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)
Connections within Mathematics
Making connections to other topics within this year group
Number and place value
- use negative numbers in context, and calculate intervals across zero
- round any whole number to a required degree of accuracy
When working on addition and subtraction and/or number and place value there are opportunities to make connections between them, for example:
Finding temperature increases, decreases and differences, e.g. the temperature one Monday morning in January was -6.5°. It had risen by 9.5 degrees by lunchtime. What was the temperature at lunchtime?
Rounding numbers to the nearest tenth, one, ten etc. as an approximation of the answer to an addition or subtraction and also to check the solution, e.g. Bertie scored 2458 points on the computer game. Cindy scored 3856. How many points did they score altogether? (Rounding provides an approximation – i.e. 2500 + 3900 = 6400. So precise solution can be compared to approximate value for checking. ) How many more points did Cindy score? (Rounding provides an approximation – i.e. 3900 – 2500 = 1400. So, if precise answer is not close to 1400 it cannot be correct.)
- solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate
When working on addition and subtraction and/or measures there are opportunities to make connections between them, for example:
Finding totals and differences of different measurements, e.g. Kirsty cycled 25.75km, her brother cycled a further 4.125km. How far did her brother cycle? How far did they cycle altogether?
- interpret and construct pie charts and line graphs and use these to solve problems
When working on addition and subtraction and/or statistics there are opportunities to make connections between them, for example:
Making up and solving problems from a line graph, e.g. How many miles did the lorry driver travel between the end of the first hour and the end of the 6th hour?
Programme of Study: Algebra
- from Notes and guidance (non-statutory)
- pupils should be introduced to the use of symbols and letters to represent variables and unknowns in mathematical situations that they already understand, such as:
- missing numbers, lengths, coordinates and angles
- generalisations of number patterns and number puzzles (e.g. what two numbers can add up to)
When working on addition and subtraction and/or algebra there are opportunities to make connections between them, for example:
Solving missing number problems by balancing each side so making use of the idea of equivalence, e.g.
||y + 35
|(add 13 to both)
||2y -13 + 13
||y + 35 + 13
|(calculate numerical elements)
||y + 48
Solving number puzzles, e.g. write down five possible values of a + b in these equations:
- a + b = 8.75
- a - b = 23 985
Making connections to this topic in adjacent year groups
- add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
- add and subtract numbers mentally with increasingly large numbers
- use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
- solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.
- Pupils practise using the formal written methods of columnar addition and subtraction with increasingly large numbers to aid fluency (see National Curriculum in England Framework Document, Mathematics Appendix 1).
- They practise mental calculations with increasingly large numbers to aid fluency (e.g. 12 462 – 2 300 = 10 162).
Key Stage 3
- understand and use place value for decimals, measures and integers of any size
- use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
- recognise and use relationships between operations including inverse operations
- appreciate the infinite nature of the sets of integers, real and rational numbers
Cross-curricular and real life connections
Learners will encounter addition and subtraction in:
Almost everything! Addition and subtraction are skills used in many problem solving activities in subjects across the curriculum.
Within the science curriculum there are opportunities to connect with addition and subtraction, for example in the introduction of the Upper Key Stage 2 Programme of Study it states that pupils should select the most appropriate ways to answer science questions using different types of scientific enquiry, including observing changes over different periods of time, noticing patterns, grouping and classifying things, carrying out comparative and fair tests and finding things out using a wide range of secondary sources of information. The children could, for example, interpret graphs and charts and find totals and differences in pieces of data, including measurement.
Within the geography curriculum there are opportunities to connect with addition and subtraction. In the introduction of the Key Stage 2 Programme of Study it states that pupils should extend their knowledge and understanding beyond the local area to include the United Kingdom and Europe, North and South America. This will include the location and characteristics of a range of the world’s most significant human and physical features. Children could, for example, find and compare distances between countries or cities, compare population statistics, temperatures, lengths of rivers, heights of mountains etc.
See, for example:
Within the history curriculum, there are opportunities to connect with addition and subtraction, for example in the introduction of the Key Stage 2 Programme of Study it states that pupils should continue to develop a chronologically secure knowledge and understanding of British, local and world history, establishing clear narratives within and across the periods they study. The children could find differences between the duration of the different periods, such as the Stone Age and Iron Age or find the lengths of the reigns of different British monarchs.
The NCETM Primary Magazine provides some useful starting ideas for linking mathematics with the Romans.