pcMaths Package

YEAR

STRAND : OBJECTIVE

Addition & Subtraction

Missing Link 1

Missing Link 2

Totally Pyramids 1 2

Totally Pyramids 3 4

Add & Sub Races1 to 7

Subtract Wh Nos 1

Subtract Wh Nos 2

Subtract Wh Nos 3

4

Secure knowledge of number facts that can be recalled quickly and used and applied appropriately

Use knowledge of addition and subtraction facts and place value to derive sums

Calculate efficiently and accurately

Add or subtract mentally pairs of two-digit whole numbers, e.g. 47 + 58, 91 – 35

5

Calculate efficiently and accurately

Use the standard written methods for addition and subtraction of two-digit and three-digit whole numbers

Secure knowledge of number facts that can be recalled quickly and used and applied appropriately

Use knowledge of place value and addition and subtraction of two-digit numbers to derive sums and differences

6

Calculate efficiently and accurately

Use the standard written methods for addition and subtraction of whole numbers

Calculate mentally with whole numbers and decimals, e.g. U.t ± U.t

Consolidate the use of standard written methods to add, subtract, multiply and divide integers

6 to 7

Calculate efficiently and accurately

Use standard written methods to add and subtract whole numbers

Bidmas Puzzles 1

Bidmas Puzzles 2

6 to 7

Calculate efficiently and accurately

Use the order of operations, including brackets

÷ by 10 100 1000

4

Calculate efficiently and accurately

Multiply or divide numbers to 1000 by 10 and then 100 (whole number answers), understanding the effect; relate to scaling up or down

5

Calculate efficiently and accurately

Use understanding of place value to multiply and divide whole numbers and decimals by 10, 100 or 1000

Chunking Word probs

6 to 7

Calculate efficiently and accurately

Use standard written methods to add and subtract whole numbers and decimals, and to multiply and divide three-digit by two-digit whole numbers; extend to multiplying and dividing decimals with one or two places by single-digit whole numbers

Simple Division 123

4

Calculate efficiently and accurately

Develop and refine written methods for multiplying and dividing a two-digit number by a one-digit number, to include division with remainders, e.g. 15 × 9, 98 ÷ 6

5

Calculate efficiently and accurately

Use the standard written methods for multiplication and division calculations of HTU × U, U.t × U, TU × TU and HTU ÷ U

6

Calculate efficiently and accurately

Calculate mentally with whole numbers and decimals, e.g. U.t ± U.t, TU × U, U.t × U, HTU ÷ U, U.t ÷ U

Consolidate the use of standard written methods to add, subtract, multiply and divide integers and decimal numbers; calculate the answer to HTU ÷ U and U.t ÷ U to one or two decimal places

6 to 7

Calculate efficiently and accurately

Use standard written methods to add and subtract whole numbers and decimals, and to multiply and divide three-digit by two-digit whole numbers; extend to multiplying and dividing decimals with one or two places by single-digit whole numbers

Equivalent Multiplication

6

Secure knowledge of number facts that can be recalled quickly and used and applied appropriately

Use knowledge of place value and multiplication facts to 10 × 10 to derive related multiplication and division facts involving decimal numbers, e.g. 0.8 × 7, 4.8 ÷ 6

Learning Number Bonds

4

Secure knowledge of number facts that can be recalled quickly and used and applied appropriately

Derive and recall multiplication facts up to 10 × 10, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple

5

Secure knowledge of number facts that can be recalled quickly and used and applied appropriately

Recall quickly multiplication facts up to 10 × 10, use to multiply pairs of multiples of 10 and 100 and derive quickly corresponding division facts

6 to 7

Secure knowledge of number facts that can be recalled quickly and used and applied appropriately

Consolidate the rapid recall of number facts, including multiplication facts to 10 × 10 and the associated division facts

x10 Dec (1 to 5)

4

Calculate efficiently and accurately

Multiply or divide numbers to 1000 by 10 and then 100 (whole number answers), understanding the effect; relate to scaling up or down

5

Calculate efficiently and accurately

Calculate mentally with whole numbers and decimals

6

Secure knowledge of number facts that can be recalled quickly and used and applied appropriately

Use knowledge of place value and multiplication facts to 10 × 10 to derive related multiplication and division facts involving decimal numbers

6 to 7

Calculate efficiently and accurately

Consolidate and extend mental methods of calculation to include decimals, fractions and percentages

Equivalent Fractions

from Times Tables

Fractions from Pictures

4

Count, compare and order numbers, and describe relationships between them

Use fractions to identify subsets of a set of objects; use diagrams to identify equivalent fractions, e.g. 6¤8 and 3¤4, or 70¤100 and 7¤10;

Calculate efficiently and accurately

Find fractions of numbers, quantities or shapes, e.g. 1¤5 of 30 plums, 3¤8 of a 6 by 4 rectangle

5

Count, compare and order numbers, and describe relationships between them

Express a smaller whole number as a fraction of a larger one; find equivalent fractions, including equivalent improper fractions and mixed numbers

6

Count, compare and order numbers, and describe relationships between them

Express a larger whole number as a fraction of a smaller one; simplify fractions;

Express one quantity as a percentage of another, e.g. express £400 as a percentage of £1000;

find equivalent percentages, decimals and fractions

Calculate efficiently and accurately

Find fractions and percentages of whole-number quantities, e.g. 5¤8 of 96, 65% of £260

6 to 7

Calculate efficiently and accurately

Consolidate and extend mental methods of calculation to include decimals, fractions and percentages

Fraction of an Amount

Fractions 1 & 2

4

Calculate efficiently and accurately

Find fractions of numbers, quantities or shapes, e.g. 1¤5 of 30 plums, 3¤8 of a 6 by 4 rectangle

5

Calculate efficiently and accurately

Find fractions using division, e.g. 1¤100 of 5 kg, and percentages of numbers and quantities, e.g. 10%, 5% and 15% of £80

Use a calculator to solve problems, including those involving decimals or fractions, e.g. to find 3¤4 of 150 g; interpret the display correctly in the context of measurement

6

Calculate efficiently and accurately

Find fractions and percentages of whole-number quantities, e.g. 5¤8 of 96, 65% of £260

Consolidate and extend mental methods of calculation to include decimals, fractions and percentages

Fraction Scales

4

Count, compare and order numbers, and describe relationships between them

Use fractions to identify subsets of a set of objects; use diagrams to identify equivalent fractions, e.g. 6¤8 and 3¤4, or 70¤100 and 7¤10

5

Count, compare and order numbers, and describe relationships between them

Express a smaller whole number as a fraction of a larger one; find equivalent fractions,

Calculate efficiently and accurately

Find fractions using division, e.g. 1¤100 of 5 kg

6

Count, compare and order numbers, and describe relationships between them

Express a larger whole number as a fraction of a smaller one; simplify fractions; order a set of fractions by converting them to fractions with a common denominator

find equivalent percentages, decimals and fractions

Decimals 1 & 2

4

Count, compare and order numbers, and describe relationships between them

Use decimal notation for tenths and hundredths, relating the notation to money and measurement;

5

Use and apply mathematics

Solve one and two-step problems involving whole numbers and decimals and all four operations, choosing and using appropriate methods, including calculator use

Secure knowledge of number facts that can be recalled quickly and used and applied appropriately

Use knowledge of place value and addition and subtraction of two-digit numbers to derive sums and differences, doubles and halves of decimals, e.g. 6.5 ± 2.7, halve 5.6, double 0.34

Calculate efficiently and accurately

Use understanding of place value to multiply and divide whole numbers and decimals by 10, 100 or 1000

Use a calculator to solve problems, including those involving decimals or fractions, e.g. to find 3¤4 of 150 g;

6

Use and apply mathematics

Solve multi-step problems, and problems involving fractions, decimals and percentages, choosing and using appropriate and efficient methods at each stage

Secure knowledge of number facts that can be recalled quickly and used and applied appropriately

Calculate mentally with whole numbers and decimals, e.g. U.t ± U.t, TU × U, U.t × U, HTU ÷ U, U.t ÷ U

6 to 7

Secure knowledge of number facts that can be recalled quickly and used and applied appropriately

Consolidate and extend mental methods of calculation to include decimals, fractions and percentages

Decimal Ordering

Decimal Scales

4

Count, compare and order numbers, and describe relationships between them

Use decimal notation for tenths and hundredths, relating the notation to money and measurement; position one- and two-place decimals on a number line

Measure accurately using appropriate units, interpret and compare scales

Interpret intervals and divisions on partially numbered scales and record readings accurately, where appropriate to the nearest tenth of a unit

5

Count, compare and order numbers, and describe relationships between them

Count from any given number in whole number steps and decimal number steps, extending beyond zero when counting backwards; relate the numbers to their position on a number line

Explain what each digit represents in whole numbers and numbers with up to two decimal places, and partition these numbers

Measure accurately using appropriate units, interpret and compare scales

Estimate measurements of length, mass and capacity to a required degree of accuracy, e.g. the nearest centimeter; interpret a reading that lies between two unnumbered divisions on a scale

6

Count, compare and order numbers, and describe relationships between them

Use decimal notation for tenths, hundredths and thousandths, partition and order numbers with up to three decimal places, and position them on the number line

Measure accurately using appropriate units, interpret and compare scales

Read scales and record results to a required degree of accuracy, recognising that the measurement made is approximate

Measure accurately using appropriate units, interpret and compare scales

Read and interpret scales on a range of measuring instruments; compare readings on different scales, e.g. when using different instruments

Percentages 1 to 4

% + Calculator

5

Count, compare and order numbers, and describe relationships between them

Understand percentage as the number of parts in every 100 and express tenths and hundredths as percentages

Calculate efficiently and accurately

Find fractions using division, e.g. 1¤100 of 5 kg, and percentages of numbers and quantities, e.g. 10%, 5% and 15% of £80

6

Use and apply mathematics

Solve multi-step problems, and problems involving fractions, decimals and percentages, choosing and using appropriate and efficient methods at each stage, including calculator use

Calculate efficiently and accurately

Find fractions and percentages of whole-number quantities, e.g. 5¤8 of 96, 65% of £260

Add & Subtract

Decimals 1

5

Count, compare and order numbers, and describe relationships between them

Count from any given number in whole number steps and decimal number steps, extending beyond zero when counting backwards; relate the numbers to their position on a number line

Secure knowledge of number facts that can be recalled quickly and used and applied appropriately

Use knowledge of place value and addition and subtraction of two-digit numbers to derive sums and differences, doubles and halves of decimals, e.g. 6.5 ± 2.7, halve 5.6, double 0.34

6

Calculate efficiently and accurately

Calculate mentally with whole numbers and decimals, e.g. U.t ± U.t, TU × U, U.t × U, HTU ÷ U, U.t ÷ U

6 to 7

Calculate efficiently and accurately

Consolidate and extend mental methods of calculation to include decimals, fractions and percentages

Number Properties: 1 2 3

Number Properties: 4 5 6

4

Secure knowledge of number facts that can be recalled quickly and used and applied appropriately

Derive and recall multiplication facts up to 10 × 10, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple

5

Secure knowledge of number facts that can be recalled quickly and used and applied appropriately

Identify pairs of factors of two-digit whole numbers and find common multiples, e.g. for 6 and 9

6

Secure knowledge of number facts that can be recalled quickly and used and applied appropriately

Recognise that prime numbers have only two factors and identify prime numbers less than 100; find the prime factors of two-digit whole numbers

Use knowledge of multiplication facts to derive quickly squares of numbers to 12 × 12 and the corresponding squares of multiples of 10

6 to 7

Secure knowledge of number facts that can be recalled quickly and used and applied appropriately

Recognise the square roots of perfect squares to 12 × 12

Recognise and use multiples, factors, divisors, common factors, highest common factors and lowest common multiples in simple cases

Rounding

Whole Numbers

Rounding Decimals

4

Secure knowledge of number facts that can be recalled quickly and used and applied appropriately

Use knowledge of rounding

5

Secure knowledge of number facts that can be recalled quickly and used and applied appropriately

Use knowledge of number facts, place value and rounding to estimate

6

Count, compare and order numbers, and describe relationships between them

Round numbers, including those with up to three decimal places

Number Vocabulary

4 to 6

all of the above (and more)

Paints 1 to 4

Which Paint?

4

Count, compare and order numbers, and describe relationships between them

Use the vocabulary of ratio and proportion to describe the relationship between two quantities, e.g. 2 to every 3, and between part and whole, e.g. 2 in every 5; estimate proportion, e.g. ‘for every 1 red car there are about 4 silver cars’, or ‘I’m asleep for about ⅓ of the day’

5

Count, compare and order numbers, and describe relationships between them

Use sequences to scale numbers up or down; solve problems involving proportions of quantities and measurements, e.g. decrease quantities in a recipe designed to feed six people

6

Count, compare and order numbers, and describe relationships between them

Use fractions, percentages and the vocabulary of ratio and proportion to describe the relationships between two quantities and solve problems, e.g. identify the quantities needed to make a fruit drink by mixing water and juice in a given ratio

6 to 7

Count, compare and order numbers, and describe relationships between them

Understand the relationship between ratio and proportion, solve problems involving proportions; use ratio notation, reduce a ratio to its simplest form and divide a quantity into two parts in a given ratio