mathematics key learning indicators of performance: … · including making nets. child f can...

Mathematics

Key Learning Indicators of Performance: Exemplification for Year 6 (Secure)

© Lancashire County Council (2016)

Number – number and place value Number – addition and subtraction Number – multiplication and division

Count forwards or backwards in steps of integers, decimals,

powers of 10.

Child F joins in with class counting. She is confident with

counting in decimal steps and uses her mental calculation

strategies to help her identify the next term, such as in the

sequence 3.242, 3.257, 3.272. She can also count forwards and

backwards through 0.

Read, write, order and compare numbers up to 10 000 000 and

determine the value of each digit.

Through all of her written work, Child F demonstrates the

ability to read and write both whole numbers with up to eight

digits, understanding the value of the digit according to its

place.

Identify the value of each digit to three decimal places.

Child F consistently identifies the value of decimal digits. She

understands tenths, hundredths and thousandths and knows

that ten thousandths has the same value as one hundredth etc.

Identify, represent and estimate numbers using the number line.

See Sample A

Order and compare numbers including integers, decimals and

negative numbers.

See Sample B

See Sample C

Find 0.001, 0.01, 0.1, 1, 10 and powers of 10 more/less than a

given number.

During starter sessions, Child F is able to identify numbers

which are 0.001, 0.01, 0.1, 1, 10, 100, 1000, 10 000 and 100 000

more or less than a given number, including where boundaries

are crossed. She uses her mental calculation skills to help her.

Round any whole number to a required degree of accuracy.

See Sample D

Round decimals with three decimal places to the nearest whole

number or one or two decimal places.

See Sample E

See Sample F

Multiply and divide numbers by 10, 100 and 1000 giving

answers up to three decimal places.

See Sample G

Choose an appropriate strategy to solve a calculation based

upon the numbers involved (recall a known fact, calculate

mentally, use a jotting, written method).

See Sample K

Select a mental strategy appropriate for the numbers in the

calculation.

See Sample L

Recall and use addition and subtraction facts for 1 (with

decimals to two decimal places).

See Sample M

Perform mental calculations including with mixed operations

and large numbers and decimals.

See Sample N

Add and subtract whole numbers and decimals using formal

written methods (columnar addition and subtraction).

See Sample O

Use estimation to check answers to calculations and determine,

in the context of a problem, an appropriate degree of accuracy.

Use knowledge of the order of operations to carry out

calculations.

See Sample P

Solve addition and subtraction multi-step problems in

contexts, deciding which operations and methods to use and

why.

See Sample Q

Solve problems involving all four operations, including those

with missing numbers.

See Sample H

See Sample I

See Sample M

See Sample P

See Sample Q

See Sample X

Choose an appropriate strategy to solve a calculation based

upon the numbers involved (recall a known fact, calculate

mentally, use a jotting, written method).

See Sample K

Identify common factors, common multiples and prime

numbers.

See Sample R

Use partitioning to double or halve any number.

During starter sessions, Child F uses partitioning strategies to

support her doubling and halving, for example, she was able to

halve 0.76 by partitioning it into 0.6 and 0.16 and halving each.

Perform mental calculations, including with mixed operations

and large numbers.

Child F uses her knowledge of tables, related facts, doubling,

halving and partitioning to help her to mentally multiply and

divide. When asked how she would solve 942 ÷ 6, she replied

‘I’d do it mentally. I can partition it into 600, 300 and 42

because they are all multiples of 6. 600 ÷ 6 is 100, 300 is half of

600 so 300 ÷ 6 is 50 and 42 ÷ 6 is 7 so the answer is 157.’

She was also asked to solve the problem ‘Three pens cost one

pound fifty pence altogether. How much would seven pens

cost? She knew the answer was £3.50 and when asked how she

knew, she replied ‘I have to find the cost of one pen first, so

that is 50p because it is £1.50 divided by 3. Then I timesed it by

7to make £3.50.’

See Sample N

Multiply multi-digit numbers up to 4 digits by a two-digit

whole number using the formal written method of long

multiplication.

See Sample S

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

whole numbers.

See Sample T

Divide numbers up to 4 digits by a two-digit whole number

using the formal written methods of short or long division, and

interpret remainders as whole number remainders, fractions, or

by rounding, as appropriate for the context.

See Sample U

Mathematics



Number – number and place value (continued)

Number – multiplication and division (continued)

Use negative numbers in context, and calculate intervals across

zero.

See Sample I

Describe and extend number sequences including those with

multiplication and division steps, inconsistent steps, alternating

steps and those where the step size is a decimal.

See Sample H

Solve number and practical problems that involve all of the

above.

See Sample H

See Sample I

See Sample J

Use written division methods in cases where the answer has up

to two decimal places.

See Sample V

Use estimation and inverse to check answers to calculations

and determine, in the context of a problem, an appropriate

degree of accuracy.

Use knowledge of the order of operations to carry out

calculations.

See Sample P

Solve problems involving all four operations, including those

with missing numbers

See Sample W

See Sample X

See Sample Y

See Sample Z

Child F can confidently answer questions such as, “I’m thinking

of a number. I multiply it by 7 and then subtract 5. The answer

is 58. What is my number?” She understands the concept of

inverse and can solve these problems mentally.

Mathematics



Number – fractions Geometry – properties of shapes Measurement

Compare and order fractions, including fractions > 1 (including

on a number line).

See Sample AA

Use common factors to simplify fractions; use common multiples

to express fractions in the same denomination.

Child F effectively uses her knowledge of factors and multiples to

enable her to change the forms of fractions.

See Sample AA

See Sample AB

Recall and use equivalences between simple fractions, decimals

and percentages, including in different contexts.

When asked to calculate the cost of a £20 item in a 5% off sale,

Child F explained ‘To find 5%, you can find 10% and then halve

it. 10% is the same as 10100

, or 110

. So I divide 20 by 10 which is 2

and then halve it to get 1. £20 take away £1 is £19.’

See Sample AC

Associate a fraction with division and calculate decimal fraction

equivalents (e.g. 0.375 and 3

8).

Add and subtract fractions with different denominators and

mixed numbers, using the concept of equivalent fractions.

Child F knows that fractions have to have the same denominator

to enable them to be added or subtracted. She effectively uses

her knowledge of multiples to do this.

See Sample AD

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

simplest form (e.g. 1

4 x

1

2 =

1

8).

See Sample AE

See Sample AF

Divide proper fractions by whole numbers (e.g. 1

3 ÷ 2 =

1

6).

Find simple percentages of amounts.

See Sample AG

See Sample AH

Solve problems involving fractions.

See Sample AI

Solve problems which require answers to be rounded to

specified degrees of accuracy.

Solve problems involving the calculation of percentages (e.g. of

measures and such as 15% of 260) and the use of percentages

for comparison.

See Sample AJ

Compare/classify geometric shapes based on the

properties and sizes.

See Sample AK

Draw 2-D shapes using given dimensions and angles.

See Sample AL

Illustrate and name parts of circles, including radius,

diameter and circumference and know that the diameter

is twice the radius.

Child F can name the parts of a circle correctly. Through

investigation she identified the relationship between

radius and diameter.

See Sample AM

Recognise, describe and build simple 3-D shapes,

including making nets.

Child F can recognise, name and describe the properties

of cube, cuboid, pyramid (variety of different shaped

bases), sphere, hemisphere, cone, cylinder, prism (variety

of different shaped end faces), tetrahedron, octahedron

and dodecahedron. She identifies faces and curved

surfaces on shapes. She can identify where faces are

parallel or perpendicular to one another.

See Sample AN

Recognise angles where they meet at a point, are on a

straight line, or are vertically opposite, and find missing

angles.

See Sample AO

See Sample AP

See Sample AQ

Find unknown angles in any triangles, quadrilaterals,

regular polygons,

See Sample AP

See Sample AQ

Use, read and write standard units of length, mass, volume and

time using decimal notation to three decimal places.

Child F understands what the abbreviations mm, cm, m, km, g, kg

and cm3 stand for and uses them in her work. She can also record

time to two decimal places.

Convert between standard units of length, mass, volume and time

using decimal notation to three decimal places.

Child F uses her knowledge of place value and multiplying and

dividing by 10, 100 and 1000 to convert between metric

measures. She knows the relationship between seconds, minutes,

hours and days, and uses her mental multiplication and division

strategies and knowledge of related facts to convert these.

See Sample G

Convert between miles and kilometres.

See Sample AR

Recognise that shapes with the same areas can have different

perimeters and vice versa.

See Sample AS

Calculate the area of parallelograms and triangles.

See Sample AT

See Sample AU

Recognise when it is possible to use formulae for area and

volume of shapes.

See Sample AT

See Sample AU

See Sample AV

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 (e.g. mm3 and km3).

See Sample AV

See Sample AW

Calculate differences in temperature, including those that involved

a positive and negative temperature.

Child F uses a number line to calculate differences in

temperature. When calculating between negative and positive

temperatures, she uses two jumps, one from the negative to the

0, and one from the positive to the 0.

Solve problems involving the calculation and conversion of units

of measure, using decimal notation up to three decimal places

where appropriate.

See Sample AX

Geometry – position and direction

Describe positions on the full coordinate grid (all four

quadrants).

See Sample AY

Draw and translate simple shapes on the coordinate

plane, and reflect them in the axes.

See Sample AY

See Sample AZ

Mathematics



Ratio and Proportion Algebra Statistics

Solve problems involving the relative sizes of two quantities

where missing values can be found using integer

multiplication/division facts.

See Sample BA

Solve problems involving unequal sharing and grouping using

knowledge of fractions and multiples.

See Sample BB

Solve problems involving similar shapes where the scale factor is

known or can be found.

See Sample BC

Use simple formulae.

See Sample AT

See Sample AU

See Sample AV

See Sample BD

Generate and describe linear number sequences.

See Sample H

See Sample BE

Express missing number problems algebraically.

See Sample BF

Find pairs of numbers that satisfy an equation with two

unknowns.

See Sample BD

Enumerate possibilities of combinations of two variables.

Continue to complete and interpret information in a variety of

sorting diagrams (including sorting properties of numbers and

shapes).

Child F uses her knowledge of properties of numbers and

shapes to sort them in both Carroll and Venn diagrams.

See Sample AK

Interpret and construct pie charts and line graphs and use these

to solve problems.

See Sample BG

See Sample BH

Solve comparison, sum and difference problems using information

presented in all types of graph.

See Sample BG

See Sample BH

Calculate and interpret the mean as an average.

See Sample BI

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A B

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C D

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E F

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G H

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I

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J K

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L M

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N O

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P Q

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R S

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T U

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V W

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X Y

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Z AA

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AB AC

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AD AE

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AF AG

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AH AI

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AJ AK

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AL AM

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AN AO

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AP AQ

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AR AS

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AT AU

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AV AW

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AX AY

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AZ

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BA

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BB

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BC BD

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BE BF

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BG BH

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BI

mathematics key learning indicators of performance: … · including making nets. child f can...

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