LEARNING ABOUT MATH

FOR K TO 5Dorset Public

SchoolApril 6, 2016

6:30 pm – 8:00 pm

presented by Kathy Kubota-Zarivnijkathkubo@rogers.com

TODAY’S MATH TOOLS FOR MATH LEARNING

colour square tiles dice playing cards tangram

KKZ, 2016

Hexalink cubes bingo chips

NIM (ANCIENT CHINESE)Getting Ready to Play�Put 10 bingo chips in an array (2

rows x 5 columns = 10 tiles).

Playing the Game�Players taken turns taking either 1 or 2 bingo chips at

a time from the array.�Player left with the last 1 or 2 bingo chips from the

array wins!

Playing the Game to Learn�How do you know if you are going to lose?�How did you decide if you would take 1 or 2 bingo

chips?�How many square tiles do you need the other people

to leave for you to ensure you will win?

MATERIALS2 to 4 (pairs) players10 blue or 10 red square tiles

GAME GOALHave the last 1 or 2 square tiles

MATH LEARNING GOALUse problem solving strategies and reasoning skills.

Any Age

KKZ, 2015

COUNTERS GONE Kindergarten

MATERIALS2 to 4 (pairs) players10 square tiles, 1 die

GAME GOALHave the greatest number of counters.

MATH LEARNING GOALCounting forwards and backwards.

Getting Ready to Play�Start with a pile of 10 counters.

Playing the Game�Players take turns taking rolling the die and removes

the number of counters indicated by the die.�Game ends when there are no more counters in the

pile.

Playing the Game to Learn�What strategy did you use to count the counters you

took from the pile?�What happens to the number of counters in the pile

as the counters are removed?KKZ, 2015

WHAT’S THE DIFFERENCE?Getting Ready to Play� Divide the cards equally among 2 to 4 people into piles.

Playing the Game�Players face up 1 card (1-digit) or 2 cards (2-digit) at the

same time. �Player with the larger number identifies the difference

between the 2 numbers and claims all cards if correct.� If the cards have the same number, they are placed in a

common pile. When a player has no cards left, the cards in the pile are shuffled and divided equally among all the players.

Playing the Game to Learn�What strategies did you use to figure out the difference

between the 2 cards?�How does “difference” relate to subtraction?

MATERIALS2 to 4 (pairs)10 blue or 10 red square tiles

GAME GOALHave the greatest number of cards

MATH LEARNING GOALSubtract 1-digit or 2-digit whole numbers using mental strategies.

Grades 1/2

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ADDITION CONCENTRATIONGetting Ready to Play� Face down 1 deck of playing cards in an array (4 rows x 13 columns =

52 playing cards)

Playing the Game�Players take turns facing up 2 cards (two 1-digit numbers)

or 4 cards (two 2-digit numbers) at a time. �Only add number on cards if they are different

-one-digit numbers have two cards 2, 5 -> 2+5=7; -two-digit numbers have four cards 2,3,5,7 -> 73+52=125)

� If number on cards are the same, are returned face down.�Game ends when there are no cards left face down.

Playing the Game to Learn�What strategies did you use to figure out the difference

between the 2 cards?�How does “difference” relate to subtraction?

MATERIALS2 to 4 (pairs)1 deck playing cards whereaces (1), face cards (10)

GAME GOALGreatest sum

MATH LEARNING GOALAdd 1-digit or 2-digit whole numbers using mental strategies.

Grades 2/3

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WHAT’S THE VALUE OF MATH GAMESFOR LEARNING MATHEMATICS?Mathematics game playing:� improves learners’ awareness of how to use rules and

constraints, within a natural and enjoyable way � encourages observation, analysis and constant revision of

thinking. � develops reasoning, decision-making, analysis and

development of strategies� involves both chance and skill, incorporates estimation,

prediction, risk-taking, collaboration and competition.

(Oldfield, 1991; Sarama and Clements, 2009)KKZ, 2015

SETTING THE MATHEMATICS CONTEXTMULTIPLICATION FROM GRADES 1 TO 3

-Gr1 - solve problems involving the addition and subtraction of single-digit whole numbers, using a variety of mental strategies (e.g., doubles); -Gr2 - represent and explain, through investigation using concrete materials and drawings, multiplication as the combining of equal groups (e.g., use counters to show that 3 groups of 2 is equal to 2 + 2 + 2 and to 3 x 2)-Gr3 - relate multiplication of one-digit numbers to real- life situations, using a variety of tools and strategies (e.g., place objects in equal groups, use arrays, write repeated addition; multiply to 7x7, using a variety of mental strategies

Doubles 4Repeated additionEqual Size Groups

ArrayMultiplication expression defined as multiplicand x multiplier

2 groups of 4

4 x 2

0

2 rows x 4 columns

size of 1 group number of groupsmultiplicand multiplier

LINE UP FOURGetting Ready to Play� Player 1 (8 blue square tiles) � Player 2 (8 red square tiles)

Playing the Game� Players take turns placing a square tile onto one empty square

at a time on a 4x4 square grid game board � Game ends when player makes four in a row.

Playing the Game to Learn� Why is it important to pay attention to the other player’s

moves?� What can you do to keep the other player from lining up four

tiles in a row?� If you begin by placing your square tile in a corner, how many

ways are there to line up 4 tiles in a row?

MATERIALS2 to 4 (pairs) players8 red square tiles and 8 blue squares and 4x4 square grid

GAME GOALMake 4 square tiles in a row (horizontal, vertical, diagonal)

MATH LEARNING GOALUse spatial reasoning to make predictions and strategies.

Any Age

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EFFECTIVE MATHEMATICS GAMESHAS THESE FEATURES:�has solution-centered activity with the game player in charge of

the process�uses the game player’s current mathematical knowledge�involves a challenge against an opponent�organized by a definite set of rules�freely engages players�has a definite number of solutions�has an ending or finishing point�provokes specific mathematics learning goals�has the capacity for several game-playing variationsKKZ, 2015

SQUARE TILES COVER-UPGetting Readyto Play� What different rectangles are made of 12 square units?

2x6=12 3x4=12

Playing the Game

Playing the Game to Learn� What is the greatest size of an array made from 2 dice rolls?� What is the least size of an array that could be made from 2 dice rolls?

Variations� Change grid size to 3x3, 5x5, 6x6.� Change the shape of the game board (e.g., t-shape, l-shape, c-shape using square grids).

MATERIALS2 Players30 red square tiles and 30 blue squares and 10x10 square grid

GAME GOALCover the largest area on 10x10 square grid with rectangles.

MATH LEARNING GOALRepresent multiplication of 1-digit whole numbers using an array. Add 1-and 2-digit whole numbers using mental strategies

Grades 3 to 4

3x53 rows x 5 columns

4 x 54 rows x 5 columns

5 columns

5 columns

3 rows

4rows

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SETTING THE MATHEMATICS CONTEXTMULTIPLICATION FROM GRADES 4 TO 6Grade 4multiply to 9x9 using a variety of mental strategies; solve problems involving the multiplication of one-digit whole numbers, using a variety of mental strategies (e.g., 6 x 8 can be thought of as 5 x 8 + 1 x 8);

multiply whole numbers by 10, 100, and 1000, using mental strategies;

multiply two-digit whole numbers by one-digit whole numbers, using a variety of tools (e.g., base ten materials or drawings of them, arrays), student-generated algorithms, and standard algorithms;

Grade 5

� solve problems involving the multiplication of whole numbers, using a variety of mental strategies (e.g., use the commutative property: 5 x 18 x 2 = 5 x 2 x 18, which gives 10 x 18 = 180);

�multiply decimal numbers by 10, 100, 1000, and 10 000, using mental strategies

�multiply two-digit whole numbers by two-digit whole numbers, using estimation, student-generated algorithms, and standard algorithms;

Grade 6

� use a variety of mental strategies to solve, multiplication, problems involving whole numbers (e.g., use the commutative property: and distributive property

� multiply whole numbers by 0.1, 0.01, and 0.001 using mental strategies

� multiply decimal numbers by 10, 100, 1000, and 10 000 using mental strategies

� multiply decimal numbers to tenths by whole numbers, using concrete materials, estimation, algorithms, and calculators (e.g., 4 x 1.4)

� solve problems involving the multiplica-tion of whole numbers (four- digit by two-digit), using a variety of tools (e.g., concrete materials, drawings, calculators) and strategies (e.g., estimation, algorithms);

KKZ, 2015

MULTIPLICATION NUMBER BATTLE AGetting Ready to Play� Players split a deck of cards into 2 piles (one pile per player)

Playing the Game� Players simultaneously flip

over 2 cards from the top of their piles. Numbers on each card are multiplied.

� Highest product wins all 4 cards. � If the cards have the same value, the cards are returned to the pile.� Player with the greatest umber of cards win.

Playing the Game to Learn� What strategies did you use to determine the product of the 2

numbers?� Is it possible that some card combinations could have the same

product? How could you know that before playing the game?

MATERIALS2 to 4 (pairs) players1 deck playing cards (aces (1) ; face cards are worth 10

GAME GOALGreatest number of playing cards

MATH LEARNING GOALMultiplying pairs of numbers and add 1-digit and 2-digit whole numbers

Grade 4

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MULTIPLICATION NUMBER BATTLE BGetting Ready to Play� Players split a deck of cards into 2 piles (one pile per player).� Aces are worth 11, face cards are worth 10.

Playing the Game� Players simultaneously flip over 3 cards from the top of their piles. � Multiply the number on each card to get a product Highest product wins all 6

cards. If the cards have the same value, the cards are returned to the pile.� Player with the greatest umber of cards win.

Playing the Game to Learn� What strategies did you use to determine the product of the two 2-digit whole

numbers?� Is it possible that some card combinations could have the same product?

How could you know that before playing the game?

MATERIALS2 to 4 (pairs) players1 deck playing cards (aces (11) ; face cards are worth 10

GAME GOALGreatest number of playing cards

MATH LEARNING GOALMultiplying 2-digit whole numbers by 10 using mental strategies.

Grades 5

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ADDITION OR MULTIPLICATION TARGETSGetting Ready to Play� Choose a target number.� Decide on the type of numbers the dice rolls represent (e.g., 1

dice -> 1-digit whole number; 2 dice -> 2-digit whole number; 3 dice – 3-digit whole number)

Playing the Game� Roll 4 dice or face up 4 playing cards.� Players make a number expression that is equal to the target

number. Use any combination of addition, subtraction, multiplication or division operations.

� Player who makes an accurate number expression to the target number wins the round and either gets points the same quantity as the target number or keeps 4 cards.

Playing the Game to Learn� What strategies did you use to make the target number?

MATERIALS2 to 4 (pairs)2 to 4 dice or playing cards

GAME GOALHave the greatest number of of points or playing cards

MATH LEARNING GOALUse 1-digit and 2-digit whole numbers to carry out number operations

Grades 2 to 6

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TOWERING TOWERS

Getting Ready to Play�Make different rectangular prisms.�Which rectangular prisms have the greatest

volume in cubic units..

Playing the Game�Roll 2 dice to identify the volume in cubic units.�Make the rectangular prism using the hexalinks.

Playing the Game to Learn�What strategies did you use to make the

rectangular prism with the greatest volume?

MATERIALS2 to 4 (pairs)2 to 4 dice and hexalinks

GAME GOALMake the tallest rectangular prism

MATH LEARNING GOALRepresent the volume of rectangular prisms and multiplication

Grades 2 to 6

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MAKING A TANGRAM BY PAPER FOLDING�Make a tangram by paper folding.�Use known angle relationships and area

relationships between the 7 tangram pieces.�Angles à 900 (right angles), 450 (half of a right

angle)�Area of 1 large triangle is ¼ of the large square.

MATERIALS4x4 square grid paper

GAME GOALUse spatial reasoning to make 2D shapes

MATH LEARNING GOALCompose shapes using 2D shapes.

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Grades 4 to 6

TANGRAM COVER-UP Getting Ready to Play�Players divide up tans from 2 sets of tangrams

Playing the Game�Players take turns covering up

the game board with 1 tan at a time.�Tangram pieces must be placed

completely and not overlap.�Scoring – each tan is worth specific

points. Game ends when all tans are placed or no spaces are left on the board.

Playing the Game to Learn� What strategies did you use to create different bird designs?� What different ways could these bids be sorted and classified in

terms of geometric attributes (i.e., angles, sides, line of symmetry)?

MATERIALS2 to 4 (pairs)2 sets of tangrams

GAME GOALAchieve the greatest number of different bird designs.

MATH LEARNING GOALUse rotations, translations and reflections to rotate 2D shapes.

K to Grade 6

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SHAPE MAKER AGetting Ready to Play� Identify the types of shapes and sizes of shapes of the 7 tans. (e.g., 2

large triangles, 1 medium triangle, 2 small triangle, 1 small square, 1 small parallelogram)

Playing the Game� Make shapes with 3 sides, 4 sides, 5

sides and 6 sides. Use 1 to 7 tangram pieces.

� Trace tangram shapes on paper.� 1 point for each shape made. � Each player adds their points.

Playing the Game to Learn� How are the shapes made with tangrams the same? How are

they different? � Which shapes were made the most? (3 sided?, 4-sided?)

MATERIALS2 to 4 (pairs) players2 sets of tangrams

GAME GOALAchieve the greatest number of points.

MATH LEARNING GOALCompose shapes using 2D shapes.

Kindergarten, Grade 1

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SHAPE MAKER BGetting Ready to Play� Identify the types of shapes and sizes of shapes of the 7 tans. (e.g., 2

large triangles, 1 medium triangle, 2 small triangle, 1 small square, 1 small parallelogram)

Playing the Game� Make shapes with 3 sides, 4 sides,

5 sides and 6 sides. Use 1 to 7 tangram pieces.

� Trace tangram shapes on paper.� Scoring: 3 points for 3 sided shape,

4 points for 4-sided shape, 5 points for 5-sided shape. Add total points.

Playing the Game to Learn� How are the shapes made with tangrams the same? How are

they different? � Which shapes were made the most? (3 sided?, 4-sided?)

MATERIALS2 to 4 (pairs) players2 sets of tangrams

GAME GOALAchieve the greatest number of points.

MATH LEARNING GOALCompose shapes using 2D shapes.

Grades 2 and 3

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TANGRAM SHAPES (POLYGONS)

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SHAPE MAKER CGetting Ready to Play�Create a bird using one set of tangrams

Playing the Game�Players create different bird designs

using all 7 tangrams. �Flip, slide and turn parts or

tans on the bird.�Player with the greatest number of

different bird designs wins.

Playing the Game to Learn� What strategies did you use to create different bird designs?� What different ways could these bids be sorted and classified

in terms of geometric attributes (i.e., angles, sides, line of symmetry)?

MATERIALS2 to 4 (pairs)2 sets of tangrams

GAME GOALAchieve the greatest number of different bird designs.

MATH LEARNING GOALUse rotations, translations and reflections to rotate 2D shapes.

Grades 4, 5 and 6

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TANGRAM BIRD DESIGNS

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ROCK, PAPER, SCISSORSGetting Ready to Play� On the count of 3, say

“Rock, Paper, Scissors” – reveal either rock (fist), paper (open hand) or scissors (2 extended fingers).

Playing the “NEW” Game� Player A – wins if all 3 players make the same hand shape� Player B – wins if exactly if 2 players make the same hand

shape.� Player C – wins if none of the players make the same hand

shape.

Playing the Game to Learn� Is the original and new game fair?� How is the new version different than the original version?

MATERIALS2 to 3 people

GAME GOALGet highest number of points.

MATH LEARNING GOALMake inferences and predictions from data and apply basic concepts of probability.

Any Age

KKZ, 2015

WHAT MATHEMATICS ARE OUR STUDENTS LEARNING? WHY?�Conceptual Understanding - understanding of mathematical concepts,

operations, and relations; enables the learning of new ideas by making mathematical connections to ideas already known through reasoning, proving and communication; supports retention and prevents common errors

�Procedural Fluency - carrying out procedures flexibly, accurately, efficiently, and appropriately for different and particular purposes

�Strategic Competence - formulating, representing and solving mathematical problems in different ways relevant to particular contexts

�Adaptive Reasoning - capacity for logical thought, reflection, explanation and justification in relation to different problem solving contexts and ways of thinking

�Productive Disposition - seeing oneself as an effective learner and doer of mathematics through perseverance (i.e., a steady effort in learning mathematics pays off); perceiving mathematics as being useful, worthwhile and accessible.