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Contents Introduction Key principles of Collins International Primary Maths How Collins International Primary Maths supports Cambridge Primary and the Cambridge Primary Mathematics Curriculum Framework
Collins International Primary Maths Stage 2 units iv
iv
The components of Collins International Primary Maths: • • • • •
Teacher’s Guide Student’s Book Workbook Collins Connect DVD
Collins International Primary Maths Stage 2 units and recommended teaching sequence Collins International Primary Maths Stage 2 units link to Cambridge Primary Mathematics Curriculum Framework Cambridge Primary Mathematics Curriculum Framework Stage 2 link to Collins International Primary Maths units
viii xvi xvi xvii xvii
Geometry Measure
Handling data
27
2 Whole numbers 2
38
3 Whole numbers 3
49
4 Fractions
55
5 Addition and subtraction 1
66
6 Addition and subtraction 2
77
7 Addition and subtraction 3
88
8 Multiplication and division 1
99
9 Multiplication and division 2
105
10 Multiplication and division 3
116
11 2D shape
127
12 3D shape
133
13 Patterns and symmetry
139
14 Position and movement
145
15 Money 1
151
16 Money 2
157
17 Length
163
18 Mass
169
19 Capacity
175
20 Time
181
21 Handling data
187
Resource sheets
198
Answers
260
xviii
xxi
xxxi
Refresh activities Number
1 Whole numbers 1
Numbers and the number system 1 Calculation: Mental strategies, Addition and subtraction 7 Calculation: Mental strategies, Multiplication and division 11 Shapes and geometric reasoning Position and movement Money Length, mass and capacity Time
16 19 20 22 25
Organising, categorising and representing data
26
Tracking back and forward through the Cambridge Primary Mathematics Curriculum Framework 274 Stage 2 Record-keeping charts
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Introduction Key principles of Collins International Primary Maths Collins International Primary Maths is a mathematics course that ensures complete coverage of the Cambridge Primary Mathematics Curriculum Framework. The course offers: • a rigorous and cohesive scope and sequence of the Cambridge Primary Mathematics Curriculum Framework, while at the same time allowing for schools’ own curriculum design • a problem-solving and discovery approach to the teaching and learning of mathematics • lesson plans following a highly effective and proven lesson structure • a bank of practical hands-on learning activities • controlled, manageable differentiation with activities and suggestions for at least three different ability groups in every lesson
• extensive teacher support through materials which: – promote the most effective pedagogical methods in the teaching of mathematics – are sufficiently detailed to aid confidence – are rich enough to be varied and developed – take into account issues of pace and classroom management – give careful consideration to the key skill of appropriate and effective questioning – provide a careful balance of teacher intervention and learner participation – encourage communication of methods and foster mathematical rigor – are aimed at raising levels of attainment for every learner • manageable strategies for effective monitoring and record-keeping, to inform planning and teaching.
How Collins International Primary Maths supports Cambridge Primary and the Cambridge Primary Mathematics Curriculum Framework Cambridge Primary is typically for learners aged 5 to 11 years. It develops learner skills and understanding through the primary years in English, Mathematics and Science. It provides a flexible framework that can be used to tailor the curriculum to the needs of individual schools.
The Cambridge approach supports schools to develop learners who are:
Cambridge Primary Mathematics Curriculum Framework:
• reflective as learners, developing their ability to learn
• provides a comprehensive set of learning objectives in Mathematics for each year of primary education
• innovative and equipped for new and future challenges
• focuses on developing knowledge and skills which form an excellent foundation for future study
• engaged intellectually and socially, and ready to make a difference in the world.
• focuses on learners’ development in each year
The Cambridge Primary Mathematics Curriculum Framework is organised into six stages. Each stage reflects the teaching targets for a year group. Broadly speaking, Stage 1 covers the first year of primary teaching, when learners are approximately five years old. Stage 6 covers the final year of primary teaching when learners are approximately 11 years old.
• provides a natural progression throughout the years of primary education • is compatible with other curricula, internationally relevant and sensitive to different needs and cultures • is suitable for learners whose first language is not English
• confident in working with information and ideas – their own and those of others • responsible for themselves, responsive to and respectful of others
• provides schools with international benchmarks.
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Unit
1
Whole numbers 1
More than, less than Learning objective Code
Learning objective
2Nn7
Find 1 or 10 more/less than any two-digit number.
Number – Numbers and the number system
Resources 100 interlocking cubes (per pair and a set for the teacher); 100 counters (per learner); two containers (per pair)
What to do • Display towers of interlocking cubes. As a class, count how many cubes are in the tower(s) and ask pairs to build a tower with the same number of cubes. • Say: Now build another tower(s) with one/ten less/more. How can you check? Take feedback. • Repeat using towers of different single- and two-digit number combinations.
Variation • Learners work in pairs. They will each need one container and 100 counters. Learner 1 counts out any number of counters into their dish (up to 90). They then choose to say either one more/one less/ten more/ten less. Learner 2 then counts out the correct number of counters into their container. Ask them to check by grouping the counters into twos, fives or tens.
Number line Learning objectives Code
Learning objective
2Nn9
Say a number between any given neighbouring pair of multiples of ten, e.g. 40 and 50.
2Nn10
Place a two-digit number on a number line marked off in multiples of ten.
Resources Resource sheet 1: 0–100 number cards
What to do • • • •
Set up the Number line tool from 0–100, with an increment of 10 between each number. Call a learner to the front of the class to move the frog to a given number from 0–100 on the number line. Ask a different learner to move the snail to a different number from 0–100 on the number line. Now ask the learners to write any number on a whiteboard that falls between the two numbers on the number line.
Variations • Position the frog and the snail on neighbouring multiples of 10 (for example, 50 and 60) and ask learners to write down any three numbers which fall between the two multiples of 10. • Give each learner a number card from 1 to the number of learners in the class. Learners make a number line by first finding the learners with the smallest and largest numbers and then fitting the other numbers between them. Ask learners to sort themselves so they are now showing a number line that skip-counts in twos/fives/tens. What do they notice? Are there any learners who are in two or more of the lines?
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Unit
2
Whole numbers 2
Refresh activities More counting
/
Code
Learning objective
2Nn3
Count on in ones and tens from single- and two-digit numbers and back again.
2Nn4
Count in twos, fives and tens [and use grouping in two, fives or tens to count larger groups of objects].
Number – Numbers and the number system
Learning objectives
Resources mini whiteboard and pen (per pair)
What to do • Learners work in pairs. Each pair decides whether to count in twos, fives or tens. Clap three times, asking learners to count in their chosen unit on each clap. Learners write the number they reached on their mini whiteboards and hold them up. Repeat with different numbers of claps. • Next, learners swap between counting forwards and backwards in ones/tens each time you clap.
Variations • Ask a learner to pick a single- or two-digit number. The class counts on from that number in twos, fives or tens until you get to 100 or just over, then count back again. Repeat with a different starting number. • Learners count forwards in ones to 100, then backwards in ones from 100 to zero. When you raise your arms, they count loudly. When you lower your arms, they count quietly.
Base 10
/
Learning objective Code
Learning objective
2Nn6
Know what each digit represents in two digit numbers; partition into tens and ones.
Resources mini whiteboard and pen (per pair); Resource sheet 1: 0–100 number cards; Base 10 equipment
What to do • Make a representation of a two-digit number using the Base 10 tool. • Ask the learners to work out which number it represents with a partner, and to write the number on a whiteboard. • Repeat this several times, ensuring that you include numbers that are multiples of 10 and numbers that have the same digits in both the tens and ones position. • Reverse the activity by writing a two-digit number and asking individual learners to make it using the Base 10 tool.
Variations • Write a number and make it or a different number using the Base 10 tool. The learners must say whether the Base 10 number matches the written number or not. • Give pairs of learners a set of two-digit number cards from Resource sheet 1 and some Base 10 blocks. Learners pick a number card. One learner makes the tens and the other learner makes the ones. They swap roles and repeat this with another number.
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Unit
2
Whole numbers 2
Larger or smaller?
/
Learning objective Code
Learning objective
2Nn12
Order numbers to 100; compare two numbers using the < and > signs.
Number – Numbers and the number system
Resources Resource sheet 1: 0–100 number cards
What to do • Set up the Number cards tool to show five random numbers from 1–99. Spread these out on the board out of order. • Ask the learners to discuss with a partner which number would come first and which would come last if the numbers were ordered, from smallest to largest. Agree on these as a class and move these two cards into position. • Now ask individual learners to put the other number cards in order between the smallest and largest numbers. • Repeat this with a different set of numbers.
Variations • Display the Number square tool and give each learner a 0–100 number card. Hold up a number card yourself. Everyone with a number larger than your number must put their hands on their heads, and everyone with a smaller number must touch their toes. Repeat, holding up different cards. • Pairs of learners share 20 two-digit number cards between them, then both put a number card down in front of them at the same time. The learner with the larger number keeps both cards. Continue until one learner has run out of cards. • Set up the Number cards tool to show two random numbers from 1–99. Ask: Which number is greater? Which number is smaller? Discuss with the learners whether you would put < or > between the two cards and why.
Rounding circle Learning objective Code
Learning objective
2Nn8
Round two-digit numbers to the nearest multiple of 10.
Resources Resource sheet 1: 0–100 number cards (cards 16 to 94 only per pair); Resource sheet 10: Rounding circle (per pair)
What to do • The learners shuffle the number cards. Player 1 takes a card at random. They round their two-digit number card to the nearest ten and place it in the correct part of the rounding circle, they score one point if they are able to place their card. Player 2 then takes a card and does the same. If a rounding space has already been taken up by another card then that player misses a turn. The game ends when the circle is complete and the winner is the player with the most points.
Variations • Only play with cards 16 to 44 to make the game shorter. • If learners are able, adapt the game to make it a rounding game to the nearest 100.
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Unit
3
Whole numbers 3
Refresh activities How many birds? Code
Learning objective
2Nn4
Count in twos, fives and tens and use grouping in two, fives or tens to count larger groups of objects.
2Nn5
Begin to count on in small constant steps such as threes and fours.
Number – Numbers and the number system
Learning objectives
What to do • • • •
Use the Tree tool to put four trees on the board and ask a learner to put three birds in each tree. Ask learners how they could count the birds. Elicit that they could be counted in ones or groups of three. Count the birds in threes, then count them in ones to check the answer. Repeat this with a different starting number of trees.
Variations • Put 2, 4 or 5 birds in each tree and count them in twos, fours or fives. • Put learners into groups of four to six. Each learner holds up three fingers. Together, they count them to work out how many fingers are being held up in each group. Repeat this with four fingers each.
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Unit
4
Fractions
Refresh activities Halving and sharing Number – Numbers and the number system
Learning objectives Code
Learning objective
2Nn16
Recognise that we write one half 1 [, one quarter 1 and three quarters 3].
2Nn18
Recognise which shapes are divided into halves [and quarters] and which are not.
2
4
4
Resources up to 50 interlocking cubes (per pair); mini whiteboard and pen (per pair)
What to do • Give each pair of learners up to 50 interlocking cubes. Ask them to share the cubes equally between themselves. Ask: How do you know you both have exactly half? How can you check?
Variations • Learners work with a partner and make a list of things in the classroom that could be shared into two pieces. They write their lists or draw the items on their mini whiteboards. • For Lesson 8: Each pair of learners has 12 interlocking cubes. Learner A halves the tower to find half of 12, then Learner B halves one of the resulting towers to find half of six. Ask: Can you halve three? Discuss responses. • Learners share 40 cubes equally between four people.
Shapes in half
/
Learning objective Code
Learning objective
2Nn19
Find halves and quarters of shapes and small numbers of objects.
Resources Resource sheet 13: Fraction cards (sheet 1 only, per learner); up to 40 counters (per pair)
What to do • Display the Symmetry tool. Choose a shape and put it on the board (start with a square, triangle or rectangle). • Ask a learner to come to the front and draw a line where they would divide the shape into halves. • Ask if anyone can see anywhere else that the shape could be divided into halves. If so, invite them to draw the line on the shape. • Click on ‘show lines’ to check if the learners were correct. • Repeat the exercise with a different shape.
Variations • For Lesson 4, repeat the above but with quarters. • Give each learner a 12 card, a 14 card and an X card from Resource sheet 13 – sheet 1. Draw a shape on the board or use the Symmetry tool and draw lines to divide it into two or four. Learners decide if it is in halves, quarters or unequal pieces and hold up a 12 card, a 14 card or X to indicate this. • Give pairs of learners even numbers of counters. They divide the counters between them, then count how many they have each. Then they double the amount to find how many counters they started with.
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Unit
5
Addition and subtraction 1
Refresh activities Number bonds Code
Learning objective
2Nc1
Find and learn by heart all number pairs to 10 and pairs with a total of 20.
2Nc3
Find all pairs of multiples of 10 with a total of 100 and record the related addition and subtraction facts.
Resources number cards from 4 to 9 (or 14 to 19) taken from Resource sheet 1: 0–100 number cards (per pair); Resource sheet 7: 1–6 spinner (per pair); Resource sheet 9: Multiples of 10 cards; Resource sheet 16: Multiples of 10 spinner; up to 20 interlocking cubes (per learner/pair)
What to do • Learner A picks a number card at random and puts it face up on the table. • Learner B spins the spinner until they get the number that makes 10 when added to the number card. • They swap roles and repeat this.
Variations
• Variation 2: Give the learners number cards from 14–19 and ask them spin the spinner to make 20 rather than 10. • Give each learner a tower of 1–9 interlocking cubes. They work out how many more cubes they need to make ten, then find someone with that number of cubes. They put their towers together and count to check that they have ten. • Lesson 2: Give pairs of learners nine interlocking cubes. They make 9 in as many different ways as they can, by making two towers. • Lesson 3: Learners work in pairs. Learner A says a number between zero and ten. Learner B says the number that makes ten when added to it. Learners repeat several times alternating roles.
• Variation 1: Give the learners multiples of 10 cards from 40 to 90 and a multiples of 10 spinner and ask them to make 100.
Adding and subtracting
/
/
Learning objectives Code
Learning objective
2Nc8
Add four or five small numbers together.
2Nc11
Add and subtract a single digit to and from a two-digit number.
Resources
Variations
Resource sheet 4: 100 square (optional, per learner); Resource sheet 19: 0–30 number line (per pair); 2 counters (per pair); Resource sheet 7: 1–6 spinner; mini whiteboard and pen (per group)
• Pairs of learners each put a counter on zero on a 0–30 number line. They take turns to spin a spinner and move their counter forwards by the amount shown on the spinner. The winner is the first learner to reach 30. • Line learners up in teams of about six. Give the learner at the front of each line a mini whiteboard with 32 written on it, and a pen. They count on three, rub out 32 and write the number they reached in its place.
What to do • Set up the Busy Ant School game set to level 1. • Challenge learners to come to the board to answer the addition and subtraction questions, reminding them that they can use a 100 square for support if necessary. Remember to go over the strategies for adding or subtracting a single digit to a two-digit number (start on the two-digit number and count on/back). • Use the game in speed tracker mode to challenge more-able learners to work out the answers quickly and accurately.
Then they pass the whiteboard to the next learner who does the same. This continues until everyone has counted on three.
Number – Calculation: Mental strategies, Addition and subtraction
Learning objectives
What number did they finish on? Did all groups finish with the same number? If so, why? If not, why not? Lesson 7: As above but this time each learner must take away four by counting back.
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Unit
6
Addition and subtraction 2
Refresh activities Adding tens
/
Number – Calculation: Mental strategies, Addition and subtraction
Learning objectives Code
Learning objective
2Nc6
Relate counting on/back in tens to finding 10 more/less than any two-digit number and then to adding and subtracting other multiples of 10, e.g. 75–30.
2Nc11
Add and subtract a single digit to and from a two-digit number.
Resources Resource sheet 4: 100 square (per pair); number cards from 20 to 40 from Resource sheet 1: 0–100 number cards (per pair); Resource sheet 7: 1–6 spinner (per group)
What to do • Ask a learner to pick a two-digit number on the Number square tool. Colour it so that it can be clearly seen. • Ask the learners to find the same number on their 100 squares with a partner. • Now ask the learners to add or subtract a multiple of ten to or from the starting number and to colour the answer. • The learners hold up their 100 squares for you to check.
Variations • As above, but ask learners to add a single-digit to the starting number instead of a multiple of ten. • Divide learners into teams of six and have each team stand in a line. Show each of the learners at the front a different ‘teen’ number. They say the number that is ten more to the learner behind them, who says the number ten more than that to the learner behind them, and so on until the end of the line is reached. Ask: What number did you reach? What was the starting number? • Lesson 3: Pairs of learners spread number cards from 20 to 40 face down on the table. They take turns to pick a card. Learner A aims to find the number that is two more than 22 and Learner B aims find the number that is three more than 22. The first learner to find their card wins. • Lesson 6: Divide learners into teams of six and have each team stand in a line. Show each of the learners at the front a different two-digit number greater than 60. They say the number that is ten less to the learner behind them, who says the number ten less than that to the learner behind them, and so on until the end of the line is reached. Ask: What number did you reach? What was the starting number? • Lesson 7: Learners spin a spinner twice to generate two numbers. They subtract the smaller number from the larger number, saying the answer to their partner. Learners repeat several times each.
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Unit
6
Addition and subtraction 2
Refresh activities /
Learning objectives Code
Learning objective
2Nc13
Find a small difference between pairs of two-digit numbers.
2Nc15
Understand subtraction as both difference and take away.
Resources Resource sheet 1: 0–100 number cards (per class); up to 100 interlocking cubes (per pair); Resource sheet 7: 1–6 spinner (per group)
What to do • Ask a learner to pick a two-digit number. Write it on the board in a subtraction with another two-digit number of your choice (this number should be no more than 20 more or less than the number chosen by the learner). • Ask a learner to set up the Number line tool to find the difference between the two numbers, starting on the smallest number and finishing on the largest number with increments of 1. • Move the frog along the number line (forwards or backwards) whilst counting the spaces between the two numbers to find the difference. • Variation: Ask the learners to solve the subtraction by counting taking away instead of by finding the difference.
Variations • Pairs of learners each take a handful of interlocking cubes. They count their cubes to find who has more. They count on from the smaller number until they reach the larger number to find how many more cubes one has than the other. • Lesson 8: Pairs of learners each spin one spinner. They find the difference between the two numbers, saying the answer to their partner. Learners repeat several times each.
Number – Calculation: Mental strategies, Addition and subtraction
Finding the difference
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Unit
7
Addition and subtraction 3
Refresh activities Adding pairs of two-digit numbers / Number – Calculation: Mental strategies, Addition and subtraction
Learning objective Code
Learning objective
2Nc12
Add pairs of two-digit numbers.
Resources cards 0–9 from Resource sheet 1: 0–100 number cards (per learner); Resource sheet 21: 0–20 number line; Resource sheet 11: 0–9 number fan (per learner); up to 10 counters (per pair)
What to do • Each learner picks two single-digit number cards, writes the numbers in an addition number sentence and adds them together, either mentally or using a 0–20 number line. If the answer has two digits, they partition it into tens and ones. Repeat with two new number cards.
Variations • Lesson 6: Learner A uses a number fan to show their partner a number from 0 to 20. Learner B finds the number that must be added to it, to total 20, and shows it on their number fan. They swap roles and repeat, several times. • Lesson 7: Learners work in pairs. One learner puts between two and ten counters on the table and closes their eyes. The other learner takes some of the counters. The first learner opens their eyes, counts their counters and works out how many are missing. They swap roles and repeat. • Write an addition involving two two-digit numbers (both below 50) on the board. Ask a learner to partition the two numbers on the board. Now ask one half of the class to add the tens together and the other half of the class to add the ones together. Ask a volunteer from each half of the class to write their answers on the board. Now add the ones total to the tens total by counting on with the learners.
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Unit
8
Multiplication and division 1
Refresh activities Times tables / Code
Learning objective
2Nn4
Count in twos, fives and tens.
2Nc4
Learn and recognise multiples of 2, 5 and 10.
2Nc17
Understand multiplication as describing an array.
Resources cards 0 to 9 from Resource sheet 1: 0–100 number cards (per learner); Resource sheet 21: 0–20 number line; Resource sheet 11: 0–9 number fan (per learner); up to 10 counters (per pair)
What to do • Lesson 2: Play the Times Table Topple game (level 1) in practice mode with the learners, supporting them in solving the twos multiplications. • Lessons 3 and 4: Play the Times Table Topple game at level 2 or 3 to practise 5 or 10 times table facts instead of twos. • Variation: Play the Times Table Topple digital game in speed tracker mode to challenge the learners to recall the multiplication facts as quickly as possible.
Variations • Set up the Tree tool with no trees. Write a two times table multiplication on the board and ask learners to make an array of apples to match the multiplication. Count the apples in twos to solve the multiplication with the class. • Lessons 3 and 4: Make arrays to match five or ten times table multiplications.
Number – Calculation: Mental strategies, Multiplication and division
Learning objectives
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Unit
9
Multiplication and division 2
Refresh activities Match the doubles Learning objective
Number – Calculation: Mental strategies, Multiplication and division
Code
Learning objective
2Nc5
Find and learn doubles for all numbers up to 10 and also 15, 20, 25 and 50.
Resources mini whiteboard and pen (per pair); 20 counters (per pair); 1–10 number cards from Resource sheet 1: 0–100 number cards
What to do • Divide the board in half and write the following numbers on one half: 3, 5, 10, 15, 20, 25, 50. • On the other side of the board, write these numbers: 40, 6, 50, 10, 100, 14, 30. • Challenge the learners to work in pairs to match the numbers on the first half of the board to their double on the other side of the board. They should do this by copying the numbers onto their whiteboards and drawing lines to connect the starting numbers with their matching doubles. • Variation: Give learners the numbers to 10 to double.
Variation • Learners work in pairs. Give each pair 20 counters and a set of 1–10 number cards. They each pick a number card and count out that many counters, then they count both sets of counters together to find how many there are in total.
2s, 5s and 10s
/
/
Learning objectives Code
Learning objective
2Nn4
Count in twos, fives and tens and use grouping in twos, fives or tens to count larger groups of objects.
2Nc4
Learn and recognise multiples of 2, 5 and 10 [and derive the related division facts].
Resources 50 counters (per pair)
What to do • Divide learners into three groups and allocate a multiple (two, five or ten) to each group, without the other groups knowing what it is. Count to 100 in ones with learners. Whenever a group’s multiple is said, they clap. Learners must work out what multiples are that the other groups are clapping on. • Variation: Invite two learners to come to the front. Ask them a multiplication fact relating to the 2×, 5× or 10× tables. The first learner to give the correct answer stays at the front, the other learner goes back to their seat, and a new learner comes to the front to compete to answer a new question first. Repeat until all learners have had a turn.
Variations • Learners work in three teams: twos, fives and tens. Give each team 50 counters. Count on in ones from zero to 100 with learners, pointing to the numbers on the Number square tool. The teams take a counter every time a multiple of their number is said. • Learners count on in twos from zero until you say: Stop! Display the Number square tool and point to the number they reached. Then count how many multiples of two they said before you stopped them. Repeat for counting on from zero in with fives and tens. • Chant the two, five and ten times tables with learners. For example, say: Five multiply two is … and learners reply with ‘ten’.
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Unit
Grouping and sharing
9
Multiplication and division 2
/
Code
Learning objective
2Nc18
Understand division as grouping and use the ÷ sign.
2Nc23
Understand that division can leave some left over.
Number – Calculation: Mental strategies, Multiplication and division
Learning objectives
Resources mini whiteboard and pen (per learner); 20 counters or small objects (per pair)
What to do • Tell learners that you are going to divide the amount of children in the class between 2. • Gather the learners at the front of the class and send them to alternate sides of the classroom one by one. Count the learners on each side at the end to find the answer. Were there any learners left over? Why/why not? • Repeat this, dividing the learners between 5, then 10. How many learners were left over each time? • Ask learners to write the matching division number sentences on their whiteboard.
Variations • Ask pairs of learners to choose a multiple of two up to 20. They count out that number of objects and share them equally between themselves. They repeat this with other multiples of two. • As above, but with odd numbers of counters and multiples of 2, 5 and 10 so that there is a remainder.
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