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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 1 units iv
iv
The components of Collins International Primary Maths: • • • • •
Teacher’s Guide Student’s Book Workbook Collins Connect DVD
viii xvi xvi xvii xvii
Collins International Primary Maths Stage 1 units and recommended xviii teaching sequence Collins International Primary Maths Stage 1 units link to Cambridge Primary xxi Mathematics Curriculum Framework Cambridge Primary Mathematics Curriculum Framework Stage 1 link to Collins International Primary xxxii Maths units
Refresh activities Number
Geometry Measure
Handling data
Numbers and the number system Calculation: Mental strategies, Addition and subtraction Calculation: Mental strategies, Multiplication and division Shapes and geometric reasoning Position and movement Money Length, mass and capacity Time Organising, categorising and representing data
1 6 8 11 14 15 17 20 22
Number Introduction to number
24
1 Whole numbers 1
26
2 Whole numbers 2
37
3 Whole numbers 3
48
4 Fractions
54
5 Addition and subtraction 1
65
6 Addition and subtraction 2
76
7 Addition and subtraction 3
87
8 Multiplication and division 1
98
9 Multiplication and division 2
109
Geometry 10 2D shape
120
11 3D shape
126
12 Patterns and symmetry
132
13 Position and movement
138
Measure 14 Money 1
144
15 Money 2
150
16 Length
156
17 Mass
162
18 Capacity
168
19 Time 1
174
20 Time 2
180
Handling data 21 Handling data 1
186
22 Handling data 2
192
Resource sheets
198
Answers
233
Tracking back and forward through the Cambridge Primary Mathematics Curriculum Framework 247 Stage 1 Record-keeping charts
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Unit
14 Money 1
Refresh activities How much? (1) Code
Learning objective
1GP1
Recognise all coins and work out how to pay an exact sum [using smaller coins].
1Pt3
Find many combinations[, e.g. combinations of three pieces of different coloured clothing].
What to do
Variation
• Display the Money tool showing 1 × 10 cents, 3 × 5 cents and 5 × 1 cent coins. • Invite individual learners to choose two coins and, as a whole class, total them. • Repeat with three coins. Change the order of the coins and total together again. • Play at a pace, giving individual learners support tools for counting if necessary.
• As learners’ mental skills for combinations develop, increase the number and/or value of the coins.
Measure – Money
Learning objectives
How much? (2) Learning objectives Code
Learning objective
1GP1
Recognise all coins and work out how to pay an exact sum [using smaller coins].
1Pt2
Explore number problems and puzzles.
1Pt3
Find many combinations[, e.g. combinations of three pieces of different coloured clothing].
1Pt9
Make a sensible estimate of a calculation, and consider whether an answer is reasonable.
Resources 5 × 1 cent, 3 × 5 cents, 1 × 10 cents coins (per pair); number lines/100 squares/beads or other counting tool (per pair at teacher’s discretion) Unit 15, Measure – Money 2: 5 × 1 cent, 10 × 5 cents, 5 × 10 cents coins (per learner); 2 × 25 cents and 1 × 50 cents coins (per Challenge 3 learner)
What to do • This is a quick teacher-led activity but learners work in pairs to find the answer using the coins in front of them. • Use the repetitive phrase: I went to the shops and bought an orange/lollipop/hat/drink and I used two coins. Ask: What could the coins be? What could the total value be? • Choose some answers to share and make with the Money tool.
• Repeat the phrase either saying you used two different coins or three coins, as long as time allows. At the start of the unit, focus on making number pairs to 10 (always including some questions in each session for Challenge 1 learners), and later in the unit use it as a way to support learning of the difficult ‘teens’, that is 11, 12, 13.
Variation • For Unit 15: Measure – Money 2, increase the total value of items to up to 20 cents. Challenge 3 learners could buy things up to the total value of 25 cents and 50 cents, using the challenge of smallest number of coins and exercising their abilities to count on in fives and tens.
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Unit overview
Unit 1: Whole numbers 1 Learning objectives
Number – Numbers and the number system
Code
Learning objective
1Nn1
Recite numbers in order (forwards from 1 to 100, backwards from 20 to 0).
1Nn2
Read and write numerals from 0 to 20.
1Nn3
Count objects up to 20, recognising conservation of number.
1Nn4
Count on in tens from zero or a single-digit number to 100 or just over.
1Nn5
Count on in twos [, beginning to recognise odd/even numbers to 20 as ‘every other number’].
1Nn9
Order numbers to at least 20 positioning on a number track[; use ordinal numbers].
1Nn11
Give a sensible estimate of some objects that can be checked by counting, e.g. to 30.
Strand 5: Problem solving 1Pt2
Explore number problems and puzzles.
1Pt7
Describe and continue patterns such as count on and back in tens, e.g. 90, 80, 70.
1Pt8
Identify simple relationships between numbers [and shapes], e.g. this number is ten bigger than that number.
Unit overview In this unit, learners will work with numbers, counting forwards and backwards in one, twos and tens. They will be reading, writing and ordering numbers to 20, and counting objects. They will estimate ‘how many’ objects there are in a group, then check their estimates by counting the objects.
Common difficulties and remediation Some learners may believe that you must start counting on from number 1 or 0, and/or finish on number 10. Remedy this by asking learners to choose a number to start counting from, for example, 4; or to finish counting on, for example, 18. Learners may not understand that, when counting a group of objects, each number said is a label for each object, and that each object must be counted only once. Practise organising objects so that they are easier to count accurately (into lines or pairs) and counting slowly and deliberately together as a class, using one number name for each object. There can be some confusion around the terms ‘numbers’, ‘numerals’ and ‘digits’. In Stage 1, it is sufficient to use the term ‘numbers’ with learners when talking about a number as an amount you have in your head or see written down as numerals. It is necessary, however, to speak about one- and twodigit numbers and to explain that ‘digit’ refers to one of the ten symbols that is used to make up a number. Of these three words, ‘numerals’ is the least important for learners to hear and understand at this stage, and will be introduced at a later stage, so ‘numbers’ can be used in its place where necessary.
In Stage 1, some learners may struggle to understand the concept of estimation, choosing a number at random as their estimate rather than looking at the group of objects and thinking carefully about how many there may be. To help learners with this, show them a group of ten objects, a group of two objects and a group of 50 (or more) objects so that they have a basis for comparison. Ask questions such as: Has this group got more or less than ten in it? whilst encouraging learners to compare it with the group of ten objects. Some learners may struggle when counting in the teen numbers as 11, 12, 13 and 15 do not follow the same naming pattern as the other teen numbers, for example, fifteen not fiveteen. Give lots of practice counting and identifying these numbers.
Promoting and supporting language Display the key words for each lesson and discuss them with learners. Use and refer to these words throughout the whole lesson, and encourage learners to use these words too, prompting them when necessary. Knowing the number names is important for this unit. It is good practice to display both numerals and their corresponding number words around your classroom to expose learners to numbers in as many ways as possible. For example, you could display a number line around the classroom, number the seats learners sit at, number the windows and so on. Refer to these numbers on display as often as possible. Use every opportunity you can to count with learners, for example counting learners as they line up for lunch or counting out resources. Physically show learners the meaning of the vocabulary, if possible, for example walk forwards or move your hand forwards on a number line to demonstrate the meaning of ‘forwards’.
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Student’s Book page 3
Unit
1
Whole numbers 1
Workbook page 3
Lesson 1: Counting in 1s Code
Learning objective
1Nn1
Recite numbers in order (forwards from 1 to 100, backwards from 20 to 0).
Strand 5: Problem solving 1Pt7
Describe and continue patterns such as count on and back [in tens, e.g. 90, 80, 70].
Prerequisites for learning
Vocabulary
Learners need to: • know the number names from 0 to 20 and some number names from 20 to 100 • be able to count forwards from 0 to 20.
count on, count back
Resources three number cards between 10 and 90 from Resource sheet 1: 0–100 number cards (per class)
Success criteria Learners can: • count forwards to 100 from any starting number • count backwards to 0 from any starting number that is less than 21.
Refresh
Practise
• Use the activity Counting rhymes from the Refresh activities. Use this to make an initial assessment of each learner’s knowledge of numbers to 100. Note any learners who may need additional practice and those who are already working at Stage 1.
• Workbook: Counting in 1s page 3 • Refer to Activity 1 from the Additional practice activities.
Discover • Direct learners to the picture in the Student’s Book. Ask: Does anyone know what this is? (snakes and ladders board game) Ask: Why does the board need numbers? Take feedback. Point to a number on the picture and say to learners: Say the numbers with me from ... to ...
Teach and Learn • Display the Number square tool. Explain that the 100 square helps us to count. Point to each number in turn, and, as a class, get learners to recite the number names to 100. • Explain that a number track can also help us to count. Count along the stars in the Student’s Book with learners, then the balloons, encouraging them to touch each picture as they count. Ask: What happens when you reach a number that ends with 0? Count to 100, asking learners to clap every time they say a number that ends with 0. • Refer to the Number square tool and show learners how the numbers follow the same pattern on every row. Now count back from 20 to 1 using the tennis balls in the Student’s Book.
Apply • The first learner counts forwards from 1, saying one number name for each of their fingers and thumbs. The second learner continues the count from 11, in the same way. They repeat this until they reach 100.
Review
Number – Numbers and the number system
Learning objectives
• Arrange learners in a circle. Give three learners a number card between 10 and 90. Learners count forwards from 1 around the circle. When someone with a number card is reached, the count stops and they (or if necessary the teacher) say the number on the card. The learner next to them must continue counting forwards from the number on the card.
Assessment for learning • What number comes after/before...? • Count forwards from... [a number between 1 and 99]. • Count backwards to 0 from... [a number between 10 and 20]. • What number comes after 29/89? Before 10/20? (Note if learners are able to cross tens boundaries when counting forwards/backwards.)
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Unit
1
Student’s Book page 4
Whole numbers 1
Workbook page 4
Lesson 2: Reading numbers to 20 Learning objectives
Number – Numbers and the number system
Code
Learning objective
1Nn2
Read [and write] numerals from 0 to 20.
Strand 5: Problem solving 1Pt7
Describe and continue patterns such as count on and back [in tens, e.g. 90, 80, 70].
Prerequisite for learning
Resources
Learners need to: • be able to count from 0 to 20.
0–20 number cards from Resource sheet 1: 0–100 number cards (one card for each learner) (Note: Prior to the lesson, stick one number card underneath each learner’s chair); large 0–20 number cards (per class)
Success criteria Learners can: • read any number from 0 to 20.
Vocabulary number
Refresh
Apply
• Use the activity Counting people from the Refresh activities.
• Ask learners to find a number card from 0 to 20 that you stuck under their chairs before the lesson began. Call out a number and an action (for example, hop around the classroom). Everyone with that number card must do the action that number of times. Repeat with the other numbers. When applicable, discuss what happens for those learners with a zero number card.
Discover • Direct learners to the picture in the Student’s Book and display Slide 1. Tell learners that your friend lives at number 16. Ask them to discuss how they would work out which house that is. Elicit that they need to be able to read the numbers.
Review Teach and Learn • Refer to the numbers in the Student’s Book and tell learners that they will be looking at the numbers 0 to 20. Display Slide 2, count from 0 to 10, touching each number as you count. Then ask what happens on the next row of numbers, eliciting that the number pattern repeats itself but with a 1 in the tens position. • Talk about how the ones digit sounds the same in 14, 16, 17, 18 and 19, but is different in 13 and 15 and that 11 and 12 are different because they aren’t called ‘oneteen’ and ‘twoteen’. Then count from 11 to 20, pointing to each number as you count.
• One by one, hold up large 0 to 20 number cards, slowly revealing the number from behind a book or scarf. Learners must call out the number when they have worked out what it is.
Assessment for learning • Tell me what number this is. • Read this number. • Point to the number 17/8/12...
Practise • Workbook: Reading numbers to 20 page 4 • Refer to Activity 2 from the Additional practice activities.
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Student’s Book page 5
Unit
1
Whole numbers 1
Workbook page 5
Lesson 3: Writing numbers to 20 Code
Learning objective
1Nn2
[Read and] write numerals from 0 to 20.
Strand 5: Problem solving 1Pt7
Describe and continue patterns such as count on and back [in tens, e.g. 90, 80, 70].
Prerequisites for learning
Vocabulary
Learners need to: • be able to count from 0 to 20 • recognise numbers to at least 20.
number
Resources mini whiteboard and pen (per learner)
Success criteria Learners can: • write any number from 0 to 20.
Refresh
Apply
• Use the activity Recognising numbers from the Refresh activities.
• Direct learners to the picture in the Student’s Book and display Slide 1. Ask: What does the picture show? Why are the numbers on the list important? What would happen if you wrote the wrong number on the list?
• Ask two learners to come up to the board. Ask a question where the answer is between 0 and 20, for example: How many learners are sitting at the table by the door? Learners compete to write the correct number on the board. Look for who has formed the number correctly. The rest of the class practise writing the same number on their mini whiteboards. Choose another two learners and repeat.
Teach and Learn
Review
• Give learners mini whiteboards and pens and tell them that they will be writing numbers from 0 to 20. Display the Number square tool and count from 0 to 20, pointing out the patterns that the numbers follow. Write the numbers together, referring to the formation pictures in the Student’s Book. Learners hold up their whiteboards to show their numbers. • Spend time on the teen numbers, stressing that the 1 always goes at the start of the number in the tens position, and talking about the numbers 11, 12, 13 and 15 and how they sound different from how you would expect. • Finally, call out numbers from 0 to 20 and ask learners to write them as carefully as possible and then to hold up their whiteboards.
• Ask volunteers to ‘pretend’ to write a number from 0 to 20 on the class whiteboard with their finger. Can the rest of the learners work out which number they have ‘written’?
Discover
Number – Numbers and the number system
Learning objectives
Assessment for learning • Write the number ... • Where do you start when you write the number ...?
Practise • Workbook: Writing numbers to 20 page 5 • Refer to Activity 2 from the Additional practice activities.
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Unit
1
Student’s Book page 6
Whole numbers 1
Workbook page 6
Lesson 4: Counting objects Learning objectives
Number – Numbers and the number system
Code
Learning objective
1Nn3
Count objects up to 20, recognising conservation of number.
Strand 5: Problem solving 1Pt7
Describe and continue patterns such as count on and back [in tens, e.g. 90, 80, 70].
Prerequisites for learning
Vocabulary
Learners need to: • be able to recite the numbers from 1 to 20 • have experience of counting a small number of objects.
count, same
Success criteria Learners can: • count a group of 1 to 20 objects accurately • recognise that the number of objects in the group is the same when they are arranged differently.
Resources 20 interlocking cubes (per learner); about 20 small counters or buttons (per learner); Resource sheet 2: Object counting (one card per group); at least 15 pencils, eight books, three erasers, 18 counters (per group)
Refresh
Practise
• Use the activity Counting people (Variation 3) from the Refresh activities. Learners count up to 20 counters into an empty container.
• Workbook: Counting objects page 6 • Refer to Activity 2 from the Additional practice activities.
Discover
Apply
• Direct learners to the picture in the Student’s Book. Ask: How could the boy find out how many there are? How could he make counting them easier?
• Give each learner 20 interlocking cubes. One learner takes a small number of their cubes and gives them to their partner to count. This learner then gives their partner a small number of their cubes to count. They continue this with increasing numbers of cubes every time (a few, a handful, two handfuls, all). Extend this by supplying 50 cubes each.
Teach and Learn • Discuss the two groups of children on the Student’s Book page. Ask: Does each house show the same number of children? • Ask various numbers of learners to stand together in groups. Model counting the groups of learners, but make some deliberate mistakes – either overcounting, or under-counting. Let learners correct your mistakes. Ask: How could you make it easier to count accurately? Elicit that you could line everyone up, pointing at each learner as you count. Demonstrate and write the number of learners on the board. Ask the group to stand in different positions. Ask: How many people are there now? Count again. Explain that if nobody leaves or joins the group, the number will be the same. • Discuss the two groups of fish in the fish tanks on the Student’s Book page. Elicit that there are the same number of fish in each tank.
Review • Arrange learners into groups and give each group one card from Resource sheet 2. • Each group collects the correct number of objects and lays them out on their table. The first group to collect the correct number of objects is the winner.
Assessment for learning • Count these objects. • How could you make counting easier? • I have moved these objects. How many are there now?
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Unit
1
Whole numbers 1
Additional practice activities Challenge
2
Learning objective • Recite numbers in order (forwards from 1 to 100, backwards from 20 to 0).
Resources
Variations
chalk (per class); Resource sheet 1: 0–100 number cards (per class); stone or similar (for the Variation – per learner)
Challenge
Challenge
3
What to do • Draw a 100 square grid outside using chalk. Each square must be large enough for a learner to jump in. • Ask learners to jump along the numbers counting in ones. Encourage learners to count forwards from any number, not just from one. • Ask learners to count backwards from 20 as they jump backwards along the track or number square.
Activity 2
1
If a 100 square is too difficult for a group, draw a 0 to 20 number track instead. Can learners count backwards from the number their stone lands on?
Adapt for indoor use by using Resource sheet 1: 0–100 number cards and sticking the cards to the floor.
Challenge
or
2
Learning objectives • Read and write numerals from 0 to 20. • Count objects up to 20, recognising conservation of number.
Resources
Variations
order pad (per group or pair); toy food or other countable items (per group or pair); plastic plates or bowls (per group or pair)
Set up a café role-play area where learners undertake the activity. The customers write their order on the order pad and give it to the waiter to read. Challenge
What to do • One learner in each group or pair is the waiter and has an order pad. • The other members of the group/pair must decide what they want and how many. The waiter writes down their orders (for example 6 apples/12 buttons). If learners are not confident to write words, they can draw the objects, as long as they write the correct number down. • The waiter then goes and fetches the order, counting the objects onto plates and giving them to the customers to count and check. • Swap roles and repeat.
1 Challenge
3
Number – Numbers and the number system
Activity 1
Adapt the activity to make it teacher-led. Learners can order more than 20 objects.
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Unit
1
Whole numbers 1
Additional practice activities Activity 3
Challenge
2
Number – Numbers and the number system
Learning objectives • Count on in 2s, [beginning to recognise odd/even numbers to 20 as ‘every other number’]. • Count on in tens from 0 to 100.
Resources
Variations
long sheet of paper (per learner); paint in trays (per group); Resource sheet 4: 10s snake jigsaw (per pair); for the jigsaw: cards, coloured pencils/crayons, scissors, glue
Learners could make pairs of fingerprints instead of hand prints.
What to do
The teacher should glue the snake to some card, laminate it and cut out the pieces so they can be reused.
Challenge
1
Limit the stamps to six or fewer.
Challenge
• Learners dip both hands in paint then, ‘stamp’ their hands along the paper as many times as they can until the paint fades. • They then count how many hand prints they made by counting them in twos. Who made the most hand prints?
2
Ask learners to count on in tens from 0 to 100 to complete the jigsaw of the snake. They should fit the pieces together so that they make a tens number track from 0 to 100. Extend the challenge by asking pairs or groups of three or four learners to put their sheets of paper together and count on in twos to find out how many hand/fingerprints there are. Challenge
3
Activity 4
Challenge
2
Learning objective • Order numbers 0 to 20 on a number track
Resources
Variations
Resource sheet 5: 0–20 number track (per learner); scissors (per learner); glue (per learner); coloured pencils (per learner); chalk (per class)
Draw a number track from 0 to 20 outside using chalk. Only fill in some of the numbers. Challenge learners to write in the missing numbers.
What to do
Ask learners to count in twos on their number track and colour each number they land on in the same colour.
Challenge
2
Challenge
• Give each learner a copy of the top half of Resource sheet 5 and the cut out numbers from the bottom half of the sheet. • Learners use the number track to order the number squares. When they are happy that they have ordered the numbers correctly they glue them to the number track. • Learners can refer to their number track during the lesson to help them order numbers from 0 to 20.
3
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