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Contents Introduction
Collins International Primary Maths Stage 5 units
Key principles of Collins International Primary Maths
iv
How Collins International Primary Maths supports Cambridge Primary and the Cambridge Primary Mathematics Curriculum Framework
iv
The components of Collins International Primary Maths: • • • • •
Teacher’s Guide Student’s Book Workbook Collins Connect DVD
viii xvi xvi xvii xvii
1 Whole numbers 1
61
2 Whole numbers 2
72
3 Decimals 1
78
4 Decimals 2
84
5 Fractions
90
6 Percentages
96
7 Ratio and proportion
102
8 Addition and subtraction 1
108
9 Addition and subtraction 2
114
10 Addition and subtraction 3
125
11 Multiplication and division 1
131
12 Multiplication and division 2
142
13 Multiplication and division 3
153
14 2D shape, including symmetry
164
15 3D shape
170
16 Angles
176
17 Position and movement
182
18 Length
193
Refresh activities
19 Mass
199
Number
20 Capacity
205
21 Time
211
22 Area and perimeter
217
23 Handling data
223
Resource sheets
234
Answers
261
Tracking back and forward through the Cambridge Primary Mathematics Curriculum Framework
280
Stage 5 Record-keeping charts
299
Collins International Primary Maths Stage 5 units and recommended teaching sequence Collins International Primary Maths Stage 5 units link to Cambridge Primary Mathematics Curriculum Framework Cambridge Primary Mathematics Curriculum Framework Stage 5 link to Collins International Primary Maths units
xviii
xxi
xxxvii
Numbers and the number system 1 Calculation: Mental strategies, Addition and subtraction 17 Calculation: Mental strategies, Multiplication and division 25
Geometry
Shapes and geometric reasoning 37 Position and movement 43
Measure
Length, mass and capacity Time Area and perimeter
47 53 55
Organising, categorising and representing data
57
Probability
60
Handling data
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Unit
1
Whole numbers 1
Refresh activities Sequences Code
Learning objective
5Nn1
Count on and back in steps of constant size [, extending beyond zero].
Number – Numbers and the number system
Learning objectives
Resources paper (per learner) or mini whiteboard and pen if available
What to do • Learners sit in a circle. Distribute paper and pencils. Suggest a number sequence beginning from zero that counts on in steps of 2, 3, 4, 5, 9 or 10. • Say: The number sequence will begin on my left and move around the circle clockwise. As the turn passes, say the next number in the sequence. • Give learners 15 seconds before the game begins to predict and write their number in the sequence. • The game begins, the turn passing around the circle. Learners say the number that they have written on their paper, holding it up. If it is correct, they score a point. The next round begins with a different sequence and a different starting position, shifted one place to the right of the previous position.
Variations • Start counting on from a number other than zero. • Introduce backward sequences that extend beyond zero.
Reverse Learning objective Code
Learning objective
5Nn12
Recognise and extend number sequences.
What to do • Learners sit in a circle. • The teacher announces a sequence, for example: adding 4, subtracting 5 or multiples of 3. • The teacher also announces a ‘reverse’ number, for example: ‘any number ending in 4’ or ‘any two-digit number in which both digits are identical’. • When it is the turn of a learner to say a ‘reverse’ number, they must say ‘reverse’ instead. The turn immediately reverses, passing the opposite way around the circle. • The teacher begins the game and the turn passes clockwise. If a learner makes a mistake, or fails to use the ‘reverse’ number at the correct point, they sit out of the game. The winner is the last learner in the game.
Variation • The game can be played without the ‘reverse’ action, focusing on the sequence announced.
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Unit
1
Whole numbers 1
Dice digits Learning objectives
Number – Numbers and the number system
Code
Learning objective
5Nn2
Know what each digit represents in five- and six-digit numbers.
5Nn3
Partition any number up to one million into thousands, hundreds, tens and units.
Resources 1–6 dice or Resource sheet 4: 1–6 spinner (per learner); mini whiteboard and pen or paper (per learner)
What to do • Learners roll a dice five times and write the numbers on their whiteboard. • Ask learners to create the largest and smallest numbers they can from their set of five digits. • As a class, work out who has the largest and smallest number. Ask: Are you sure these are the largest and smallest numbers? Learners check to make sure. • Choose individual learners to display their numbers and ask the class: How would we partition this number? Take feedback. Point to a digit and ask: What is the place value of this digit? Continue until you are sure all learners can recall how to partition numbers and are confident with place value. • Repeat with six digit numbers.
Variation • Learners tell their partner the value of each digit in the number.
Values together Learning objectives Code
Learning objective
5Nn2
Know what each digit represents in five- and six-digit numbers.
5Nn3
Partition any number up to one million into thousands, hundreds, tens and units.
Resources 1–6 dice or Resource sheet 4: 1–6 spinner (per learner); mini whiteboard and pen or paper (per learner); Resource sheet 5: Arrow cards (per learner)
What to do • Learners roll a dice four times, each number representing the number of thousands, hundreds, tens or ones digit. • The learners then write their numbers on their whiteboards in expanded notation, for example: 2000, 300, 10, 9. • Ask individual learners to demonstrate what they have done and say the place value of each digit in their number. • Next, ask five learners to each roll one number. Say: We are going to partition this five-digit number using the Place value tool. Ask individual learners to say which arrow cards you need to drag on to the screen. Repeat with different five- and six-digit numbers. • Learners roll their dice five (or six) times and use the place value arrow cards to display their numbers in expanded notation form. If time allows, let individual learners use the Place value tool to partition their five- or six-digit number.
Variation • Less able learners can work with three- or four-digits only.
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Unit
1
Whole numbers 1
Multiply or divide Code
Learning objective
5Nn5
Multiply and divide any number from 1 to 10 000 by 10 or 100 and understand the effect.
Number – Numbers and the number system
Learning objective
Resources 1–6 dice or Resource sheet 4: 1–6 spinner (per pair); mini whiteboard and pen or paper (per pair); a counter with a multiplication symbol drawn or taped on one side and a division symbol on the other (per pair); Resource sheet 3: Blank place value grid (per learner)
What to do • Remind learners they already know that when they multiply a number by 10 the digits move one place value to the left and when multiplying by 100 the digits move two place values to the left. In division, when they divide a number by 10 the digits move one place value to the right and when dividing by 100 the digits move two place values to the right. If necessary, demonstrate this by drawing a place value grid on the board and modelling some simple two-digit by three-digit calculations. • In pairs, learners roll a dice up to five times. They write the number in their copy book or on a mini whiteboard. • Without telling their partner, each learner should decide whether to multiply or divide the number by 10 or 100. Or, to make this a more random choice, learners can flip a counter with a multiplication symbol drawn or taped on one side and a division symbol on the other. Each learner then does their calculation individually. • Learners use Resource sheet 3: Blank place value grid, to help calculate their answer. • Learners reveal their multiplied or divided figure to their partner who must say whether they have multiplied or divided by 10 or 100.
Variation • Less able learners use a five-digit number, with zeros in the tens and ones places.
Rounding Learning objective Code
Learning objective
5Nn6
Round four-digit numbers to the nearest 10, 100 or 1000.
Resources 1–6 dice or Resource sheet 4: 1–6 spinner (per class); paper (per learner)
What to do • • • •
Roll a dice four times. Write the digits on the board to form a three-digit number. Ask learners to round it to the nearest 10 or 100. Learners compare their answer with a partner. Repeat.
Variation • For less able learners, roll the dice three times to create a three-digit number.
3
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Unit
1
Whole numbers 1
Comparing numbers Learning objective Code
Learning objective
5Nn8
Order and compare numbers up to a million using the > and < signs.
Number – Numbers and the number system
Resources 1–6 dice or Resource sheet 4: 1–6 spinner (per class); paper (per learner)
What to do • • • • •
Roll the dice to form two three-digit numbers. Write the numbers on the board. Learners copy the numbers and write the correct symbol of comparison, < or >, between them. They suggest a number that comes between the two numbers. Repeat.
Variations • Roll the dice to create five three-digit numbers, then place these numbers in order of size. • Create four- or five-digit numbers to compare and order.
Odd or even Learning objective Code
Learning objective
5Nn13
Recognise odd and even numbers and multiples of 5, 10, 25, 50 and 100 up to 1000.
Resources 1–6 dice or Resource sheet 4: 1–6 spinner (per class); paper (per learner)
What to do • Explain that on the command you will ask the learners to arrange themselves in four random groups of any size. • Give the command: Ready, set, go! • After learners have settled in their groups, ask them to state the total number in their group and say whether it is an odd or an even number.
Variation • Ask two groups to join together and say whether the sum of the groups is odd or even. Repeat for groups that are: odd + odd; even + even; odd + even. Ask: Do you get the same odd/even result every time? Learners investigate and discuss the results.
4
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Unit
2
Whole numbers 2
Guess the steps Code
Learning objective
5Nn1
Count on and back in steps of constant size, extending beyond zero.
Number – Numbers and the number system
Learning objective
What to do • Learners sit in a circle. • A volunteer is chosen to be the ‘guesser’. They leave the circle and stand at a distance, with their back to the other learners. • The teacher whispers a step sequence to the learners, for example ‘forwards in steps of four’ or ‘backwards in steps of six’. • The guesser is invited to return to the circle. • The teacher indicates for the sequence to begin. • The guesser has to work out the rule of the step sequence.
Variation • Introduce forwards or backwards sequences that extend beyond zero.
Up above, down below Learning objective Code
Learning objective
5Nn9
Order and compare negative and positive numbers on a number line and temperature scale.
What to do • Divide the class into two teams. • Say: Think of an island. The trees on the island are above sea level. The fish swimming around the island are below sea level. I will tell you the height of the top of a tree, a positive number of metres, and the depth of a fish, a negative number of metres. You have to work out the distance between the top of the tree and the fish. • Begin the game with: ‘The tree is five metres tall; the fish is at minus four metres.’ • Invite the first learners to put up their hands to respond. If correct, they score a point for their team. • Repeat with different heights above and below sea level. The team with higher score wins.
Variation • Provide a number line to assist learners.
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Unit
2
Whole numbers 2
Temperature change Learning objective Code
Learning objective
5Nn9
Order and compare negative and positive numbers on a number line and temperature scale.
Number – Numbers and the number system
What to do • • • • • •
Display the Thermometer tool, with two thermometers both set with the scale from –20 to 30. Divide the class into two teams. Place the markers of the two thermometers at different positive readings. Ask: What is the difference between the two readings? Repeat with different questions. Teams take turns to answer, scoring a point each time they are correct. The team with the higher score is the winner.
Variation • Use both negative and positive scale readings.
Odd and even guess Learning objective Code
Learning objective
5Nn14
Make general statements about sums, differences and multiples of odd and even numbers.
What to do • • • •
Display the Spinner tool, with the sectors labelled 1 to 8. Learners work with a partner. Click ‘spin’ for a start number. Learners tell their partner their prediction for whether the sum of the start number and the next number spun will be odd or even. They score a point if correct. • The game continues with the teacher spinning new numbers and learners predicting the cumulative sum. The learner with the higher score wins the game.
Variation • Reduce the range of sector numbers to 1 to 4.
6
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Unit
3
Decimals 1
Fraction finder Code
Learning objective
5Nn4
Use decimal notation for tenths and hundredths and understand what each digit represents.
What to do • • • • • •
Display the Fractions tool, set to 10 or 100 parts (no fraction label). Shade one or more parts. Ask: What fraction of the shape has been shaded? Learners take turns to tell their partner the fraction shown. Click ‘show fraction’ to confirm the answer. Repeat with different fractions.
Variation 3 • Display fraction bars divided into tenths or hundredths. Shade to show mixed numbers, for example: 1 10 .
Between the numbers Learning objective Code
Learning objective
5Nn4
Use decimal notation for tenths and hundredths and understand what each digit represents.
What to do • Display the Number line tool, set from 0 to 10 in increments of 0·1; sub-divide: 0·1 or 0·01. (Tick ‘show only end numbers’ if 0·1 is chosen.) • Position pointers above two divisions. • Ask: What two decimals are highlighted? Name a decimal that comes between them. • Repeat with different decimal positions.
Variation
Number – Numbers and the number system
Learning objective
• Learners name the decimal position of each pointer, not numbers between.
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Unit
3
Decimals 1
Counting in tenths and hundredths Learning objective Code
Learning objective
5Nn4
Use decimal notation for tenths and hundredths and understand what each digit represents.
Number – Numbers and the number system
What to do • • • • •
Display the Place value tool, from 27·1. Learners count forwards from 27·1 as the teacher displays the corresponding decimals. Stop at 27·9 and ask: What comes next? (28) Continue counting to 30, then count back to 27·1. Repeat for different decimal number steps.
Variation • Learners begin at 27·9 and count in hundredths to 27·99, stopping to discuss counting through 28 and continuing the sequence to 28·3.
Place value Learning objective Code
Learning objective
5Nn4
Use decimal notation for tenths and hundredths and understand what each digit represents.
5Nn5
Multiply and divide any number from 1 to 10 000 by 10 or 100 and understand the effect. [Decimals answers to one and two decimal places]
What to do • Divide the class into two teams. Display the Number line tool, set 0 to 2 with divisions of 0·1. • Say: I am thinking of a ‘secret number’, a decimal tenth between zero and two (for example, 1·7). • Each team is allowed to ask one question and make one guess at the ‘secret number’ per turn. Allow up to ten questions. • All questions must be of the closed type, demanding only a ‘yes’ or ‘no’ response, for example: Is the number between 0·5 and 0·9? Is it less than 0·8? • The first team to guess the ‘secret’ number scores points equivalent to 11 minus the number of questions asked.
Variation • Choose a decimal tenth as the ‘secret number’. Use an interval of 0·2, for example 0·45 to 0·65 or 1·21 to 1·41.
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