Mathwire

Problem Solving: Valentine's Day Treat

2012-02-10T11:14:00.001-05:00

Valentine's Day Treat challenges students to list all of the possible sundaes that can be made if students choose one ice cream and one topping from the cafeteria list. Note that students must choose a topping for this problem, otherwise they are simply buying ice cream which doesn't count as a sundae.

This problem may be solved using various methods and is accessible to students of all levels. Some students may simply list the various combinations. Other students might elect to use a probability tree. Others might use a more developed concept of combinations in counting and naming the various combinations. All are valid methods of solving this problem and reflect students' current understanding of the concept of combinations.

Download Valentine's Day Treat which includes the student handout and a sample solution.

Valentine Quilt

2012-02-09T09:26:00.001-05:00

This Valentine Quilt is a great culminating activity for a study of the geometry of quilts. Each student designs a 9-square paper quilt patch using only red, pink and white paper. Students may elect to use a traditional quilt pattern or design their own original pattern and name it. Assemble all of the quilt squares into a class quilt.

See Mathwire's Mathematical Quilting menu to view and download resources for teaching a unit on the mathematics of quilts.

Heart Paths

2012-02-08T09:42:00.002-05:00

Heart Paths challenges students to find all the different paths that spell HEART if they can only move from a letter to one of the two letters directly below it. Students use the Heart Path worksheet to record each path, making it easy to check for duplicates.

This problem is best solved using systematic counting, an organized approach to solving the problem. While many students might not use this approach independently, it is beneficial for the teacher to spotlight students who successfully used this approach. Or, the teacher might model the approach as students check their own solutions, adding paths they might have missed in a more haphazard approach.

Download the Heart Paths worksheet which includes the problem sheet, worksheet and solution.

Snowman Probability

2011-12-16T15:38:00.001-05:00

This activity is designed as a fun, seasonal data collection activity that introduces students to the probability of a spinner. Although each piece of the snowman is equally likely to be spun, the actual game results are often quite different.

In this game, students spin to win all of the pieces to create the snowman. Students may place a transparent spinner over the spinner template, or use a pencil and paper clip to create a spinner.

Before playing, ask students to estimate how many spins they think they will need to collect all of the pieces for their snowman. Call on students to share both their number of spins and why they think that is a reasonable number. Record these estimates for later discussion.

Give each student a copy of the game mat and insert the mat into a clear sheet protector. Students may then use dry erase pens to draw the pieces as they collect them.

Have students use the Snowman Probability Recording Sheet to collect data on how many spins it takes to get all of the pieces. Insert this sheet in a clear sheet protector for a renewable activity. Be sure to collate the class data and analyze this larger sample to get an approximate number of spins required.

Download the Snowman Probability Game file which includes the game mat, spinner, directions and recording sheet.

Last Snowman Standing Game

2011-12-15T14:01:00.000-05:00

The snowmen face off in this game of addition facts. But beware! A toss of the die may mean the sun melts a snowman. Students practice addition facts as they try to be the last snowman standing because in this game the first person to remove all of his/her snowmen loses the game!

Download the Last Snowman Standing Game for directions and game mats for three different versions of the game:

Sum of Two Dice Version to practice addition facts
Difference of Two Dice Version to practice subtraction facts
One Die Toss for a simplified version to analyze the probability of a die toss

Data Collection: The directions for each version also include directions for data collection and analysis of the outcomes of the games. Be sure to incorporate these activities, if at all possible, as games offer a highly motivational study in probability. Students love to "play games" to collect data. They're also eager to analyze games so that they learn how the game works and what strategies they can use to improve their odds of winning.

Differentiation: This game offers many opportunities to differentiate the activity. First of all, teachers are able to select from three different versions. Secondly, each teacher should differentiate the game analysis to meet the instructional level of his/her students. Most students can handle the questions with teacher guidance. Older students and talented primary students may be challenged to analyze the game and answer the questions in small groups.

Read about the Last Snowman Standing game on Mathwire.

Hundred Board Puzzles

2011-12-13T16:25:00.000-05:00

Students learn the patterns in the hundred board by assembling puzzles. Teachers are able to assess student use of patterns in rows and columns by observing the student at work.

This task is easily differentiated to accommodate the varied levels in a first grade class by changing the number of pieces and the shape of the pieces. Puzzle bags should be sequentially lettered so that students progress through harder versions of the task.

Finally, students are asked to create their own puzzles for classmates to solve.

Download a hundred board template to copy onto card stock and then cut apart to create puzzles.

Elf Glyph

2011-12-12T15:13:00.000-05:00

This Mathwire elf glyph comes complete with legend and downloadable patterns to create your student glyphs. As with all glyphs, teachers should feel free to adjust the legend to best fit the information on your students.

Creating their own glyphs requires students to follow a legend. However, teachers should be sure to also provide opportunities for students to analyze the class glyphs with questions that require them to identify specific information in the glyphs such as:

Does anyone have a "twin glyph" or someone whose glyph is exactly like yours?
How many people in the class like to make snowmen?
Do more people like warm weather or cold weather?
How many girls like to go sledding?

Gingerbread Graph Ideas

2011-12-09T10:28:00.000-05:00

It is very easy to incorporate graphing into a gingerbread man unit. Consider these possibilities to get the creative juices flowing. Remember to include different kinds of graphs as suggested below.

Gingerbread Info.: As an introduction to the unit, graph how many students have eaten a gingerbread cookie, baked a gingerbread cookie or decorated a gingerbread cookie. [clothespin graph with simple yes/no options]
Gingerbread Bites: Ask students to take one bite of their gingerbread cookie. Graph or tally how many students bit off the head, the right arm, left arm, right leg or left leg. [bar graph, as shown, or pictograph using pieces]
Gingerbread Taste Test: Have children taste several different gingerbread cookies, including homemade and store-bought. Ask students to vote for their favorite cookie. [bar graph]
Gingerbread Man Stories: After reading several different versions of the classic story, ask students to vote on their favorite. [pictograph using book die cuts]
Gingerbread Unit: At the conclusion of the gingerbread unit, have students vote on their favorite activity. [bar graph]

Catch the Gingerbread Man Game

2011-12-08T17:15:00.000-05:00

For this game, students toss two dice (one regular and one marked A-B-C-D-E-F), form an ordered pair (e.g. B5), then remove the gingerbread man from that space, if there is one. Play continues until the timer rings or until one player has caught 10 gingerbread men. Students love playing the game and they get to practice their coordinate graphing skills in the process.

Coordinate Pairs: This seasonal version of the classic Battleship game provides practice in forming coordinate pairs, identifying the x-coordinate (A-F), then the y-coordinate (1-6) so that spaces are identified as C3 or E6. Hopefully, lots of practice will help students transition to the algebraic ordered pairs (x,y) where x and y are both numbers. Just be certain to reinforce the notion that the x-coordinate (across) comes before the y-coordinate (up or down). The alphabetical cues (across comes before up or down) help some students remember the order.

Download Catch the Gingerbread Man Game which includes game mat, directions and game pieces.

Gingerbread Man Problem Solving

2011-12-06T19:07:00.000-05:00

Students are asked to use words, pictures and numbers to solve these gingerbread problems:

Gingerbread Bake Sale challenges students to figure out how many different gingerbread men Ruby can make for the holiday bake sale.

Gingerbread Man Chains requires students to calculate how many gingerbread men will be needed to create chains across the bulletin board. Students also need to figure out how many sheets of brown construction paper will be needed for the project.

Creative Extension: Ask students to write original problems that involve the gingerbread man. Encourage them to think of measurement and patterns as well as numbers and operations as they create their word problems. Provide time for students to type in, print out and decorate their problems. Assemble them into a class Gingerbread Man booklet that may be shared with other classes as well.

Gingerbread Man Math

2011-12-06T10:00:00.000-05:00

Gingerbread men and gingerbread houses enjoy special popularity around the holidays, but many of these gingerbread activities are timeless and complement literature titles that teachers use at the beginning of school or after the holidays. It's very easy to incorporate mathematics into a study of gingerbread men, and students will enjoy the data collection activities and games while learning math skills and deepening their understanding of important mathematical concepts.

Look through these math activities and add some to your repertoire. Consider broadening the gingerbread math to include measurement, games and problem solving this year.

Check out Mathwire's Gingerbread Man Math collection, part of Mathwire's themed math activities collection.

Gingerbread House Math

2011-12-05T08:11:00.000-05:00

Introduce elementary students to coordinate graphing through seasonal coloring activities. This winter Gingerbread House activity requires students to use the grid code and crayons or markers to create a gingerbread house on a blank 11x11 grid. The use of letters on the horizontal axis and numbers on the vertical axis introduces young students to coordinate pairs without the confusion of the standard (h,v) format. Notice that it is important that elementary students become accustomed to listing the horizontal coordinate first as this will transfer to the Cartesian coordinates they will use in later grades.

See more Mathwire Gingerbread House activities.

Counting Game: Run, Gingerbread Men, Run!

2011-12-02T09:10:00.000-05:00

This game was designed to introduce students to the randomness of spinners and dice. Each color gingerbread man starts at the same place and has the same chance of winning by crossing the finish line, but does it work out that way? Students will enjoy playing the game AND use a clothespin graph [see sample on right] to collect some useful data on the winners.

Once students have collected class data from playing many games, they will come together to analyze the clothespin graph results. Students will be asked to discuss whether or not they think the game is fair for all of the gingerbread men and explain their reasoning.

Download the Run, Gingerbread Men, Run! game so that students can get started playing and collecting data. The pdf file contains the spinner, gameboard, clothespin graph icons, and an optional tally sheet.

Dice in the Classroom

2011-11-29T10:07:00.000-05:00

There are so many effective math games and data investigations that involve tossing dice. One way to help young students toss dice is to place the dice in a clear jar. Students simply shake the jar, place it down on its lid, and read the dice toss. Teachers may place 1-4 dice in the jar and they're ready to go. HINT: This also works for coin tosses!

Some teachers prefer to use the small trays in which vegetables and fruits are sometimes packed or small boxes or box lids. The sides stop the dice from rolling off the student desk. If noise is a concern in the classroom, place a sheet of craft foam in the bottom of the tray and the dice tosses will be silent.

Now check out some activities from the Mathwire collections:

Data Analysis: One Die Toss
Data Analysis: Two Dice Toss

Integers: Elevator Model

2011-11-28T09:10:00.000-05:00

Students intuitively use this model to describe riding up (+) and down (-) in an elevator. This real-life application is one some students might have encountered if they live in a large city or have visited taller buildings. Generally problems involve starting at one floor and going up (+) or going down (-) floors to get to another location within the building. This provides a gentle introduction to integers in a familiar format.

The Elevator Template may be laminated or placed in a clear sheet protector for student use. Students use dry erase markers to number the starting floor. They may then move up or down, as dictated by the problem, using a clothespin to mark the ending floor. NOTE: The template was purposely left unnumbered so that it works for all types of uses and ranges of numbers.

The Elevator Problems set suggests students use an elevator template to track multiple moves from floor to floor, recording each change as an integer. Ultimately students work through these moves to identify the final floor.

Some teachers create a fictional store with special floors (e.g. 2 - Kids' Clothing, 3 - Furniture, 4 - Toys, etc.) so that students experience this real-life application of integers. It's easy to generate integer problems using this model: If I get back on the elevator at the 2nd floor, ride up 5 floors, then back down 1, what floor am I on now?

Challenge students to write their own Where in the building am I now? problems.

Read more about Integers: Elevator Model on Mathwire.

Fact of the Day

2011-11-26T09:56:00.001-05:00

Help students master basic facts by posting a Fact of the Day or Fact of the Week conspicuously in the classroom. Some teachers post a fact by the clock or on the front wall where students will see the fact several times throughout the day. Stop periodically for a choral recitation of this fact. Students look at the fact and recite it slowly three times. Then students close their eyes and recite the fact from memory 3 times and/or write it on white boards 3 times.

To start slowly or for particularly troublesome basic facts, use a Fact of the Week and follow the same posting and choral recitation procedures.

Download the Fact of the Day/Fact of the Week template. Laminate the template or place in a clear sheet protector for easy reuse.

Number Sentences

2011-11-22T10:37:00.000-05:00

This activity originated in the Games magazine and has floated around the internet in various forms. Teachers may use this as a fun number sense activity, challenging students to think about numbers in everyday life. From experience, it's usually best to pair students or have them work in small groups.

Try your hand at these samples:

26 = L. of the A. [letters of the alphabet]
4 = Q. in a G.
13 = O.C.

Stumped or easy? Download the Number Sentences handout and answer key. It's a fun activity for those crazy days when play practice or assemblies alter the schedule. Or, split these up and use a few a day as a challenge.

Eli and the Magic Peanuts

2011-11-21T14:43:00.000-05:00

This model was developed and used in the CSMP (Comprehensive School Mathematics Program) and remains a wonderful introduction to integers for young children. Eli is an elephant who loves peanuts. As he travels through the jungle, he picks up each and every peanut he sees and places them in his bag.

The trouble is that some of the peanuts are magic peanuts. They look the same as regular peanuts, so Eli doesn't know if he's picking up a regular or a magic peanut. The problem is that when a regular and a magic peanut get together, they disappear. Eli is always disappointed to find fewer peanuts in his bag when he stops for a snack.

Read more about Integers: Eli and the Magic Peanuts Model on Mathwire. This latest addition to the Mathwire collection includes pictorial directions for introducing Eli to young students. You may also download an Eli math mat and problem set.

NOTE: I regularly used craft foam peanuts and magic peanuts for classroom presentations of Eli and the Magic Peanuts. You can easily use the downloadable demo-size peanuts as a template or simply print several of these demo-size peanuts for student use.

See how the CSMP curriculum presented Eli and the Magic Peanuts and the simple notation they used with first graders. NOTE: You will have to scroll through the document to Lesson F114, page 4-473 for a multi-page presentation. Here you'll find the original representations and story.

Thanksgiving Probability

2011-11-18T09:27:00.000-05:00

How about a little probability for Thanksgiving? This handout is a simple review of probability using the letters in Thanksgiving. Students must explain their answers to provide practice in writing and explaining their thinking. There is a challenge question that might be thought about and explained in different ways, so it's always interesting to see which route students choose to use.

Download Thanksgiving Probability.

Turkeys and Cows

2011-11-17T08:28:00.001-05:00

In honor of Thanksgiving, here is a turkey and cow problem, an adaptation of the familiar chicken and cows problems. In these problems, students are given the number of heads and the number of legs and must figure out how many chickens and cows there are. Central to the solution of these types of problems is the fact that chickens have two legs and cows have four legs.

The following method is a simple pictorial way to solve these types of problems. Very young first and second graders have used this method to successfully tackle these problems, itching for more challenges.

PROBLEM: Farmer Brown counted the turkeys and cows in his barnyard.

There were 5 heads.
There were 14 legs.

How many turkeys and how many cows were in Farmer Brown's barnyard?

First, the students concentrate on the number of heads. In this case there were 5 heads, so the students draw 5 circles to represent the heads.

Second, the students give each head 2 legs to make them turkeys.

Now the student checks the number of heads and legs he has drawn. The student has 5 heads (correct) and 10 legs (not enough). Farmer Brown saw 14 legs, so the student needs to add 4 more legs. He must add 2 legs at a time because a cow has 4 legs.

Again, the student counts and checks his drawing. He has 5 heads (correct) and 14 legs (correct), so he now labels each drawing either T (turkey) or C (cow).

It is now easy to see that the solution to this problem is that Farmer Brown had 3 turkeys and 2 cows in his barnyard.

Teachers should model this method with students. It might be very helpful to model this solution on chart paper or chalkboard, so that students may refer back to this model as they solve problems on their own. Next, let pairs of students work together to solve another problem. After that, students may work individually or as pairs to solve additional problems involving turkeys and cows.

Download Mathwire's Turkeys and Cows problem set.

CHALLENGE: Students may be challenged to create their own turkey and cow problems for their classmates to solve. Each problem should also have a solution attached for easy checking.

Number Line Madness Game

2011-11-16T08:44:00.000-05:00

This game was designed to provide practice in adding integers, using the number line model. In this model, students move to the right for a positive integer and to the left when adding a negative integer.

Each player starts at 0. The first player spins the spinner, then adds that number to her current position. The second player spins and moves accordingly. Play continues back and forth until one of the players reaches +15 or -15 or beyond these endpoints.

Download the Number Line Madness Game. The PDF file includes extra number lines and optional spinners to differentiate levels of challenge to best meet the needs of varied learners.

Changes in Temperature Template

2011-11-15T15:53:00.001-05:00

Changes in temperature are a real-life application of integers in mathematics. 3 degrees warmer would be represented as +3 while 5 degrees colder would be represented as a change of -5. This change in temperature use of positive and negative integers is in addition to the absolute temperatures on a thermometer which might read below 0 in some climates.

Students use this template to record data to solve changes in temperature problems. Using the 5-day forecast, the teacher tells students Monday's temperature and the change (+ or -) for each day of the week. Students use this information to figure out the actual temperature for each day of the week. Note that the change should reflect the change from the previous day. For example, a change of -3 for Wednesday means that the temperature went down 3 degrees from Tuesday's temperature. Additionally, if the teacher uses the actual changes in the 5-day forecast for the area, the students can also assess the accuracy of a 5-day forecast as the week's weather plays out.

Place the template in a clear sheet protector and provide dry erase markers for students to use.

The thermometer strip is available as a visual representation for students to use in solving the changes in temperature problems. Students write Monday's temperature in the START space. They may then simply count up or down spaces to get to the next day's temperature.

The template was designed so that students could use a clothespin to mark the daily change for ease in recording on the template pictured above. The clothespin simply clips onto the appropriate space as a placeholder while students write in the temperature and record the information in the weekly chart.

Download the Changes in Temperature Template which also includes thermometer strips that may be laminated for student use in these lessons.

Introducing Integers: Good Weather

2011-11-14T08:39:00.000-05:00

The mathematical introduction of integers as positive and negative numbers on the number line is easily accomplished through the real-life application of weather changes in temperature. We are all accustomed to hearing how the temperature will be up or down over the course of the week. Given Monday's temperature, and a series of up and down daily changes, students are challenged to find Friday's temperature.

Teachers might use the 5-day weather forecast for your area on Monday. Give students Monday's temperature, then tell them how the temperature will change each day, going up or down from the previous day. Challenge students to find the predicted temperature on Friday, then check it against Friday's actual temperature as part of daily routines.

The Good Weather problem is a formal assessment of students' proficiency in using integers to describe the changes in temperature and predict the Friday temperature. It is simple to adjust this problem to reflect the current temperatures in any area, depending on the season.

Download the Good Weather assessment.

Candy Corn Pattern

2011-11-11T11:41:00.000-05:00

Candy Corn presents a triangular numbers problem using a candy corn pattern. Younger students might use candy corn or other manipulatives to model the problem. A sample solution shows how older students might use an input-output table to model the pattern and find the solution without the use of manipulatives.

Download the Candy Corn pattern problem.

Subtraction Trick

2011-11-09T19:59:00.000-05:00

This is a great modification for students who have difficulty with these types of problems. Students simply rewrite the problem using the numbers that come before the original numbers in the problem. They may then subtract without the difficult regrouping process necessary in problems with all of these 0s.

Add this method to students' repertoire. They'll think they're getting away with something and you'll get lots of subtraction practice. You may even want to split the class in half and have a subtraction challenge: half the class uses the traditional method while half the class tries the subtraction trick. Check answers and see how accurate each group is. Allow students to choose the method that works best for them.

Download the Subtraction Trick handout.

Pattern Block Fraction Design

2011-11-08T20:03:00.000-05:00

These open-ended assessments require students to use pattern blocks to fill the shape so that it has a line of symmetry. Students must draw a dotted line to show the line of symmetry and they must write a fraction to represent the part of the whole for each color pattern block used in the design.

Download the Pattern Block Fraction Design handouts.

Who Has? Fraction Deck

2011-11-04T21:04:00.000-04:00

This deck was designed to provide practice in using the area model of fractions. The teacher distributes the cards and picks any student to begin the round. In the case above, the sequence would go:

[red shading] I have 1/12. Who has 3/8?
[green shading] I have 3/8. Who has 4/5?
[yellow shading] I have 4/5. Who has 5/12?

The beauty of all of the Who Has? games are that students remain active participants throughout the game. Even after they have read their card aloud, they continue to attend to the card at hand, so students get lots of practice.

Differentiation: Teachers may differentiate the game to accommodate learners with special needs by:

specially selecting cards when distributing them so that each learner may be successful in naming his/her fraction
allowing partners to work together to participate, thus providing the opportunity for gentle prompting for students who need this help to successfully participate in this activity.

Materials: Download the Who Has? Fraction deck which is designed to be printed on 2x4 inch labels which may then be affixed to index cards to easily create a classroom deck of cards.

Variation: Students may play this game in groups of 2-4. They simply deal out all of the cards and place them face up on their desks. One player begins, reading a card, then turning it over. Whoever has the answer to that card, reads it and then turns it over. Play continues in this way until one player has turned over all of his/her cards. He/she is the winner.

Of course, this is totally random, based on the distribution of the cards and the selection of the starting card, but students are fascinated with this version and willingly play and practice fractions in this game format. Make the game available in the math center and schedule time for students to play.

Learn More: Read more about using Who Has? decks to practice basic facts, scan some classroom management strategies for maximizing the potential benefits of these simple activities or download additional Who Has? decks in Mathwire's Who Has? collection.

Spin to Win Game

2011-11-02T20:09:00.001-04:00

Landmarks are an important concept in the study of fractions. Students need to have a conceptual understanding of whether a fraction is close to 0, close to 1/2, close to 1, larger than 1, etc. in order to correctly evaluate fractions and check the reasonableness of their answers. The Spin to Win Game was designed to practice these skills in a fun game.

Students should be encouraged to use various methods of comparing the fractions (e.g. drawing pictures, folding paper, fraction strips, etc.) It's not uncommon for students to use a more sophisticated approach. Your fraction is larger than 1/2. My fraction is less than 1/2, so my fraction is closer to 0.

Directions for Spin to Win Game

Students play in pairs.
Each student draws a card from the fraction deck.
One student spins the spinner.

In this case, the spinner landed on closer to 0. Students decide whose fraction is closer to 0. That player wins both cards.
NOTE: If the spinner lands on closer to 1/2 or closer to 1, then the player whose fraction is closest to these landmarks wins both cards.
If the spinner lands on PLAY for 4! Draw new cards, then both players pick another fraction card, place it on top of their original card, then spin the spinner. The player whose new fraction card best matches the spinner wins all 4 cards.
If the players turn over equivalent fractions, then they drawn new cards, spin the spinner and the player whose new fraction card best matches the spinner wins all 4 cards.
Teachers may set the end of the game to be most points in 5 minutes, first player to get 10 points, etc. to fit available time and best meet student needs.

Download the Spin to Win Game directions and spinner.

Download Fraction Cards.

DIFFERENTIATION: It may be helpful to provide this fraction strip handout for students still struggling with the size of fractions. Slip the handout into a clear sheet protector and provide dry erase markers. Students may then use the fraction strips to compare their fractions to see who is closer to the landmark.

Download Fraction Strip handout from the internet.

Fall Fraction Words

2011-11-01T21:13:00.000-04:00

This activity requires students to put together fractional parts of words to create a new word. It's a verbal take on the fractional set model. If correctly solved, the fractional parts spell out a fall word.

Extension: Students may enjoy creating their own fraction words, using local clues, seasonal prompts or even holidays. Use student-generated fraction word activities as an easy do-now exercise at the beginning of class. It's a great way to develop understanding of the set model of fractions.

Download the Fall Fraction Words handout and answer key.

Pascal's Ghosts

2011-10-28T09:04:00.000-04:00

How Many Ghosts Do You See?

This activity encourages students to apply the patterns in Pascal's Triangle. A teacher instructional plan with mathematical background, answer and challenge is included to explain how to present this problem, which is also an outgrowth of the Rutgers Discrete Math Institute.

A recording sheet is also included as part of the teacher packet so that students are able to record all different solutions using a systematic counting method, which is a goal of discrete mathematics.

Download Pascal's Ghosts problem, instructional plan, student recording sheet and answer key.

Be sure to check out Pascal's Pumpkins in an earlier post. This is an easier introduction to the patterns in Pascal's triangle.

Fall Problem Solving

2011-10-27T09:21:00.000-04:00

These open-ended assessments require students to apply mathematical concepts and skills to solve problems and explain their thinking using words, pictures and/or numbers.

Candy Corn presents a triangular numbers problem using a candy corn pattern. Younger students might use candy corn to model the problem. A sample solution shows how older students might use an input-output table to model the pattern and find the solution without the use of manipulatives.

Annual Fall Parade challenges students to use the triangular pattern to figure out how many students are in the fourth grade. Given the number of full rows, students must apply the pattern and use effective recording (picture, table, etc.) to explain their reasoning.

Pumpkin Picking is a pattern problem that can be solved using a picture or an input/output table. [contributed by Shannon Collier, Joseph C. Caruso School, Keansburg, NJ]

Trick or Treat requires students to create a table of values and identify the pattern or rule to solve the problem.

Grade 2 Halloween Word Problems were written by Tammie Holcombe and Karen Zeigler, second grade teachers at Port Monmouth Road School in Keansburg, NJ.

Younger students will enjoy analyzing and completing Fall Patterns. They should then classify the pattern and explain their reasoning as part of the class discussion. It is possible that students will see different patterns in some of the items so their explanation and justification are very important mathematical discourse.

Measurement Man

2011-10-26T09:28:00.000-04:00

Create Measurement Man scarecrows to visually represent the relationship between gallon, quart, pint, cup. This conceptual image provides a visual body cue when students need to use these references in the future or on state testing.

Measurement equivalents are always a tough challenge in elementary classrooms. This visual helps students master the equivalent units and helps them compare and rename these common measurement units.

Symmetric Faces

2011-10-25T07:35:00.000-04:00

Halloween masks become a math activity when students create Symmetric Faces. Students demonstrate a working knowledge of symmetry as they make these unique masks using 1.5 sheets of construction paper, scissors and glue. Students outline the features on the half-sheet of paper, then carefully cut the pieces, and position them on the opposite side to create a symmetric face in opposite colors.

Download directions for making Symmetric Faces.

Don't limit this mask activity to Halloween, as these versions would be equally effective opportunities to introduce this symmetry project:

Patriotic masks created in red, white and blue
Mardi Gras masks using yellow, green, and purple construction paper combinations to simulate Mardi Gras colors.
School Spirit masks created in school colors
Valentine masks created in red, pink and white
Or...you get the idea!

Be sure to check out the Symmetric Faces Photo Gallery for more inspiration.

Estimation Station

2011-10-24T13:35:00.000-04:00

Establish a regular center in the room which changes weekly. A simple clear plastic container is filled with different items each week. These items should vary in size to challenge students' developing concept of volume, as it relates to smaller or larger units. Use seasonal items: acorns, leaves, candy corn, popcorn kernels, pumpkin seeds, etc. to spark student interest. Keep a class journal of these activities in which students may record their estimates. Record the item and the actual count along with a digital picture, if possible, of the container and the student(s) whose estimates were closest. Some classes involve parents by asking for volunteers to send in appropriate items to be counted. It is important to use the same container for several weeks so that students build an understanding that size matters in estimating how many items there are in the jar.

Download Estimation Station Recording Sheets to use for this activity. Keep sheets in a binder to provide a growing record of student growth in estimating.
Suggestions for using recording sheets: Have each student write his/her name and estimate on Page 2. After counting, circle or color in the student(s) whose estimates were closest. Teachers may elect to print in names at the beginning of the year and simply copy each week so that student names are always in the same location for easy checking.
Take a picture: Use a digital camera to record the winner(s) holding the jar each week. Add the picture to page one by simply covering the estimation jar clip art.

Math-Literature Connection - Estimation: The Biggest Pumpkin Ever by Stephen Kroll would be a great literature connection for a Huge Pumpkin Estimation Station or to introduce a class pumpkin sorting activity.

Read more about these pumpkin activities in Pumpkins, Pumpkins Everywhere.

Math-Literature Connection - Estimation: The Candy Corn Contest by Patricia Reilly Giff would be a great literature connection for a Candy Corn Estimation Station, as described in the book. The sneaky teacher in this story required that students read a page in a library book for each guess they submitted. Math teachers might vary this requirement to include some fun math practice as a way to earn guessing rights. Either way, incorporating the actual candy corn jar estimation is a great seasonal variation of the Estimation Station described above.

Spider Names

2011-10-21T10:50:00.000-04:00

Ms. Collier's and Ms. Rachko's classes created Name-Collection spiders for Halloween. These fourth grade students extended the Everyday Math name-collection box routine to writing 8 different names for each number, one for each spider leg.

This activity builds on students' ability to recognize and create different names for the same number. NCTM originally proposed the open-ended activity:

Students are encouraged to write questions drawn from all areas of mathematics for which the answer is 24. Here's an example of a student's response:

This activity is easily used as a transition activity. Students complete the activity as the teacher checks homework or distributes materials. Make it a once a week activity, copy the best responses onto chart paper and post it in the classroom for student reference.

Bats on Parade

2011-10-20T12:29:00.000-04:00

This book is a literary introduction to square numbers and the patterns they form as square arrays. The bats march in parade formation and different sections of the band, being different sizes, march in different arrays: "In nine rows of nine those trombones reported, while there, right behind them, the tubas retorted." The pictures and rhyme reinforce the mathematics of the patterns and teachers can easily ask students to predict how many bats will be in the next section or ask them to figure out how many bats are in the whole band before reading those pages. Add this book to your collection of problem-solving literature prompts.

Multiplication Arrays: The book is a great introduction to multiplication arrays. Use the book illustrations to show students how to use an array to model a multiplication problem then ask students to create arrays for different multiplication facts.
Class on Parade Book: Challenge students to design an array and a rhyme for an original page in theClass on Parade book. Decide on a theme and let pairs of students work on both the math and the language for a page.

Bat Jamboree by Kathi Appelt

Bat Jamboree introduces the triangular number pattern as bats assemble for the final number beginning with 10 bats in the bottom row, 9 in the next row, etc. to the very top row with 1 bat. Students are introduced to the 55 bats in formation and their various acts but the book "isn't over until the bat lady sings." Students will enjoy this introduction to an important mathematical pattern. Teachers can find many problems that build upon this triangular number pattern and extend the experience.

Student Written Problems: ask students to write original problems that use the triangular number pattern. Being able to write similar problems and solve them require higher-order thinking skills as students apply, synthesize and evaluate both the problems and the solutions.

Bats Around the Clock by Kathi Appelt

Take a humorous dance through time. Click Dark and American Batstand introduce a new dance each hour. Students move through time, enjoy some rhyme and learn the names of some oldie-but-goodie dances along the way.

Making Time: For the second reading, give students individual clocks and ask them to move the hour hand to the next hour and say the time before reading the book section for that hour.
School Time: Provide copies of the School Time Template and have students choose a time in the school day, draw the hands on the clock, write a verse and draw an illustration that shows what the class does during that hour. Assemble the individual hours into a class booklet or booklets, depending on the number of students in the class. This activity is easily differentiated to feature time on the hour, or to use the real time schedule of activity changes the class follows. The template clock deliberately shows no hands, allowing teachers to customize the activity to the appropriate mathematical level of students in the class.

Fat Bat Game

2011-10-17T19:51:00.000-04:00

Students roll a die to see how many insects their bat eats. Students may continue rolling, in this Bat version of Pig, until they elect to stop, or until they roll a 1. But be careful! If your bat is still eating (collecting points) when a one is tossed, you are a Fat Bat and lose all of your points for that round.

This game is designed to provide a fun experience in the experimental probability of a single die toss. However, students get lots of practice adding a string of single digit numbers, as they total up their winning points for each round. A data analysis option is included to formally extend the analysis of the game's probability for older students.

Download Fat Bat for the student recording sheet, directions for whole class play, and data analysis option for extending the game.

Bat Probability

2011-10-16T18:39:00.000-04:00

There Was An Old Lady Who Swallowed A Bat!
by Lucille Colandro

After reading the book, investigate Batty Old Lady Probability. Students spin to collect all of the items the Batty Old Lady swallowed, and tally each spin on the recording sheet. They then calculate the total spins it took them to get all 7 items, and add that figure to the class data. Teachers may help students analyze the class data and learn about probability in the process. The pdf document includes directions, game mat, picture cards, spinner, recording sheet and writing to learn handout.

Pumpkin Graphing

2011-10-14T13:36:00.000-04:00

This month's featured graphing format is the clothespin graph which captures data from simple yes-no questions. Use a piece of oaktag or foam board to construct the actual graph part that is reused. Write the question on a sheet of paper and attach it to the top of the board. Provide clothespins for students to use to affix to the yes or no side of the graph. Some teachers write student names on the clothespins so that it is easy to see who did or didn't vote yet.

Do you like pumpkin pie?
Have you ever gone to a pumpkin farm to pick out a pumpkin?
Do you like to eat pumpkin seeds?
Have you ever carved a jack-o-lantern?

A clothespin graph may also be used to record data for any two-choice option.

Will your holiday costume be friendly or scary?
Did heads or tails win the game?
Will you go away for Thanksgiving or eat at home?

Pumpkin Jumble Game

2011-10-12T07:09:00.000-04:00

Students toss a die to get pattern blocks to add to create a jack-o-lantern face. The first person to complete his/her jack-o-lantern wins the game. This game develops the concept of probability of a single die as students also have opportunities for Lucky or Unlucky tosses that add a twist to the game.

Data Collection & Analysis: This simple game provides a great opportunity for data collection and analysis of the probability of a one-die toss.

Have students use the recording sheet to capture each die toss. After completing the game, students may add their results to a class data table to see if each number does indeed have an equal chance of winning.

Download the Pumpkin Jumble game mat.
Download the recording sheet to capture data for class analysis.

Pascal's Pumpkins

2011-10-11T17:01:00.000-04:00

Pascal's Pumpkins encourages students to look for patterns in Pascal's Triangle. The handout develops awareness of this important mathematical pattern through a timely seasonal activity.

Students who take higher math courses will meet Pascal again in many different applications, including probability. This handout is an outgrowth of the Rutgers Discrete Math Institute.

Download Pascal's Pumpkins handout and solution.

Heads & Tails Game

2011-10-09T22:20:00.003-04:00

The Heads & Tails Game was designed to introduce young students to the probability of a single coin toss. By playing the game and adding results to a class tally, students will learn that the outcomes of heads and tails are equally likely.

To start the game, each player places a penny on the star of the snake. The heads player places the penny heads side up. The tails player places the penny tails side up.

The heads player tosses a coin. If it is heads, he moves the penny one space toward the head of the snake. If it is tails, he does not move but the tails player moves her coin one space toward the tail.

Next, the tails player tosses a coin. If it is tails, she moves her penny one space toward the tail of the snake. If it is heads, she does not move but the heads player moves his penny one space toward the head of the snake.

Play continues back and forth until one of the players reaches either the head or the tail of the snake, thereby winning the game.

The players post their results on the classroom tally, adding to the Heads Won or Tails Won count. Players should play several games, if possible, to create a large sample which more closely approximates the actual probability.

Download the Heads & Tails game mat.

Handful of Pennies

2011-10-08T19:32:00.000-04:00

The student rolls a die and places that many pennies in the blue hand. She rolls the die again and places that many pennies in the red hand. Next, the student writes a number sentence for the number of pennies in each hand.

Students may work independently on this activity to practice their math facts. Students enjoy both dice and money so it's a great way to provide practice in basic facts. Students who need concrete practice may simply count the pennies, then write the corresponding sentence.

MATERIALS:

Students create their own mats by tracing their hands onto a piece of oaktag or card stock. Students may elect to color the hands blue and red, as pictured.
Insert the mat into a page protector and use dry erase markers for easy cleaning and re-use.
Create a blank template for the overhead.

EXTENSIONS:

Ask the student to write the other three number sentences for each number family.
Challenge students to complete this activity with 3-4 handfuls of pennies by linking together 2 mats.
Have students roll 2 dice instead of one die and place that many pennies on the hand. Repeat for the other hand.

Writing in Math Class

2011-10-07T06:55:00.000-04:00

Often students who have difficulty writing in math class have less difficulty telling the teacher what they think. Capitalize on this oral strength by incorporating the think-pair-share strategy more often into math lessons as a prelude to writing.

Think-Pair-Share: Some students are reluctant to write at first and benefit from practice sharing thoughts with a partner and hearing that partner put thoughts into words. Reluctant students get to "practice" in a small setting with a partner before speaking to the whole class. These students can also choose to share their thoughts, their partner's thoughts, or a combination of the two.

The basic steps of Think-Pair-Share are:

Question: Ask an open-ended question and tell students that they will think-pair-share the answer.

Think: Give students 1-2 minutes to think quietly about their response to the question. Walk around the room to reinforce this quiet, on-task response.

Pair: Ask students to share thoughts with their partners and ask questions if they don't understand what their partner is saying. Circulate around the room, listening to student conversations.

Share: Ask for student volunteers to share as you begin this process. Later, you should call on non-volunteers to increase student accountability in this cooperative learning strategy. Reinforce the expectation of active listening by requiring students to acknowledge the thoughts of classmates by saying:

I agree with [name's] answer...,
I don't agree with [name's] answer...,
I started the problem like [name] but then I...

NOTE: It is not necessary and, in fact, it is usually not time-effective to have each group share. As you circulate around the room during the Pair share, identify students who have used different strategies or great models for thinking about an important concept. Call on these students or their partners to share with the class.

Grab the Candy Corn Game

2011-10-04T21:42:00.000-04:00

This game requires students to toss two dice, form an ordered pair, and remove a candy from that space, if possible. The game can be played with counters or with real candy for a holiday treat that is appropriate from Halloween through Thanksgiving. The file contains the gameboard, directions, candy counters and a recording sheet.

There is also an M & M version of the game available for classrooms that use these candies for data collection. Both games were designed to provide fun practice of coordinate graphing for young students.

Download the Grab the Candy Corn game mat, counters, directions and recording sheet.
Download the Grab the Candy (M&M version) game mat, counters, directions and recording sheet.

Mad Monster

2011-10-03T10:05:00.000-04:00

This is another coordinate graphing activity from the Mathwire seasonal collection. Students will enjoy seeing the monster come to life as they color in the squares according to the key.

This activity is designed to introduce students to coordinate graphing in the square, similar to the popular Battleship game of old. Later, students will transition from the letter-number ordered pair to the traditional two number ordered pair and graph the point at the intersection.

Download the Mad Monster activity.

Check out more fall math activities in the Mathwire collection.

Pumpkin Coordinate Graphing

2011-10-02T15:51:00.000-04:00

This activity requires students to use coordinate pairs to correctly color in the squares of the grid to create a jack-o-lantern. This is an activity from the Mathwire season fall collection.

Introduce young students to coordinate pairs using letters and numbers, reinforcing the concept that the letter (horizontal) coordinate is listed first in an ordered pair. Younger students begin by graphing in the space. Later, students transition to ordered pairs, graphing the point at the intersection.

Download the Jack-O-Lantern coordinate graphing activity.

See more Mathwire seasonal activities.

Counting Money

2011-09-26T14:10:00.000-04:00

The NCTM Illuminations site offers Coin Box, an application that allows students to count money, using coins and/or coins on the hundred board. The app allows students to move the coins as they count. Students may opt to place similar coins in a row for easier counting, etc. The game also prompts students that their answer is too little or too much, allowing them to try again.

Students may use this application in school or at home to practice counting money, making change, and exchanging coins. Be sure to include this free site in resources for parents.

School Day Count Routine

2011-09-07T08:55:00.000-04:00

Each day a student adds one straw or craft stick to the ones pocket or cup. The student holds up each straw in the ones pocket and leads the class in an oral count. The student and class decide if they have enough straws to make a bundle (of ten) to move to the tens place. Students will quickly begin to make predictions that "tomorrow is a bundle day" or "Friday will be a bundle day."

After leading the class in an oral count of straws in all pockets, the student makes the change in the posted number so that it reflects how many days they have been in school and how many straws they have collected in the school day count pockets. If students use labeled cups to hold straws, then use a school day count poster to write the days. Laminate the poster and let students use dry-erase markers to change the number of days.

Download a School Day Count poster that may be laminated or inserted in a sheet protector so that students may use dry erase markers to record the appropriate digits for the day's count.

Back-to-School Problem Solving

2011-09-06T14:32:00.002-04:00

September is a great time for data collection activities as students are naturally curious about their new classmates. Ask questions that require students to analyze data and support their conclusions.

Challenge students to solve some of these problems to practice collecting, organizing and analyzing data in real-life applications. Require students to explain their reasoning and solution to develop mathematical communication skills.

See all Back-to-School Word Problems.

Here's a sample 3rd grade problem that targets student understanding of probability:

Third graders cut apart each of the letters in THIRD GRADERS and place
the squares in a bag. Kevin pulls out one square and looks at the letter.

What is the probability that the letter he pulls out will be the letter, D? Explain how you know.
What is the probability that the letter he pulls out will be S? Explain.
On Friday, his teacher says that if anyone can correctly predict which tile he or she will pull out the bag of THIRD GRADERS squares, the class will not have any homework over the weekend. She asks Kevin's table to predict for the class. They are nervous because the class is counting on them to say the right letter.

Which letter should Kevin’s team predict that they will pull from the bag?
Explain how you know that the students should predict this letter.

Note: It is very important that students explain how they know their answers are correct. They may use pictures, words and numbers to explain their thinking.

Math Train

2011-09-03T18:26:00.000-04:00

Eric Marcos, a math teacher at Lincoln Middle School in Santa Monica, California, supports students as they create their own videos of important math concepts and skills. Math Train is the result of this classroom initiative in which students teach students. Here's how Math Train started:

Bookmark this site for middle school students and their parents. Chances are when a student runs into difficulty at home, he just might find an appropriate video that deals with that concept on Math Train.

What's Your Favorite Number?

2011-09-02T13:06:00.000-04:00

Alex Bellos is fascinated with numbers. As an author of books on numbers, he's been asked countless times what his favorite number is. He decided to conduct a survey to find out what numbers people most liked. He promises to publish the results of this worldwide survey in 2012.

Students can also take part in the survey which simply asks you to input your favorite number and explain why it is your favorite. It would be fun for students to take part in this easy survey and they'd surely be interested in the results when they are available. Visit the Alex Bellos Blog to read about the survey idea and to enter your favorite number.

Extension: Extend this online activity by conducting a classroom survey of favorite numbers. You might use the same format that Bellos uses online. Students would collect data, then organize the data presenting it in graphical form before analyzing the results. Students might elect to organize a schoolwide survey to see if the classroom results match this larger sample.

Active Participation Strategy: Let Go and Let Students...

2011-08-23T13:09:00.000-04:00

Let go and let students...: This phrase reminds teachers to put students in charge of their learning and in charge of explaining themselves. This practice incorporates multiple effective strategies to support student learning:

Give students the chalk or marker and ask them to come to the board or overhead to explain their thinking. Resist asking students to tell you what they did while you write what they did. Asking students to write as they explain allows them to organize their thinking and provides insight to teachers about what strategies and organizational methods students use effectively and independently. This strategy also provides practice for the expected independent test performance.
Ask another student to repeat a student's explanation or insight. Resist the urge to repeat or paraphrase each student's response. Ask classmates to do this instead, fostering active participation/listening skills in all students.
Ask students to read directions or problems aloud rather than reading them yourself. Once again, this practice encourages students to develop effective reading skills for math activities and tests. If reading levels are an issue in your classroom, you might begin with buddy reading, pairing students to effectively mitigate this issue.
Ask students to define math vocabulary terms in their own words. Post the best definitions around the room.
Post samples of effective problem-solving solutions that meet tough requirements of the problem-solving rubric you use to grade student responses. Make overheads of student samples and review them regularly so that all students see examples of effective ways to organize solutions and explain thinking.
Expect students to be capable of some independent work. Voice this expectation to students as in "I want to see how each of you does on Math Boxes #3 and #4 today, so please begin with those boxes. I believe that everyone can do these by themselves and I will be around to check. After you finish these two math boxes, you may do the others in any order you choose."
Quickly spin off students who are capable of independent work. Provide enrichment activities that go beyond current grade-level expectations and require higher-order thinking skills for solutions. Encourage these students to play harder versions of math games (i.e. more cards, larger numbers, etc.)
Differentiate and scaffold instruction to effectively meet the varied needs of learners in your classroom. Provide enrichment activities for talented students while you work with small groups who need additional instruction or scaffolded support/encouragement during independent practice. Use flexible grouping based on informal assessment of student responses during instruction.

More Active Participation Strategies

Download Mathwire's Active Participation Strategies for Math Classes: a one-page text-only summary of the strategies discussed above.

Download Mathwire's Active Participation Strategies for Math Classes: the full text of this section with pictures.

Morning Math Routines

2011-08-22T23:34:00.000-04:00

Many teachers incorporate morning math routines into their daily math lesson. The most popular activities include posting the date on the calendar, adding a straw or penny to the days in school count, tallying the day's weather, choosing coins for the date, etc. These every day routines develop real life math skills and reinforce our base ten number system throughout the 180 day school year.

Mathwire offers a short description of the most common morning math routines for teachers to check out. Your math series may also prescribe many of the same activities so be sure to read through the introduction of your teacher's manual for more information.

Teachers use many different charts and organizational practices to streamline these routines, so Mathwire added a Morning Math Routines: Photo Gallery. This photo gallery reflects how different teachers integrate these routines into real classrooms. Teachers use many charts and varied organizational methods to provide visual cues for these important mathematical routines. Hopefully, this photo gallery will provide ideas for teachers looking for different ways to integrate these mathematical routines into daily classroom bulletin boards.

Most importantly, however, is the student role in morning math routines. Your goal, as a teacher, is to introduce and structure these activities so that students become the active participants. Some teachers post names next to each station so that student leads the activity for the day or week. Remember, that these activities are designed to build number sense in students, so it is imperative that students are in control and have the opportunity to demonstrate their understanding and proficiency in number operations. Kindergarteners are capable of leading their peers and almost all students enjoy the opportunity to be teacher for a day, so let go and let the students take charge. You'll learn a lot by observing.

What's Your Number Sense?

2011-08-19T15:37:00.001-04:00

Panamath

A person's number gut, or Approximate Number System (ANS), specializes in the "ballpark" figure rather than an outright calculation. It's what lets us see which grocery line in a store is longer, or which part of the movie theater has fewer people. Animals have this ability as well, without any training from humans: a bird picks the branch with the greatest amount of berries or a baboon decides he's better off not fighting a gang of six. The ANS empowers us to decide the most efficient course to take in everyday situations and may impact our performance in school mathematics.

Panamath measures your ANS through a simple task. You're repeatedly flashed two groups of dots -- one blue and one yellow. After each flash, you're asked, "Which one had more?" This enables Panamath to calculate how precise your ANS is. [from the Panamath website]

Try taking the free online test to measure your own number sense. You are repeatedly shown a slide with blue and yellow dots for a very short time. You simply have to say whether there were more yellow or blue dots. You'll get a correct or incorrect response before moving to the next screen, so you know how well you're doing. It's a fun experiment and you will get results immediately upon completion of the 2-part trial.

There's a lot of research on the site and suggestions for teachers who might want to use the test with students. The basic premise is that a person's ANS (Approximate Number System) predicts his success in mathematics. What do you think?

Try the Panamath Test.

Enjoy Your Summer

2011-07-18T00:19:00.000-04:00

Hopefully everyone gets some time to get away this summer and enjoy the summer break. I know that teachers are always thinking and planning, so I've reposted the summer Mathwire resource page for your reflection.

Enjoy a well-deserved rest before the new year starts in gear. Keep an idea journal and jot down those thoughts for later...

The Mathwire blog will be on a summer break until early August. Thanks for reading!

Data Analysis: TV Survey

2011-06-08T10:54:00.000-04:00

TV Survey is an open-ended problem that was designed to introduce students to this real-life application of sampling. Because TV is a part of students' daily life, this scenario is accessible to all students. And, because students often exhibit a keen sense of "fairness," they are sometimes disconcerted by the notion that a small group of people get to decide what all of us get to watch on TV.

TV Survey was also designed to address different Bloom levels so that students have to use higher-order thinking skills to analyze, synthesize and evaluate information about the sampling method.

Download the TV Survey open-ended assessment.

See more Mathwire Sampling Activities.

Problem Solving: Pattern Blocks

2011-06-07T09:36:00.000-04:00

Pattern blocks are a familiar manipulative in most elementary classrooms. Students learn a lot of geometry from informally interacting with pattern blocks. These problem-solving activities were specifically designed to target important mathematical concepts using these available manipulatives.

In Pattern Block Symmetry students must create a pattern block design to satisy the given conditions involving line symmetry and the number of different pattern block pieces used.
Pattern Block Design (Grade 3) requires students to create a design to meet specified criteria.
Pattern Block Design (Grade 4) requires students to create a design to meet specified criteria.
Hexagon Dragons challenges students to use an input-output table to record dragon growth, then analyze the pattern and write a rule for dragon growth.
In Fir Tree, students must use an input-output table to record and analyze data, then write a rule for this growing pattern.
Symmetric Snowflake challenges students to use pattern blocks to complete the snowflake design so that it has line symmetry.

Problem Solving: Fractions 2

2011-06-02T15:52:00.000-04:00

Students sometimes find the set model of fractions harder to understand and use. These problems were designed to help students concretely work with the set model to solve problems.

Let's look at a sample problem:

Mrs. Puglisi’s third graders visited the park nature center to see the tadpoles and

frogs. They counted 20 animals in the tank.

• 3/4 of the animals had already changed to frogs.

• The rest were still tadpoles.

• How many frogs were in the tank?

• How many tadpoles were in the tank?

• Explain how you know your answers are correct.

Concretely Solving the Problem:

Students should begin by counting out 20 manipulative objects they will use to solve the problem.
Next, students look at the fraction 3/4. The denominator tells us that the animals were divided into 4 groups. NOTE: It is often helpful to use a piece of paper that is folded into quarters so that students may sort the manipulatives evenly into each of the 4 spaces.
Students deal out the manipulatives as if they were cards, placing one in each of the 4 spaces and repeating until all of the manipulatives have been distributed.
Students check to make sure that each quarter has the same number of animals.
Now students look back at the fraction 3/4. The denominator of 4 told students how many groups. The numerator of 3 in this case tells students how many of the groups had already changed to frogs.
Students count the total number of frogs in 3 groups.
The other group are still tadpoles. Students count how many animals are still tadpoles.
Finally, students may use words, pictures and numbers to record their thinking and explain how they knew their answer was correct.

Extension: After students have mastered this concrete approach to solving fraction problems using the set model, they may move to a paper-and-pencil semi-concrete solution method.

The student draws a square on his paper.
He checks the denominator of the fraction to see how many groups are needed. The student divides the square into that many identical parts.
The student then makes dots or tally marks in each section, as above, dividing the total number of objects evenly among the groups.
The student checks the numerator of the fraction to see how many groups he must label for his answer.

NOTE: The beauty of this method is that students may easily use this approach in standardized testing situations. It's completely portable!
Students may also simply draw four circles to represent the 4 groups and proceed as above.

Practice Problems:

Tadpoles and Frogs requires students to use fractions to figure out how many tadpoles and frogs there were in the tank.
Animal Shelter requires students to use fractions to figure out how many cats and dogs were available for adoption at the animal shelter.
Ask students to write original problems, peer solve and edit, then add to your classroom collection for future use.

Problem Solving: Fractions

2011-06-01T13:45:00.001-04:00

Problem solving activities help students develop conceptual understanding of fractions as they use appropriate fraction models to think about and solve the different tasks. These Mathwire open-ended assessments were designed to measure students' conceptual understanding of fractions.

Pattern Block Fraction Design requires students to fill a shape with pattern blocks to create a design that meets certain requirements. Students must also write a fraction that describes the part of the total design represented by each different color pattern block.

Fraction Game simulates a Fraction War game but students must draw a representation of each fraction and explain who won, based on the drawings. This assessment was designed for students in an Everyday Math program. Students may draw any representation that helps them decide which fraction is larger and explain their thinking.

Mrs. Meatball challenges students to solve pizza fraction problems pictorially. The problems are listed on one page, but students should use lots of room to draw pictures, label and explain how they solved each problem pictorially. NOTE: This task was originally designed for a teacher in-service class where participants were not allowed to use any previous fraction knowledge to solve the problems. They were instructed to use only words, pictures and numbers to solve the problems and explain their thinking. They were not allowed to use any fraction algorithms, etc.

Problem Solving: Multiplication Arrays

2011-05-31T08:33:00.000-04:00

Arrays are one graphical representation of multiplication that students must understand. These problems were created to provide practice in creating arrays.

Ants Marching assesses student understanding of the concept of multiplication as arrays.
Third Grade Parade also assesses student understanding of the concept of multiplication as arrays.
Cheerleader Competition was designed to assess student understanding of multiplication as an array.

Online Resource: Probability Spinners

2011-05-25T10:41:00.001-04:00

Math Playground: Spinner
This online site allows users to customize a spinner by colors, then spin for trials. There is a graph option to display the results by color as they are generated. This is an effective online resource for data collection. Students may easily generate data from larger trials than through the use of a real spinner.

Many teachers use this kind of online generator after student's initial experience with classroom spinners and discussion of the resulting data from this small trial. Students generate hypotheses which may be easily investigated using this online resource to capture more data. A resulting data analysis confirms or disputes the hypotheses and should include a discussion of the use of online generators and randomness.

Note: This site allows the user to customize the spinner by adding labels to each section (e.g. numbers, names, etc.) and to select how many different outcomes there will be.

Check out Math Playground's Probability Spinner.

Tessellations: Online Resources

2011-05-24T15:48:00.001-04:00

Tessellations.org: Check out Tessellations.org for additional information on creating tessellations. Be sure to visit the online galleries to view Escher-like tessellating pieces designed by students. The site also hosts several different methods for creating these tessellating pieces.

Bookmark this online tessellation site as a wonderful resource for your tessellation unit. It would be a great introduction to an Escher unit as well.

M.C. Escher Official Website: http://www.mcescher.com/

Tessellation World of Makoto Nakamura: this artist creates colorful Escher-like tessellations, then animates many of them. This is an incredible site not to be missed in any discussion of Escher and Escher-like tessellations. Check out this Tessellation World for great inspiration. You'll be astounded at both the art and the mathematics inherent in these designs.

Creating Original Escher-Type Tessellations

2011-05-23T09:08:00.000-04:00

These directions support students as they create tessellating pieces that slide to tessellate the page. Creating the tessellating piece is the easy part of this activity. Students traditionally have a tougher time deciding what their creation can be. Use the suggested ideas to help students develop an Escher eye for form.

Help students Develop Escher Eyes to identify the hidden creature(s) in their tessellating pieces. Remember days of cloud watching where you tried to find shapes in clouds? Replicate this experience by placing the cut-out tessellation pieces on an overhead and rotating or flipping them to encourage students to think outside the box and identify many possibilities for their original form. This is an excellent introductory activity before students create their own Escher-type tessellations as it helps students see the possibilities in their own shapes. Project the images so that the whole class can brainstorm together! Encourage students to go for quantity as they try to see many different possibilities in the same shape.

See Directions for creating an Escher-type tesselation. The original PowerPoint file was converted to PDF format for easy viewing. Teachers may use this document to lead students step-by-step through creating their own original tessellating pieces.

Read more about tessellations on Mathwire.com, including a collection of links to tessellation art and activities available on the internet.

Problem Solving: Number Patterns

2011-05-18T09:31:00.001-04:00

Mathematics is full of patterns and mathematicians analyze data, searching for patterns that will allow them to draw conclusions and make hypotheses.

These problems were specifically designed to reinforce common mathematical patterns. Some patterns are easily identified. Others are best solved using an input/output table to collect and analyze mathematical patterns.

Grades 1-2:

Bay Street requires students to analyze the pattern of house numbers on Bay Street. Students write down the pattern they see and use this number pattern to write in the missing house numbers.
King Street requires students to analyze the pattern of house numbers on King Street. Students write down the pattern they see and use this number pattern to write in the missing house numbers.

Grades 3-4:

Baseball Season is a pattern problem that can be easily solved using a table of values.
Anthony's Allowance provides additional pattern practice.

It is important that students identify the patterns they see, using their own words to describe these patterns. Supply mathematical terms as you summarize their findings, adding terms such as odd, even, Fibonacci sequence, repeating pattern, growing pattern, etc. Add these terms to the math word wall so that students may consult this list in future problem solving.

Intervention Strategies: Teen Numbers

2011-05-17T09:49:00.002-04:00

It is very common for young students to have difficulty with the numbers 11- 19. Their names do not follow the common rule and they are the sight words/ numbers of mathematics. Teachers must ACTIVELY help students develop meaning for both the words and the corresponding numerals. It may help to emphasize that the teen numbers are between 10 and 20.

Do some informal assessment to decide where to begin on this continuum:

Rote Counting:

Identify the student's comfort zone: add 1-2 numbers at a time to the 1-10 sequence until the student can reliably count on using the correct names.
Sing songs and extend counting songs: for example, Ten Little Indians can be modified and extended to be 11 little, 12 little, 13 little teddy bears (or dinosaurs or valentines, etc.). Singing is great reinforcement for many students and helps them acquire fluency with these extended numbers more easily than simply counting aloud. [Think about the A-B-C song for learning the alphabet.]
Who Has The Number?: Give students the large demo-size cards (#10-20) and have them hold up the cards as you sing the song so that students hear and see the numbers.
Teen Line-up: distribute the large demo-size cards (#10-20) and ask students to line up in the correct order. NOTE: numbers 10 and 20 of the teen demo cards are boxed in bright orange [see picture above] to visually reinforce the notion that the teen numbers are between 10 and 20. Reinforce this notion often when working with the teen demo cards.
Build the Hundred Board: students need to build the hundred board by placing the numbers or tiles in the correct order. Again, build slowly by varying the number of tiles the student uses to match the individual comfort zone of each student. Alternatively, print out small number cards, attach magnetic tape, and use metal surfaces such as heaters, sides of file cabinets or cookie sheets so that students can build the hundred chart with these number cards.
Classroom Applications: Have student perform classroom duties which support the development of one-to-one correspondence: attendance head count, passing out/collecting papers, paper plates, napkins, etc.

Tally Ho! Game

2011-05-16T07:50:00.000-04:00

This game was created to help kindergarten students learn to use tally marks to count. The game mat was specially designed to support young learners who must master the skill of tally counting.

Tally marks are made in groups of five (four upright and the fifth goes across the four) for easy counting. The game mat has four dots to prompt students to mark four upright tallies. Then the dotted line prompts students to close the gate by drawing the fifth tally across the group of four, Finally, each group of five is in its own box.

Now, students practice making tally marks in a game format. They roll a die and add that many tally marks to their game mat. For ease of use, place the Tally Ho! game mat in a sheet protector and use dry erase pens to make the tally marks. They are easily erased to play again.

Download the Tally Ho! game mat.

Differentiation: Use this dot and dashed line approach as an accommodation for students having difficulty making tally marks correctly in groups of five in classroom activities.

Counting Game: Car Race

2011-05-13T13:07:00.000-04:00

In the counting game, Car Race, students toss a die and move cars that many spaces. First player to cross the finish line wins the game. This is a simple counting game that reinforces counting 1-6 spaces and one-to-one correspondence.

Download the directions, game mat and center icons for Car Race.
The game mat is printed in 3 sections which should be taped together.
Students enjoy using small cars as their game pieces.
NOTE: This game was developed by a Monmouth University student for the Probability Fair.

Hundred Board Puzzles

2011-05-12T10:44:00.000-04:00

The hundred board or chart holds a prominent place in primary math classrooms. The chart is a visual representation of the patterns in our mathematical system of numbers.

Students are able to learn the patterns in the hundred board by assembling puzzles. Teachers are able to assess student use of patterns in rows and columns by observing the student at work.

Differentiation:

This task is easily differentiated to accommodate the varied levels in a first grade class by changing the number of pieces and the shape of the pieces. Puzzle bags should be sequentially lettered so that students progress through harder versions of the task.

Extensions:

Have students and their families create their own hundred board puzzles.
Challenge students to fill in missing numbers on hundred board pieces or whole hundred boards as practice using the patterns in the hundred board.

Materials:

Download a hundred board template.

Active Participation: Let Go and Let Students...

2011-05-11T09:46:00.000-04:00

This phrase reminds teachers to put students in charge of their learning and in charge of explaining themselves. This practice incorporates multiple effective strategies to support student learning:

Give students the chalk or marker and ask them to come to the board or overhead to explain their thinking. Resist asking students to tell you what they did while you write what they did. Asking students to write as they explain allows them to organize their thinking and provides insight to teachers about what strategies and organizational methods students use effectively and independently. This strategy also provides practice for the expected independent test performance.
Ask another student to repeat a student's explanation or insight. Resist the urge to repeat or paraphrase each student's response. Ask classmates to do this instead, fostering active participation/listening skills in all students.
Ask students to read directions or problems aloud rather than reading them yourself. Once again, this practice encourages students to develop effective reading skills for math activities and tests. If reading levels are an issue in your classroom, you might begin with buddy reading, pairing students to effectively mitigate this issue.
Ask students to define math vocabulary terms in their own words. Post the best definitions around the room.
Post samples of effective problem-solving solutions that meet tough requirements of the problem-solving rubric you use to grade student responses. Make overheads of student samples and review them regularly so that all students see examples of effective ways to organize solutions and explain thinking.

Expect students to be capable of some independent work. Voice this expectation to students as in "I want to see how each of you does on Math Boxes #3 and #4 today, so please begin with those boxes. I believe that everyone can do these by themselves and I will be around to check. After you finish these two math boxes, you may do the others in any order you choose."
Quickly spin off students who are capable of independent work. Provide enrichment activities that go beyond current grade-level expectations and require higher-order thinking skills for solutions. Encourage these students to play harder versions of math games (i.e. more cards, larger numbers, etc.)
Differentiate and scaffold instruction to effectively meet the varied needs of learners in your classroom. Provide enrichment activities for talented students while you work with small groups who need additional instruction or scaffolded support/encouragement during independent practice. Use flexible grouping based on informal assessment of student responses during instruction.

Mathwire Materials:

Download Active Participation Strategies for Math Classes: a one-page text-only summary of the strategies discussed above
Download Active Participation Strategies for Math Classes: the full text of this section with pictures

Hidden Butterfly

2011-05-09T09:26:00.000-04:00

Sneak Preview

A new Butterfly Themed Math Activities is under development at Mathwire.com. Here's a sneak peak at one of the new activities.

Hidden Butterfly challenges students to use the clues provided to figure out which number the butterfly has hidden behind. Students read each clue and eliminate the numbers that don't fit, crossing them off on the number grid. They continue clue by clue until only one number remains.

Download the Hidden Butterfly PDF document which includes 6 logic problems, answer key and a blank template for students to create their own Hidden Butterfly logic problems to challenge their classmates.

Active Participation Strategy: Show Me The Answer

2011-05-04T17:44:00.000-04:00

Look for opportunities to incorporate visual components into student responses. For example:

Use student digit cards to have students form the largest or smallest number from those digits. Or dictate a number and have students form the number using their digit cards. The teacher may then ask students to hold up the digit in the hundreds place or in the ten-thousands place. See More Place Value Activities for additional suggestions.
Give students small response cards: even/odd, prime/composite, yes/no, area/perimeter and ask students to hold up the correct card to respond to questions.

Math Competitions

2011-05-03T12:51:00.000-04:00

The end of the school year is a great time to try out new activities and strategies. Your students are accustomed to your procedures and expectations. Teachers are able to get immediate feedback on these activities, then tweak them to best fit the needs of students in the class. Then, the activities are ready for immediate implementation in the fall.

These activities are also well-suited to use during the end of the school year when schedules often become chaotic with students missing class for assemblies, choral practice, field trips, etc. The games accommodate varied number of students and may easily be implemented by substitute teachers or used in combined classes.

See the new May 2011 issue of Mathwire for specific information on these games and suggestions for implementing grade level competitions as a way to motivate students to master basic facts and develop number sense.

Thirteen Ways of Looking at a Half

2011-05-02T15:59:00.001-04:00

This online Cyberchase activity challenges students to find the 13 different ways to shade in the figure to show one-half.

Download a Thirteen Ways recording sheet so that students can shade in their solutions to find all 13 before entering them into the computer.
Visit the Thirteen Ways of Looking at a Half website to enter all of the one-half shaded solutions you found.

Math-Literature Connection: Give Me Half!

2011-04-29T18:51:00.000-04:00

Give Me Half by Stuart J. Murphy

This book takes a humorous look at splitting things in half. Follow a reading and discussion with this worksheet where students practice splitting shapes (area fraction model) and groups of shapes (set fraction model) into half fairly.

Download Give Me Half! worksheet.

Folded Fractions

2011-04-28T16:57:00.000-04:00

Students need many concrete experiences with fractions to develop a deep understanding of the three models of fractions: area, linear and set models. Teachers need to address all three models in well-designed instructional activities so that students develop a rich concept of fractions that they can use to make sense of numbers, operations, measurement and probability.

Folded Fractions: For this area model, students use 4 pieces of construction paper to create this set of fraction manipulatives. Students fold the paper following instructions, unfolding to easily see how many pieces are now in the whole. After marking each piece with the correct fraction part, students cut apart the fractional pieces.

This model is easily created from classroom materials and students should keep their sets in their desks. Students may use the fraction pieces during instruction, in problem solving or to play games. By using the yellow "1" or "whole" mat, students may easily combine different fractional pieces to create a whole, etc., placing pieces on top of the yellow mat to see different ways of making a whole.

Download directions for making Folded Fractions.

Other Area Models

Students divide shapes into the appropriate number of equal sections given by the denominator, then shade in the appropriate number of sections, given by the numerator to create a picture of the fraction. Equivalent fractions are also developed using this area model. Teachers may also use any of these manipulatives to develop the area model:

pattern blocks
circular fraction regions
pizzas
geoboards
spinners

Problem Solving: Fractions

2011-04-27T11:08:00.000-04:00

Students are challenged to solve these problems by drawing pictures rather than using traditional fraction algorithms. This is an extremely effective strategy to develop student conceptual understanding of fractions, fractional parts and fraction operations.

Tadpoles and Frogs requires students to use fractions to figure out how many tadpoles and frogs there were in the tank.
Animal Shelter requires students to use fractions to figure out how many cats and dogs were available for adoption at the animal shelter.
Fraction Game simulates a Fraction War game but students must draw a representation of each fraction and explain who won, based on the drawings.
High Number Game requires that students apply their knowledge of fractions, decimals and percents to decide whose number card is highest.
Pattern Block Fraction Design requires students to use pattern blocks to fill the shape so that it has a line of symmetry. They must then write a fraction for each color pattern block used in the design.
The Adventures of Mrs. Meatball problem set challenges students to draw pictures to solve each problem and prove their answers.
Monkey Business challenges students to work backwards to solve this fraction division problem.
Bake Sale challenges students to work backwards to solve another fraction division problem involving disappearing cookies.

Fractions: Spin to Win Game

2011-04-26T12:26:00.000-04:00

It is important that students develop numerical sense in fractions. One excellent activity is sorting fractions as close to 0, close to 1/2, close to 1. This activity forces students to think about fractions in a whole different way and enriches student understanding.

The Spin to Win Game was developed to provide fun practice in this skill. Students play in pairs. Each student draws a card from the fraction deck. One student spins the spinner. If the spinner lands on "closer to 0" then the student whose fraction is closer to 0 wins both cards. The same holds true for "closer to 1/2" or "closer to 0." If the students turn over equivalent fractions, they pick another card and spin to win all 4 cards.

Materials:

Download Spin to Win Game directions and spinner.
Download Fraction Cards.

Writing to Learn: Fractions

2011-04-25T10:47:00.000-04:00

Headline: 3 out of 2 people don't understand fractions.

Journal entries, student-illustrated definitions and open-ended problems help students use writing to learn fractional concepts and terms. Students should be encouraged to draw pictures to illustrate fraction concepts or to solve problems.

These are some sample writing prompts to probe student understanding of fractions:

Explain what the numerator and denominator of a fraction tell you. Give 2-3 different examples that include numbers, pictures and words.
Is 1/4 or 1/8 larger? Use words, pictures and numbers to explain your thinking to someone who doesn't understand. Can you write a general rule that helps you decide quickly?
John says that 1/100 is the smallest fraction. Do you agree or disagree? Use words, pictures and numbers to support your position.
Is 7/8 or 9/10 closer to 1? Use words, pictures and numbers to explain your thinking to someone who doesn't understand. Can you write a general rule that helps you decide quickly?
Sort the fraction cards into groups of close to 0, close to 1/2 or close to 1. What strategies did you use to quickly sort the cards into these groups? Which fractions were harder to place? Why?

Teachers might elect to use the Think-Pair-Write-Share strategy with these prompts.

Think: Ask students the question, then provide some quiet think time for students to grapple with the concept and organize their thinking, perhaps selecting an appropriate fraction model to explain their thinking.
Pair: After a few minutes, student pairs discuss their thinking. This is especially beneficial for the reluctant writer as they often find it easier to "talk" a solution. Students also benefit from hearing different approaches to the problem, adding to their repertoire of strategies they have available for future tasks.
Write: Each student writes (words, pictures, numbers) to explain their thinking in response to the prompt.
Share: Teachers use a variety of strategies for this sharing session. Sometimes teachers select students to represent the different ways of thinking about the prompt, asking those students to read their responses aloud. Other times, teachers might circulate around the room as small groups discuss their responses.

Math-Literature Connection: A Quarter from the Tooth Fairy

2011-04-22T11:02:00.000-04:00

In this book, Caren Holtzman [Hello Math Reader, Level 3] recounts in verse how a young boy spends the quarter he got from the Tooth Fairy for his tooth. He first buys a monster for his quarter but then decides it wasn't quite right and returns it, getting 2 dimes and 1 nickel back. Each time he buys and returns an item, he gets his 25 cents back in a different combination of coins, making this book an excellent introduction to the problem of how many different ways students can make 25 cents.

Challenge: What other ways could the character have gotten his 25 cents in change?

Try to find all of the different ways.
How did you organize your answer to be sure you had found all of the ways?
Download the How Many Different Ways Can You Make 25 Cents? student worksheet and answer key.

Writing Extension: Each student writes additional pages for the story that describe what the character buys and what combination of coins he gets back when he ultimately returns the item.

Math-Literature Connection: Pezzettino

2011-04-21T10:56:00.000-04:00

Pezzettino by Leo Lionni is a great introduction to the concept of area as how many small squares cover a surface. In this book, small squares are used to create the characters.

After reading the book, have students use color tiles or paper squares to first estimate how many squares will cover an object then actually use the squares to measure the object.
Students can also create their own Pezzettino characters using colored construction paper squares. The class discussion should focus on comparing the "sizes" of these Pezzettino characters based on their area or the number of squares used to construct each character.

Download the Pezzettino Characters handout and squares template. The squares template can be used to copy squares onto construction paper that has been trimmed to 8.5 x 11 inch size to use in a copier. Ellison pattern block square cutouts will also produce small squares from construction paper.

Developing Number Sense

2011-04-20T09:59:00.000-04:00

Students in Everyday Math classes play a game called Name That Number. Make It Count is a very similar online game. Students are dealt number cards, given operations and a target number. The students must use only those cards (all or some) and the given operations to produce the target number. They click on Submit to check their solution and get immediate feedback. If the student is stumped by a particular combination of cards, they may click on See Answer to view a possible solution

These games provide practice of basic facts. The real beauty is that students rehearse many different options in the search for one successful combination, developing number sense. There are often several possible solutions, so students believe they will be successful, motivating them to search for a solution when one is not initially evident.

After a class presentation of the game, students often benefit from playing as pairs, generating mathematical discussion and debate in the search for a solution. This online game might also be added to Parent Resources as students may play for free at home.

Play Make It Count online.

The Make the Number template may be downloaded and used in class as a warm-up or Do Now! activity. For renewable use, students insert the template into a clear sheet protector and use dry erase markers to write in the target number and the number cards. They use the white space to write down and check possible solutions.

NOTE: Teachers may opt to make an overhead of this template so that students are able to record different solutions they find. If the overhead is also inserted into a sheet protector, students may use dry erase markers to record their solutions. The sheet protector is easy to clean and the overhead may be kept in a teacher binder for easy retrieval as needed.

Extension: The Contig game is a natural extension of this activity and it develops number sense as students search for the best possible solution that will win them the most points. Students should know multiplication and division facts, but older students are easily challenged by this game. Try it!

In the Contig Game students toss three dice. They use those three numbers and any operations to form a number on the game mat. Players earn an extra point for each covered number the new number touches, so students quickly learn to search for the best move that will yield the maximum possible points. The instructional benefit of the game is that students try many different combinations in search of that best move.

Contig Jr. is designed to provide that same format for younger students who need to develop mastery of addition and subtraction facts.

Suggestions:

Introduce these games to students and provide students time for supervised play.
Make the games available in the math center for use during center time or indoor recess or game day.
Insert the game mats into clear sheet protectors and use dry erase markers for renewable play.
Home Connection: Send a copy of the game mat home for students to teach parents and play at home for additional practice.

Earth Day Math Activities

2011-04-18T01:21:00.000-04:00

In a time when environmental activists are urging every American to make small changes, there are many online lesson plans and activities that help students think about the environment and how daily choices and practices impact our earth either positively or negatively.

Mathwire has assembled a collection of links to online activities. Be sure to check out the Earth Day Math Activities when planning your classroom celebration.

Math-Literature Connection: Ladybugs

2011-04-15T12:58:00.003-04:00

The Grouchy Ladybug
by Eric Carle

Download Vicki Blackwell's Grouchy Ladybug clock.
See NCTM Illuminations lesson plan for this book which develops students understanding of time based on activities in their days.
View an entire ladybug unit from Homeschool Share.

Ladybug on the Move
by Richard Fowler

See NCTM Illumination's Ladybug Lengths unit that helps students develop the concept of measurement through the use of nonstandard units including a ladybug tape that may be downloaded from the site.
Let students play with the Hiding Ladybug applet to practice measurement skills.
Ladybug Leaf is another online version of this applet game that requires students to estimate distances in a Logo-like environment.

Lots of Ladybugs
by Michael Dahl

This book was designed to provide practice in counting by fives, offering yet another way to include math in a ladybug unit. Each page adds five more spots to count until you reach 50.

Download Ladybug Counting worksheets.

NOTE: The worksheet is designed as a companion to the Lots of Ladybugs book.

Worksheet 1 has all numbers in a traceable font.
Worksheet 2 has some missing numbers. Printed numbers are in traceable font.

Ladybug Scramble

The ladybug cards are all scrambled and students must put them in the correct order. This deck is designed to be printed on card stock, cut apart and stored in plastic bags for use in a math center.

Download Ladybug Scramble cards in color.
Download Ladybug Scramble cards in black-white.

Differentiation: This activity is easily differentiated by varying the number of cards given to students to accommodate the varied learning levels in the class. Consider creating A, B, C sets in baggies that contain different number of cards. Students may move to the harder level once they have mastered the first set.

Ladybug Links

2011-04-14T12:15:00.000-04:00

For those who remember the Logo language, NCTM Illuminations offers a similar experience for students today. The Ladybug Adventures unit requires students to use geometric and measurement skills to program a sequence to move the ladybug under a leaf or through a maze.

Students use NCTM's Hiding Ladybug applet to design a path that will take the ladybug beneath the leaf for a great problem solving experience. This online applet encourages students to refine their paths until they are ultimately successful.
Making Triangles and Making Rectangles require students to teach the ladybug to use specific angles to create shapes that will hide the ladybug under the leaf.
Finally, Ladybug Mazes challenges students to develop a series of moves that will successfully navigate the ladybug through the given maze.

These online applets are exceptional tools to help students think about and experience geometric concepts. Students are motivated by the challenge and get immediate feedback on their success. The applets allow students to refine their initial attempts, another plus in motivating students to successfully master the skills to meet a challenge.

There are additional Ladybug Links available on Mathwire's Ladybug Themed Activities.

Ladybug Game

2011-04-13T00:10:00.000-04:00

The Ladybug, Fly Away Home! game uses a one-die toss to move that numbered ladybug one space closer to her home. Students add their results to the Class Recording sheet by adding a tally mark for the winning ladybug. Class discussion focuses on the fairness of the game by asking if each ladybug has an equal chance to win? PDF file includes directions, game mat, recording sheet and math center icons

Download the Ladybug, Fly Away Home! directions, game mat, recording sheet and math center icon.

Ladybug Patterns

2011-04-12T00:07:00.001-04:00

Ladybug Patterns introduces students to the algebraic concept of growing patterns or functions. In this case, the dots on the ladybug change with age. Students may use the picture and a function table to analyze the pattern's growth and write a rule in words and/or variables/numbers.

Download the Ladybug Patterns student handout.
Download a blank Ladybug Patterns handout so that students can create their own original patterns to challenge their classmates.
NOTE: teachers may use an overhead of the blank pattern handout to create additional patterns for students to analyze (e.g. double the age, 2 more than age, etc. )

Ladybug Odd & Even Numbers

2011-04-11T09:02:00.000-04:00

Students use counters and their ladybug mats. Count out the correct number of counters for the given number. Place counters, alternating sides, onto the ladybug mat until all counters are placed. If there are the same number of counters on each side of the ladybug, then the number is an even number. If one side has an extra counter (spot), then the number is an odd number.

Download Ladybug Math for directions for Odd and Even Ladybugs, recording sheet, number cards and Odd/Even Recording Sheet.
B/W Ladybug Mat includes mat, recording sheet and number sentence template.
Color Ladybug Mat may be used with round counters or black foam circles.

Suggestion for Morning Math Routines: Place a ladybug template in a sheet protector or laminate the ladybug. Use a dry-erase marker to add a new spot each day. Discuss whether the ladybug has an odd or even number of spots, based on whether there are the same number of spots on each side of the ladybug. Incorporate this practice into morning routines to reinforce odd and even numbers.

Question of the Day

2011-04-05T15:40:00.000-04:00

Collecting, organizing and analyzing data are essential skills in today's world. Some teachers incorporate daily practice by including a question of the day in the morning routines. Students have markers with their names, and they are accustomed to completing this task when they arrive in the classroom, placing their marker in the correct spot. If students are non-readers, assign one student to be the interviewer, repeating the question to classmates as they arrive in the classroom.

Suggestions:

Vary the format of the data organization, providing practice by using bar graphs, clothespin graph, Venn diagram, tally chart, line plot, glyph, etc.
Use seasonal, weather, holiday prompts to collect data.
Coordinate math question of the day to current literature, science or social studies units.
Extend assembly and field trip experiences by graphing data about the particular theme.
Check out this list of data questions for young learners.

Free the Animals Game

2011-04-04T10:25:00.000-04:00

Who will free their animals first? Students toss two dice, calculate the difference and free an animal from that number cage. Younger students will enjoy this animal version of the Release the Prisoners game and learn subtraction facts as well. Both the 6-sided dice game mat and the 12-sided dice game mat are included with directions.

Download the Free the Animals game directions and game mats for 6-sided dice to practice easier subtraction facts or 12-sided dice to practice harder subtraction facts.
Download the Free the Animals game recording sheet designed so that students can track how many animals each player places in his/her cages and who wins. Hopefully, students will learn something about probability while mastering subtraction facts.

Money: Coin Values

2011-04-01T14:02:00.000-04:00

Coin Race
Mrs. Higgins and Ms. Gillespie's first graders at Port Monmouth Road School in Keansburg, NJ, use large magnetized coin cutouts to make the correct money amount. This activity provides a platform for discussing different ways to make the same amount as student pairs often choose different coin combinations. Students at their seats use coins to create combinations as well and record them on whiteboards, if desired.

Many Coins, Many Ways
Challenge students to find all of the different ways to use coins to express the day's date. Students may start this challenge haphazardly, but this activity presents older students the opportunity to learn the value of using an organized approach to solving these types of problems so that they will be confident that they have found all of the possibilities. Teachers might model the use of a chart, for instance, to record combinations. Students should be prompted to talk about the orderly approaches they used.

Place Value Game

2011-03-29T06:30:00.000-04:00

Games provide extended place value practice for students and allow them to use their conceptual understanding to develop appropriate strategies to win the game. The best games encourage students to try out many options in search of the best solution. This search for the best solution prompts additional practice in a highly-motivational setting.

Place Value Game: Students use number cards to create the largest number possible.

Materials:

Deck of digit cards for each set of partners (2-4 each of #0-9, depending on the level of students and the size of the numbers they will create) Note: Spinners with #0-9 may be used instead of cards, if desired.
Place value mat for each player.
Recording sheet, if desired.

Directions:

Partner A turns over the first card and decides where to place that card on his/her place value mat. Once the card is placed, it may not be moved.
Partner B turns over a card and decides where to place that card on his/her place value mat. Again, the card may not be moved once it is placed.
Play continues with each partner turning over a card and deciding where to place it on the place value mat in hopes of building the largest number.
When all slots are filled on the place value mats, partners compare numbers to see who created the larger number. That partner wins a point for the round.
Partners record both numbers on their recording sheet and circle the larger number
Students clear their mats, shuffle the cards and play additional rounds, as time allows.

Variations: Students try to form numbers to meet specified criteria (which will vary from these suggestions, based on the number of digits used):

Students try to form the smallest number.
Students try to form a number that is closest to 500 (or 2000 or...)
Students try to form a number that is less than 1000.
Students form numbers and earn a different number of points, depending on the range within which the number falls (e.g. 1 point for numbers from 0-500, 2 points for numbers from 501-1000, etc.)

Mathwire Who Has? Deck Collection

2011-03-28T11:15:00.000-04:00

Several decks are available on Mathwire for downloading as PDFs. All decks are 30 cards so that there are enough cards for most classes. In fact, some students will probably need to have two cards to use the complete deck. The decks are designed to print onto 2x4 inch labels (10 to a page). These can then be affixed to index cards to create each deck. If labels are not available, simply cut and paste the printout to create card decks.

More or Less Deck: this deck was developed to help students develop mental math proficiency. Students will learn to mentally add or subtract a one-digit number or a multiple of 10. Regular practice helps students develop proficiency in mental addition and subtraction.

Download the More or Less Deck

Coins Deck: Two decks are available for this series.

Coin Deck uses clip art of actual coins on each card. Students answer the question Who has 40 cents? by stating I have 4 dimes, reading the coins on their cards to correctly answer the question. Note that this 20-card version uses both heads and tails of coins.
Coin Deck with Antennas is the same deck as above, but antennas have been added to coins for an easy coin-counting modification for struggling learners. Read more about the coin antenna strategy in Mathwire's Money Activities & Strategies collection.

Doubles Deck

This doubles deck was developed to provide practice in doubles facts. This 20-card deck is straightforward practice of these important facts. Regular practice helps students develop mastery of doubles.

Base Ten Deck

The Base Ten deck provides practice in recognizing numbers pictured in base ten block representation.

Mathwire Who Has? Collection

These are a few samples from the Mathwire collection. See Who Has? Activities to read more about using these decks in the classroom and to download additional decks for fractions, geometry, etc.

Who Has? Decks: Multiplication Facts

2011-03-24T20:57:00.000-04:00

Once students have developed conceptual understanding of the basic operations they need to develop fluency with the facts. One quick way to include daily practice and motivate students to master these basic facts is through the use of the Who Has? card decks. These decks can be created for virtually any topic and frequent use as both a whole class practice or as a center activity for partners or small groups will provide facts practice in a highly-motivating format.

Classroom Management Strategies

There are several strategies that have proven successful when implementing this activity:

Distributing Cards: Distribute one card to each student, then distribute the extras to strong students in the beginning and to random students as the class becomes more familiar with the deck.
Class Play: As you distribute the cards, encourage students to begin thinking about what the question for their card might be so that they are prepared to answer. When all cards are distributed, select the "0" card or any student to begin. Play continues until the game comes back to the original card. That student answers and then says "stop" to signal the end of the game.
Timed Play: Consider using a stopwatch to time the class game. Record the time on the board so that students try each game to beat their current best time. This practice encourages students to stay attentive and prompts students to practice basic facts so that the class time improves.
Calling Out Answers:Discourage this practice by adding 5 seconds onto the class time whenever you hear an answer from someone who does not hold the card. Use the same penalty for students who express vocal displeasure with delays by other students.
Partner or Small-Group Play:
- One student deals out the cards to all players.
- Players arrange the cards face-up in front of them. Students will find that arranging the cards in order from least to greatest will help them locate cards quickly.
- Play begins with the "0" card or any card held by the player to the dealer's left.
- Play continues as in the class game. Whoever has the card that answers the question reads that answer and then reads the question on that card.
- Students turn over the cards after reading them.
- The first person to turn over all his/her cards, wins the game. [Note: this is completely random but don't tell the students!]
- Shuffle the cards and repeat the game.

The current record for the multiplication deck was held by a fourth grade class in New Jersey who completed the deck in 59 seconds.

Mrs. Leanne Cherosky's 5th grade class at Buffalo Elementary just e-mailed that they broke the record with a time of :56.593. Congratulations, 5th graders!!!

If your class beats this record, be sure to leave a comment on this post with grade level, school and the time.

Writing in Mathematics

2011-03-23T10:59:00.000-04:00

Getting Started

Often students who have difficulty writing in math class have less difficulty telling the teacher what they think. Capitalize on this oral strength by incorporating the think-pair-share strategy more often into math lessons as a prelude to writing. Using either of these options will increase the active participation of all students in the class. The pause after a teacher's question provides think time for students, accommodating different learning styles and requiring all students to engage and reflect.

Think-Pair-Share: Some students are reluctant to write at first and benefit from practice sharing thoughts with a partner and hearing that partner put thoughts into words. Reluctant students get to "practice" in a small setting with a partner before speaking to the whole class. These students can also choose to share their thoughts, their partner's thoughts, or a combination of the two.

The basic steps of Think-Pair-Share are:

Question: Ask an open-ended question and tell students that they will think-pair-share the answer.
Think: Give students 1-2 minutes to think quietly about their response to the question. Walk around the room to reinforce this quiet, on-task response.
Pair: Ask students to share thoughts with their partners and ask questions if they don't understand what their partner is saying. Circulate around the room, listening to student conversations.
Share: Ask for student volunteers to share as you begin this process. Later, you should call on non-volunteers to increase student accountability in this cooperative learning strategy. Reinforce the expectation of active listening by requiring students to acknowledge the thoughts of classmates by saying:
- I agree with [name's] answer...,
- I don't agree with [name's] answer...,
- I started the problem like [name] but then I...
NOTE: It is not necessary and, in fact, it is usually not time-effective to have each group share. As you circulate around the room during the Pair share, identify students who have used different strategies or great models for thinking about an important concept. Call on these students or their partners to share with the class.

Think-Write-Pair-Share: Once students are comfortable with the Think-Pair-Share strategy, introduce the Think-Write-Pair-Share strategy. This strategy incorporates writing into the thinking process. As students think about the question, they also write their response to the question using a variety of techniques: webbing, words, pictures, numbers, examples. Teachers might start with a prompt poster that students can use for reference when they don't know where to start. Effective prompts use successful pre-writing strategies such as:

Make a web.
Draw a picture and label.
Write a definition in your own words.
Create examples of the skill/concept and explain.
Write about a real-life use of this math concept or skill.
Connect the concept/skill to concepts/skills you already learned and use.
Reflect on your understanding of this concept/skill on a scale of 1-5 and explain.
Create a K-W-L chart of what you already know, what you want to know and what you have learned about the concept/skill.

Students then share their written responses with partners during which time students might elect to edit their own written response, choosing to replace certain words with better mathematical vocabulary, or add ideas and statements from their partner's writing. Finally the teacher selects some students to share written responses with the class. This process encourages students to get something down on paper and allows them some editing functions through the partner pairing. Additionally, students benefit from regular listening to classmates sharing their own writing.

More Organized Counting

2011-03-22T15:40:00.000-04:00

Houses in a Row

This problem challenges students to figure out how many different color combinations are possible for a row of houses, if no two houses can be painted exactly alike. Use large color squares and triangles to model this problem for students as an introduction to combinations.

Download Houses in a Row student worksheet and solution.

NOTE: Have students explain their thinking and how they organized their information. It is also important to ask students how they knew that they had found all of the possible combinations.

Problem Solving: Organized Counting

2011-03-21T21:15:00.000-04:00

Stoplights challenges students to figure out how many different stoplights they can create with 3 different color linking cubes if each stoplight must have one cube of each color. Use linking cubes so that students can assemble all possible stoplights.

NOTE: You may choose to have students use any three different colors so that each student pair has enough linking cubes to assemble all possible combinations using one of each color to create the stoplight.

Discussion: In these types of problems, it is important that students know when they have found all of the possible combinations. Be sure to ask students to explain how they know they have all of the combinations. How did they know when they could stop looking?

Try to let students work on the problem without organizing their thinking. Let pairs of students work together. Ask students to explain their method and their thinking. Peer explanations are so powerful in problem solving.

You may be surprised at how students organize the challenge. I remember a first grader telling me that he knew when he had them all because each color got to be on top twice. He simply switched the bottom two cubes, then let another color be on top, etc. To him, it was like being in the front of the line. It was such a succinct explanation from a young learner. Amazing!

Download Stoplights which includes the student handout and a brief explanation. Be sure to make extra copies available to students, so they aren't led into believing they must find 6, which is the correct answer.

Suggestion: To keep this task truly open-ended, hand out blank paper and have students draw their answers. This method does not prompt students and also mimics state testing.

Scrambled Eggs Game

2011-03-18T05:36:00.000-04:00

Successfully skip counting by 5s is an important mathematical foundation for the 5 times table, for counting nickels, for rounding numbers, etc. Counting by 5s and counting by 10s are often the first rote skip counting a student learns. While some students will naturally learn the count through classroom activities, other students will need deliberate intervention to master this sequence.

Scrambled Eggs Game

Distribute large cards with multiples of 5 to students. Ask students to quietly assemble themselves in correct order, holding the card in front of them. Time the class in this activity, if this motivates your class to master the sequence.

NOTE: Cheap, white paper plates work well for this activity. Write large numbers with a black sharpie pen. Paper plates stack easily for storage and also hold up well through repeated use.

Partner Game: Each partner shuffles a set of count by five cards and turns them face down. On the word "GO!" each partner turns over the first card and places it roughly before him/her. Each student turns over one card at a time, ordering the cards before him/her until all cards are in correct order. First student to correctly order the sequence of cards wins the game.

Download Count by 5 Cards for individual student use. Copy on card stock, cut apart, and place in baggies for partner game use.

Shamrock Paths

2011-03-17T10:23:00.000-04:00

Shamrock Paths challenges students to use Pascal's Triangle to figure out how many different ways there are to spell Shamrock. Included in the PDF file are an explanation of how this problem relates to Pascal's Triangle and the numerical solution to the challenge.

Download the Shamrock Paths student handout, explanation, and the solution.

Domino Flash Game

2011-03-16T06:48:00.000-04:00

Play Domino Flash to help your students master the domino (and dice) patterns. Each student needs a domino mat and counters. Teachers may use overhead dominoes or Domino Flash Cards (copied on card stock, and cut apart) for this game.

Domino Patterns: The teacher shows a domino for a count of 5-10 seconds, depending on the ability level of the students, then covers it. Students look at the domino as it is shown, then build the domino from memory, using a domino mat and counters. The teacher circulates around the room as students work, to observe student performance. After some time, the teacher asks students to describe the domino they saw and how they remembered the patterns to build. Finally, the teacher shows the domino again so that students are able to self-correct.

Fact Family Practice: The teacher shows a domino for a count of 5-10 seconds, depending on the ability level of the students, then covers it. Students look at the domino as it is shown, then build the domino from memory, using a domino facts template inserted in a sheet protector. Students use dry erase markers to write the fact family for the given domino.

Center Activity: make the Domino Flash Game materials available for students to play as pairs or triads at center time. Students love to rotate playing teacher for this game!