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.