Saturday, December 18, 2010

Gingerbread Man Math Activities

Check out Mathwire's Gingerbread Man Math collection for timely math gingerbread activities to accompany this seasonal unit.  The collection includes activities to develop measurement, probability, symmetry, problem solving, games and literature links to popular gingerbread books.

Older students will practice coordinate graphing skills as they play Catch the Gingerbread Man, a Battleship-type game where students try to capture their opponent's gingerbread men.

Younger students will enjoy the Run, Gingerbread Man, Run! game which comes with a colored spinner, gameboard and directions for small group play.  Students will practice simple counting skills as they try to be the first to move through the colored board.

Students may use a copy of the gameboard to analyze the results of winners:
  • Did the red, yellow, blue or green gingerbread man win more often?
  • Does each color have an equal chance of winning?  Explain your thinking

Problem solving activities involve combinations.  Gingerbread Bake Sale challenges students to figure out if Ruby can make each of the 12 gingerbread cookies on a cookie sheet different, given the possible eyes and noses.  Gingerbread Man Combinations is a harder version of this problem, with more choices to challenge older students.  Gingerbread Man Chain requires students to use measurement skills to figure out how many gingerbread men will be needed to create borders at the top and bottom of a bulletin board.

Thursday, November 18, 2010

Turkey Glyph

Students in Mrs. Bestle's class in Keansburg, NJ, created turkey glyphs that tell a story about how they celebrate Thanksgiving and what foods they like to eat on that special day.  It's great to have students create the legend(key) for what different parts of the turkey glyph mean (e.g. like white or dark meat, eat home or away, like gravy, feather colors for different vegetables, etc.)

Glyphs are a great visual display of data and may be used to create a seasonal bulletin board of student work.  Be sure to use the display for some data analysis activities. 
  • Will more people in this class eat at home or away for Thanksgiving?
  • Do more people in this class like corn or potatoes
  • How many people in this class like yams?

Developing the legend(key) with students allows teachers to customize the activity to fit individual classes.  Creating a legend for a glyph is a higher-order thinking skill that develops critical thinking skills. 
See turkey glyph for one teacher's legend and lesson plan for this activity.

Saturday, November 6, 2010

Guess My Rule Game

This function machine game was created to give students practice in saying and writing the rule, given an input/output table. One student has the rule which the other student has to guess. The guesser records an input number in the table. The rule person must apply the rule and tell the output number. Student pairs repeat this until the guesser correctly identifies the rule by saying and writing it. Students then switch places and repeat the activity.

Download three different levels of rules for play: simple addition & subtraction, multiplication or two-step rules.

Differentiation:  This game is easily differentiated by varying the rule cards provided to students.  Use simple one-step addition and/or subtraction for basic skills students and challenge better students by graduating them to 2-step rules.  Consider printing the different level rules on different color paper so that students may easily select the proper level from the math center.

Enrichment:  Provide blank cards for students to create their own rules to challenge their peers.  Be sure that students try their rule on at least 3 other students to be sure that they have written it correctly.

Wednesday, November 3, 2010

Investigating Growing Patterns

Introduce elementary students to the concept of functions by investigating growing patterns. Visual patterns formed with manipulatives are especially effective for elementary students and allow them to concretely build understanding as they first reproduce, then extend the pattern to the next couple of stages. Finally, students explain the pattern in words and try to write a rule that works for any stage.

See Mathwire's Investigating Growing Patterns for specific suggestions on using these patterns to help elementary students develop a concept of functions. The article includes activities with handouts that teachers can use to introduce this topic to elementary students. A Function Scrapbook of function ideas is included and examples of function problems created by elementary students will be added as they are completed. Literature connections and web links to relevant sites on the internet are also included in the article.

Thursday, October 28, 2010

Math App: Motion Math

This app targets students' understanding of fractions.  As students work their way back into space, they must sort fractions by tilting the iTouch (iPhone, iPad) so that the ball bounces in the proper spot.

The app provides practice in different representations of fractions.  Students must drop the ball at the correct location on a number line in one level.  Another level presents a visual representation of the fraction which students must also bounce at the correct location.

Still other levels ask students to sort fractions as less than, equal to, or more than the given fraction.  These sorts may contain fractions, visual representations, percents, and decimals so that students become accustomed to equivalent representations of fractions.

This is a great app for fraction practice.  Students are playing AND learning at the same time.  Students only need to move the iTouch to make the ball bounce in the correct location.  Correct responses generate a corresponding marking on the number line.  Incorrect responses prompt an arrow indicating which way the user should bounce the ball the next try.

The app is available through iTunes for 99 cents.  It's certainly worth the price to provide fraction practice in a game mode.  Be sure to check out more about the game and the research behind this app at Motion Math.

Wednesday, October 27, 2010

Pattern: Triangular Numbers

Bat Jamboree by Kathi Appelt 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.

  • 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.
  • 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.
  • See more Bat Activities in Mathwire's Math Activity Themes:  Bats collection.

Sunday, October 24, 2010

Symmetric Faces

Halloween masks become a math activity when students create Symmetric Faces. See Symmetric Faces in the Geometry Section for directions to make these unique masks using 1.5 sheets of construction paper, scissors and glue.

Thursday, October 21, 2010

Introduction to Coordinate Graphing

Introduce elementary students to coordinate graphing through seasonal coloring activities. The fall Jack-O-Lantern activity requires students to use the grid code and crayons or markers to create a jack-o-lantern on a blank 9x9 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.

Download the Mathwire Jack-o-Lantern graphing activity.

Download the Mathwire Mad Monster graphing activity.

Monday, October 18, 2010

Name-Collection Spiders

Students in Everyday Math classes are familiar with Name-Collection Boxes which challenge students to write different mathematical expressions for a given number.  This activity is easily adapted to create name-collection spiders.  Each leg sports a different name for the given number. 

Thanks to Ms. Collier and Ms. Rachko for creating this activity for their students at Joseph C. Caruso School in Keansburg, NJ.

See more Mathwire Spider Math Activities.

Sunday, October 17, 2010

Fall Math Activities

Many teachers elect to integrate seasonal activities into lesson plans.  Mathwire has several collections of appropriate math activities to target current objectives and skills.  Be sure to check out the Fall Math Activities in the Mathwire Seasonal Math Activities for new games and problem solving activities to add to your seasonal repertoire.

Wednesday, October 13, 2010

Calculation Nation

NCTM's Illuminations site includes Calculation Nation.  Students may play the games to challenge themselves, playing against the computer, or they may challenge another online player. 

The games practice multiplication facts, factors, prime numbers, area, perimeter and other upper elementary through middle school concepts and skills.  All games add an element of strategy so that students are prompted to try several possible moves before selecting the best move that garners the most points.  Students won't realize they're really doing math as they PLAY these games and they'll keep playing to try to improve their scores and beat the computer or their online opponent.

Add this free resource to your online sites and encourage students to practice regularly.  They may enjoy playing each other, parents, older siblings or students from other schools.

Tuesday, October 12, 2010

Pumpkin Problem Solving

Take advantage of the seasonal preoccupation with pumpkins to include some problem solving activities.  These seasonal activities include the student handout and a detailed possible solution, both in PDF format for easy downloading and printing.

  • Pascal's Pumpkins is an activity from the Rutger's Discrete Math collection, revised by Mathwire, that challenges students to analyze the patterns in order to complete the array. The file contains the student handout as well as an explanation of the different patterns students may find and the solution.
  • Pumpkin Picking challenges students to solve a pattern problem. The solution provided details how students might use a table to organize the data and easily identify the correct answer to this problem.
  • Pumpkin Farm is a sneaky way to get students to analyze the meaning of remainders in long division. Students must figure out which character will be the 100th to be printed on a neon signboard. The file contains the student handout as well as a detailed possible solution.
  • Jack-o-Lantern Combinations challenges students to figure out how many different pumpkins may be made, given the assortment of eyes, noses and mouths. This problem provides an opportunity to expose students to the concept of orderly counting where they exhaust all possibilities for one component before moving to the next, so that they exhaust all possibilities without duplication.
Be sure to check out more fall math activities on

Thursday, October 7, 2010

Clothespin Graphs

Use a clothespin graph for a simple daily graphing experience.  Many teachers write each student's name on a clothespin that students then use in classroom data collection activities.  This is a simple visual data collection that lends itself to picture cues for younger students or questions for readers.

Add this graphing model to your fall classroom activities:
  • Do you like fall or winter best?
  • Do you help rake leaves?
  • Have you ever bobbed for apples?
  • Do you prefer red or green apples?
  • Will you carve a pumpkin for Halloween?
  • Will your jack-o-lantern be cute or scary?
The list could go on and on.  It's easy to divide a student white board into halves or quarters for four choices.  Students may easily clip their clothespins to the space that represents their choice.  Did heads or tails win the game? 

This data collection activity lends itself to other curricular areas as well.  For example, students might vote on their favorite version of a familiar story or vote on whether or not they were born in the same state where they currently live, etc.

Preschool and primary teachers often find that a clothespin graph is a great way to take attendance.  As students enter the classroom and get settled, they move their clothespin to the Here side.  This makes it easy for teachers to check attendance and students easily see how many people are absent(not here) that day. 

Think about ways to add a clothespin graph to math class.  Please share your ideas on using this simple yet powerful data collection tool.

Sunday, October 3, 2010

Math Number Pull

Michelle La Follette submitted an original activity based on Mathwire's Number Line-Up.  Michelle graciously gave permission for Mathwire to share her activity in PDF format.  Math Number Pull is a great mini-assessment of student's number sense.

Thanks, Michelle, for sharing!

Thursday, September 30, 2010

Climb the Ladder

Some students need prompts to help them write mathematical expressions for target numbers.   Climb the Ladder is an activity that prompts students to move from all addition or subtraction problems and include many mathematical topics to generate equivalent names.   The student starts at the bottom of the ladder and completes the first rung using the prompt provided.   He/she then moves up to the next rung, etc. and works to complete as many rungs as possible in the allotted time.   The teacher may also include a traditional name-collection box for students to use after they reach the top so that they continue to generate equivalent expressions of their choice.   Many students write more diverse mathematical expressions as a result of using this prompted approach.

Classroom Management Suggestions:
  • Have students write equivalent expressions for the day's date.
  • Ask students to write equivalent expressions for the school day count.
  • Pick a random number from a hundred board.
  • Insert the Climb the Ladder template into clear sheet protectors and have students use dry-erase markers so that the form may be reused each day.

 Differentiation Strategies:
  •  Let pairs of students or small groups work together to generate as many different expressions as possible in a given amount of time.

  • Read more about Mathwire's Climb the Ladder and download different versions of the  templates.

Sunday, September 26, 2010

Factor Blaster

Students must think about the factors of each number as they play this game.   Students quickly learn the value of selecting prime numbers as a strategy.   The beauty of the game design is that students will review the factors of many numbers and mentally add the sum of these factors together in search of the "best move." 

Basically, start with the numbers 1-25.  The first student may choose any number and gets that many points.  The second student identifies and keeps any factors of that number that are still on the board.  Play then switches with the second student picking any number, and the first student identifying and taking any factors of the chosen number that still remain on the playing board.

This means that students have to think carefully about the number they choose, mentally identifying and tallying any factors left on the board.  So, the game provides lots of practice in identifying all of the factors of these numbers.  Students quickly strategize and learn that prime numbers make great early picks that provide no points for their opponent.

Note:  Factor Blaster is very close to Factor Game, but Factor Blaster allows students to take numbers, even if there are no factors left on the board.  Students not only learn factors; they also master the prime numbers which is a great skill for prime factorization.

Classroom Management Suggestions:
  • Introduce the game by playing against the class or by dividing the class into two teams and playing on the overhead or using large numbers on the board.
  • Use cheap cookie sheets and magnetic number cards to create easy versions of the game for partner play.  All of the numbers fit on the cookie sheet and the cookie sheets nest within each other for easy storage.  Dollar stores are a great place to find cheap cookie sheets for this purpose. 

  • Use different ranges of numbers to challenge students or remove a couple of numbers to shake up the usual game
  • Allow basic skills students to use lists of factors as they begin to play the game OR begin with the numbers 1-12 and increase the range as students master the factors of these numbers 

Check out Factor Blaster on Mathwire for additional discussion of the rules, classroom management suggestions and to download number cards and directions for the game.

Wednesday, September 22, 2010

Measurement Man

Students typically have difficulty in class and on testing with measurement topics.   Consider sprinkling measurement instruction over the course of the year so that students have a chance to use the measurement units and to become more familiar with these units. 

Measurement Man is a great hands-on activity as students assemble the pieces which build on student experience with cut-paper fractions.   Students are able to visualize the relationship among these different units of capacity as they cut and assemble the figure.   While they can't bring Measurement Man into testing, many students can see him in their mind which helps them visualize the units more clearly.   Some teachers also encourage students to view their own arms and legs as quarts and pints.   They just need to remember that they only have four fingers or toes on each hand and foot.   Maybe the crows got one? 

Download Measurement Man directions.  Consider adding a pointed cap and some raffia straw to create a field of scarecrows, just perfect for fall decorations.

See more pictures of Measurement Men decorating school classrooms and hallways.

Monday, September 20, 2010

Coin Combinations

It is important that students recognize that there are often different combinations of coins for any  particular value.  Many problem-solving activities incorporate this skill as students search for all of the different ways to make 50 cents, for example.

One teacher uses these large coin cut-outs, available at teacher supply stores, to challenge students to find different combinations for the same value.  The students love being at the board, manipulating the large coins,  and coming up with different combinations.  Students at their seats work with small bags of coins to complete the same task.

Consider adding this station to the daily math routines.  Challenge students to find many different coin combinations for the date.  Repeated practice in the primary grades would help build flexibility with coin combinations, an important skill in counting coins and making change.

Teachers might use A Quarter from the Tooth Fairy as an introduction to the concept of coin combinations. 

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:  Try to find all of the different ways to make 25 cents with coins.  Students may use the Student Worksheet to keep track of all of the different ways.

Sunday, September 19, 2010

Who Has? Coin Cards

The coin card deck provides practice for students to count coins and determine the amount pictured.  Give each student a card and hand out any extras to better students, as the whole deck must be used.  Allow students time to figure out the value of the coins on their cards.

Pick a student to start the game.  The student reads the coins on his/her card.  Because other students cannot see the coins on the card, it is important for the student to read the coins.  For example, the student with the card pictured above would read:  I have one quarter and two pennies.  Who has 13 cents?

The student with the card that has a value of 13 cents would then answer.  I have one dime and three pennies.  Who has 32 cents.   The game continues until the original student answers the question Who has 27 cents?

Classroom Management Suggestions:

Teachers can easily differentiate the game to accommodate varied ability levels by carefully distributing the cards, giving simpler coin combinations to struggling students so that they may successfully participate.

The game is designed to be an ongoing loop, so teachers may select any student to begin and the play will eventually come back to that student.  All cards must be used to complete the loop.

In the beginning, teachers may find it helpful to follow the Who Has? Coin Deck Loop to easily monitor student responses.  Teachers might ask the starting student to come to the front of the class to start.  This way, it's easy to know when the play comes back to the starter.

Once students are proficient at this deck, start timing the class performance.  Record the time on the board and challenge students to better their time the next day.The beauty of the Who Has? card decks is that students mentally check everyone's response, performing 20 calculations in the course of the game.  Students enjoy the game more than completing a similar worksheet and they are strongly motivated to participate and give the correct answer in order to better the class time.

Download the Who Has? Coin Deck which may be printed onto 2x4 inch labels to affix to index cards to create an easy deck.  Teachers may also print the cards on card stock and cut them apart to create a smaller deck.

If students are currently using coin antennas to determine the value of coin combinations, Mathwire has a deck for them.  Download the Who Has? Coin Deck with Antennas to use with young learners.  The game is played in the same way.  The antennas are added as an appropriate modification for struggling learners.  This deck is exactly the same sequence as the regular deck, so teachers could choose to insert the coin antenna cards only for struggling students.
Mathwire Who Has? Collection:  Check out all of the card decks in the Mathwire Who Has? collection which includes addition, subtraction, multiplication facts, geometry, doubles, etc.  The web page also details classroom management suggestions.
Small Group Play:  Place extra decks in the math center.  Allow 2-4 students to play the game in pairs or small groups.  Students deal out the cards and place them face up in front of them on the table.  The person to the left of the dealer picks any card to begin.  He/she reads that card and then turns it over.  The student with the correct answer reads his/her card and then turns it over.  Play continues until all cards are turned over.  The person who turns over all cards first is the dealer for the next round.

Saturday, September 18, 2010

Clean up the Money Game

This 2-player game challenges students to toss 2 dice, form a coordinate pair, then collect the coin from that space, if there is one.   First students alternate placing quarters, dimes, nickels and pennies on the gameboard. Then students toss a regular die and a special die (A-B-C-D-E-F) to form the coordinate pair and remove the coin from the matching space.  
Variations of the game are given but students must always find the value of their coins to identify the winner of the game so they get plenty of practice sorting and counting coins. NOTE: Buy wooden cubes at craft stores to create the ABCDEF die or use labels to cover the faces of a regular die.

Download the directions, game mat and recording sheet for the Clean up the Money game.
See more Mathwire Money Games.

Friday, September 17, 2010

Math-Literature Connection: Money Madness

Money Madness by David A. Adler

This book is a great introduction to a money unit.  "It's hard to imagine a world without money," Adler says.  He then delivers a mini-economics lesson taking readers from a life without money to today's credit cards and digital money.

Along the way, students learn about trading and bartering as well as the natural progression from metal coins to paper money to the credit cards and digital money that are widely used in today's world.  It's a quick read that provides a simple introduction to the history of money and its importance. 

See more books in Mathwire's Math-Literature Connections:  Money.

Thursday, September 16, 2010

Using Antennas to Count Coins

Students draw antennas on coin pictures to represent the value. Each antenna is worth 5 cents. This means a dime has two antennas, a nickel has one antenna, a penny has no antennas, etc. This strategy capitalizes on students' strength in counting by fives. They simply point to each antenna as they count by 5s, then count on by ones to include any pennies.

This method is also efficient because students do not need to sort and reaarange coins; they simply draw antennas on coins in the order given. This method is especially effective for K-2 regular and special ed. students who will eventually outgrow the need for antennas. NOTE: some teachers call the antennas "hairs" and talk about the penny as "bald" because it has no hair. Whatever works for you and your students is the best strategy.

See more Mathwire Money Activities & Strategies including money games.

Wednesday, September 15, 2010

Using the Hundred Board to Count Money

Hundred Chart: students who confidently use the hundred chart and its patterns to solve problems can utilize this tool to work with coins: 

Counting coins: Use a hundred chart to help students count coins.   Have students place coins on the correct number.   For instance, given 3 dimes and 1 nickel, students would place dimes on 10, 20, 30 and the nickel on 35. The last coin tells students how much money they have altogether.   This method is effective for having students figure out which coins to use to pay for an item.

Making change for a dollar: Place a counter on the price of the object.   Place pennies on each square to get to the nearest multiple of 5.   Use nickels, dimes or quarters to get to $1.00.   Students should begin with whatever combination of coins they wish then work toward using the least number of coins as they become more proficient at making change.

Tuesday, September 14, 2010

Hundred Board Puzzles

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.

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

Extension:  Use a 101-200 number grid so that students extend patterns and become more familiar with 3-digit numbers.

  • See Hundred Board Activities on Mathwire to download a hundred board template that may be used to create the hundred board puzzles.
  • Copy the template onto card stock to make the puzzles heavier and easier to assemble.

Friday, September 10, 2010

Math Templates

Using math templates during instruction keeps each student actively involved and allows the teacher to informally assess each student's proficiency with the skills and concepts addressed in the day's lesson. Many teachers regularly use whiteboards to have students record answers, write terms, draw pictures, etc. The use of templates in sheet protectors extends this practice and eliminates the time spent drawing diagrams, etc., allowing students more time to demonstrate mathematical proficiency. Teachers who regularly use math templates include planned task items that assess student proficiency. Careful observation of student responses allows teachers to form flexible small groups for additional instruction or enrichment and also better plan for instruction.

The Mathwire Template Library is a collection of generic math templates available in PDF format for easy downloading and printing.  Students insert each template into a clear sheet protector, then use dry erase pens and erasers to extend the life of these templates.

Tuesday, September 7, 2010

Number Line-Up

This activity was designed to practice place value.  In its simplest form, students with the demo digits are asked to form a specific number.  Students arrange themselves to form that number.  The teacher may then ask students what number is in the hundreds place, or the thousands place, etc. 

Ask the students to form number answers for these challenges:
  • the largest number
  • the smallest number
  • a multiple of 25
  • a multiple of 4
  • an even number greater than 4000
  • an odd number less than 5200
  • the largest even number
  • the smallest odd number
  • the largest multiple of 5

Build a Number
To extend the activity, next ask students to use the digits 2,3,7, 8 to form:

  • the greatest number
  • the smallest number
  • a number between 3000 and 7000
  • an even number
  • an odd number between 2000 and 3000
  • the largest even number
  • the smallest odd number

Students at their desks work with small decks to digit cards to produce similar results.  Students may work individually or in pairs, rearranging their small digit cards to produce numbers to satisfy each condition.  It's best to have students working in pairs because they will "talk math" as they figure out how to rearrange their number cards AND they will also discuss how their solution is the same/different than the standing group AND whether they are both possible solutions.

Materials:  Visit Mathwire to read more about Number Line-Up and Build A Number.  There you may download both demo size and individual size digit cards to print out for use in your classroom.  I suggest that you print them on cardstock or laminate them for classroom use.  The demo digits may also be placed in sheet protectors, if desired.

Math Warm-Up Activity:  use the digit cards for quick warm-up activities in the week(s) following initial instruction.  Pose conditions that fit the level of instruction and have students quickly assemble a solution on their desks.  Students enjoy this break from pencil and paper tasks and the digit cards are an easy visual for a teacher to  check quickly as he/she walks around the room.

Differentiation:  this activity is easily differentiated by varying the number of digit cards used (the size of the numbers) and the difficulty level of the task conditions.  Teachers may also pair students to increase the likelihood of success.

Saturday, August 28, 2010

Data Collection: Tossing Two Dice

Students LOVE working with dice, almost forgetting that they're doing math.  While standard probability lessons ask students to calculate the probability of tossing an even number, a sum of 10, etc., students are more highly motivated when they generate their own experimental data.

The Mathwire collection contains many examples of both one-die toss activities and two-dice toss activities.  These data investigations begin with a game but make data collection an integral part of the activity, so that students begin to examine the underlying probability of the game and can use appropriate strategies in future play.

Students will generate their own small set of data, which should be combined with the whole class data for a larger set.  Teachers may ask questions to help students draw conclusions and make generalizations about the probability of dice tosses.

After this initial hands-on data collection and analysis, extend the activity by asking students to use online dice simulators to generate even more data to test their hypotheses and generalizations.  This option allows students to quickly generate large sets of random data.  It is helpful to pair students for this activity:  one student at the computer keyboard and the other student recording the results of each simulated dice toss.  Again, ask students to post their results to a class data collection display (e.g. tally chart, graph, etc.) so that the class is able to analyze the larger sample.

Check out these online dice-toss simulators:
  • Coins & Dice:  A Probability Simulator records the results of each dice toss, making it easy for students to record the result of each dice toss
  • Dice Roll displays the results in a bar graph so that students visually see the results of extended dice tosses
This data collection and data anaylsis approach provides students with hands-on data collection activities that generate real-life data for analysis.  Students then take advantage of technology to simulate the activity, quickly collecting larger sets of random data.  It's the best of both worlds!

Sunday, August 8, 2010

Writing in Math Class

Teachers incorporate writing in math class to help students reflect on their learning, deepen their understanding of important concepts by explaining and providing examples of those concepts, and make important connections to real-life applications of the math they are learning. Teachers use the writing assignments to assess student understanding of important concepts, student proficiency in explaining and using those concepts and each student's attitude toward learning mathematics.

Writing in mathematics is a win-win for both teacher and student. Although it may be difficult to introduce this practice, it is well worth the effort. Look for simple ways to incorporate short writings throughout daily lessons and longer writings over the course of weeks or math units.

  • Use whiteboards often throughout a lesson.  Ask students to define a term in their own words, explain why an answer is correct/incorrect, show their thinking using words, pictures, numbers, etc.  For some students, the "forgiveness" of an erasable whiteboard encourages them to write more.  For others, the color and novelty motivate active participation.
  • Plan regular Think-Write-Pair-Share opportunities:  plan to stop instruction to include these student-controlled learning opportunities in which students are asked to think (nonverbally respond to a question or prompt), write their response, pair share their responses, then share responses with the class.  This strategy is particularly effective for shy or struggling students as they have time to practice their response on a peer, hear their partner's response, and finally combine responses to share with the class.  This practice also helps students make the connection between oral and written responses. Teachers may elect to chart responses in bullet format to post for student review.

Read more about strategies for including Writing in Mathematics Class with links to additional internet resources.

Sunday, August 1, 2010

Three Strikes and You're Out!

Summer means baseball games so capitalize on this favorite sport with the game Three Strikes and You're Out!  The game was designed to practice addition and subtraction facts while incorporating a basic introduction to probability outcomes. 

Players will enjoy choosing the numbers for their players and their strikes.   As they play the game, they'll learn which numbers are best for placing players and which numbers are best left as strikes, developing a basic understanding of probability.  They'll practice addition or subtraction facts while learning that the dice toss is often unpredictable and random.

The game uses the sum of two dice to practice addition facts, but may easily be adapted to practice subtraction facts by using two 12-sided dice and finding the difference. The game handouts include directions, variations in play and scoring, game boards for both the addition and subtraction games, as well as game pieces that may be used to support the baseball theme.  

Download the directions and gameboards for Three Strikes and You're Out.

Friday, July 30, 2010

Summer Basic Facts Practice

Students may easily lose fact mastery over the summer without some kind of regular practice.  Parents may help students retain mastery by utilizing small moments of time on a daily basis.  Here are some suggestions:
  • Mad Minute:  insert a facts worksheet into a page protector.  The student uses a dry-erase marker to complete as many facts as possible in one minute.  Many students respond positively to this experience as it's only a minute.  They can practice graphing skills by graphing the number of correct facts for each day.
  • Who Has? Card Decks:  read about and download Who Has? cards from Mathwire's collection, print out the labels and apply to index cards to easily create a deck.  Shuffle the deck and deal out the cards.  Each player turns over his/her cards.  The person who has the I have 0. card begins.  After reading a card, the player turns over that card, and play continues.  The first player to read all of his/her cards wins.  NOTE:  This is a totally random winning, but students seem to be challenged by the prospect of "winning."
  • Contig:  Play this game to help older students develop fact fluency with addition, subtraction, multiplication and division facts.  The beauty of the Contig game is that students will practice facts for several options, searching for the move that yields the most points.  Download the Contig game mat and directions from Mathwire.

Thursday, July 15, 2010

The Game of Pig

Pig is one of my favorite probability games.  I have played the game with kindergarten through college level students and used it in teacher training sessions.  Everyone LOVES the game and it's fun to watch who plays it safe and who's the risk-taker.  

In my own classroom experience, I have found that this is best introduced as a class activity. Students collect points for each toss of the die unless a ONE is tossed, which means they lose all of the points they have collected in the round. To prevent losing their points, students may elect to stop at any point in the game before a ONE is tossed and they get to keep the points they collected but get no further points. Students love the game and begin to appreciate that theoretical probability and experimental probability are often quite different! 

I devised a method that uses only one die tossed by the teacher, so this is a great transition activity that quiets a class as they strain to hear and record the results of the die toss AND decide if they will stop or continue to play.   It's a win-win because students feel that they're playing, but they're actually learning a lot about the probability of a one-die toss.

  • Download Pig directions.
  • Download Pig template or Pig Tally template, and place in a sheet protector to record die tosses.  Students may use dry erase markers for a reusable recording sheet.  The Pig Tally template requires students to use tally marks to record each toss of the die.  This recording sheet is a very visual presentation of the results and proves extremely useful when students devise winning strategies, as described below.
Results:  Younger students may use calculators to total each column.  Older students should use mental math to find the sum of the die tosses.  Students should write the total of all 3 columns in the upper right hand corner of the template and circle it.

Extending the Data Collection & Analysis:
  • Ask pairs or small groups of students to talk about the game and come up with a winning strategy.  For example, some groups decide to stop once they have 20 points.  Another group decides to stop when they get 3 of any number.
  • Have each group share their winning strategy and explain why they think it is a winner.
  • Play the game again.  Groups MUST play according to their winning strategy.
  • Discuss the results and allow groups to refine their strategies, if desired, before playing 1-2 more times.
  • Finally, ask students to write about what they learned from this game.  Is there really a winning strategy that works all the time?  Explain your thinking.

Friday, July 9, 2010

Heads and Tails Investigation

Explore the probability of a one-coin toss using the Heads and Tails Game.  This is an easy game for young learners.  All you need to play is the Heads and Tails gameboard, two coins for markers and another coin to flip.  Use a coin toss to decide who will be heads and who will be tails.  Then the fun begins!

Both players place their marker coins on the star on the snake.  The player who is HEADS flips the coin first.  If the flip is HEADS, the player moves his/her marker one space toward the head.  If the flip is TAILS, the player doesn't move. 

Next, the TAILS player, flips the coin, moves one space if it lands on TAILS, stays put if it comes up HEADS.

Play continues switching back and forth until one of the players' markers reaches the head of tail of the snake to win the game.


  • Do both players have an equal chance of winning?  Try keeping a record of several games to see if HEADS and TAILS really both win.

  • Does it matter who goes first?  Sometimes let HEADS go first; other times, let TAILS go first.

  • Use a simple tally sheet to record whether HEADS or TAILS wins each game.

  • EXTENDED PLAY OPTION:  The HEADS player tosses the coin.  If it comes up HEADS, the player moves the coin one space toward the head and tosses again.  If it comes up TAILS, the player stops and does not move.   The TAILS player now tosses the coin.  If the toss comes up TAILS, the player moves the coin one space toward the tail and tosses again.  The player continues as long as the toss comes up TAILS.  The game continues until a player's marker reaches the HEAD or TAIL of the snake.


  • Do both players still have an equal chance of winning? 

  • Does the game go faster this way?  Explain.

  • What was the longest move either HEADS or TAILS got on one turn?

  • If young players have trouble tossing the coin, use a small container and let them drop the coin into the container. 

  • OR place the coin in a small see-through container such as a clear plastic jar with lid.  Players then simply shake the jar and place it down on the table on its lid.  It's easy to see  whether it landed on HEADS or TAILS without opening the jar.

  • Buy larger coins at the dollar store.  Remember that these are not the same weight as real coins and any imperfections may affect the outcome of the games.  This could prove an interesting investigation for older players.  Are some coins HEADS-winning coins and others TAILS-winning coins or are they all fairly equal?

Monday, May 17, 2010

Guess The Number

Introduce younger students to logic problems using Mathwire's Guess the Number collection.  Give students more practice in using the hundred board to solve number clue problems. Once again, students solve the problem clue by clue. With this set, however, students must use multiplication, money, and measurement facts to correctly solve the problem and guess the number.

Here's a sample problem:
  • The number is greater than the number of pennies in a quarter.
  • The number is less than the number of pennies in five dimes.
  • The number is an odd number.
  • If you count by 5s, you say the number.
  • The sum of the digits is 8.
What is the number?

Check out Guess the Number on Mathwire to download more problems and their solutions.  Be sure to read suggestions for using these problems in math classes.  After solving several, encourage students to write their own original Guess the Number logic problems.

Saturday, May 15, 2010

Hundred Board Logic Problems

These original Mathwire Hundred Board Logic problems are designed to help students use a hundred board to solve problems.  Students read each clue, then eliminate numbers on the hundred board that do not fit the clue.  After reading through all clues, students should be left with only one solution.  They should check their solution by rereading each clue to be sure their solution fits.  These problems were field-tested in Grades 3-8 classrooms and students loved the experience because the step-by-step process enabled them to be successful at solving these problems.

Enrichment:  After students have solved several of these problems, they may be challenged to create their own original problems.  Provide blank 100 board and logic problem templates.  Students should start by circling their target solution.  They then write clues that will eliminate all other numbers.  Finally, students should exchange problems and use peer review to edit their problems, clarifying and modifying clues to eliminate any confusion.

Creating original problems is a higher-order thinking skill (Synthesis on Bloom's Taxonomy) that extends students' problem solving ability and requires flexible thinking about mathematical concepts, skills and vocabulary terms.  Student-created problems may be added to the classroom math center and used on game days as a problem-solving center.  Additionally, these problems may be used in the initial lesson in subsequent years.  Consider publishing the problems with the author's name and copyright year.  Students love seeing their names in print!

  • Read more about Hundred Board Logic Problems including classroom management suggestions and ideas for a cooperative learning lesson.  The discussion includes PDF documents for all problems and templates needed for this lesson.