KS2-KS3 Maths Transition: Build confidence and secure skills from Year 7 by Collins

Introduction – KS2–KS3 Maths Transition

Curriculum coverage table Domain

KS2 National Curriculum Attainment Target Year 5

Prerequisites for KS3 National Curriculum Understand and use place value for integers of any size Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value [KS3 Working mathematically] Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value [KS3 Working mathematically]

Y5 unit number

Number – number and place value KS3 Number KS3 Working mathematically

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

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

Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers

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

Round numbers and measures to an appropriate degree of accuracy

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

N/A

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

Number – addition and subtraction KS3 Number

Solve number problems and Select and use appropriate practical problems that involve all calculation strategies to solve of the above increasingly complex problems [KS3 Working mathematically]

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

Select and use appropriate calculation strategies to solve increasingly complex problems [KS3 Working mathematically]

Add and subtract numbers mentally with increasingly large numbers

Select and use appropriate calculation strategies to solve increasingly complex problems [KS3 Working mathematically]

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

Use approximation through rounding to estimate answers and calculate possible resulting errors

KS3 Maths Transition © HarperCollinsPublishers 2022

Introduction – KS2–KS3 Maths Transition Domain

Number – multiplication and division KS3 Number

KS2 National Curriculum Attainment Target Year 5

Prerequisites for KS3 National Curriculum

Y5 unit number

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

Select and use appropriate calculation strategies to solve increasingly complex problems [KS3 Working mathematically]

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

Use the concepts and 11 vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property Use the concepts and 12 vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property Use the concepts and 13 vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property

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

Establish whether a number up to 100 is prime and recall prime numbers up to 19

Multiply and divide numbers mentally, drawing upon known facts

Select and use appropriate calculation strategies to solve increasingly complex problems [KS3 Working mathematically]

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

Select and use appropriate calculation strategies to solve increasingly complex problems [KS3 Working mathematically]

Multiply numbers up to four digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers

Select and use appropriate calculation strategies to solve increasingly complex problems [KS3 Working mathematically]

KS3 Maths Transition © HarperCollinsPublishers 2022

Introduction – KS2–KS3 Maths Transition Domain

Number – fractions (including decimals and percentages) KS3 Number

KS2 National Curriculum Attainment Target Year 5

Prerequisites for KS3 National Curriculum

Y5 unit number

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

Select and use appropriate calculation strategies to solve increasingly complex problems [KS3 Working mathematically]

Recognise and use square numbers and cube numbers, and the notation for squared (2) and cubed (3)

Use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations

Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes

Select and use appropriate calculation strategies to solve increasingly complex problems [KS3 Working mathematically]

Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign

Select and use appropriate calculation strategies to solve increasingly complex problems Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

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

Interpret fractions and percentages as operators

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

Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction

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

Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real number

Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

KS3 Maths Transition © HarperCollinsPublishers 2022

Introduction – KS2–KS3 Maths Transition Domain

KS2 National Curriculum Attainment Target Year 5

Prerequisites for KS3 National Curriculum

Y5 unit number

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

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers

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

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers

Read and write decimal numbers as fractions

Work interchangeably with terminating decimals and their corresponding fractions

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

Understand and use place value for decimals, measures and integers of any size

Round decimals with two decimal Round numbers and measures places to the nearest whole to an appropriate degree of number and to one decimal place accuracy [for example, to a number of decimal places or significant figures]

Read, write, order and compare Understand and use place numbers with up to three decimal value for decimals, measures places and integers of any size

Solve problems involving number Use the four operations, up to three decimal places including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

Define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%

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 fraction

KS3 Maths Transition © HarperCollinsPublishers 2022

Introduction – KS2–KS3 Maths Transition Domain

Measurement KS3 [Ratio, proportion and rates of change] [Geometry and measures]

KS2 National Curriculum Attainment Target Year 5

Prerequisites for KS3 National Curriculum

Y5 unit number

Solve problems which require knowing percentage and decimal equivalents of , , , ,

and those fractions with a denominator of a multiple of 10 or 25

Work interchangeably with terminating decimals and their corresponding fractions Select and use appropriate calculation strategies to solve increasingly complex problems

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

Use standard units of mass, length, time, money and other measures, including with decimal quantities [Ratio, proportion and rates of change]

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

Change freely between related standard units Use standard units of mass, length, time, money and other measures, including with decimal quantities [Ratio, proportion and rates of change]

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

Calculate and solve problems 36 involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes

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

Calculate and solve problems 37 involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes

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

Derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)

Solve problems involving converting between units of time

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

KS3 Maths Transition © HarperCollinsPublishers 2022

Introduction – KS2–KS3 Maths Transition Domain

KS2 National Curriculum Attainment Target Year 5

Prerequisites for KS3 National Curriculum

Y5 unit number

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

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D

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

Draw and measure line segments and angles in geometric figures, including interpreting scale drawings

Draw given angles, and measure them in degrees

Draw and measure line segments and angles in geometric figures, including interpreting scale drawings

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

Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles

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

Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures

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

Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures

Geometry – position and direction KS3 Geometry and measures]

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

Identify properties of, and describe the results of translations, rotations and reflections applied to given figures

Statistics

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

Construct and interpret 48 appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data

Geometry – Identify 3-D shapes, including properties of cubes and other cuboids, from 2shapes D representations KS3 Geometry and measures]

KS3 Maths Transition © HarperCollinsPublishers 2022

Introduction – KS2–KS3 Maths Transition Domain

KS2 National Curriculum Attainment Target Year 5

Prerequisites for KS3 National Curriculum

Y5 unit number

Complete, read and interpret information in tables, including timetables

Construct and interpret 49 appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data

Domain

KS2 National Curriculum Attainment Target Year 6

Prerequisites for KS3 National Curriculum

Y6 unit number

Number – number and place value

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

Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value Understand and use place value for integers of any size

Round any whole number to a required degree of accuracy

Round numbers and measures to an appropriate degree of accuracy

Use negative numbers in context, and calculate intervals across 0

Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers

Solve number and practical problems involving number and place value

Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multistep problems

Perform mental calculations, including with mixed operations and large numbers

Select and use appropriate calculation strategies to solve increasingly complex problems

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

Use approximation through 6 rounding to estimate answers and calculate possible resulting errors

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

Select and use appropriate calculation strategies to solve increasingly complex problems

Divide numbers up to four digits by Select and use appropriate a two-digit whole number using the calculation strategies to solve formal written method of long increasingly complex problems division

KS3 Number

Number – addition, subtraction, multiplication and division KS3 Number

KS3 Maths Transition © HarperCollinsPublishers 2022

Introduction – KS2–KS3 Maths Transition Domain

KS2 National Curriculum Attainment Target Year 6

Prerequisites for KS3 National Curriculum

Divide numbers up to four digits by Select and use appropriate calculation strategies to solve a two-digit number using the formal written method of short increasingly complex problems division where appropriate, interpreting remainders according to the context

Number – Fractions (including decimals and percentages)

Y6 unit number 9

Identify common factors, common multiples and prime numbers

Use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property

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

Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals

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

Select and use appropriate calculation strategies to solve increasingly complex problems

Solve problems involving addition, subtraction, multiplication and division

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

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

Compare and order fractions, including fractions > 1

Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real number

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

Use the four operations, including 16 formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers

KS3 Number

KS3 Maths Transition © HarperCollinsPublishers 2022

Introduction – KS2–KS3 Maths Transition Domain

KS2 National Curriculum Attainment Target Year 6

Prerequisites for KS3 National Curriculum

Multiply simple pairs of proper fractions, writing the answer in its simplest form

Use the four operations, including 17 formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers,

Divide proper fractions by whole numbers

Use the four operations, including 18 formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers,

Identify the value of each digit in Understand and use place numbers given to three decimal value for decimals, measures places and multiply and divide and integers of any size numbers by 10, 100 and 1000 giving answers up to three decimal places

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers,

Use written division methods in Use the four operations, cases where the answer has up to including formal written two decimal places methods, applied to integers, decimals, proper and improper fractions, and mixed numbers,

Associate a fraction with division and calculate decimal fraction equivalents for a simple fraction

Work interchangeably with terminating decimals and their corresponding fractions Interpret fractions and percentages as operators

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

Round numbers and measures to an appropriate degree of accuracy

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

Work interchangeably with terminating decimals and their corresponding fractions

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

Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction

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

Ratio and proportion KS3 Ratio, proportion

Y6 unit number

KS3 Maths Transition © HarperCollinsPublishers 2022

Introduction – KS2–KS3 Maths Transition Domain

KS2 National Curriculum Attainment Target Year 6

and rates of change

Solve problems involving the Interpret fractions and calculation of percentages and the percentages as operators use of percentages for comparison

Algebra

Prerequisites for KS3 National Curriculum

Y6 unit number 26

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

Use scale factors, scale diagrams 27 and maps

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

Use ratio notation, including reduction to simplest form Divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio

Express missing number problems Use and interpret algebraic algebraically notation

Find pairs of numbers that satisfy an equation with two unknowns

Understand and use the concepts 30 and vocabulary of expressions, equations, inequalities, terms and factors

Enumerate possibilities of combinations of two variables

Substitute numerical values into formulae and expressions, including scientific formulae

Generate and describe linear number sequences

Generate terms of a sequence 32 from either a term-to-term or a position-to-term rule Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors

Use simple formulae

Substitute numerical values into formulae and expressions, including scientific formulae

Use standard units of mass, length, time, money and other measures, including with decimal quantities [KS3 Ratio, proportion and rates of change]

Measurement Read, write and convert between standard units of length, mass, KS3 volume and time, using up to three Geometry decimal places and

KS3 Maths Transition © HarperCollinsPublishers 2022

Introduction – KS2–KS3 Maths Transition Domain

KS2 National Curriculum Attainment Target Year 6

Prerequisites for KS3 National Curriculum

Y6 unit number

measures

Convert between miles and kilometres

Change freely between related standard units Use standard units of mass, length, time, money and other measures, including with decimal quantities [KS3 Ratio, proportion and rates of change]

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

Calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes

Solve problems involving the conversion of units of measure

Use standard units of mass, length, time, money and other measures, including with decimal quantities

Calculate the area of parallelograms and triangles

Calculate, estimate and compare the volume of cubes and cuboids

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

Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons

Describe, sketch and draw using 41 conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures

KS3 Ratio, proportion and rates of change

Geometry – properties of shapes KS3 Geometry and measures

KS3 Maths Transition © HarperCollinsPublishers 2022

Introduction – KS2–KS3 Maths Transition Domain

KS2 National Curriculum Attainment Target Year 6

Prerequisites for KS3 National Curriculum

Y6 unit number

Draw 2-D shapes using given dimensions and angles

Derive and use the standard ruler and compass constructions

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

Use the properties of faces, 43 surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D

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

Apply the properties of angles at 44 a point, angles at a point on a straight line, vertically opposite angles Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons

Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius

Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures

Geometry – position and direction KS3 Geometry and measures

Describe positions on the full coordinate grid

Work with coordinates in all four quadrants

Draw and translate simple shapes Identify properties of, and on the coordinate plane and reflect describe the results of them in the axes translations, rotations and reflections applied to given figures

Statistics

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

Construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data

Calculate and interpret the mean as an average

Describe, interpret and compare 49 observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

KS3 Maths Transition © HarperCollinsPublishers 2022

Diagnostic test 1

Diagnostic test 1 Calculations 1. 8546 – 1999 = 2. 0∙8 × 7 = 3. 7 2 4 9 × 26 4. 1344 ÷ 32

5. 18 7830

6. 80 – 56 ÷ 8 =

7 3 = 10 20

2 7 = 8. 2 + 3 12 1 3 9. 1 - = 3 4

10.

1 1 ´ = 3 5

11.

5 ¸5 = 6

KS2–KS3 Maths Transition © HarperCollinsPublishers 2022

Diagnostic test 1

12. 3∙16 × 4 =

13. 781 ÷ 4 =

14. 20% of 2400 = 15. 95% of 640 =

KS2–KS3 Maths Transition © HarperCollinsPublishers 2022

Diagnostic test 1

Number – number and place value 16. Write three million, twenty-four thousand and three in numerals.

17. In the number 5 678 209, write the value of the: a) 6 digit b) 8 digit 18. Round 3∙285 to the nearest: a) whole number b) tenth 19. What number is 9 less than 6? 20. The table shows the populations of some European countries. Country

Population

Albania

2 886 026

Armenia

2 993 900

Cyprus

847 000

Lithuania

2 849 317

a) Write the countries in population order, from most to least. __________________________________________________________ b) Round the population of Albania to the nearest 100 000.

c) Round the population of Armenia to the nearest 1000.

d) Write the population of Cyprus as a decimal of millions.

KS2–KS3 Maths Transition © HarperCollinsPublishers 2022

Diagnostic test 1

KS2–KS3 Maths Transition © HarperCollinsPublishers 2022

Diagnostic test 1

Number – addition, subtraction, multiplication and division 21. Circle the correct answer. Use estimation to show how you know. a) 9∙85 × 5∙03 = 45∙5455

b) 9∙85 × 5∙03 = 49∙5455

c) 9∙85 × 5∙03 = 495∙455

d) 9∙85 × 5∙03 = 4∙95455

22. Work out 3867 ÷ 12, giving the remainder as a fraction.

23. Choose a number from the box. You do not need to use them all. 1

a) Find a common factor of 20 and 32. b) Find a common multiple of 2 and 3. c) Find a prime number. 24. Work out the missing digits in the subtraction. 9 –

3 4

7 0

25. Bottles of fizzy water are packed in packs of 24. 16 packs fit into a box. Sam has 5766 bottle to pack. How many full boxes can he fill? boxes.

Diagnostic test 1

Number – fractions (including decimals and percentages) 26. Simplify

50 fully. 60

27. Order these fractions, from smallest to largest.

4 5

4 9

2 3

7 12

7 to a decimal using division. Use dot notation for recurring 11 decimals.

28. Change

29. Fill in the correct number to make each calculation correct. a) 2∙4 ×

= 2400

b) 35∙89 ÷

= 0∙3589

30. What is the value of the digit 3 in the number 5∙293?

31. A library fits an average of 24 books on a shelf. How many shelves are needed for one thousand books? shelves 32. Write the fractions, decimal and percentage on the number line. A

3 5

B 0.45

C 72%

13 20

Diagnostic test 1

Ratio and proportion 33. A drink is made by diluting 25 ml of lime juice with water. How many drinks can be made from a 1·5-litre bottle of concentrated lime juice? drinks 34. Here are two similar shapes. Find the length of side PQ.

PQ =

35. Josie and Erin shared 35 marbles in the ratio 2 : 3. How many more marbles did Erin have? marbles

Diagnostic test 1

Algebra 36. Work out the value of n in this equation. 2n + 5 = 11

37. pq = 24. What is the value of p when q = 8? 38. List three different solutions for 2x – y = 0. a) x =

b) x =

c) x =

39. Fill in the missing numbers in the sequence. 90

40. The formula to find the area, A, of a parallelogram is A = bh. What is the area of trapezium b = 9 cm and h = 11 cm?

Area =

cm2

Diagnostic test 1

Measurement 41. Write the equivalent measurements. a) 1·7 kg =

b) 340 cm =

42. 5 miles = 8 km. Change 250 miles into kilometres. km 43. The two fields, A and B, both have an area of 36 m2, but different perimeters. What could their perimeters be? Find two possibilities. A

Perimeter of A =

Perimeter of B =

44. Is it possible to use the formula

1 base x height to find the area of this 2

triangle?

45. Calculate the volume of the cuboid.

Volume = 46. How much more than 780 ml is 1·2 litres? Give your answer in litres.

Diagnostic test 1

litres

Diagnostic test 1

Geometry – properties of shapes 47. a) Label the isosceles trapezium to show the parallel sides, the equal sides and the equal angles.

b) Compare an isosceles trapezium with an isosceles triangle. What is the same? _________________________________________ What is different?

_________________________________________

48. a) Name this 3-D shape. ______________________________________

b) How many faces does it have? c) How many vertices does it have?

Diagnostic test 1

49. Draw this triangle accurately. The base has been drawn for you. The diagram is not drawn to scale.

50. Which shape will the net make? _________________________________

51. Find the value of the angle marked x.

52. The radius of a circle is 4·2 cm, what is the length of its diameter? cm

Diagnostic test 1

Geometry – position and direction 53. Reflect the shape in the y-axis and write the coordinates of the vertex marked with a cross in the reflected shape.

Diagnostic test 1

Statistics 54. A group of children were asked how many brothers and sisters they have. The results are shown in the pie chart.

If 60 children have two siblings, how many children were in the survey? children 55. Work out the mean mass. 1·6 kg mean:

1·55 kg

900 g

1 kg 750 g

Number – number and place value

Unit 1:

Read, write, order and compare numbers up to 10 000 000 and determine the value of each digit Content domain reference: 6N2/6N3

Prerequisites for learning

Key vocabulary

Read, write, order and compare numbers up to 1 million

million, place value, digit

Know the value of digits in numbers up to 1 million

Resources

Learning outcomes

sets of 0–9 digit cards; Resource 1: Place-value grids; mini whiteboards and pens

Understand numbers up to 10 million

Background knowledge • Our number system is a decimal system, so it is base 10. Each ‘place’ is ten times the value of the place to the right of it. The value of each digit is determined by its position in the number. Larger numbers are grouped in threes, separated by a space: 1 234 567. As long as pupils can read a threedigit number, they should be able to read any larger number. • Confusion often arises where there are several zeroes as place holders, such as four hundred thousand and six and 2 000 015. Help children to consider how many digits are needed: a number beginning with ‘million’ will be a seven-digit number, one number followed by two lots of three numbers separated by a space: __ __ __ __ __ __ __. For whole numbers, the more digits a number has, the larger it must be: any four-digit whole number is larger than any three-digit whole number. This is not true, however, of decimal numbers: 0·5 is larger than 0·46, for example.

Teaching Activity 1a (15 minutes) Understand numbers up to 10 million • Shuffle a set of digit cards, without the zero. Lay them out to form a six-digit number (smaller if necessary), separating the two sets of three cards with a small gap. Practise reading it together, pointing to the gap as you say ‘thousand’. Ask the children what the value of each digit is. Emphasise that they only need to be able to read three-digit numbers in order to read larger numbers. • Repeat with a seven-digit number, leaving a small gap between the first and second digit and the fourth and fifth. Point to the first gap as you say ‘million’. Ask children to give the value of selected digits. Rearrange the same cards, then read it again. Point to a number and ask: What is the value of this number now? • Replace one of the digits with a zero card and repeat. Rearrange the cards, putting the zero card in a different place. Repeat, until the zero card has been in all of the places (except millions). Ensure that children read these numbers correctly.

• Repeat with zeroes in several place holders, reading them carefully, for example, 2 009 005; 3 090 021. • Now say a seven-digit number and ask children to show that number, using digit cards or by writing it on a whiteboard. Repeat, ensuring you include some numbers involving zero, for example, two million, four thou-sand and eighty; three million, fifty thousand and five. • Ask each child to write an ‘interesting’ sevendigit number on a whiteboard; order the numbers by moving the boards to show from smallest to largest or largest to smallest. Ask: How do you know that this number is larger? Why is this number smaller than this one? How many ten thousands/ hundreds does this number have? • Repeat, but ask children to start their number with a specified number of millions, then ask for a specified number of millions and hundred thousands. Order again. Ask: Which digit do you have to look at to know which is the larger number?

• Write 5 000 000 + 400 000 + 30 000 + 8000 + 700 + 10 + 9. Ask: Can you write this number straight down without actually adding the numbers? Point out that this a place-value addition, so it is simply 5 438 719. • Repeat with the numbers not in place-value order and then with some missing, so that children have to use a zero in a place holder: 900 000 + 700 + 40 + 6 000 000 = 6 900 740.

Teaching Activity 1b (15 minutes) Understand numbers up to 10 million • Using Resource 1: Place-value grids, write some digits in the columns, starting with a sixdigit number, or smaller if necessary, and with no zero digits, for example, 123 456. Write the value of each digit, using the words at the top of the columns for support. (one hundred thousand, two lots of ten thousand: twenty thousand, three thousand…) Write the number on a whiteboard as a sum of the separate columns: 100 000 + 20 000 + 3 000 + 400 + 50 + 6. • Tell the children that, if they can read a threedigit number, then they can read any number. On the resource sheet, point out the bold line between the thousands and hundreds columns. Explain that this line represents the word ‘thousand’. Read the number together, emphasising the way the thousands are read as HTO with the word ‘thousand’ after it. Say: One hundred and twenty-three thousand, four hundred and fifty-six. • Repeat with a zero as one digit, then include more zeroes, for example, 457 019; 302 008; 700 016.

• Give the children six-digit numbers to write on their whiteboards. • Write a seven-digit number on the place-value grid. Ask: What word does this bold line represent? (million) Write the number as a sum on the whiteboard. Read the numbers together, ensuring that ones with zeroes are read correctly. • Give the children some seven-digit numbers to write down. • Ask each child to write an ‘interesting’ sevendigit number on a whiteboard; order the numbers by moving the boards to show from smallest to largest or largest to smallest. Ask: How do you know that this number is larger? Why is this number smaller than this one? How many ten thousands/ hundreds does this number have? • Repeat, but ask children to start their number with a specified number of millions, then ask for a specified number of millions and hundred thousands. Order again. Ask: Which digit do you have to look at to know which is the larger number? • Write 5 000 000 + 400 000 + 30 000 + 8000 + 700 + 10 + 9. Ask: Can you write this number straight down without actually adding the numbers? Point out that this a place-value addition, so is simply 5 438 719. • Repeat with the numbers not in place-value order and then with some missing, so that children have to use a zero in a place holder: 900 000 + 700 + 40 + 6 000 000 = 6 900 740.

Number – number and place value

Unit 1

Number – number and place value

Practice

Unit 1: Read, write, order and compare numbers up to 10 000 000 and determine the value of each digit 1. Write these numbers in numerals. a) three hundred and forty thousand, five hundred and six b) eight hundred thousand and four c) five million, nine hundred and sixty-four thousand, seven hundred and twenty d) two million, five thousand and thirty 2. Write these numbers in words. a) 609 013 ___________________________________________________ b) 8 091 105 _________________________________________________ 3. Calculate, using place value. a) 400 000 + 500 = b) 50 000 + 70 = c) 300 000 + 50 000 + 7000 + 800 + 20 + 1 = d) 6 000 000 + 700 000 + 40 000 + 1000 + 600 + 50 + 9 = e) 80 000 + 6 + 4 000 000 + 5000 + 300 = 4. What is the value of the 6 in these numbers? a) 4 369 215

b) 7 615 004

c) 8 426 119

d) 6 927 354

5. Write these numbers in order, from largest to smallest. a) 978 935

1 245 742

99 999

987 276

__________________________________________________________ b) 5 475 312

5 457 321

5 475 321

5 457 231

Number – number and place value

Practice

__________________________________________________________

Number – number and place value

Quick Practice Test

Unit 1: Read, write, order and compare numbers up to 10 000 000 and determine the value of each digit 1. Write these numbers in numerals in the place-value grid. a) five hundred and seventy-six thousand and fourteen b) three million, eight hundred and ninety thousand, four hundred and five c) three hundred and eighty thousand, one hundred and twelve d) four million, five hundred and twenty thousand, two hundred and ten e) four hundred and thirty thousand and ninety-one f) five million and forty-five Million Hundred thousand Ten thousand

Thousand

Hundred

Ten

2. What is the value of the 9 in these numbers? a) 3 196 385 b) 8 904 215 3. Write these numbers in order, from smallest to largest. 2 150 001

2 090 003

2 125 786

2 089 998

Ones

Number – number and place value

Practice