Making Connections
Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects.
Connections within Mathematics
Making connections to this topic in adjacent year groups
Year 5 – Number and place value

count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000

interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers through zero

solve number problems and practical problems that involve all of the above
Notes and guidance
They should recognise and describe linear number sequences, including those involving fractions and decimals, and find the termtoterm rule.
Year 5 – Multiplication and division

solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign

solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.
Notes and guidance
Distributivity can be expressed as a(b + c) = ab + ac in preparation for using algebra.
Year 5 – Measurement

measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres

calculate and compare the area of squares and rectangles including using standard units, square centimetres (cm^{2}) and square metres (m^{2}) and estimate the area of irregular shapes

use all four operations to solve problems involving measure (e.g. length, mass, volume, money) using decimal notation including scaling.
Notes and guidance
Pupils calculate the perimeter of rectangles and related composite shapes, including using the relations of perimeter or area to find unknown lengths. Missing measures questions such as these can be expressed algebraically 4 + 2b = 20 for a rectangle of sides 2 cm and b cm and perimeter of 20cm.
Making connections to this topic in adjacent year groups
Key Stage 3 – Algebra:

read and interpret algebraic notation

express known relations, including spatial generalisations, algebraically using accurate notation, including prioritisation of operations

recognise an arithmetic progression, and find the nth term

interpret mathematical relationships both algebraically and graphically.

use formulae by substitution to calculate the value of a variable, including for scientific formulae

begin to model simple contextual and subjectbased problems algebraically
General guidance

When discussing different mental calculation methods:

explore with pupils the structure behind them;

invite pupils to make up similar examples;

model how these structures might be recorded using algebra and encourage pupils to record them using letters or other symbols.
e.g. 4 × 27 = 4 × 20 + 4 × 7
or 4 × 27 = 4 × 25 + 4 × 2
or 4 × 27 = 4 × 30 + 4 × 3
leading to 4(x + y) = 4x + 4y or a(b + c) = ab + ac

Explore ‘quick’ ways of doing calculations which rely on the algebraic structure within them.
e.g. Do this calculation as quickly as you can;
173 – 35 + 36
Write down a few more calculations like this (and the answers to them) which use the same idea. Be creative!

When solving problems that involve finding an unknown quantity (e.g. a missing number in a number puzzle, a missing length or angle in a shape, etc.) encourage pupils to record it using letters or other symbols – e.g. 25 + ⬜ = 32; 180 = ? + 134; x + 9 = 23, etc.
Crosscurricular and real life connections
Learners will encounter algebra in:
Recipes or formulae such as: Child’s dose = Age × Adult dose
Age + 12
or F = 9⁄5 C + 32
Working out the reading age of a particular text – e.g.
where N is the number of onesyllable words in a passage of 150 words.

FORECAST formula

FOG index
where A = no. of words in passage
n = no. of sentences
L = no. of words containing 3 or more syllables (excluding the'ing' and 'ed' endings).
More information on reading age formulae, can be found here