RIC-20326_Maths_games_for_the_Australian_Curriculum_Year_3_Game_7_Division_facts_fluency

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Maths games for the Australian Curriculum (Book 2)
Published by R.I.C. Publications ® 2014 under licence from Didax Inc.
Copyright © Gail Gerdemann with Kathleen Barta 2014
RIC–20326
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copyright under the Copyright Act 1968 (Cth) and is owned
by the Australian Curriculum, Assessment and Reporting
Authority 2014.
For all Australian Curriculum material except
elaborations: This is an extract from the Australian
Curriculum.
Elaborations: This may be a modified extract from the
Australian Curriculum and may include the work of other
authors.
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particular, ACARA does not endorse or verify that:
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and subject;
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have been used; and
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Curriculum content descriptions for the relevant year
and subject.
You can find the unaltered and most up to date version of
this material at
http://www.australiancurriculum.edu.au/
This material is reproduced with the permission of ACARA.
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Foreword
Students are more engaged when they are having fun, and the collection of activities will improve student
understanding and strengthen skills through lively, collaborative and interactive games.
Games assist students with computational fluency and greater conceptual understanding as each in-depth unit
includes warm-up activities, one or more games, ideas for differentiation and develops mathematical capabilities.
Contents
Teachers notes .................................... iv – vi
Curriculum links ......................................... vii
Strategies for developing fluency with
multiplication within 100
Game 1 Double trouble
Multiplying by twos and fours................ 2–11
Game 2 Think about ten
Multiplying by tens, fives, and nines.... 12–21
Game 3 Triple trouble
Multiplying by threes and sixes............ 22–30
Game 4 Using facts you know
Multiplying by sevens and eights ....... 31–37
Game 5 Putting it all together
Multiplication facts fluency ................. 38–41
Place value understanding and properties of
operations – Multi-digit arithmetic
Game 8 Let’s get a-round to it
Rounding.............................................. 51–55
Game 9 The multiples of ten
Multiply by multiples of ten................. 56–59
Game 10 That’s ‘sum’ difference
Add/Subtract within
1000 – Fluency...................................... 60–64
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Develop understanding of equivalent
fractions and compare fractions
Game 11 Match the fractions
Equivalent fractions.............................. 65–68
Relationship of multiplication/division and
fluency with division within 100
Game 6 Is that a fact?
Relationship of
multiplication/division......................... 42–46
Game 12 Wild card fractions
Comparisons of fractions.................... 69–72
Reproducibles .............................. 73–113
Game 7 Let’s divvy it up
Division facts fluency............................ 47–50
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Maths games for Australian Curriculum Book 2
Maths games for the Australian Curriculum iii
iii

Teachers notes
Introduction
Maths games for the Australian Curriculum series targets:
• Operations and algebraic thinking
• Number and operations in Base Ten
• Number and operations—fractions
These games are designed to help students understand key concepts and strengthen skills.
Developing number sense can take time. We all know that students are more engaged when
they are having fun, and these games are designed for both substance and fun.
The games and activities program is also designed to be straightforward for teachers.
Supplies include standard equipment like paperclips and coloured markers, as well as copies
of blackline masters. All materials for the year may be duplicated and organised in about
one hour. Basic manipulatives such as tiles and fraction pieces are recommended but not
required.
Each game provides:
• Ideas for more support and some challenges
• Discussion questions to help students make connections between the game and
mathematical concepts
• Straightforward directions
• Blackline masters
These games can also be used for home-school activities.
Materials
Step 1: Duplicate blackline masters and place them in file folders.
Step 2: Duplicate cards* on card stock; cut out the cards.
Step 3: Gather the recommended manipulatives.
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* Number cards (0–9): Regular playing cards may be substituted. Remove Kings, Jacks and
10s. Use the Ace as 1 and the Queens as zero. (‘Q’ looks similar to ‘O’).
* Fraction cards: Only the eighths cards are required but others are recommended.
Student-created fraction cards may be substituted.
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Maths games for the Australian Curriculum
v

Curriculum links
Content descriptions
Overview of games and activities
Year 2
Investigate number sequences, initially those increasing and decreasing
by twos, threes, fives and ten from any starting point, then moving to
other sequences. (ACMNA026)
Recognise, model, represent and order numbers to at least 1000
(ACMNA027)
Group, partition and rearrange collections up to 1000 in hundreds, tens
and ones to facilitate more efficient counting (ACMNA028)
Games
1 2 3 4 5 6 7 8 9 10 11 12
– – – – – – – –
– – – – – – – – – – –
– – – – – – – – – –
Explore the connection between addition and subtraction (ACMNA029) – – – – – – – – – –
Solve simple addition and subtraction problems using a range of
efficient mental and written strategies (ACMNA030)
Recognise and represent multiplication as repeated addition, groups
and arrays (ACMNA031)
Recognise and represent division as grouping into equal sets and solve
simple problems using these representations (ACMNA032)
Recognise and interpret common uses of halves, quarters and eighths of
shapes and collections (ACMNA033)
– – – –
– – – –
– – – – – – – – – – –
– – – – – – – – – –
EXTENSION – – – – – – – – – –
Year 3
Investigate the conditions required for a number to be odd or even and
identify odd and even numbers (ACMNA051)
Apply place value to partition, rearrange and regroup numbers to at
least 10 000 to assist calculations and solve problems (ACMNA053)
Recognise and explain the connection between addition and
subtraction (ACMNA054)
– – – – – – – – – –
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– – – – – – – – – – –
– – – – – – – – – – –
Recall addition facts for single-digit numbers and related subtraction
facts to develop increasingly efficient mental strategies for computation
(ACMNA055)
Recall multiplication facts of two, three, five and ten and related division
facts (ACMNA056)
Represent and solve problems involving multiplication using efficient
mental and written strategies and appropriate digital technologies
(ACMNA057)
Model and represent unit fractions including 1 ⁄2, 1 ⁄4, 1 ⁄3, 1 ⁄5 and their
multiples to a complete whole (ACMNA058)
– – – – – – – – – – –
– – – – –
– – – – –
– – – – – – – – – –
EXTENSION – – – – – – – – – – –
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Maths games for the Australian Curriculum
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Let’s divvy it up
Game 7
Fluently divide within 100, using strategies such as the relationship between
multiplication and division or properties of operations.
Mathematical understanding and skills
Fluently multiply within 100, using strategies such as the relationship between multiplication
and division or properties of operations.
Prerequisite skills
Students should have strategies for multiplying all facts within 100, but may not yet have
automaticity for all facts.
Maths vocabulary
dividend
divisor
quotient
Materials
For each pair of students:
• ‘Divide by …’ spinners A, B & C (pages 92–94)
• Multiplication chart (page 105)
• Deck of number cards 1–9 (page 104)
• Product/Divisor cards (pages 106–107)
• ‘Let’s divvy it up’ game board (page 95)
Warm-up
‘Let’s divvy it up’
game
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16 3
54 6
21 30
42 9
48 36
24 24
12 18
42 27
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Let’s divvy it up
Game 7
Warm-up: Divide by …
Number of players: 2
Materials:
For each pair of students:
• ‘Divide by …’ spinners A, B and C (pages 92–94)
• Multiplication chart (page 105)
Object: Get 16 or more quotients right out of 20 spins for each spinner.
Directions:
1. Pick a spinner. (Teacher assigns or students choose.)
2. Spin for the dividend.
3. Divide by the divisor for that spinner.
4. Each player writes the quotient.
5. Players compare their quotients. Check using the multiplication chart, if needed. If both
are correct, circle the quotient.
6. Spin again. Do 20 spins. If players get 16 correct out of 20, it’s time for a new spinner.
12
18
3
21 15
27
9
÷ 3
6 24
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63
35
7
56
÷ 7
14 28
42 49
21
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Let’s divvy it up
Game 7
Explaining the game
Number of players: 2
Materials:
For each pair of students:
• Deck of number cards 2–9 (remove the 5), called ‘divisor cards’ in this game
(page 104)
• One set of product/divisor cards, called ‘dividend cards’ in this game
(pages 106–107)
• Game board (page 95)
Object: Win cards by making division facts.
How to play:
1. Place the divisor and dividend card decks on the game board. Place one divisor card
face up.
2. Players take turns dividing the dividend by the divisor, if possible.
3. If the cards can be used to make a division fact (for example, 42 and 6), the player says
the fact: ‘42 divided by 6 equals 7’. If correct, the player puts the dividend card in his/
her ‘win pile’. Then it is the other player’s turn.
4. If the cards cannot be used to make a division fact, the player whose turn it is draws a
new divisor card and divides. If the new cards cannot be used, the player’s turn is over.
5. Play continues until all of the dividend cards are used. The winner is the player with the
most cards.
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Variation
The same rules as ‘Let’s divvy it up’, except: A player may collect any dividend
card that is a square number at the beginning of his/her turn, even if he/she
does not have the divisor card. The player just has to correctly identify its factors.
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Let’s divvy it up
Game 7
Differentiation
Warm-up: Divide by . . .
Challenge
• Play a divide-withremainders
version: Pick any
spinner. Use the divisor cards
2–9. Spin for the dividend. Turn
over a card for the divisor.
What is the quotient? Is there a
remainder?
Ask the class
It is possible to:
• Share an odd number of items with an even number of
people?
• Share an even number of items with an odd number of
people?
• Share an odd number of items with an odd number of
people?
• Share an even number of items with an even number of
people?
• Put an odd number of items evenly into an odd number
of groups; for example, 25 items into 5 or 7 groups?
(Sometimes it is, sometimes it isn’t.)
Give examples for each.
Do you agree or disagree? Why?
Let’s divvy it up game
More support
Deepening the understanding
• Additional time with the warm-up
exercise can provide an opportunity to
develop fluency with each of the divisors.
• Begin by using just the product/divisor
cards 12, 14, 16, 18, 21, 24, 27, 28, 32 and 36.
• Have the multiplication chart available
facedown to check answers as needed.
Mathematical capabilities
Reason abstractly and quantitatively.
Construct viable arguments and critique the
reasoning of others.
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For a dividend of 24, what are possible divisor/quotient pairs?
What are other dividends in the multiplication chart that have
more than one divisor/quotient pair?
Reason abstractly and quantitatively.
Construct viable arguments and critique the
reasoning of others.
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Let’s divvy it up
Game 7
‘Divide by …’ spinner A
Spinner for the divisor ‘2’ Spinner for the divisor ‘3’
2 10
16
6
8
÷ 2
14
Spinner for the divisor ‘4’ Spinner for the divisor ‘5’
4 28
20
18
12
9
12 18
21 15
4
27
12 30
35
5
3
÷ 3
6 24
20
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÷ 4
36 24
16 8
32
÷ 5
45 10
15 25
40
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Let’s divvy it up
Game 7
‘Divide by …’ spinner B
Spinner for the divisor ‘6’ Spinner for the divisor ‘7’
36 6
24
30
42
÷ 6
12
Spinner for the divisor ‘8’ Spinner for the divisor ‘9’
8
72
35
63
56
18 54
42 49
48
21
54 9
24
40 27
36
7
÷ 7
14 28
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56
÷ 8
16
32 64
48
81
÷ 9
72
45 18
63
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Let’s divvy it up
Game 7
‘Divide by …’ spinner C
Spinner for divisor ‘4’ or ‘8’
4 28
32 24
16 8
72 56
20 12
36 48
32 64
24 40
Spinner for divisor ‘3’ or ‘6’
15 3
54 6
21 30
Can you divide by 4 and
get a 1-digit quotient?
or
Can you divide by 8 and
get a 1-digit quotient?
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42 9
48 36
24 24
Can you divide by 3 and
get a 1-digit quotient?
or
Can you divide by 6 and
get a 1-digit quotient?
12 18
42 27
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Let’s divvy it up
Game 7
Game board
÷ Divisor
=
card,
face up
Deck of
dividend
cards,
face up
dividend divisor quotient
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Deck of
divisor
cards,
face
down
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0–10 number cards
0
4
1 2
5 6
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3
7
8 9
10
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Multiplication chart
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 18 21 24 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 18 24 30 36 42 48 54 60
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7 0 7 14 21 28 35 42 49 56 63 70
8 0 8 16 24 32 40 48 56 64 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0 10 20 30 40 50 60 70 80 90 100
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12
24
14
27
16
28
18
32
21
36
Product/Divisor cards – 1
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36
56
42
63
48
64
49
72
54
81
Product/Divisor cards – 2
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