Toronto Catholic District School Board from the ... Family...Toronto Catholic District School Board from the Mathematics Department ... 1 deck of cards 1 dice ... • Compare your

Toronto Catholic District School Board from the Mathematics Department

thinkMATH@home FAMILY MATH ACTIVITIES for Kindergarten to Grade 8

using Math Learning Tools

cards/dice 2 colour counters interlocking cubes pattern blocks square tiles tangrams

Version 2 - November 2015

© TCDSB 2014 - thinkMATH@home Family Math Activities, K to 8 2

Superintendents of Education Cristina Fernandes, Early Learning

Patrick Keyes, Student Success Dan Koenig, Curriculum & Accountability

Mathematics Department

Kathy Kubota-Zarivnij (program coordinator) Luciano Lopez

Grace Mlodianowski Stefana Penelea

Adrian Pope Wilma Simmons

© 2014 Toronto Catholic District School Board 80 Sheppard Avenue East, Toronto, Ontario M2N 6E8


Helping Your Child LEARN and LOVE Mathematics! Learning Mathematics Successfully What does it mean to learn mathematics successfully? Learning mathematics successfully or with mathematical proficiency includes the five components or strands of competencies: • Conceptual Understanding – understanding of

mathematical concepts, operations, and relations; integrated and functional grasp of mathematical ideas that enables students to learn new ideas by connecting to ideas they already know through reasoning, proving and communication; supports retention and prevents common errors

• Procedural Fluency - carrying out procedures flexibly, accurately, efficiently, and appropriately.

• Strategic Competence - formulate, represent, and solve mathematical problems.

• Adaptive Reasoning - capacity for logical thought, reflection, explanation, and justification

• Productive Disposition - is habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy. (National Research Council, 2001)

About Student's Mathematical Learning Students learn math best through experiences that allow them to explore new ideas, solve problems using information they have gathered themselves, reflect on what they have discovered, as well as through their own thinking, and explain their solutions through reasoning. Students learn more easily when they connect mathematical concepts and procedures with their own experience. The seven mathematical processes (i.e., Problem Solving, Reasoning and Proving, Reflecting, Selecting Tools and Computational Strategies, Connecting, Representing, Communicating) support students’ acquisition and application of mathematic knowledge and skills. By solving problems in different ways, using reasoning skills, and making connections between mathematical concepts and strategies, students develop a deeper understanding of mathematics.

Also, when students analyse other students’ solutions to problems, they are compelled to reflect on their own mathematical thinking and the thinking of others and how their mathematical ideas strategies are connected. What Can Parents/Guardians Do At Home? Parents/guardians, school and the local community have the shared task of nurturing our students’ confidence in loving and learning mathematics and in applying their mathematical knowledge to solve real-life problems. The disposition of appreciating and enjoying mathematics is necessary for our students to persevere in learning mathematics with depth and precision and to continuously improve the clarity of their mathematical communication. It is common knowledge that parent's and/or guardian's attitudes toward mathematics has an impact on children's attitudes towards mathematics. In fact, students whose parents/ guardians show an interest in and enthusiasm for mathematics around the home will be more likely to develop that enthusiasm themselves and persevere to learn and succeed in mathematics. Ways to participate in your child's mathematics learning are as follows: • show a positive attitude towards learning

mathematics by talking positively about it • expect your child to complete mathematical

activities and solve problems • encourage your child to persevere when the

mathematical work becomes difficult • appreciate different ways to make calculations

and solve math problems • listen carefully to your child's explanation of a

solution to a lesson problem • estimate and count anything in different ways

(forwards, backwards, by 2s, 5s, 10s, 100s) • play board and card games • solve jigsaw, number and logic puzzles • build models with different materials (e.g.,

legoTM, stacking blocks, rolled newspaper tubes) • involve your child in household activities that

involve math. (e.g. measuring in the kitchen, setting the table, pairing socks)

• look for and describe mathematics in the books you read with your child. (e.g., find patterns, count objects, find shapes, identify probability)

• support homework completion by being a co-learner and encourage perseverance to think


thinkMATH@home About the Family Math Activities

Educational Goals Parents/guardians will: • experience different strategies for engaging their children in mathematics learning

(e.g., solving math problems, playing math games, using mental math challenges) • develop an awareness of the range of mathematical concepts across kindergarten to

grade 8 using different mathematics learning tools • use and develop their mathematical communication strategies Family Math Activities Parents/guardians and students will preview and collaboratively engage in math take-home activities using math learning tools, such as: • solving math problems • playing math games • solving mental math challenges Table of Contents Cards and Number Cubes (Dice) ……………………………………………………. 5 2 Colour Counters …………………………………………………………………… 13 Interlocking Cubes …………………………………………………………………… 21 Pattern Blocks ………………………………………………………………………… 29 Square Tiles ………………………………………………………………………….. 37 Tangrams ……………………………………………………………………………… 45


thinkMATH@home from the TCDSB Math Dept

WHICH NUMBER COMES UP THE MOST? Kindergarten Learning Goal Describe probability using informal language

Materials 1 deck of cards 1 dice

Problem to Solve Materials – Take out the jacks, queens and kings; aces are worth 1 Problem – Which number comes up the most with rolling 1 dice or drawing from a deck of playing cards? Solving the Problem • Look at the numbers in 1 deck of cards or 1 dice. • Predict which number (1 to 10) will come up most often when drawing a card from 1 deck of

playing cards and when rolling 1 dice. • Roll the dice 10 times. Record the number that came up from each dice roll. • Draw 10 cards. Record the number that came up after each card drawn. • Compare your prediction with the numbers you recorded. What did you find out? • Roll the dice 20 times again. Record the numbers that came up from each dice roll. • Draw 20 cards. Record the number that came up after each card drawn. • Compare your prediction with the numbers you recorded. What did you find out? Questions to Ask to Probe Mathematical Thinking • Why do some numbers come up more often than others? • Do the same numbers come up more than when rolling 1 dice or when drawing playing cards? Math Activity Variations • Roll 2 die at the same time. • Use half of the deck of playing cards.


ADDITION GO FISH Kindergarten Learning Goal Composing whole numbers to 7

Materials 1 deck of playing cards

Math Game Instructions Players – 2 to 4 Materials – Remove all cards higher than 7; aces are worth 1 Goal – highest number of pairs at end of game (all cards matched) Playing the Game • Deal out 5 cards to each player and keep remaining cards in a draw pile. • All players lay down pairs of cards that sum (add) to 7 (i.e., 6+1; 5+2; 4+3). • Player to right of the dealer asks other players, one at a time for a card that he/she needs to

make a sum of 7. Player can keep asking for cars until no further matches • When no other matches can be made, player is told to “Go Fish” and draw a card from the pile.

The next player takes a turn trying to make pairs of cards that sum to 7. • When a player runs out of cards, he chooses 5 cards from the draw pile. • Game ends when all cards have been matched into pairs. Questions to Ask to Probe Mathematical Thinking • How did you know when a pair of playing cards made (summed to) 7? • Is possible that not all of the laying cards will pair up to make 7? Math Activity Variations • Change to sum to a higher number, like 8, 9 or 10 (then remove cards higher than 8, 9 or 10).


thinkMATH@home from the TCDSB Math Dept MORE THAN, LESS THAN, OR SAME? Kindergarten Learning Goal Comparing whole numbers as more than, less than and the same

Materials 1 deck of cards or 2 die

Mental Math Activity People – 2 people Materials – Use 1 deck of playing cards, aces to 10 only; divide cards into black and red card piles Using Mental Math • Each person shuffles their set of cards (black or red set) • Each person faces up one card. Compare the numbers on the cards. If red card number is greater

than the black card number, put both cards in one pile (called red pile). If black card number is greater than the red card number, put both cards in second pile, called the black pile

• Tf the same number comes up for black and red, the cards are put in a separate pile. • Mental math practice ends when 1 player has no more cards.

Questions to Ask to Probe Mathematical Thinking • How do you know when 1 number is more than another number? • How do you know when 1 number is less than another number? • Which pile (red or black) had the greatest number of pairs? Why?

Math Activity Variations • Roll 2 die rather than face up cards from 2 piles or roll 1 die and face up 1 card from 1 deck. • When compare numbers on cards, focus on number less than the other number.


MAKING TENS Grades 1 and 2 Learning Goal Add 1 digit whole numbers to make ten

Materials 1 deck of playing cards

Problem to Solve Jane and Kyle are playing a game with 1 deck of playing cards. The jacks, queens and kings are removed. The player who makes the greatest number of pairs of cards that sum to 10 wins the game. For example, Kyle faces up 2 cards to show an ace and 9 to make 10. Jane faces up 2 cards to show a 2 and 5, so she returns them to her pile and shuffles her cards. What are the greatest number of pairs of cards that sum 10 that Jane and Kyle can make? How do you know? Questions to Ask to Probe Mathematical Thinking • What are the possible pairs of cards that make 10? • Is it possible that some cards will not be paired to make a ten? Why?

Math Activity Variations • Pairs of cards make odd numbers or even numbers. • Use 2 decks of cards.


thinkMATH@home from the TCDSB Math Dept ADDITION CONCENTRATION Grades 1 and 2 Learning Goal Add 2 digit whole numbers using mental strategies

Materials cards, number cubes (dice)

Math Game Instructions Players – 2 to 4 Materials – 1 deck for 2 players; jacks, queens and kings are worth 10; aces are worth 1 Goal – Highest sum at the end of the game (no cards left) Playing the Game • Face down 1 deck of playing cards in an array (4 rows x13 columns cards = 52 playing cards) • Take turns facing up 2 cards at a time. If the cards have 4 different number, player can make 2

sets of numbers and add them together (e.g., 4, 6 -> 4+6=10; 10, 5 -> 10+5=15 • Any cards that are the same number are returned face down. • Keep track of points by totaling the scare after each turn. • Game ends when there are no cards left to face up.

Questions to Ask to Probe Mathematical Thinking • What addition strategy did you use? • How did you decide how you made numbers from the cards to add together? Math Activity Variations • Subtract the 2 cards to get the difference; difference is the number of points gained. • Each player faces up a card at the same time, smaller card gets the sum of the 2 cards for points

thinkMATH@home from the TCDSB Math Dept WHAT’S THE DIFFERENCE? Grades 1 and 2 Learning Goal Subtract 1 digit whole numbers using mental strategies


Mental Math Activity Persons - 2 Materials – 1 deck of cards or 2 die for 2 players; aces are worth 1; remove jacks, queens and kings Mental Math Challenge • Divide the cards equally among the people. • Each person faces up 1 card at the same time. • The person with the larger number identifies the difference between the 2 numbers. • When the 2 cards have the same number, they are placed in a pile. • When a person has no cards left, the cards in the pile are shuffled and divided equally between the

2 people. • Mental math practice ends when there are no more cards to compare.

Questions to Ask to Probe Mathematical Thinking • What strategies did you use to figure out the difference between two cards? • What does “difference” mean? How does “difference” relate to subtraction? Math Activity Variations • Person with the smaller number identifies the difference between the 2 numbers. • Add 1 ten to one of the whole numbers.



WHAT’S THE NEXT CARD? Grades 3 and 4 Learning Goal Predicting the frequency of an outcome

Materials cards, numbered 1 to 10

Problem to Solve Kathy has ten cards, numbered 1 to 10. She mixes them up and faces them down in a row. She shows the first four cards … 8, 3, 2, 5. What is the chance that the next number (5th card) will be lower than 5? How do you know? Questions to Ask to Probe Mathematical Thinking • If the 5th card is 1, what is the probability that the 6th card will be lower than 5? Explain. • If the 6th card is 4, what is the probability that the 7th card will be lower than 5? Explain. • Is it possible for another 8 to come up by the 7th card? How do you know?

Math Activity Variations • Carry out the problem with 10 cards, number 1 to 10. How does your experiment compare with

your prediction? •

thinkMATH@home from the TCDSB Math Dept MULTIPLICATION CONCENTRATION Grades 3 and 4 Learning Goal Multiplying pairs of numbers and add 1 digit and 2-digit whole numbers.

Materials 1 to 2 decks of playing cards

Math Game Instructions Players – 2 to 4 Materials – 1 deck for 2 players; 2 decks for 4 players; remove 8s and up; aces are worth 1 Goal – Highest sum at end of the game (no cards left) Playing the Game • Face down 1 deck of playing cards in an array . • Take turns facing up 2 cards. If the cards have the same number, player can multiply the numbers to

get points (e.g., 2x2 = 4 points). • If cards are not the same number, the 2 cards are returned face down. • Keep track of points by totaling the scare after each turn. • Game ends when there are no cards left.

Questions to Ask to Probe Mathematical Thinking • How did you know which cards to choose to make points? • What did you think about to multiply 2 same numbers, like 3x3 or 5 x 5? • What strategies did you use to add 1 and 2 digit whole numbers?

Math Activity Variations • Gain points if turn up pairs of same numbers (e.g., 2 x 2=4 points) and lose points if turn up pairs of

different numbers (2x3=6 lose 6 points). • Name and description of variation 2.


thinkMATH@home from the TCDSB Math Dept WHO’S CLOSER TO 100 Grades 3 and 4 Learning Goal Add and subtract 2 digit whole numbers using mental strategies

Materials 1 deck of cards

Mental Math Activity Persons – 2 or 2 groups of 2 students Materials – face up 5 cards Mental Math Challenge • Shuffle a deck of cards. Face up 5 cards. • Use numbers on those cards to create any 1 and 2 digit whole numbers to add up and subtract as

close to 100 as possible. • Mental math practice ends where there are less than 5 cards left. Questions to Ask to Probe Mathematical Thinking • Describe the addition and subtraction strategies that you used. • How did you decide which numbers to make using the cards?

Math Activity Variations • Use 4 cards to make 50. • Include multiplication of 1 digit whole numbers.


IS THIS A FAIR GAME? Grades 5 and 6 Learning Goal Comparing theoretical and experimental probability

Materials 2 die

Problem to Solve Stefana and Grace are playing the “Multiplying Dice Game.” Here are the rules: • Roll 2 die and multiply the two numbers. • If the product is even, Stefana wins 1 point. • If the product is odd, Grace wins 1 point.

Is this a fair game? Does Stefana and Grace both have an equal chance of winning? How do you know? Questions to Ask to Probe Mathematical Thinking • What does a fair game mean within the context of this game, “Multiplying Dice?” • What does a unfair game mean within the context of this game, Multiplying Dice?”

Math Activity Variations • Scoring – if product is equal to and greater than 24, half the score. • Scoring – if the product is equal to and greater than 12 triple the score>


thinkMATH@home from the TCDSB Math Dept AIM TO BE LAST Grades 5 and 6 Learning Goal Multiply and add 1 and 2 digit whole numbers using mental strategies


Math Game Instructions Players - 2 Goal – highest score at the end of the game Playing the Game • Shuffle the deck and place 13 cards face down in a circle. • Players take turns picking up 1 or 2 cards at a time (their choice) to make 1 or 2 digit number with 1

or 2 cards. (e.g., pick up 9, make 9; pick up 3 and 6, make 63 or 36) • Players record the cards they picked up, the number they made and the score for the turn and the

cumulative score by the end of that turn. • Player who picks up the last card scores 50 additional points • Deal another 13 cards for additional rounds (3 more). • Game ends when there are no cards left.

Questions to Ask to Probe Mathematical Thinking • Is it best to be the last player? Why or why not? • How do you decide whether to make a 1 digit or 2 digit number? Math Activity Variations • If an odd 1 digit or 2 digit whole number is made from 1 or 2 cards (, player has the option to have

the other player deduct that amount from their total score. • If 2 cards are drawn with the same number, player makes double the 2 digit number (e.g., 3, 3 are

drawn, so points is 33x2=66).

thinkMATH@home from the TCDSB Math Dept WHAT’S THE FINAL NUMBER? Grades 5 and 6 Learning Goal Add, subtract, multiply and divide 1 digit numbers using mental strategies


Mental Math Activity Persons – 2 to 4 Mental Math Challenge • Start with <card 1 or dice 1>. • Double it. • Add <card 2 or dice 2>. • Subtract <card 3 or dice 3>. • Multiply by <card 4 or dice 4>. • Divide by <card 5 or dice 5>. • What’s the final number? Questions to Ask to Probe Mathematical Thinking • Describe the strategies you used to add, subtract, multiply and/or divide? • Why are some final numbers estimates rather than actual results? Math Activity Variations • Use only addition and subtraction. • Make a number cube with operations and roll it to randomly determine the operation for each card

or dice roll.



IS THIS A FAIR GAME? Grades 7and 8 Learning Goal Compare the theoretical and experimental probability of a compound event

Materials 3 dice

Problem to Solve Have you played Rock, Paper and Scissors? Players A, B and C simultaneously display the rock, paper or scissors sign of their choice. Here’s a different way to score: • Player A gets 1 point – all the signs are the same (e.g., rock, rock, rock) • Player B gets 1 point – 2 signs match (e.g., rock, rock, paper) • Player C gets 1 point – no signs match (e.g., rock, paper, scissors)

(a) Wilma predicted that this game is not fair. How did she figure that out? (b) Play the game and see if your prediction is true. Roll dice to play the game. Rock (1 or 3), Paper (2 or 4) and Scissors (3 or 6). Roll 3 dice at the same time and keep track of the outcomes. What did you find out? (c) Do all 3 players have an equal chance of winning? Explain. Questions to Ask to Probe Mathematical Thinking • What are the total possible outcomes when playing rock, paper, scissors with 3 people? • How could this 3 player game be made fair? Math Activity Variations • 2 players with points for either same or different signs. • 3 players with player A and C getting 3 points and player B getting 1 point

thinkMATH@home from the TCDSB Math Dept CLOSEST TO +1 Grades 7 and 8 Learning Goal Adding positive and negative 1-digit integers

Materials cards

Math Game Instructions Players – 2 to 4 players Materials – red card is negative and black card is positive; jacks are 11, queens are 12 and kings are 13 Goal – player with the most cards wins Playing the Game • Shuffle and deal 6 cards per player. Remaining cards are in the “pick-up pile.” • Players take turn laying down a card until a positive 1 is made. (e.g., • Player who makes positive 1wins all the cards. • When a player runs out of cards, pick up 6 cards from the pick-up pile. • Game ends when one player has no more cards and there are no more cards to pick up. Questions to Ask to Probe Mathematical Thinking • Question 1 (Sample Response – • Question 2 (Sample Response - Math Activity Variations • player with no cards left wins • players lay down 2 cards at a time to make 2 digit integers


thinkMATH@home from the TCDSB Math Dept MAKE THE TARGET Grades 7 and 8 Learning Goal Use order of operations with integers

Materials 1 deck of cards

Mental Math Activity Persons – 2 to 4 Materials – ace is 1, jack is 11, queen is 12 and king is worth 13; red card is negative, black card is positive Mental Math Challenge • Shuffle cards and deal 4 cards to each player. • People select order of operations for the 4 numbers (from the cards) to make a result closest to 24). • Discuss and compare choice of operations and order of operations from other people. • Mental math practice ends when 4 cards cannot be dealt to each person.

Questions to Ask to Probe Mathematical Thinking • What mental math strategies did you use to select operations? • What strategies did you use to determine the order of operations?

Math Activity Variations • 3 or 5 cards are dealt to each player. • Change the target to a different integer, such as -24 or 13.



SPILL THE NUMBERS Kindergarten

Learning Goal Describe number relationships to 10

Materials 2 colour counters

Problem to Solve What different ways can you show 10 with red and yellow counters? How many times • Grab 10 counters and spill them on a surface. • How many red counters? How many yellow counters? • Record the number of red and yellow counters in a chart. • Repeat again until you have all different ways to make ten

using red and yellow counters.

Questions to Ask to Probe Mathematical Thinking ● How do you know that you have all different ways to make ten? ● How many times did you have to spill the counters to get all the combinations for 10?

Math Activity Variations ● Show 5 in different ways. How is 5 related to 10? ● Show 4 in different ways. Show 8 in different ways. How is 4 related to 8? ●


COUNTER - OH - OH! Kindergarten

Learning Goal Counting forwards and backwards

Materials 2 colour counters 1 dice

Math Game Instructions Players – 2 or more Goal – player with the most counters wins. Playing the Game • Start with a pile of 10 counters, the first player rolls the dice and removes the number of counters

indicated by the number cube roll. Each player takes a turn. • The game ends when there are no more counters in the pile. • Players count their counters; the winner is the player with the most counters. • Players can use paper and pencil to keep track of the number of turns.

Questions to Ask to Probe Mathematical Thinking • What strategy did you use to count the counters that you took from the pile? • What happens to the number of counters in the pile as the counters are removed?

Math Activity Variations • Change the starting pile to 5. Did the game end faster or slower than the first game? Why


thinkMATH@home from the TCDSB Math Dept QUICK! GUESS MY NUMBER! Kindergarten

Learning Goal Recognizing without counting quantities (subitizing)


Mental Math Activity People – 2 Mental Math Challenge • One person arranges up to 7 counters on a surface (e.g., far apart and/or close together, in an

array) while the other players cover their eyes. • One person challenges the other person, “Quick, Guess my number!” Other person guesses the

number of counters in the arrangement as quickly as they can. • Players then count the number of counters to see if they are right. • Repeat with different number of counters. Change roles of arranging the counters and guessing the

counters. • Questions to Ask to Probe Mathematical Thinking • How did you know the number of the counters that were covered? What did you see? • What other ways could you see the counters in order to count them differently?

Math Activity Variations • Use 5 counters. • Use 10 counters.


SHARING COUNTERS Grades 1 and 2 Learning Goal Dividing by sharing equally


Problem to Solve How can you equally share counters? • Place 20 counters in a bag. With a partner, take one turn each to pull out one handful of counters. • Count out the number of counters each partner has. • How many do you have altogether? Who has more?.. Equally share the counters. • Show more than one way to equally share the counters.

Questions to Ask to Probe Mathematical Thinking • What action did you use to share your counters? • How is knowing ways to share 20 counters equally help you to know different ways to share 40

counters equally?

Math Activity Variations • Share 30 counters equally. How does knowing about sharing 30 counters equaly help you now

different ways to share 60 counters equally?



COUNTER - OH - OH! Grades 1 and 2

Learning Goal Counting forwards and backwards


Math Game Instructions Players – 2 or more Gaol – player with the most counters wins. Playing the Game • Start with a pile of 50 counters, the first player rolls the dice and removes the number of counters

indicated by the number cube roll. Each player takes a turn. • The game ends when there are no more counters in the pile. • The players count their counters; the winner is the player with the most counters. • Players can use paper and pencil to keep track of the number of turns.

Questions to Ask to Probe Mathematical Thinking • What strategy did you use to count the counters that you took from the pile? • What happens to the number of counters in the pile as the counters are removed?

Math Activity Variations • Increase the starting pile to 20


QUICK IMAGES Grades 1 and 2 Learning Goal Estimate the number of objects in a set and check by counting

Materials 2 colour counters blank 8-1/2 x 11” paper

Mental Math Activity Persons - 2 Mental Math Challenge • Grab a large handful of counters and drop them on the table and cover them with paper. • Uncover the counters for 5 sec then cover again. • How many counters did you see? How do you know? • Uncover the counters to check. • Return the counters and repeat the activity.

Questions to Ask to Probe Mathematical Thinking • Compare the number of counters you grabbed, the number of counters you saw, and then the

number of counters you counted. How close was your estimate. • How could you improve the accuracy of your count?

Math Activity Variations • How many counters are there, if you imagine double its amount. • How many counters are there, if you imagine half its amount.



SKIP COUNTING PATTERNS Grades 3 and 4 Learning Goal: Count by 2s and 5s

Materials 2 colour counters BLM3 Hundreds Chart

Problem to Solve How many numbers do you have to count to get to 100? Use a 100 chart and the counters to represent the 2 patterns • Start at 0 and add 2 each time until I get to 100. • Start at 0 and add 5 each time until I get to 100. • What numbers are counted in both number patterns?

Questions to Ask to Probe Mathematical Thinking • What are the numbers when you start at 0 and add 3 each time? • What are the numbers when you started at 0 and added 4 each time?

Math Activity Variations • Start a 1 and add 2 each time to get to 100. Start at 1 and add 5 each time to get to 100.

What numbers are counted in both number patterns? • Start at 3 and add 3 each time to get to 100. Start at 3 and add 5 each tie to get to 100.

What numbers are counted in both number patterns?


WHERE IS IT? Grades 3 and 4 Learning Goal Locating objects on a coordinate grid (area) map

Materials 2 colour counters BLM4 Interlocking Cube Paper

Math Game Instructions Players – 2 or more Materials – Use the BLM Interlocking Cube Paper to make an area grid map Goal – guess the coordinates of the hidden counter Playing the Game • Each player gets one coordinate grid and 3 counters spaced out on the grid. • Set up a divider so that players cannot see each other’s grid. • Players place 3 counters on the grid. • Take turns guessing the coordinates of each other’s counters and give

feedback like, “found”( if correct guess), “keep looking” (if far) or “very close” (It’s 1 space away)

• Keep playing until one player guesses all of the other players coordinates Questions to Ask to Probe Mathematical Thinking • Explain how to use the coordinate grid map to identify location of an object on it. • What location or positional words did you use to give feedback about the guesses. Math Activity Variations • Place the 3 counters close together rather than spaced out. • Use only 1 counter.



SEING FRACTIONS AS A SET Grades 3 and 4 Learning Goal Represent and compare fractions in a set

Materials 2 colour counters paper and pencil

Mental Math Activity • Take 5 counters, shake them and spill them Record how many red and yellow counters in the set of

5 counters. What fractions do you see? Record the fractions • Shake and spill 5 counters again, until you have represented all possible fractions using 5 counters • Repeat the entire activity with 10 counters • Compare the fractions you see with 5 counters and with 10 counters. How are the fractions similar

and how are they different?

Questions to Ask to Probe Mathematical Thinking • Explain 2 different fractions with 5 counters and with 10 counters. • What is the relationship between the fractions you see with 5 counters and the fractions you see

with 10 counters?

Math Activity Variations • Use 4 counters sand then 8 counters • Use 3 counters then 6 counters and then 12 counters.

thinkMATH@home from the TCDSB Math Dept HOW MANY COUNTERS TO START? Grades 5 and 6 Learning Goal Represent fractions in a set


Problem to Solve Ben, Jack and Emma were playing a game with a box of 40 counters they were not using all of them. They each had a small pile of counters. ● Ben passed a third of his counters to Jack. ● Jack passed a fourth of his counters to Emma. ● Emma passed a fifth of her counters to Ben. ● Then, they all passed on more than one counter. After passing on 1 counter, Ben, Jack and Emma all had the same number of counters. How many counters could Ben, Jack and Emma each have at the start? Show your work. Questions to Ask to Probe Mathematical Thinking • What does a third of his counters mean? Fourth of his counters? Fifth of her counters mean? • Is it true that you need 36 counters were needed to solve this problem? • What strategy did you use to solve this problem? Math Activity Variations • Is it true that this problem could be solved with 12 total counters? Explain. • Is it true that this problem could not be solved with 40 total counters? Explain.


thinkMATH@home from the TCDSB Math Dept THE SUM OF TWO DICE Grades 5 and 6 Learning Goal Add decimal amounts to hundredths

Materials 11 2 colour counters 2 die BLM 1 Game board

Math Game Instructions Players – 2 or more Materials – 11 counters and 1 game board per player Goal – fewest rolls wins Playing the Game • Each numeral represents hundredths (e.g., 2 means 2

hundredths or 0.02). Each number on the dice represents hundredths

• Each player arranges 11 counters on the game strip and records their arrangement.

• Players can place more than one counter on a number if they choose. • Once the counters are arranged, players take turns rolling the dice. • For each roll, a player can remove one counter, if it is on the sum rolled. • Players keep track of the number of rolls of the dice it takes to clear their game board. • Fewest rolls wins.

Questions to Ask to Probe Mathematical Thinking • How did your arrangement change from one game to the next? • Why where some sums harder to roll than others? Math Activity Variations • Players can choose to remove a counter (subtract hundredths) from their board or add (hundredths)

a counter to their opponents board that matches the sum rolled.

thinkMATH@home from the TCDSB Math Dept WHAT’S THE PATTERN RULE? Grades 5 and 6 Learning Goal Describing pattern rules in words


Mental Math Activity • What is staying the same? • What is changing? • What’s the pattern rule? • What’s the term value for the 10th figure (at term number, 10)?

Questions to Ask to Probe Mathematical Thinking • What would the table of values be for this growing pattern? • What is the changing variable in this growing pattern? Math Activity Variations • Change the term number where the original figure 1 (term number is 1) and now figure 0 or term

number is 0. • What if there are 2 yellow counters at every term number. How does that change the patterning

rule?

1 2 3 4



DIVIDING FRACTIONS Grades 7 and 8 Learning Goal Divide a whole number by a fraction


Problem to Solve • Why is 6 ÷4 not the same as 6 ÷ ¼? • Use colour counters to show your solution

Questions to Ask to Probe Mathematical Thinking • What does 6 ÷4 mean, in terms of the size of one group and the number of groups? • What does 6 ÷¼ mean, in terms of the size of one group and the number of groups? Math Activity Variations • Why is 60 ÷4 not the same as 60 ÷ ¼? • How does the quotient of 60 ÷4 and 60 ÷ ¼ relate to the quote of 6 ÷4 and 6 ÷ ¼?


FRACTION BINGO Grades 7 and 8 Learning Goal Add and subtract fractions with simple like and unlike denominators


Math Game Instructions Players – 2 Goal – to have a score closest to 0 Playing the Game • Make a plying card by recording on a 3x3 grid, 9 fractions that are close to 0, using denominators

1, 2 3, 4, 5 or 6. • Roll a pair of dice two times. Use 1 dice roll as the numerator and the other dice roll as the

denominator of one proper fraction. Roll a second time to determine the 2nd proper fraction. • Choose the sum or difference of the two fractions is on a card, put a counter on the number on your

3x3 grid. • Take turns rolling and calculating. Check each other’s work. The winner is the first player with three

counters in a row horizontally, vertically, or diagonally. Questions to Ask to Probe Mathematical Thinking • How do you know when two fractions are equivalent? • How do you know which fraction that is the result of a sum or difference is closest to 0? Math Activity Variation • Use numbers on the dice roll as improper fractions. • Multiply fractions to get a result closest to 0.



INTEGER OPERATIONS Grades 7 and 8 Learning Goal Represent integer operations


Mental Math Activity Visualize this integer equation using colour counters. [(-6) + (+3) x (+8)] ÷(6) - (-3) = (6)

Questions to Ask to Probe Mathematical Thinking • What is the order of integer operations for this equation? • If the brackets are removed, is the final result (6) changed to a different result? Why?

Math Activity Variations • If the (-6) is changed to (-4) and (6) is changed to (4) how, is the final result changed? Explain. • If the (-6) is changed to (-2) and (6) is changed to (2), how is the final result changed? Explain.



MAKING A PATTERN Kindergarten

Learning Goal Create repeating and growing patterns

Materials interlocking cubes

Problem to Solve What different repeating patterns can be made with only 10 yellow and 10 green cubes? • Show 2 different repeating patterns, with at least 3 repetitions. Questions to Ask to Probe Mathematical Thinking • What is repeating in your pattern? • How many repeats are in your pattern? Math Activity Variations • Use 5 yellow, 5 green and 5 red cubes. • Use only 10 yellow cubes.


RACE TO FIVE OR TEN Kindergarten

Learning Goal Adding and subtracting numbers to 5 or 10

Materials interlocking cubes, 2 die BLM2 Race to 5 or 10

Math Game Instructions Players - 2 or more Materials – cover one dice with paper and write “+” or “-“ on 3 sides of the dice each, one 5-frame Goal – fill exactly one 5-frame with 5 cubes Playing the Game • Take turns rolling the number dice and +/- dice. • If the “+” comes up on the dice, then place the number of cube (as on the number dice) on the 5-

frame. • If “-” then remove the number of cubes (as on the number dice) on the 5-frame • The goal is to get exactly 5 cubes on in the frame. If a player goes over 5, then they have to start a

10-frame and aim to get exactly 10 cues on the 10-frame Questions to Ask to Probe Mathematical Thinking ● How could you keep track of the number of cubes put on and taken off the 5-frame or 10-frame? ● Do some numbers come up more often than other numbers when rolling the number dice? Math Activity Variations • If score goes over 5, add another 5 frame; if score goes over 10, add another 5 frame. •


thinkMATH@home from the TCDSB Math Dept MAKING PREDICTIONS USING PATTERNS Grades 1 and 2 Learning Goal Skip counting to solve patterning problems

Materials interlocking cubes 6 blue, 6 orange, 6 yellow

Problem to Solve • How can you make a pattern with interlocking cubes to show skip counting by two’s? Discuss your

ideas. • Predict what colour the eleventh cube will be. • Create your pattern. Record your colour pattern and number the cubes. • Was your prediction of the colour for the eleventh cube correct? Why or Why not. • Use your interlocking cubes to make a skip counting pattern of three’s. What colour is the eleventh

cube? Record your pattern. Explain how it shows a skip counting pattern for threes. • Repeat this pattern using skip counting with 5 interlocking cubes. Questions to Ask to Probe Mathematical Thinking • Explain your pattern using colours, using numbers. • How can you change your pattern of two’s (or three’s) to show skip counting by three’s (or five’s) Math Activity Variations • Create a pattern of twos so that the 7th cube will be (choose a colour) • Name and description of variation 2


MEASURING LENGTHS USING CUBES Kindergarten

Learning Goal Measure lengths using non-standard units


Mental Math Activity People – 2 Mental Math Challenge ● Look at objects around you whose length can be measured. Think about the length of paper, a

shoe, the width of a door ● Estimate (visualize) the number of cubes that match the length of an object. ● Check the estimate by lining up and counting the number of cubes (end to end) that it takes for

match the length of an object. ● How close is your estimate to the actual length of the object, using the cubes?

Questions to Ask to Probe Mathematical Thinking ● How could the estimate and actual measurement be closer when using the cubes? ● What could you do differently to estimate the length of another object using cubes? Math Activity Variations • Choose objects to measure that you estimate are less than 5 cubes long? • Choose objects to measure that you estimate are about 10 cubes long?



GUESS AND CHECK TEN Grades 1 and 2 Learning Goal Predicting the outcome of an event

Materials 20 interlocking cubes 1 brown paper bag paper, pencil, crayons

Math Game Instructions Players – 2 or more Goal – first to reach 10 points • First player reveals and then places 2 orange and 8 green interlocking cubes in a bag. • Second player reveals and then places 2 yellow, 2 red, 2 orange, 2 blue, 2 green interlocking

cubes in a bag. • Each player takes turns predicting and then drawing one colour cube from bag. • A correct prediction is worth 1 point. • Player who reaches 10 points to win.

Questions to Ask to Probe Mathematical Thinking • How did you decide which colour to predict? • Which player had a better chance of drawing a green cube? Why?

Math Activity Variations • Use 5 orange and 5 green interlocking cubes. • Use 8 orange and 2 green interlocking cubes.

thinkMATH@home from the TCDSB Math Dept WHAT DOES A 25¢ PATTERN LOOK LIKE? Grades 1 and 2 Learning Goal Making combinations of 25 using different values of cubes

Materials interlocking cubes - 6 6 6 blue, 6 yellow, 6 green

Mental Math Activity If blue cubes are 1¢, yellow cubes are 2¢ and green cubes are 5¢, then what would a pattern worth 25¢ look like? Questions to Ask to Probe Mathematical Thinking • What does the least number of cubes in a pattern worth 25¢ look like? • Which kind of pattern did you use: repeating or growing?

Math Activity Variations • Use 9 blue and 9 yellow cubes. • Use 6 blue and 12 yellow cubes.



THE STAIRCASE Grades 3 and 4 Learning Goal Describing and extending a pattern.


Problem to Solve – How can you figure out the number of cubes you need to build a staircase without counting every cube? • Build staircases with steps (see diagram) that are 3 cubes

wide using cubes. • Look for a pattern - predict the number of cubes you would

need to make a 6-step staircase.

Questions to Ask to Probe Mathematical Thinking • Describe the pattern rule for the staircase. • Is the pattern repeating or growing? How do you know?

Math Activity Variations • Make steps that are 5 cubes wide. • Predict the number of cubes to make a 10 step staircase.


LOOSE CABOOSE Grades 3 and 4 Learning Goal Making equal size groups


Math Game: Players – 2 Goal – greatest number of points wins Playing the Game • Start with a pile of 27 snap cubes • Pick a number between 1 – 10 to decide how many cubes to take from the pile. (e.g., if you

choose 6, then take away 6 cubes at a time, meaning the group size of cubes is 6) • Take turns removing a specific number of cubes from the pile of 27 cubes, until there are no more

cubes of that group size to take from the pile (e.g., group size of 6, mean that on the 5th turn, there will be 3 cubes left)

• For every group of cubes removed, 1 point is gained. • Start with another pile of cubes, like 24. Pick another number between 1-10, to determine group

size of cubes. • Take turns removing the same group size of cubes until there are no more cubes of that group size

to take away from the pile. Questions to Ask to Probe Mathematical Thinking • What numbers could you make into 2 trains with no leftover cubes? • What happened when you chose the number 1? Math Activity Variations • Start with a pile of 37 cubes. • Start with a pile of 54 cubes.



NUMBER TOWERS Grades 3 and 4 Learning Goal Adding and subtracting 2 digit whole numbers using mental strategies.


Mental Math Activity People – 2 Materials – yellow cubes represent tens and blue cubes represent ones; 1 tower is a set of cubes attached (e.g., 2 yellow, 4 blue makes a tower of 6 cubes) Mental Math Challenge • Make seven different towers of 2 digit numbers using yellow (tens) and blue (ones) cubes (e.g., 2

yellow, 4 blue represent 2 tens and 4 ones or 24). • Take turns challenging each other to add three or more addends of 2 digit numbers (e.g., How many

altogether? 2 yellow,4 blue; 4 yellow, 2 blue; 3 yellow, 3 blue à 24+42+33 = 9 tens + 9 ones = 99

Questions to Ask to Probe Mathematical Thinking • What strategy did you use to add three addends of 2 digit numbers? • Which combinations of 2 digit numbers are easier and more difficult to add?

Math Activity Variations • Determine the difference between 2 towers; that is, subtract two 2 digit whole numbers. • Increase the number of addends to four and five 2 digit whole numbers.

thinkMATH@home from the TCDSB Math Dept INVESTIGATING PATTERNS Grades 5 and 6 Learning Goal Extending growing patterns


Problem to Solve What does the 10th figure look like? • Build the three cube models as shown in the diagram. • What will the 4th figure look like? Build it. • Without building the 5th figure, build the 6th figure. • How many cubes would be in the 10th figure? Questions to Ask to Probe Mathematical Thinking • How did you decide the number of cubes for the 4th, 5th and 6th cube figure? • How do you know that the 10th cube figure you built is accurate? Math Activity Variations • Build the first three models of a different growing pattern. Challenge a friend to determine the

10th figure.


thinkMATH@home from the TCDSB Math Dept END OF THE LINE Grades 5 and 6 Learning Goal Analysing game playing strategies to improve the likelihood of winning the game.


Math Game Instructions Players – 2 Goal – to avoid taking the last cube Materials - start the game with a line of 21 connected cubes. Playing the Game • Players take turns removing 1, 2, or 3 linked cube from the line of cubes. • The player that holds the last cube in “at the end of the line” and loses the game Questions to Ask to Probe Mathematical Thinking • Does it matter which player goes first? • Why did you decide to take 1, 2, or 3 cubes on one turn? Math Activity Variations • Player taking the last cube wins • Each player can only take 2 or 3 cubes; the player who takes the last cube loses • Each player can only take 1 or 3 cubes; the player who takes the last cube loses

thinkMATH@home from the TCDSB Math Dept WHAT IS THE SMALLEST SURFACE AREA? Grades 5 and 6 Learning Goal Estimating the surface area of a cube structure


Mental Math Activity People – 2 Mental Math Challenge • Create as many different cube structures from as you can that have 12 linking cubes. • Determine the number of square faces without viewing all faces. Check by examining all faces. • Sort cube structures that have the same number of square faces

Questions to Ask to Probe Mathematical Thinking • What do you notice about the structure that has the least number of square faces visible? • What visualization strategies did you use to determine the number of faces on the structure that you

couldn’t see? Math Activity Variations • Use 16, 24, or 36 cubes. • Make only tower (straight line) structures.


thinkMATH@home from the TCDSB Math Dept BUILDING TOWERS Grades 7 and 8 Learning Goal Determining the relationship between the height, the area of the base, and the volume of prisms

Materials interlocking cubes pencils, markers BLM4 Interlocking Cubes Paper

Problem to Solve Each tower pictured here is a prism. Build each prism and determine the volume of each building by counting cubes. • Complete the table of measures for each tower

• What relationship do you notice between volume, area of the base, and height? • Make a generalization (i.e., formula) for calculating volume of a prism when you know the area of the

base and the height of the prism. • Test your formula for accuracy by building two other prism towers and determining the volume. • Sketch your towers and show calculations on this table. • Describe the accuracy of your formula and explain any adjustments that you made.

Tower Area of Base

Height of Tower

Volume counting cubes

A

B

C

Questions to Ask to Probe Mathematical Thinking • What do you notice about the structure that has the least number of linking cube faces visible?

Math Activity Variations • Try the same activity with 16 or 24 cubes.

thinkMATH@home from the TCDSB Math Dept CHAIR AND TABLE Grades 7 and 8 Learning Goal Enlarging and reducing 3D figures


Mental Math Activity • Make a table using cubes. • How many cubes did you use? • Visualize the size of the table doubled. How many cubes do you need? Check your

estimate by building a table double the original size. • Visualize the size of the table halved. How many cubes do you need? Check your estimate by

building a table half its original size. Questions to Ask to Probe Mathematical Thinking • What parts of the table did you double? • What is the relationship between the number of cubes for the original table and table doubled? Math Activity Variations • Build a different object, like a chair. • Build a tower only. (Its easier to see doubling and halving.)

Tower A Tower B Tower C


thinkMATH@home from the TCDSB Math Dept ROLLING FOR A CATERPILLAR Grades 7 and 8 Learning Goal Analysing the frequency of dice rolls in relation to game playing strategies

Materials interlocking cubes BLM5 Caterpillar Game Board, 2 die, frequency chart

Math Game Instructions (adapted from Edutopia) Players - 2 to 4 Goal - build the longest caterpillar with blocks by the end of the game. Playing the Game • Each player begins the game by placing two blocks on any two

mushroom spaces they choose. • One turn consists of a player rolling the two dice and recording the

sum on a frequency chart. • Any player with a block on a mushroom space touching the sum

rolled receives an extra block of his or her color. • Each turn also includes the opportunity to place accumulated blocks

in order to build the longest caterpillar on the board. • The game ends when there are no more spaces available on the

board. • Players then reference their dice rolls on the frequency chart to

determine the most frequently rolled number. • That number is the "bird," which eats the caterpillars at the end of

the game. • Players must remove pieces from any space around the number that

has been determined to be the bird. The player with the longest caterpillar intact at the end of this explosion is the winner!

Questions to Ask to Probe Mathematical Thinking • How do you decide if the first move is a "good" and "bad" move, in terms of where the first two

blocks are placed on mushroom spaces? • How these spaces on the board correspond to the most and least frequently rolled two dice sums?

Math Activity Variations • Changes on first move place.



HOW MANY MORE? Kindergarten

Learning Goal Creating the same shape using different combinations of 2D shapes

Materials pattern blocks BLM6 Pattern Block paper

Problem to Solve What different ways can the same shape be made? • Put 1 trapezoid and 1 hexagon together to make a shape. • Make this shape using different number and types of pattern blocks. • Sketch the different ways that the same shape is made using pattern block paper.

Questions to Ask to Probe Mathematical Thinking • How do you know your shape is the same? • Why is it possible to make the shape using several same shapes (e.g., using only green triangles)?

Math Activity Variations • Create a shape using the pattern blocks. Ask : “How can you copy my shape? you cannot use the

same blocks I did.

thinkMATH@home from the TCDSB Math Dept ATTRIBUTE CONNECTION Kindergarten

Learning Goal Covering a space using 2D shapes

Materials pattern blocks BLM6 Pattern Block paper

Math Game Instructions Players – 2 to 4 Goal – be the last player to cover a space with a pattern block Playing the Game • Each player selects 8 pattern blocks • Players take turns take turns placing a pattern block to cover a space on the game board. • When a player has placed 8 blocks, then they take another more pattern blocks. • Game ends when there is no more space on the game board to cover by a whole pattern block. • Last person to cover space on the game board wins.

Questions to Ask to Probe Mathematical Thinking • Which pattern block shape did you use more often? Why? • Which pattern block shape did you use less often? Why?

Math Activity Variations • Last person to cover the space loses. • Use only 1 type or 2 types of pattern blocks.



MAKING SAME IMAGES Kindergarten Learning Goal Using spatial relationships to compose pictures using 2D shapes

Materials pattern blocks

Mental Math Activity Persons – 2 Mental Math Challenge • Put up a visual divider, like a book between the 2 people. • 1 person makes and gives spatial directions (e.g., above, below, to the right, to the

left) to tell how to make a picture of an object (e.g., dog) using pattern blocks. • 2nd person makes the picture fro the oral directions using pattern blocks • Compare the intended picture with the picture made from the oral instructions. • Switch roles where the 2nd person makes and gives spatial directions while the 1st person makes the

picture from the oral instructions. Questions to Ask to Probe Mathematical Thinking • How did you decide which pattern blocks to use to make the picture? • How did you decide what to tell your partner so he/she could make your picture using pattern

blocks? • When you compare your picture with your partner’s picture, what parts were the same? What

parts were different? How did that happen?

Math Activity Variations • Try only using 2 types of pattern blocks. Which ones did you choose to use?


UNDER COVER Grades 1 and 2 Learning Goal Compose and decompose shapes using smaller or larger shapes

Materials pattern blocks number cube

Problem to Solve Is it possible to make the same shape with less number of pattern blocks? • Create a shape with the pattern blocks. • Trace your shape • Cover your shape using the least number of blocks? How many blocks did you use? • Now cover your shape using the greatest number of blocks? How many blocks did you use? Questions to Ask to Probe Mathematical Thinking • What strategy did you use to cover the same shape with the least number of pattern blocks? • What strategy did you use to cover the same shape with the greatest number of pattern blocks? Math Activity Variations • Double the size of the original shape. How does that change the least number of blocks used?

How does that change the greatest number of blocks used? • Change the shape.



NAME MY PATTERN Grades 1 and 2 Learning Goal Creating and describe repeating or growing patterns

Materials pattern blocks dice

Math Game Instructions Players - 2 Goal - first player to reach 10 points wins Playing the Game • Players roll dice to determine who goes first; lowest roll goes first • Player 1 rolls the number cube to indicate the number of pattern blocks to use to begin a repeating

or growing pattern. • Player 2 rolls the dice to indicate the number of shapes to use to continue the pattern started by

player 1, then describes the pattern rule (1 point if accurate) and/or pattern attributes (1 point if accurate).

• Repeat the process with player 2 starting. • First player to reach 10 points wins.

Questions to Ask to Probe Mathematical Thinking • What are the attributes of each pattern? • What changes and what stays the same in the patterns?

Math Activity Variations • Use 1 pattern block shape only. • Use 2 pattern block shapes only.


COVER THE BOARD Grades 1 and 2 Learning Goal Making Pictures and Movement


Mental Math Activity Persons - 2 Mental Math Challenge • Person 1 creates an animal using pattern blocks. • Person 2 imagines which pattern blocks to move or change so that the animal looks like it is walking. • Person 1 imagines which pattern blocks to move or change so that the animal looks like it is looking up

towards the sky. Person 1 builds the shape with the change to check. • Person 2 creates a different animal using pattern blocks. Repeat the process.

Questions to Ask to Probe Mathematical Thinking • How did you decide which pattern block to move or change to show the movement? • Which part of the shape did you use to show movement? Why? Math Activity Variations • Visualize and then discuss how to make a pattern block animal, then take turns adding one pattern

block at a time to build the picture, without communicating to one another. • Create pictures of objects in the classroom.



THE TOY FACTORY Grades 3 and 4 Learning Goal Represent money amounts to $10


Problem to Solve: Is it possible to build 2 different toys that are made of the same number and type of pattern blocks and are worth $9.75? • The values of the pattern blocks are: green triangle (5¢), blue rhombus, square, trapezoid,

parallelogram (10¢), hexagon (25¢) • Use any number or combination of pattern blocks. • Show the calculations to determine the worth of each toy.

Questions to Ask to Probe Mathematical Thinking • Which pattern block did you use most often? Why? • What strategy did you use to make 2 different toys with the same number and type of pattern

blocks?

Math Activity Variations • Change the value of each pattern block. • Use only 2 types of pattern blocks.


DON’T BREAK THE WAGON Grades 3 and 4 Learning Goal Use strategies to cover an area with the least or greatest number of 2D shapes

Materials pattern blocks BLM6 Pattern Block Paper

Math Game Instructions: Players – 2 Materials – Make the game board by drawing an outline of a wagon on pattern block paper, using the pattern block paper lines Goal – avoid placing the last block to win Playing the Game • Take turns placing blocks on the game board. The blocks must fit within the outline. • Player who places the last block on the board “breaks the wagon!” • Avoid being the last person to place a block and break the wagon. • Play again.

Questions to Ask to Probe Mathematical Thinking • Is it better to go first or second? • Did your strategy change as the board became more full? • How many pattern blocks were used the 1st time, the 2nd time? Was the game played in a shorter

amount of time the 1st or 2nd time? Why?

Math Activity Variations • Make a different shape for the wagon as game board outline. • Use only 1 or 2 types of pattern blocks.



PATTERN BLOCK WALLS Grades 3 and 4 Learning Goal Create and extend a growing pattern


Mental Math Activity Persons – 2 Mental Math Challenge • Person 1 imagines a growing pattern and explains the pattern rule. • Person 2 creates the growing pattern from person 1’s description. • Change roles and repeat the process. Questions to Ask to Probe Mathematical Thinking • What stayed the same and what changed in your growing pattern? • What information is important to include in a pattern rule?

Math Activity Variations • Growing pattern starts at 5, but changes in a way determined by the persons. • Growing pattern changes by add 5 again and again, but the person determines the start.

thinkMATH@home from the TCDSB Math Dept HOW MANY WAYS CAN YOU MAKE 360O? Grades 5 and 6 Learning Goal Creating polygons with rotational symmetry.


Problem to Solve How many ways can 360o be made? • Place combination of pattern blocks adjacent to one

another to create a design where the pattern blocks meet at one point.

• Create such a design with 1 type, 2 types, 3 types, 4 types, 5 types or 6 types of pattern blocks.

Questions to Ask to Probe Mathematical Thinking • How do you know you’ve created a set that is 360o • How does the design change as you increase the type of pattern blocks used? • What designs have a line of symmetry? How does the choice and number of pattern blocks used

contribute to creating a line or lines of symmetry within the design? • What designs have rotational symmetry? How does the choice and number of pattern blocks used

contribute to creating a rotational symmetry within the design?

Math Activity Variations • Is it possible to create a 360o design that has 1 line, 2 lines, 3 lines, 4 lines, 5 lines

or 6 lines of symmetry?


thinkMATH@home from the TCDSB Math Dept TILE IT UP! Grades 5 and 6 Learning Goal Make calculations using proportional relationships

Materials pattern blocks, dice BLM6 Pattern Block Paper

Math Game Instructions Players – 2 to 4 Materials – exclude square and the parallelogram Goal – cover the greatest area Playing the Game - • Every player chooses a different pattern block • Roll a die to determine the number of pattern blocks that can place on the Pattern Block Paper

game board in one turn. • A player skips a turn when they cannot place a pattern block on the grid. • Make a chart to keep track of the number of blocks each player places on the game board. • Determine value of the area covered by the pattern blocks using proportional reasoning (i.e., If the

triangle - $1.25, then 1 blue rhombus is $1.25 x 2 = $2.50 as 2 triangles). • When no more pattern blocks can be placed on the game board, calculate the total area covered

by your team’s blocks. • Player(s) that cover(s) the greater area wins.

Questions to Ask to Probe Mathematical Thinking • How did you choose which block you should use? • How did you decide where to place your blocks? • What strategy did you use to determine the value of the pattern blocks placed on the game

board?

Math Activity Variations • Change the values of the pattern blocks • Include the square and parallelogram and assign values for each shape.

thinkMATH@home from the TCDSB Math Dept CREATING FRACTION BLOCK FRACTIONS Grades 5 and 6 Learning Goal Represent equivalent fractions

Materials pattern blocks 2 die

Mental Math Activity ● Roll die and use one number as the numerator and the other number as the denominator of a

proper fraction. ● Visualize different pattern blocks models of the fraction (include equivalent fractions). ● Create different representations of the same fraction using the pattern blocks Questions to Ask to Probe Mathematical Thinking • How are the pattern blocks helpful for creating equivalent fractions? • Represent the fraction using pattern blocks as a set of objects, rather than as an area model. Math Activity Variations • Use 3 dice to create a mixed number (greater than one). • Make an improper fraction.


thinkMATH@home from the TCDSB Math Dept DANCING BLOCK PEOPLE Grades 7 and 8 Learning Goal Solve problems that involve determining whole number percents


Problem to Solve Is it possible that the 2 dancing people represents different fractional amounts? • The "Dancing Block People" are made out of three different pattern blocks. • What’s the value of the whole? What is the percentage of the design is

made up of each shape? Explain your thinking. • Change the value of the whole. Now what is the percentage of the design is

made up of each shape? Explain your thinking. • Is it possible to change the value of the whole again? If so, what’s the

percentage of the design is made up of each shape? Explain your thinking.

Questions to Ask to Probe Mathematical Thinking • How are the pattern block shapes related to each other? • How does the value of the whole impact the value of its fractional parts? Math Activity Variations • Number of original figures are increased to three or four. • Original shapes can be changed (e.g., house, car).

thinkMATH@home from the TCDSB Math Dept REDUCING PATTERN BLOCKS Grades 7 and 8 Learning Goal Creating composite shapes using combinations of 2D shapes


Math Game Instructions Players - 2 Goal – greatest number of combinations wins Playing the Game • Take turns creating a different combination of

pattern blocks to make the same shape. • Player that makes the greatest number of

combinations of the same shape wins the game.

Questions to Ask to Probe Mathematical Thinking • How are the pattern blocks related to one another? • How are the areas of the pattern blocks related to one another? • What strategies did you use to create combinations of the same shape?

Math Activity Variations • Use composite shapes that are made up of 4 or more pattern blocks. • Use pictures of objects made from pattern blocks.

1 Trapezoid + 2 Rhombi (3 shapes ) reduces to 1 Hexagon + 1 Triangle (2 shapes)


thinkMATH@home from the TCDSB Math Dept SHAPES, SHAPES Grades 7 and 8 Learning Goal Compare the area of 2D shapes


Mental Math Activity

Questions to Ask to Probe Mathematical Thinking • How are the areas of the shapes related? • How many triangles will make other given shapes How do you know?

Math Activity Variations • Other pattern block shapes are compared. • Compare combinations of pattern blocks shapes, rather than single pattern block shapes.



5 SQUARE TILES Kindergarten

Learning Goal Build and sort non-traditional shapes

Materials square tiles BLM7 Square Tiles Paper

Problem to Solve What different shapes can be made with 5 square tiles? List o directions ● To make shapes from square tiles, the sides must line up end to end ● Shapes may be the same, but in a different position by a reflection

or a rotation. ● Trace outlines of your shape on the square tiles paper.

Questions to Ask to Probe Mathematical Thinking ● What strategies did you use to make different shapes using 5 square tiles. ● How did you check to make sure that you did not include same shapes.

Math Activity Variations ● Use 4 square tiles only. ● Use 6 square tiles only.


One Two Three in a Row Kindergarten

Learning Goal Develop and use strategies when playing a game.

Materials 6 square tiles BLM8 3 in a Row Gameboard

Math Game Instructions Players – 2 Goal – create 3 a row of 3 tiles through the centre of the game board Playing the Game • The first player places square tile on any one of the nine circles

on the game board. • The second player then places square tile on one of the empty

circles. The players continue to take turns placing one counter at a time on a circle.

• When all six square tiles are on the board, players take turns moving one square tile at a time along a line to an empty circle. The players can not jump square tiles

• The winner is the first player to create a row of three square tiles through the centre. The game is a draw if neither player can complete a row of three square tiles

Questions to Ask to Probe Mathematical Thinking • How did you decide what direction to move the square tiles?

Math Activity Variations ● Double the square tiles for every circle. ● Double square tiles for every other circle.

yes no no



MORE OR LESS? Kindergarten

Learning Goal Estimating and counting a set of objects

Materials square tiles

Mental Math Activity Person – 2 • Grab a handful of square tiles and dump them on the table and asks, e.g., “Are their more or

less__red_ than _blue_?”, “Which has the most?”, or “Which has the least?” “How many altogether?”

• Other person makes at estimate based on visual inspection. • Check the visual estimates by counting the number of square tiles and compare the number of

colour square tiles. • Compare the estimate to the actual count. • Repeat the process again, switching roles.

Questions to Ask to Probe Mathematical Thinking • Which colour has more/less than the other colour? • What strategies did you use to estimate the number of colour square tiles.

Math Activity Variations • Select only 2 colours. • Select only 3 colours.


MAKING RECTANGLES Grades 1 and 2 Learning Goal Compare rectangles by area

Materials square tiles BLM7 Square Tile Paper

Problem to Solve How many different rectangles can you make, using only 20 rectangles? • Create different rectangles using 20 rectangles. • Sketch each rectangle that you created on the square tile paper.

Questions to Ask to Probe Mathematical Thinking • How do you know if you have all possible rectangles? • What could the rectangle look like if the 20 tiles used only to build the edges of the rectangle?

Math Activity Variations • Use 12 square tiles. • Use 40 square tiles.



WHERE’S YOUR SQUARE TILE? Grades 1 and 2 Learning Goal Describing location of objects using positional language

Materials square tiles BLM7 Square Tiles Paper

Math Game Instructions Players – 2 Materials – Assign colour tile to each player and green colour tiles to be the environment objects, 2 game boards. Goal – Locate the other player’s object first. Playing the Game • Agree to place 3 different size green rectangles on both game boards. • Put up a visual divider between the 2 game boards. • Each player places their one colour square tile on the game board. • Take turns asking each other questions about the location of each other’s colour square tile using

position language like, “Is it above the rectangle made of 3 square tiles? Is it to the right of the rectangle made of 4 square tiles?

• Game ends when a player locates the other player’s colour square tile. Questions to Ask to Probe Mathematical Thinking • Which positional words did you use most often? • Which object did you use as the reference for other objects? Math Activity Variations • Each player can place 2 colour tiles to find • Increase the number of green colour tiles as environmental objects


WHAT’S MY SHAPE? Grades 1 and 2 Learning Goal Identify a shape by its geometric properties and attributes


Mental Math Activity People – 2 Mental Math Challenge • Make a 2D shape using 5 square tiles • Describe the 2D shape, one geometric attribute at a time (e.g., My

shape has 1 side that is 2 linear units. What’s my shape) • The other person creates the shape using square tiles from each

description. • Continue until the person accurately creates the shape. • Switch roles and repeat the process. Questions to Ask to Probe Mathematical Thinking • How did you decide what description to tell first and then tell last? • What details best helped you the create the shape? Math Activity Variations • Have person 2 ask questions about the shape, rather than person 1 giving one detail at a time. • Brainstorm the possible shapes first, before visualizing the shape chosen.

yes no no



BEN’S GARDEN Grades 3 and 4 Learning Goal Measure area and perimeter of a rectangle using square and linear units.

Materials colour square tiles

Problem to Solve Ben is designing a fenced in garden that is 24 square units. Show all the different ways you can design his garden plot. Use square tiles. Which garden plot design will have the longest fence? Questions to Ask to Probe Mathematical Thinking • Will the fence be the same length for every shape of garden? • Which garden plot design will have the shortest fence? Math Activity Variations • Use 36 square units. • Use 48 square units.


AREA LOGIC Grades 3 and 4 Learning Goal Measure the area of rectangles using square units

Materials colour square tiles BLM7 Square Tile Paper

Math Game Instructions Players – 2 Materials – each player chooses 2 colours of square tiles (to designate the area they covered) Goal – Cover the greatest area on the game board Playing the Game • Players take turns rolling 2 dice. Use the product of the 2 numbers from each die to determine the

area of a rectangle. • Cover the area on the square tile paper using square tiles. • Player loses a turn when the die rolls require an area that cannot be with square tiles. • Continue taking turns until no player can cover a rectangle on the square tile paper with square

tiles. • Add up the number of square units.

Questions to Ask to Probe Mathematical Thinking • What did you notice about the arrangement of square tiles in a rectangle? • What strategy did you use to make it difficult for the other player to cover an area on the game

board with square tiles? • What strategy did you use to help you to cover an area on the game board with square tiles?

Math Activity Variations • Use 1 dice to determine the number of square tiles or area to cover on the game board (easier

version) • Add the value of 2 dice to determine the number of square tiles or area to cover on the game

board.



DOUBLES, DOUBLES, DOUBLES Grades 3 and 4 Learning Goal Measure the area of rectangles using square units

Materials colour square tiles

Mental Math Activity People – 2 Mental Math Challenge • Visualize a shape using 6 square units. • Double the number of square tiles again. • Double the number of square tiles again. • How many square tiles do you need to make that shape? • What does the rectangle look like after the second doubling? • Describe the shape to your partner so he/she can build the shape. • Have the partner predict the original rectangle (rows x columns)

Questions to Ask to Probe Mathematical Thinking • How does doubling the number of square tiles affect the area of the rectangle made from square

tiles? • Is it true that doubling 2 times means quadrupuling? Explain using your square tile rectangles.

Math Activity Variations • Visualize a shape with 10 square units. • Visual a final shape that is 60 square units and work backwards to the original shape.

thinkMATH@home from the TCDSB Math Dept AREA POSSIBILITIES Grades 5 and 6 Learning Goal Measuring the perimeter of a rectangle using linear units.


Problem to Solve Lisa plans to use 48 metres of fencing to enclose her dog’s rectangular play area. What dimensions would give the dog the largest possible play area? • Use square tiles to model different playing areas to determine which play area will have the largest

dimensions.

Questions to Ask to Probe Mathematical Thinking • What strategy did you use to find rectangles of 48 meters? • Based on the models you made, what can you say about how perimeter affects area?

Math Activity Variations • Use 25 metres of fencing. • Use 36 metres of fencing.


thinkMATH@home from the TCDSB Math Dept WHAT’S YOUR PREDICTION? Grades 5 and 6 Learning Goal Comparing predictions to the results of an experiment

Materials Square tiles paper bag paper and pencil

Math Game Instructions Players - 2 or more ● One player fills the bag with 8 square tiles ● The second player(s) take turns taking a sample from the bag, recording what they picked, and

replacing the tile in the bag. ● The second player continues until they are ready to make a prediction about how many of each

colour tile is in the bag. ● Players reveal the contents of the bag to compare to the predictions Questions to Ask to Probe Mathematical Thinking • How did you decide how many of each colour tile was in the bag? • How could you change the experiment so that your prediction is closer to the actual experimental

results? Math Activity Variations • Increase the number of tiles. • Increase the number of draws from the bag

thinkMATH@home from the TCDSB Math Dept FRACTION FLAGS Grades 5 and 6 Learning Goal Describe fractions using an area model


Mental Math Activity People - 2 • Use the 3 different colour tiles to visualize a rectangular flag designs for flags. • what fraction is represented by each of colours on your flag. • Use your visualization to tell your partner how to create your flag. Use only fractional language.

Questions to Ask to Probe Mathematical Thinking • What was your strategy for determining the fractions that represent the colours of your flag?

Math Activity Variations • Determine the percentage of space taken up by each of the colours of your flag. • Use 2, 4, or 5 square tiles.


thinkMATH@home from the TCDSB Math Dept ON THEIR OWN Grades 7 and 8 Learning Goal Organizing and interpreting data, making predictions

Materials square tiles paper bags

Problem to Solve: There are 30 colour square tiles in a bag. The tiles are red, blue, green, and yellow. How can you figure out the number of tiles of each color square tile by drawing one colour tile at a time? • Take turns sampling the tiles in the bag by drawing 1 tile from the bag without looking inside. • Each time you draw a tile, record the color and then return the square tile to the bag. Make only 10

draws. • Record your group’s predictions, the number of each color picked, and the total number of samples

you took. • Be ready to explain how you made your predictions. • Continue the experiment for 10 more draws from the bag. Draw a conclusion. Questions to Ask to Probe Mathematical Thinking • Can you predict the number of different color tiles after first, second, third drawings? • What facts support your predictions? Math Activity Variation • Different combinations of tiles’ colors placed in the bag. • Increased number of coloured tiles in a bag.

thinkMATH@home from the TCDSB Math Dept ALGE-SCRABBLE Grades 7 and 8 Learning Goal Model linear relationships using tables of values, graphs, and equations


Math Game Instructions Players – 2 to 4 Goal – highest score wins Playing the Game • Place the tiles with their blank sides facing up. Each of 2-4 players chooses 15 tiles- 5 green, 5 blue

and 5 yellow tiles at the beginning of the first turn. The red tiles can be used whenever they are needed.

• Players take turns placing tiles on the game board to form an equation with a variable, such as 3n+2=20.

• Players score points equal to the value of the variable that solves their equation. • At the end of each turn, players draw new tiles to replace the tiles used. • Players can use tiles that are already on the game board to build an equation, but the original

value of the variable cannot change. • The game is finished after five rounds. The player with the highest score wins. Questions to Ask to Probe Mathematical Thinking • What is the relation between the independent and dependent variables?

Math Activity Variations • If the game boards includes double value and triple value squares, the variable tiles can be placed

on these squares to score extra points.


thinkMATH@home from the TCDSB Math Dept RECTANGLES AND SQUARES Grades 7 and 8 Learning Goal Describe the relationship between the lengths of sides in a rectangle and in a square

Materials square tiles chart paper, markers

Mental Math Activity • Use the square tiles to make five rectangles with the dimension shown. Length (cm) Width (cm) Area (𝑐𝑚!) Square?

(yes/no) Side Length of Square (cm)

5 3 8 2 9 1 4 3 9 4

• After constructing the shape, record the area of the shape. • Try to rearrange the tiles in each rectangle to make a square. • Which rectangles can you make into square? Record the side length of each square in your table.

Questions to Ask to Probe Mathematical Thinking • Which rectangles from your chart can you make into square? • How is the area of each square related to its side length?

Math Activity Variations • Various length and widths can be given for students to investigate areas.



TANGRAM MOVES Kindergarten Learning Goal Compose picturess using 2D shapes

Materials 2 sets of tangrams

Problem to Solve A tangram has a set of 7 shapes. Different pictures cam be made with them. How many tangram pieces need to be moved in the first shape to make the second shape? original shape new shape Questions to Ask to Probe Mathematical Thinking • How are the 2 shapes similar? How are they different? • Describe the movement of the 2 shapes from the original shapes to the new shape? Math Activity Variations • Make a different boat by changing 2 tangram pieces. • Make the square using 7 tangram pieces.


SHAPE MAKER Kindergarten Learning Goal Compose shapes using 2D shapes

Materials 1 set of tangrams, blank paper

Math Game Instructions Players - 2 Goal – player with the greatest number of points wins Playing the Game • Make shapes with 3 sides, 4 sides, 5 sides and 6 sides. Use 1 to 7 tangram pieces. • Trace around your shapes on paper. • Points – 3 points for 3-sided shape, 4 points for 4-sided shape, 5 points for 5-sided shape and so

on. Add the points gained for each player.

Questions to Ask to Probe Mathematical Thinking • How are the shapes you made with tangrams the same? How are the shapes different? • Which shapes did you make the most? 3-sided? 4-sided? 5-sided?

Math Activity Variations • Change the shapes to animals, like cats. (Show one example of a cat as a starter.) • Change the shapes to objects, like boats.


thinkMATH@home from the TCDSB Math Dept SAME? DIFFERENT? Kindergarten Learning Goal Show spatial relationships and movements

Materials 2 sets of tangrams

Mental Math Activity Which tangram pieces should be moved in the first shape to make the second shape?

original shape new shape Questions to Ask to Probe Mathematical Thinking • How are the 2 shapes similar? How are they different? • Describe the movement of the 2 shapes from the original shapes to the new shape?

Math Activity Variations • Rotate the new shape and pose the mental math challenge again. • Rotate the original shape and pose the mental math challenge again


FILLING IN SHAPES Grades 1 and 2 Learning Goal Cover an outline puzzle with 2D shapes

Materials 1 set of tangrams BLM12-15 Outline Puzzles 1-4

Problem to Solve • Use all 7 tangram pieces to fill in these tangram outline puzzles. • Is it possible for a tangram outline puzzle to be filled in more than 1 way?

Questions to Ask to Probe Mathematical Thinking • Which tangram piece did you use most often to start? Why? • Which tangram piece did you use most often as the last piece? Why? Math Activity Variations • Change the orientation of an outline puzzle already solved, then challenge the students to solve the

tangram outline puzzle again.



CATS GALORE Grades 1 and 2 Learning Goal Make pictures using 2D shapes

Materials tangrams

Math Game Instructions • Here is one example of a tangram cat. • Make different cats using all 7 tangrams. Questions to Ask to Probe Mathematical Thinking • What did you keep the same and what did you change to make different cats? • Which tangram pieces better showed details of the cat shape than others?

Math Activity Variations • Make different letters of the alphabet using all 7 tangrams. • Make different people using all 7 tangrams.

thinkMATH@home from the TCDSB Math Dept CATS ON THE MOVE Grades 1 and 2 Learning Goal Describe the relative locations and movements of objects

Materials 2 sets tangrams

Mental Math Activity • Which tangram pieces should be moved to show that

the cat is sitting? Name the pieces by their shape (e.g., triangle, square, parallelogram) and their size (e.g., small triangle, medium triangle, large triangle)

• Where are the tangram pieces moved to in relation to the original tangram pieces? Use words like above, beside, below, to the right of, to the left of and so on.

Questions to Ask to Probe Mathematical Thinking • Which shape is below the small triangle? • Which shape is above the large triangle?

Math Activity Variations • Which tangram pieces should be moved to show that the cat is laying down? • Which tangram pieces should be moved to show that the cat’s head is looking downwards?



THERE’S MORE THAN 1 SQUARE Grades 3 and 4 Learning Goal Compose a 2D shape using different number of shapes

Materials tangrams

Problem to Solve Which squares can and cannot be made with tangram pieces? Predict and try each one. • Square using 1 tangram piece. • Square using 2 tangram pieces • Square using 3 tangram pieces. • Square using 4 tangram pieces. • Square using 5 tangram pieces. • Square using 6 tangram pieces. • Square using all 7 tangram pieces.

Questions to Ask to Probe Mathematical Thinking • What spatial visualization strategies did you do to make each square with different number and

types of tangram pieces? • What spatial visualization road blacks did you experience? Why?

Math Activity Variations • Is it possible to create a triangle using 1, 2, 3, 4, 5, 6 and 7 tangram pieces? • Is it possible to create a trapezoid using tangram pieces?

thinkMATH@home from the TCDSB Math Dept WHERE’S THE TAN? Grades 3 and 4 Learning Goal Identify location (by spaces) on a grid system

Materials 2 sets of tangrams BLM16 Tangram Battleship Grid (Area)

Math Game Instructions Players – 2 Goal – locate the spaces covered by the tan on the tangram battleship grid Playing the Game • Place visual barrier at the centre of the Tangram Battleship grid. • Each player places 1 tangram piece (tan) on the tangram battleship game board. • Players take turn guessing the location of the area covered by the tan. • First player to identify the entire area that the tan covers, wins. Questions to Ask to Probe Mathematical Thinking • How did you use the Tangram Battleship grid to identify the area (in square units) covered by the

tan? • What strategy did you use to choose the grid areas covered by the tan?

Math Activity Variations • Use 2 tans that are joined together to make a larger polygon. • Identify the location of 1 tan translated 3 square units to the left of the original position.


thinkMATH@home from the TCDSB Math Dept HOW TO MAKE A TANGRAM Grades 3 and 4 Learning Goal Divide whole objects into equal parts and identify the parts using fractional names

Materials tangrams

Mental Math Activity • Make the square using all 7 tangram pieces. • Examine the tangram pieces as fractions of a whole. • Visualize the size of the tangram pieces in relation to each other. • Make all 7 tangram pieces by paper folding. Questions to Ask to Probe Mathematical Thinking • Are there different ways to make a square using 7 tangram pieces? • Question 2 (Sample Response - Math Activity Variations • Is it possible to make a parallelogram that is not a square with all 7 tangram pieces? • Is it possible to make a triangle using all seen tangram pieces?


BIRD WATCHING Grades 5 and 6 Learning Goal Sort polygons according to geometric properties and attributes

Materials tangrams BLM10 Tangram Birds

Problem to Solve Students designed many different birds using all 7 tangram pieces. Here is a small sample of their bird designs.

What different ways could these birds be sorted and classified in terms of geometric properties (i.e., angles, sides and symmetry) and geometric attributes.) Use BLM XX Tangram Birds to cut out the birds. Questions to Ask to Probe Mathematical Thinking • What did you look for in the bird designs to sort them by sides, angles and symmetry? • What is the difference between geometric properties and geometric attributes? Math Activity Variations • Design other birds using all 7 tangram pieces. Sort them according to geometric properties and

geometric attributes.


thinkMATH@home from the TCDSB Math Dept WHERE’S THE TAN? Grades 5 and 6 Learning Goal Identify location (by lattice points) on a grid system

Materials tangrams BLM17 – Tangram Battleship Lattice Grid

Math Game Instructions Players – 2 Goal – locate the coordinate points of the vertices of the tan on the tangram battleship grid Playing the Game • Place visual barrier at the centre of the Tangram Battleship grid. • Each player places 1 tangram piece (tan) on the tangram battleship game board. • Players take turn guessing the location of vertices of the tan (points on the grid, A1) • Game ends when a player to identify all vertices of the tan, wins. Questions to Ask to Probe Mathematical Thinking • How did you use the grid to identify point location of all the vertices of the tan? • What strategy did you use to choose each point/vertex of the tan on the Battleship Grid? Math Activity Variations • Use 2 tans that are joined together to make a larger polygon. • Identify the location of 1 tan translated 2 linear units east of its original position

thinkMATH@home from the TCDSB Math Dept FROM SITTING TO STANDING Grades 5 and 6 Learning Goal Create and analyse designs by reflecting, translating and/or rotating a shape or shapes

Materials tangrams

Mental Math Activity • Which tangram shape or shapes would you transform to

make the bird move from its sitting position to a standing position? • Visualize the shape transformation(s) to show the bird standing? • Explain the transformation(s). • Show the transformation(s) that show the bird sitting to showing the

bird standing, using the tangrams. Questions to Ask to Probe Mathematical Thinking • How do geometric transformations show movement? • What tools could be used to verify the transformations you described?

Math Activity Variations • Which shape and which transformation(s) would you use to show the bird tilting its beak? • Which shape and which transformation(s) would you use to show the bird’s tail moving?



TANGRAMS AND FRACTIONS Grades 7and 8 Learning Goal Represent fraction operations in expressions and equations.

Materials tangrams

Problem to Solve Fraction expressions include addition, subtraction, multiplication and division operations. Write equations that represent 1 tangram and its 7 fractional parts. Use different fraction operations. (a) 1 tangram has the value of 1 (b) 1 tangram has the value of 2 (c) 1 tangram has the value of ½ (d) 1 tangram has the value of 2 ½ Questions to Ask to Probe Mathematical Thinking • How are the fraction equations for (a), (b), (c) and (d) related to each other? • How do the fractional parts relate to one another? • Is this fraction equation accurate for 1 tangram? 1= (1/7) x 7 Why or why not? Math Activity Variations • Write fraction equations that represent 5 tangrams? • Write fraction equations that represent 2 ½ tangrams?

thinkMATH@home from the TCDSB Math Dept TANGRAM COVER-UP Grades 7 and 8 Learning Goal Solve problems involving rates and fraction relationships

Materials 2 sets of tangrams BLM XX Tangram Paper

Math Game Instructions Players – 2 Goal – player with the greatest number of points wins Playing the Game • Players choose tangram pieces from 2 sets of tangrams. • Players take turns covering up the game board with one tangram piece at a time. • Tangram pieces must be completely placed on the game board grid. Tangram pieces may not

overlap. • The largest tangram piece (2 large triangles) is worth 10 points. The other tangrams are worth

double or quadruple the points of 1 large triangle. For example the small triangle is ¼ of 1 large triangle, so it is worth quadruple the large triangle points or 10 points x 4 = 40 points.

• Game ends when all the tangram pieces are placed or if there are no more spaces left for a tangram piece to be placed on the game board.

Questions to Ask to Probe Mathematical Thinking • What strategy did you focus on for winning the game: choosing small tangram pieces first to make

points or placing more tangram pieces than the other player? • How did you determine the number of points for each tangram piece? Math Activity Variations • Change the value of the tans, so that the largest tan has the greatest number of points • Use 3 sets of tangrams.


thinkMATH@home from the TCDSB Math Dept HOW TO MAKE A TANGRAM Grades 7 and 8 Learning Goal Analyse and describe designs using area and angle relationships of polygons

Materials tangrams

Mental Math Activity (a) Explain how to make a tangram by visualizing paper folding using the known angle relationships and area relationships between the 7 tangram pieces. (b) Test your explanation on a 4 x 4 square grid paper by paper folding. (c) Keep track of the paper folding steps. (d) Through paper folding, were you able to make the 7 tangram pieces accurately? Questions to Ask to Probe Mathematical Thinking • Which angles did you refer to most often when constructing a tangram? Why? • How did the 4 x 4 square grid help you in explaining the construction of a tangram? Math Activity Variations • Could the paper folding steps be done in a different order, yet still make the 7 tangram pieces

accurately? • Could you construct the tangram pieces using fractional relationships only?


BLM 1 – “The Sums Decimal Hundredths of Two Dice” Game Board


BLM 2 – Race to 5 or 10 Game Board


BLM 3 – Hundreds Chart for Interlocking Cubes


BLM 4 – Interlocking Cubes Paper


BLM 5 – Caterpillar Game Board (adapted from Edutopia)


BLM 6 – Pattern Block Paper


BLM 7 – Square Tiles Paper


BLM 8 – Three in a Row Game Board


BLM 9 - Tangrams Paper

©1996 Cuisenaire Company of America Inc Tangrams ◆ Grades K 2 91

BLANK COVER-AND-COUNT GAME BOARD

© ETA/Cuisenaire®

©1996 Cuisenaire Company of America Inc Tangrams ◆ Grades K 2 91

BLANK COVER-AND-COUNT GAME BOARD

© ETA/Cuisenaire®


BLM 10 – Tangram Birds


BLM 11 – Tangram Squares, Triangles and Other Polygons


BLM 12 – Tangram Outline Puzzle 1








BLM 16 – Tangram Battleship Grid (Area/Square Units)

A B C D E F G H I J K L

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10


BLM 17 – Tangram Battleship Grid (Lattice Points)

A B C D E F G H I J K L M

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10


Documents

Toronto Catholic District School Board from the ... Family...Toronto Catholic District School Board from the Mathematics Department ... 1 deck of cards 1 dice ... • Compare your