Teachers should use every relevant subject to develop pupils’ mathematical fluency. Confidence in numeracy and other mathematical skills is a precondition of success across the national curriculum.

Teachers should develop pupils’ numeracy and mathematical reasoning in all subjects so that they understand and appreciate the importance of mathematics.

*– National Curriculum in England Framework Document, September 2013, p10)*

### Connections within Mathematics

#### Making connections to other topics within this year group

In **fractions** work:

Pupils count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10

Pupils connect tenths to place value, decimal measures and to division by 10. They begin to understand unit and non-unit fractions as numbers on the number line and deduce relations between them such as size and equivalence (non-statutory)

In work on **measures**:

Measure and compare: lengths (m/cm/mm); Mass (kg/g); volume (l/ml)

Pupils continue to measure using appropriate tools and units, progressing to a wider range of measures, including comparing and using mixed units (e.g. 1kg and 200g) and simple equivalents of mixed units (e.g. 5m = 500cm)

The comparison of measures should also include simple scaling by integers (non-statutory)

#### Making connections to this topic in adjacent year groups

**Year 2**

- count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward
- recognise the place value of each digit in a two-digit number (tens, ones)
- identify, represent and estimate numbers using different representations, including the number line
- compare and order numbers from 0 up to 100; use <, > and = signs
- read and write numbers to at least 100 in numerals and in words
- use place value and number facts to solve problems.

**Non-Statutory Guidance**

Using materials and a range of representations, pupils practise counting, reading, writing and comparing numbers to at least 100 and solving a variety of related problems to develop fluency. They count in multiples of three to support their later understanding of a third.

As they become more confident with numbers up to 100, pupils are introduced to larger numbers to develop further their recognition of patterns within the number system and represent them in different ways, including spatial representations.

Pupils should partition numbers in different ways (for example, 23 = 20 + 3 and 23 = 10 + 13) to support subtraction. They become fluent and apply their knowledge of numbers to reason with, discuss and solve problems that emphasise the value of each digit in two-digit numbers. They begin to understand zero as a place holder.

**Year 4**

- count in multiples of 6, 7, 9, 25 and 1000
- find 1000 more or less than a given number
- count backwards through zero to include negative numbers
- recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
- order and compare numbers beyond 1000
- identify, represent and estimate numbers using different representations
- round any number to the nearest 10, 100 or 1000
- solve number and practical problems that involve all of the above and with increasingly large positive numbers
- read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of zero and place value.

**Non-statutory guidance**

Using a variety of representations, including measures, pupils become fluent in the order and place value of numbers beyond 1000, including counting in tens and hundreds, and maintaining fluency in other multiples through varied and frequent practice.

They begin to extend their knowledge of the number system to include the decimal numbers and fractions that they have met so far. They connect estimation and rounding numbers to the use of measuring instruments.

Roman numerals should be put in their historical context so pupils understand that there have been different ways to write whole numbers and that the important concepts of zero and place value were introduced over a period of time

### Cross-curricular and real life connections

Learners will encounter numbers and place value in many contexts and begin to explore their significance.

- Comparing quantities in real life contexts such as counting those present in school or having school dinners
- Comparing measures such as length, weight or volume of different objects
- Organising data can draw attention to aspects of place value for instance through collecting information about pets that others have or the distances that they travel to get to school.
- School sports day can offer opportunities for counting and measuring and comparing quantities
- Activities such as counting the number of seeds in a packet can support children’s understandings of large numbers and help them to see the value of strategies such as rounding to the nearest 10