Busy Ant Maths: Assessment Guide 5

Page 1


Assessment Guide 5

Series editor: Peter Clarke

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Contents Introduction Assessment Tasks and Exercises Key Principles of Busy Ant Maths Assessment Assessment Tasks Assessment Exercises End-of-unit Tests Pupil Self-assessments Record-keeping formats Resources to accompany the Assessment Tasks

5 7 9 12 14 16 18 23

Assessment Tasks Number – Number and place value Number – Addition and subtraction Number – Multiplication and division Number – Fractions (including decimals and percentages) Measurement Geometry – Properties of shapes Geometry – Position and direction Statistics Assessment Task Record

24 42 49 75 99, 105 117 128 132 140

Assessment Exercises Number – Number and place value Number – Addition and subtraction Number – Multiplication and division Number – Fractions (including decimals and percentages) Measurement Geometry – Properties of shapes Geometry – Position and direction Statistics Assessment Exercises – Answers and marking commentary

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141 148 152 162 176 186 194 196 200

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End-of-unit Tests Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 Unit 11 Unit 12 End-of-unit Tests – Answers and marking commentary

205 209 212 215 219 224 230 236 241 249 254 260 265

Pupil Self-assessments Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 Unit 11 Unit 12

270 272 274 276 278 280 282 284 286 288 290 292

Record-keeping formats Year 5 Whole-class National Curriculum attainment targets Year 5 Whole-class Domains (View 1) Year 5 Whole-class Domains (View 2) Year 5 Individual Pupil National Curriculum attainment targets and Domains

294 302 303 304

Resources to accompany the Assessment Tasks

307

Tracking back and forward through the Mathematics National Curriculum attainment targets – Year 5

367

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Introduction

Introduction Assessment Tasks and Exercises

Number – Addition and subtraction

Number – Number and place value

Domain National Curriculum attainment target

Assessment Task(s)/Exercise(s)

Read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit

1

Count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000

2

Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero

3

Round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000

4

Solve number problems and practical problems that involve all of the above

5

Read Roman numerals to 1000 (M) and recognise years written in Roman numerals

6

Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)

7

Add and subtract numbers mentally with increasingly large numbers

8

Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy

9

Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

Tasks: 10 and 20 Exercise: 10

Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers

11

Know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers

12 and 13

Number – Multiplication and division

Establish whether a number up to 100 is prime and recall prime numbers up to 19 Multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers

14

Multiply and divide numbers mentally drawing upon known facts

15

Divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context

16

Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000

17

2

18

Recognise and use square numbers and cube numbers, and the notation for squared ( ) and cubed (3)

Solve problems involving multiplication and division including using their knowledge of factors 19 and multiples, squares and cubes Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign

Tasks: 10 and 20 Exercise: 20

Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates

21

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Introduction Assessment Task(s)/Exercise(s)

Compare and order fractions whose denominators are all multiples of the same number

22

Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths

23

Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number (for example, 25 + 45 = 65 = 115)

24

Add and subtract fractions with the same denominator and denominators that are multiples of the same number

25

Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams

26

Read and write decimal numbers as fractions [for example, 0.71 =

71 100

]

27

Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents

28

Round decimals with two decimal places to the nearest whole number and to one decimal place

29

Read, write, order and compare numbers with up to three decimal places

30

Solve problems involving number up to three decimal places

Tasks: 31 and 40 Exercise: 31

Recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal

32

Solve problems which require knowing percentage and decimal equivalents of 12, 14, 15, 25, 45 and those fractions with a denominator of a multiple of 10 or 25

33

Convert between different units of metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)

34

Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints

35

Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres 36 37

Estimate volume [for example, using 1 cm3 blocks to build cuboids (including cubes)] and capacity [for example, using water]

38

Solve problems involving converting between units of time

39

Use all four operations to solve problems involving measure [for example, length, mass, volume, money] using decimal notation, including scaling

Tasks: 31 and 40 Exercise: 40

Identify 3-D shapes, including cubes and other cuboids, from 2-D representations

41

Know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles

42

Draw given angles, and measure them in degrees (°)

43

Identify: angles at a point and one whole turn (total 360°), angles at a point on a straight line and 12 a turn (total 180°), other multiples of 90°

44

Use the properties of rectangles to deduce related facts and find missing lengths and angles

45

Distinguish between regular and irregular polygons based on reasoning about equal sides and angles

46

Geometry – Position and direction

Calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes

Identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed

47

Statistics

Geometry – Properties of shapes

Measurement

Number – Fractions (including decimals and percentages)

Domain National Curriculum attainment target

Solve comparison, sum and difference problems using information presented in a line graph

48

Complete, read and interpret information in tables, including timetables

49

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Introduction

Assessment Exercises Purposes • To assess individual pupils’ level of mastery in a specific National Curriculum attainment target (NC AT). • To identify individual pupils’ strengths and weaknesses in a specific NC AT. • To identify those pupils who are achieving above or below expectations. • To inform future planning and teaching of individual pupils and the class as a whole.

When to use the Assessment Exercises • Any time throughout the year when teachers are uncertain about a pupil’s, or group of pupils’, level of mastery in a specific NC AT. • When requiring written evidence of a pupil’s level of mastery in a specific NC AT. • Assessment Exercises differ from the End-of-unit Tests (see pages 14 and 15) in that an Assessment Exercise is designed to assess mastery in a specific NC AT, i.e. the end-of-year level of expectation, whereas an End-of-unit Test assesses all of the NC ATs taught in a particular Busy Ant Maths unit. It is designed to assess the exact mathematical content that has been taught during the unit and therefore will not always assess the end-of-year level of expectation.

How to use the Assessment Exercises • This section provides a photocopiable pupil Assessment Exercise and accompanying teacher’s notes with answers and marking commentary for each of the NC ATs. • The way in which the Assessment Exercises are administered is entirely up to the discretion of the individual teacher. • It is advised that before pupils begin an exercise, you read through and explain the exercise to the pupils to ensure that they understand each of the questions. Also ensure that pupils have any necessary resources. • After marking the Assessment Exercise, you then decide, based on the results of the exercise, the level of mastery achieved by the pupil for that specific NC AT, i.e. ‘Not yet achieved’ (NYA), ‘Achieved’ (A) or ‘Achieved and exceeded’ (A&E). • The data collected can then be used to update either the paper or electronic versions of the Whole-class National Curriculum attainment targets record (see pages 18 and 19) and the pupil’s Individual Pupil National Curriculum attainment targets and Domains record (see page 22).

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Assessment Task 1

Number – Number and place value National Curriculum attainment target

F.

• Read, write, order and compare numbers to at least 1 000 000 and determine the value of each digit

G. H.

Prerequisite checklist Can the pupil: • read and write numbers to 10 000 in numerals and in words? • compare and order numbers to 10 000? • recognise the place value of each digit in a four-digit number? • partition four-digit numbers into multiples of 1000, 100, 10 and 1 and in different ways?

I.

Use the < and > symbols to compare two numbers to at least 1 000 000 Order numbers to at least 1 000 000 Know what each digit represents in a number to at least 1 000 000 Partition numbers to at least 1 000 000

Resources Resource 1: Four- and five-digit numbers cards Resource 2: Six- and seven-digit numbers cards Resource 3: Numbers to 3 000 000 in words Resource 4: Symbol cards pencil and paper (per pupil)

Success criteria A. Read numbers to at least 1 000 000 in numerals B. Write numbers to at least 1 000 000 in numerals C. Read numbers to at least 1 000 000 in words D. Write numbers to at least 1 000 000 in words E. Compare two numbers to at least 1 000 000

NOTE • Prior to the Assessment Task, cut out the number cards from Resources 1 and 2 and arrange them into four separate piles: four-digit numbers, five-digit numbers, six-digit numbers and seven-digit numbers.

Assessment Task Success criterion A: Read numbers to at least 1 000 000 in numerals What to do

What to say

What to look out for

Place one of the number cards from Resources 1 and 2 on the table in front of the pupil.

What is this number?

Can the pupil read four-, five-, six- and seven-digit numbers in numerals?

Repeat several times, placing different four-, five-, six- and seven-digit number cards on the table in front of the pupil. Lay out all the remaining number Point to the number cards that have not previously been [8164/635 078 …]. read face up on the table.

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Success criterion B: Write numbers to at least 1 000 000 in numerals What to do

What to say

What to look out for

Provide the pupil with paper and pencil.

Write down the number 56 936 as a [number/numeral/ figure].

Can the pupil write four-, five-, six- and seven-digit numbers in numerals?

Tell me a different five-digit number. Write this number as a [number/numeral/figure]. Repeat until the pupil has sufficiently demonstrated their ability to write four-, five-, six- and seven-digit numbers in numerals.

Success criterion C: Read numbers to at least 1 000 000 in words What to do

What to say

What to look out for

Display Resource 3 and point to a number.

What is this number?

Can the pupil read four-, five-, sixand seven-digit numbers in words?

Point to the number 1 378 263. Ensure the pupil has paper and pencil and point to another number on Resource 3.

What is this number? Write this number as a [number/ numeral/figure].

Can the pupil read four-, five-, sixand seven-digit numbers in words and write the corresponding number as a numeral?

Repeat until the pupil has sufficiently demonstrated their ability to read four-, five-, six- and seven-digit numbers in words.

Success criterion D: Write numbers to at least 1 000 000 in words What to do

What to say

What to look out for

Ensure the pupil has paper and pencil.

Write down the number 856 421 as a word.

Can the pupil write four-, five-, sixand seven-digit numbers in words?

Tell me a different six-digit number. Write this number as a word. On the sheet of paper write a four-, five-, sixor seven-digit number in numerals, e.g. 639 374.

What is this number? Write this number as a word.

Can the pupil read four-, five-, sixand seven-digit numbers in numerals and write the corresponding number as a word?

Repeat until the pupil has sufficiently demonstrated their ability to write four-, five-, six- and seven-digit numbers in words.

Success criterion E: Compare two numbers to at least 1 000 000 What to do

What to say

What to look out for

Lay two number cards from Resources 1 and 2 face up in front of the pupil.

Point to the larger number.

Can the pupil identify the larger number?

Repeat for other pairs and combinations of four-, five-, six- and seven-digit numbers, asking the pupil to identify the number that is smaller/less/bigger/more. Include pairs of numbers with: – different numbers of digits, e.g. 18 476 and 997 257 – different thousands, tens of thousands, hundreds of thousands or millions digits, e.g. 3675 and 5746; 62 543 and 18 476; 814 882 and 628 794; 1 690 296 and 2 105 348 – the same thousands, tens of thousands, hundreds of thousands and/or millions digits, e.g. 3803 and 3675; 74 127 and 74 851; 635 078 and 635 146; 2 143 682 and 2 147 456.

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Success criterion F: Use the < and > symbols to compare two numbers to at least 1 000 000 What to do

What to say

What to look out for

Provide the pupil with a ‘greater than/less than’ card from Resource 4. Ensure that the pupil realises that the ‘greater than/less than’ card can be used to represent either symbol by turning the card upside down.

Look at the two number cards in front of you. I want you to place your symbol card between these two cards so that it makes a correct statement.

Can the pupil correctly identify the greater than and less than symbols? Can the pupil correctly use the greater than and less than symbols to compare two numbers?

Choose two number cards from Resources 1 and 2 and place them in front of the pupil, leaving a space between the two cards, e.g. 635 146 813 663. When the pupil has done this, ask them to say their statement.

Can you read this statement to me?

Repeat above several times. Choose a number card and a symbol card and place them in front of the pupil, e.g. 1 702 874 < .

Look at the two cards in front of you. Choose a number card from the table and put it after the symbol card so that the statement is correct.

Can the pupil correctly identify the greater than and less than symbols? Can the pupil identify a number that correctly completes the statement?

Randomly spread a selection of the other number cards face up on the table. When the pupil has done this, ask them to say their statement.

Read me your statement.

Remove the number card the pupil has used to complete the statement and place it with the other number cards.

Can you choose another number card so that the statement is still correct?

Repeat above several times, alternating the symbol card between < and > .

Success criterion G: Order numbers to at least 1 000 000 What to do

What to say

What to look out for

Lay five number cards from Resources 1 and 2 face up in front of the pupil.

Look at the numbers in front of you. I want you to place these cards in order, smallest to largest.

Can the pupil order the numbers?

Give the pupil another number card.

Look at the cards you have just put in order. Where would you put this number so that the order is still correct?

Referring to the set of six ordered number cards, point to two consecutive numbers.

Tell me a number that lies between these two numbers.

Can the pupil identify a number that lies between two other numbers?

Repeat until the pupil has sufficiently demonstrated their ability to order numbers to at least 1 000 000. Include sets of cards with: – different numbers of digits, e.g. 74 127, 997 257, 4039, 1 690 296 and 62 543 – the same number of digits, e.g. 62 543, 74 127, 43 682, 74 851 and 16 038.

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Success criterion H: Know what each digit represents in a number to at least 1 000 000 What to do

What to say

What to look out for

Place one of the number cards from Resources 1 and 2 on the table in front of the pupil and point to a specific digit in the number.

What is the value of this digit?

Can the pupil identify the value of any digit in a four-, five-, six- and seven-digit number?

Place another four-, five-, six- or seven-digit number card on the table in front of the pupil.

Point to the digit that shows how many thousands are in the number.

Can the pupil identify the ones, tens, hundreds and thousands digit in a four-digit number?

Repeat, referring to other four-, five-, six- and seven-digit numbers, asking the pupil to identify the ones, tens, hundreds, thousands, tens of thousands, hundreds of thousands or millions digit in the number.

Point to the digit that shows how many [ones/tens/hundreds/ thousands/tens of thousands/ hundreds of thousands/millions] are in the number.

Can the pupil identify the ones, tens, hundreds, thousands and tens of thousands digit in a five-digit number?

Repeat several times, pointing to different place values in other four-, five-, six- and seven-digit numbers.

Can the pupil identify the ones, tens, hundreds, thousands, tens of thousands and hundreds of thousands digit in a six-digit number? Can the pupil identify the ones, tens, hundreds, thousands, tens of thousands, hundreds of thousands or millions digit in a seven-digit number?

Randomly spread a selection of four-, five-, six- or seven-digit number cards face up on the table.

Point to a number that has five tens. Point to a number that has eight hundreds. Point to a number that has two thousands.

Can the pupil identify a specific four-, five-, six- or seven-digit number based on the value of one (or more) of its digits?

Point to a number that has three ones and eight thousands. Point to a number that has three tens of thousands and eight ones. Point to a number that has six hundreds of thousands, four ones and seven hundreds. Repeat above for other four-, five-, six- and seven-digit numbers until the pupil has sufficiently demonstrated that they know what each digit represents in a number to at least 1 000 000.

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Success criterion I: Partition numbers to at least 1 000 000 What to do

What to say

What to look out for

On the sheet of paper write a four-, five-, six- or seven-digit number in expanded notation, e.g. 70 000 + 6000 + 800 + 70 + 4.

What is this number? Write it for me as a [number/numeral/figure].

Can the pupil identify a four-, five-, six- or seven-digit number when written in expanded notation?

Place one of the number cards from Resources 1 and 2 on the table in front of the pupil, e.g. 813 663.

Look at this number. Write it for me in the same way that I did, showing how many [hundreds of thousands, tens of thousands, thousands, hundreds, tens and ones] there are in the number.

Can the pupil partition a four-digit number into multiples of 1000, 100, 10 and 1? Can the pupil partition a five-digit number into multiples of 10 000, 1000, 100, 10 and 1? Can the pupil partition a six-digit number into multiples of 100 000, 10 000, 1000, 100, 10 and 1? Can the pupil partition a seven-digit number into multiples of 1 000 000, 100 000, 10 000, 1000, 100, 10 and 1?

Repeat for other four-, five-, sixand seven-digit numbers. Refer back to the number you had previously partitioned into multiples of 10 000, 1000, 100, 10 and 1, and on the sheet of paper write: 76 874 = 70 000 + 5000 + 1800 + 70 + 4.

I can partition this number a different way.

Refer back to the number you asked the pupil to partition.

I want you to partition this number in a different way. Can you partition this number in yet another way?

Can the pupil partition four-, five-, six- and seven-digit numbers in at least two different ways?

Repeat until the pupil has sufficiently demonstrated their ability to partition four-, five-, six- and seven-digit numbers.

What to do for those pupils working below or above expectations Refer to the ‘Tracking back and forward through the Mathematics National Curriculum attainment targets’ charts on pages 367-376.

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BUSY ANT MATHS | Assessment Guide 5 | Assessment Task Record Domain: National Curriculum attainment target (NC AT): Teacher:

Class:

Date: Name

Success criteria

A

B

C

D

E

F

G

H

I

Other observations Level of mastery of NC AT* NYA

A

A&E NYA

A

A&E NYA

A

A&E NYA

A

A&E

Future action

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Level of mastery key: NYA – Not yet achieved | A – Achieved | A&E – Achieved and exceeded

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Name:

Year 5 Assessment Exercise 1

Date:

Number and place value 1

a) 465 736 = 400 000 +

+ 5000 + 700 + 30 +

b) 1 302 581 =

+ 300 000 + 2000 +

+ 80 + 1

+ 40 000 +

c) 947 562 =

+ 500 +

+2

1 3 marks

2

a) 800 000 + 50 000 + 1000 + 600 + 90 + 2 = b) 9000 + 1 + 300 + 80 + 30 000 + 600 000 = c) 20 000 + 800 + 1 000 000 + 30 + 500 000 + 1000 =

2 3 marks

3

Write the value of the bold digit in each of these numbers. a) 278 301

b) 726 982

c) 647 361

d) 1 387 465

3 4 marks

4

Write the value of the 6 in each of these numbers. a) 574 265

b) 1 763 182

c) 628 317

4 3 marks

5

Use the < or > sign to make each statement correct. a) 465 173

465 137

c) 1 039 471

b) 826 316

1 039 570

826 406

d) 1 864 363

1 846 363

5 4 marks

6

Order the numbers, smallest to largest. a) 475 289, 475 283, 475 298, 475 238, 475 279, 475 287 ,

,

,

,

,

b) 548 154, 548 182, 548 281, 548 812, 548 128, 548 218 ,

,

,

,

,

c) 1 736 281, 1 726 281, 1 736 821, 1 736 182, 1 736 218, 1 735 281 ,

,

,

,

,

6 3 marks

â—? read, write, order and compare numbers to at least

1 000 000 and determine the value of each digit

Total:

out of 20

Mastery: NYA

A

A&E

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Name:

Year 5 Assessment Exercise 2

Date:

Number and place value Fill in the missing numbers from each number sequence.

1

17 956, 17 966, 17 976, 17 986, ,

,

,

,

,

1 1 mark

2

2249,

, 2229, 2219, ,

,

, 2189,

,

2 1 mark

3

139 615, 139 715,

, 139 915, ,

140 215,

,

,

,

3 1 mark

4

84 301,

, 84 101, ,

,

,

, 83 801,

, 83 401

4 1 mark

5

736 208,

, 756 208,

796 208,

,

, 776 208,

,

,

5 1 mark

6

, 50 609, 49 609,

,

,

,

, 44 609, 43 609,

6 1 mark

7

786 712, 886 712,

,

,

, 1 286 712,

, 1 486 712

7 1 mark

8

1 304 285, 1 204 285,

,

,

, 804 285,

704 285,

8 1 mark

9

, 6 687 698, ,

, 4 687 698, 3 687 698, , 687 698

9 1 mark

10

445 687,

, 443 687, ,

,

,

, 440 687,

, 436 687

10 1 mark

â—? count forwards or backwards in steps of powers of 10 for

any given number up to 1 000 000

Total:

out of 10

Mastery: NYA

A

A&E

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Name:

Year 5 Assessment Exercise 3

Date:

Number and place value °C

10

°C

15

°C

10

9

°C

10

°C

5

8

7

10

7

15

6

6

0

5

6 5

4

5

4

10

3

4

2

–5

2

1

3

0

0

2

0

5

–1

1

–2

0

–2

–3

–5

0

–4

–1

–10

–4

–5

–2

–6

–10

–3

–6

–5

–7 –8

–4

–15

–8

–9

–5

1

20

8

8

A

°C

9

–15

–10

B

C

–10

D

–10

E

–20

F

Look at thermometers A to F above. What is the temperature shown on each thermometer? A:

B:

C:

D:

E:

F:

1 6 marks

2

Look at thermometers A to F above. a) Which thermometer shows the coldest temperature? b) Which thermometer shows the warmest temperature? c) What is the difference in temperature between A and B?

d) What is the difference in temperature between D and E? 2 4 marks

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Name:

Year 5 Assessment Exercise 3

Date:

Number and place value 3

Look at thermometers A to F. a) The temperature reading on Thermometer E increases by 5°C. What is the new temperature?

b) The temperature reading on Thermometer A decreases by 2°C. What is the new temperature?

c) The temperature reading on Thermometer D decreases by 8°C. What is the new temperature?

d) The temperature reading on Thermometer C increases by 7°C. What is the new temperature? 3 4 marks

4

Fill in the missing numbers from each number sequence. a) −5, −4, b) −12, c)

, −2, ,

, −11,

, , −3,

, 1, ,

, −9, −8,

, 3, 4 , 6, 9, 12

,

, −5, −4, −3

4 3 marks

5

a) Count back 10 steps of 1, starting from 4. What number do you reach? b) Count back 5 steps of 4, starting from 10. What number do you reach? c) Count on 8 steps of 1, starting from −3. What number do you reach?

5 3 marks

● interpret negative numbers in context, count forwards

and backwards with positive and negative whole numbers, Total: including through zero | Page 2 of 2

out of 20

Mastery: NYA

A

A&E

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