An integer is any positive or negative whole number or zero. E.g. (−2), 0, 153 are all examples of integers.

A number is in decimal form when the decimal point is shown and there are digits to the right of the decimal point.

A digit is one of the symbols of a number system. In our number system we use the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

Checking understanding of arithmetic procedures with integers and decimals

Maths

Pupils use their understanding of place value and fluency with decimals from this unit in order to extend this understanding to fractions.  In the future unit, pupils will be asked to compare and order both fractions and decimals and will assess when conversion is required.

The prior unit on factors, multiples, squares and cubes helped pupils build on their understanding that any positive integer can be expressed as a product of its factors. This skill is used here to explore multiplying and dividing with decimals.

In this unit pupils develop their ability and efficacy with the four operations including more complicated and challenging calculations involving fractions, decimals and negative numbers. This leads into an exploration of the priority order of operations.

Arithmetic procedures with integers and decimals

Securing understanding of arithmetic procedures with integers and decimals

An integer is any positive or negative whole number or zero. E.g. -2, 0, 153 are all examples of integers.

Checking and securing understanding of negative numbers in context

The additive inverse of a number is a number that, when added to the original number, gives the sum of 0.

A number and its additive inverse make a zero pair.

The absolute value of a number is its distance from zero. E.g. 5 and (−5) are both 5 away from zero and so both have an absolute value of 5

Addition of positive and negative integers

The absolute value of a number is its distance from zero. E.g. 5 and (−5) are both 5 away from zero and so both have an absolute value of 5.

Subtraction of positive and negative integers

Metric units are based around the standard units of metre, gram and litre.

The absolute value of a number is its distance from zero. E.g. 5 and (-5) are both 5 away from zero and so both have an absolute value of 5.

Checking and securing understanding of written addition and subtraction strategies

Partitioning is the act of splitting an object or value down into smaller parts.

Checking and securing understanding of multiplication and division

Multiplication and division where only one value is negative

A product is the result of two or more numbers multiplied together.

Multiplication and division where two or more values are negative

Simplifying multiplication and division using multiples of 10

Factorising means to express a term as the product of its factors.

Multiplying with decimals

The divisor is the number by which the dividend is divided.

The quotient is the integer result of division.

Dividing with decimals

An operation is commutative if the values it is operating on can be written in either order without changing the calculation

An operation is associative if a repeated application of an operation produces the same result regardless of how pairs of values are grouped

Checking and securing understanding of the commutative and associative laws

The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.

Checking and securing understanding of the distributive law

An operation is commutative if the values it is operating on can be written in either order without changing the calculation.

Priority of operations with positive integers

Priority of operations with positive and negative integers and decimals

The associative law states that a repeated application of the operation produces the same result regardless how pairs of values are grouped.

Arithmetic procedures with integers and decimals

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These lessons will be removed by end of Summer Term 2025.