Busy Ant Maths Assessment Guide 6 by Collins

Assessment Guide 6

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, subtraction, multiplication and division Number – Fractions (including decimals and percentages) Ratio and proportion Algebra Measurement Geometry – Properties of shapes Geometry – Position and direction Statistics Assessment Task Record

24 41 67 102 110 127 137 150 155 163

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

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164 170 184 200 204 214 225 235 239 244

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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 â&#x20AC;&#x201C; Answers and marking commentary

250 256 262 266 272 279 283 290 294 301 306 311 317

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

322 324 326 328 330 332 334 336 338 340 342 344

Record-keeping formats Year 6 Whole-class National Curriculum attainment targets

346

Year 6 Whole-class Domains (View 1) Year 6 Whole-class Domains (View 2) Year 6 Individual Pupil National Curriculum attainment targets and Domains

355 356 357

Resources to accompany the Assessment Tasks

360

Tracking back and forward through the Mathematics National Curriculum attainment targets â&#x20AC;&#x201C; Year 6

426

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Introduction

Introduction Assessment Tasks and Exercises

Number – Fractions (including decimals and percentages)

Number – Addition, subtraction, multiplication and division

Number – Number and place value

Domain National Curriculum attainment target

Assessment Task(s)/Exercise(s)

Read, write, order and compare numbers up to 10 000 000 and determine the value of each digit

Round any whole number to a required degree of accuracy

Use negative numbers in context, and calculate intervals across zero

Solve number and practical problems that involve all of the above

Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication

Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context

Divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context

Perform mental calculations, including with mixed operations and large numbers

Identify common factors, common multiples and prime numbers

Use their knowledge of the order of operations to carry out calculations involving the four operations

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

Tasks: 11 and 12 Exercise: 11

Solve problems involving addition, subtraction, multiplication and division

Tasks: 11 and 12 Exercise: 12

Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

Use common factors to simplify fractions; use common multiples to express fractions in the same denomination

Compare and order fractions, including fractions > 1

Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

Multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 14 × 12 = 18]

Divide proper fractions by whole numbers [for example, 13 ÷ 2 = 16]

Associate a fraction with division and calculate decimal fraction equivalents [for example, 0·375] for a simple fraction [for example, 38]

Identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places

Multiply one-digit numbers with up to two decimal places by whole numbers

Use written division methods in cases where the answer has up to two decimal places

Solve problems which require answers to be rounded to speciﬁed degrees of accuracy

Tasks: 23 and 34 Exercise: 23

Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts

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Introduction

Measurement

Algebra

Ratio and proportion

Domain National Curriculum attainment target

Assessment Task(s)/Exercise(s)

Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts

25 and 28

Solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison

Solve problems involving similar shapes where the scale factor is known or can be found

Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

25 and 28

Use simple formulae

Generate and describe linear number sequences

Express missing number problems algebraically

Find pairs of numbers that satisfy an equation with two unknowns

Enumerate possibilities of combinations of two variables

Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate

Tasks: 23 and 34 Exercise: 34

Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places

Convert between miles and kilometres

Recognise that shapes with the same areas can have different perimeters and vice versa

Recognise when it is possible to use formulae for area [and volume] of shapes

38 and 39

Calculate the area of parallelograms and triangles Recognise when it is possible to use formulae for [area and] volume of shapes

38 and 40

Statistics

Geometry – Position and direction

Geometry – Properties of shapes

Calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm3) and cubic metres (m3), and extending to other units [for example, mm3 and km3] Draw 2-D shapes using given dimensions and angles

Recognise, describe and build simple 3-D shapes, including making nets

Compare and classify geometric shapes based on their properties and sizes and ﬁnd unknown 43 angles in any triangles, quadrilaterals, and regular polygons Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius

Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and ﬁnd missing angles

Describe positions on the full coordinate grid (all four quadrants)

Draw and translate simple shapes on the coordinate plane, and reﬂect them in the axes

Interpret and construct pie charts and line graphs and use these to solve problems

Calculate and interpret the mean as an average

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Assessment Task 1

Number – Number and place value National Curriculum attainment target • Read, write, order and compare numbers up to 10 000 000 and determine the value of each digit

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

Success criteria A. Read numbers to 10 000 000 in numerals B. Write numbers to 10 000 000 in numerals

C. D. E. F. G. H. I.

Read numbers to 10 000 000 in words Write numbers to 10 000 000 in words Compare two numbers to 10 000 000 Use the < and > symbols to compare two numbers to 10 000 000 Order numbers to 10 000 000 Know what each digit represents in a number to 10 000 000 Partition numbers to 10 000 000

Resources Resource 1: Four- and ﬁve-digit numbers cards Resource 2: Six- and seven-digit number cards Resource 3: Numbers to 10 000 000 in words Resource 4: Symbol cards pencil and paper (per pupil)

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 10 000 000 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 cards that have not been read face up on the table.

Point to the number [640 519/76 943/…].

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Success criterion B: Write numbers to 10 000 000 in numerals What to do

What to say

What to look out for

Provide the pupil with paper and pencil.

Write down the number 409 726 as a [number/numeral/ ﬁgure].

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

Tell me a different six-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 10 000 000 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?

Ensure the pupil has paper and pencil and point to another number on Resource 3.

What is this number?

Point to the number 642 165.

Write this number as a [number/ numeral/ﬁgure].

Can the pupil read four-, ﬁve-, six- and 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 10 000 000 in words What to do

What to say

What to look out for

Ensure the pupil has paper and pencil.

Write down the number 2 847 239 as a word.

Can the pupil write seven-digit numbers in words?

Tell me a different seven-digit number. Write this number as a word. On the sheet of paper write a four-, ﬁve-, six- or seven-digit number in numerals, e.g. 573 094.

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

Can the pupil read four-, ﬁve-, six- and 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 10 000 000 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/larger/more. Include pairs of numbers with: • different numbers of digits, e.g. 316 284 and 76 943 • different thousands, tens of thousands, hundreds of thousands or millions digits, e.g. 4195 and 5073; 83 056 and 25 829; 316 284 and 409 726; 3 874 235 and 8 627 941 • the same thousands, tens of thousands, hundreds of thousands and/or millions digits, e.g. 7816 and 7382; 52 364 and 52 671; 640 519 and 638 495; 6 203 817 and 6 281 394.

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Success criterion F: Use the < and > symbols to compare two numbers to 10 000 000 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. 83 056 76 943 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. 6 203 817 > .

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

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?

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

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

Success criterion G: Order numbers to 10 000 000 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 Can the pupil identify a number these two numbers. that lies between two other numbers?

Repeat until the pupil has sufﬁciently demonstrated their ability to order numbers to 10 000 000. Include sets of cards with: different numbers of digits, e.g. 574 302, 8 627 941, 851 637, 3 874 235 and 640 519 the same number of digits, e.g. 25 829, 52 671, 83 056, 52 364 and 14 738.

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Success criterion H: Know what each digit represents in a number to 10 000 000 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 or 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?

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 or tens of thousands digit in a ﬁve-digit number? Can the pupil identify the ones, tens, hundreds, thousands, tens of thousands or 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 four tens. Point to a number that has six hundreds.

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 five thousands. Point to a number that has eight tens and six thousands. Point to a number that has four tens of thousands and nine ones. Point to a number that has six hundreds of thousands, nine tens and eight thousands. 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 10 000 000.

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Success criterion I: Partition numbers to 10 000 000 What to do

What to say

What is this number? Write it for On the sheet of paper write a me as a [number/numeral/figure]. four-, five-, six- or seven-digit number in expanded notation, e.g. 80 000 + 3000 + 900 + 60 + 2. Place one of the number cards from Resources 1 and 2 on the table in front of the pupil, e.g. 574 302. Repeat for other four-, five-, sixor seven-digit numbers.

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.

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: 83 962 = 80 000 + 3000 + 800 + 160 + 2.

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.

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

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 426–442.

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BUSY ANT MATHS | Assessment Guide 6 | Assessment Task Record Domain: National Curriculum attainment target (NC AT): Teacher:

Class:

Date: Name

Success criteria

Other observations Level of mastery of NC AT* NYA

A&E NYA

A&E

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

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Name:

Year 6 Assessment Exercise 1

Date:

Number and place value 1

a) 846 523 = 800 000 +

+ 6000 + 500 + + 500 000 + 60 000 +

b) 4 563 291 = c) 9 270 346 = 9 000 000 +

+3 + 200 + 90 +

+ 70 000 +

+ 40 +

1 3 marks

a) 7 000 000 + 300 000 + 20 000 + 6000 + 50 + 4 = b) 3000 + 5 + 200 + 10 + 60 000 + 800 000 = c) 10 000 + 400 + 6 000 000 + 20 + 300 000 + 8000 =

2 3 marks

Write the value of the bold digit in each of these numbers. a) 475 298

b) 7 387 549

c) 3 857 401

d) 2 539 548

3 4 marks

Write the value of the 3 in each of these numbers. a) 843 297

b) 6 872 382

c) 5 398 210

4 3 marks

Use the < or > sign to make each statement correct. a) 286 417

284 617

c) 8 361 863

8 368 163

b) 3 476 190

3 746 190

d) 3 381 292

3 381 282

5 4 marks

Order the numbers, smallest to largest. a) 5 648 371, 5 648 731, 5 684 371, 5 648 317, 5 684 731, 5 648 137 ,

b) 4 076 284, 4 506 284, 4 570 284, 4 576 204, 4 576 280, 4 570 264 ,

c) 9 473 197, 9 437 197, 9 743 197, 9 473 179, 9 473 917, 9 471 397 ,

6 3 marks

â&#x2014;? read, write, order and compare numbers up to

10 000 000 and determine the value of each digit

Total:

out of 20

Mastery: NYA

A&E

ÂŠ HarperCollinsPublishers Ltd. 2015

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Name:

Year 6 Assessment Exercise 2

Date:

Number and place value 1

Round each number to the nearest 10. a) 3756

c) 5 287 105 e) 23 763

g) 7 182 477 i) 635 184

b) 54 879

d) 321

f) 198 478

h) 8262

j) 475

1 10 marks

Round each number to the nearest 100. a) 461 381

b) 7333

c) 718

d) 1 209 492

e) 2 491 309 g) 3251

f) 361 327

h) 376

2 8 marks

Round each number to the nearest 1000. a) 183 180

b) 165 483

c) 402 874

d) 7599

e) 3716

f) 1 394 387

3 6 marks

Round each number to the nearest 10 000. a) 3 487 198 c) 36 872

b) 863 928

d) 1 834 291

4 4 marks

Round each number to the nearest 100 000. a) 2 767 198

b) 328 173

5 2 marks

â&#x2014;? round any whole number to a required

degree of accuracy

Total:

out of 30

Mastery: NYA

A&E

ÂŠ HarperCollinsPublishers Ltd. 2015

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Name:

Year 6 Assessment Exercise 3

Date:

Number and place value –10

–9

–8

–7

–6

–5

–4

–3

–2

–1

10 °C

–5

–4

–3

–2

–1

10 °C

–20

–15

–10

–5

5 °C

–10

–8

–6

–4

–2

10 °C

–15

–10

–5

15 °C

–20

–15

–10

–5

20 °C

Look at thermometers A to F above. a) What is the difference in temperature between A and B? b) What is the difference in temperature between C and F? c) What is the difference in temperature between D and B? d) What is the difference in temperature between E and F?

1 4 marks

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Name:

Year 6 Assessment Exercise 3

Date:

Number and place value 2

Look at thermometers A to F. a) The temperature reading on Thermometer D increases by 9°C. What is the new temperature on Thermometer D? b) The temperature reading on Thermometer A decreases by 3°C. What is the new temperature on Thermometer A? c) The temperature reading on Thermometer F decreases by 7°C. What is the new temperature on Thermometer F? d) The temperature reading on Thermometer C increases by 8°C. What is the new temperature on Thermometer C?

2 4 marks

Fill in the missing numbers in each number sequence. a) −12, b)

, −8, , −15,

c) −37,

, −25,

, −4, ,

, −3, , −13,

, 0, , 5, 9 , −1,

3 3 marks

a) Start at 3. Count back 5 steps of 1. What number do you reach? b) Start at 7. Count back 4 steps of 3. What number do you reach? c) Start at −12. Count back 7 steps of 2. What number do you reach?

4 3 marks

a) −7 + 4 =

b) −2 + 6 =

c) 6 – 14 =

d) 3 – 5 + 2 – 9 =

e) 4 – 12 + 8 – 2 =

f) 4 – 7 – 2 + 3 =

5 6 marks

● use negative numbers in context, and calculate

intervals across zero | Page 2 of 2

Total:

out of 20

Mastery: NYA

A&E

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Name:

Year 6 Assessment Exercise 4

Date:

Number and place value 1

The table below shows the tallest mountain on each of the seven continents. Round the height of each mountain to the nearest 1000 m. Mountain

Continent

Height (m)

Mount Everest

Asia

8848

Aconcagua

South America

6961

Mount McKinley

North America

6194

Mount Kilimanjaro

Africa

5895

Mount Elbrus

Europe

5642

Mount Vinson

Antarctica

4892

Mount Kosciuszko

Australia

2228

Rounded to the nearest 1000 m

1 7 marks

The table below shows the estimated population of eight cities (2015). Round the population of each city to the nearest million. City

Country

Population

Shanghai

China

24 150 000

Beijing

China

21 516 000

Mumbai

India

12 655 220

Jakarta

Indonesia

9 988 329

Tokyo

Japan

9 071 577

Mexico City

Mexico

8 874 724

London

8 416 535

Los Angeles

USA

3 884 307

Rounded to the nearest million

2 8 marks

Page 1 of 2 ÂŠ HarperCollinsPublishers Ltd. 2015

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