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
- Convert between different units of measure [for example, kilometre to metre; hour to minute]
- solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days.
- recognise and show, using diagrams, families of common equivalent fractions
- count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten
- recognise and write decimal equivalents to 1/4 , 1/2 , 3/4
- find the effect of dividing a one- or two-digit number by 10 and 100, identifying the
value of the digits in the answer as ones, tenths and hundredths
Making connections to this topic in adjacent year groups
- recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
- write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods
- solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects.
- identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers.
- solve problems involving multiplication and division where larger numbers are used by decomposing them into their factors
- know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
- establish whether a number up to 100 is prime and recall prime numbers up to 19
- multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers
- multiply and divide numbers mentally drawing upon known facts
- divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context
- multiply and divide whole numbers and those involving decimals by 10, 100 and 1000
- recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
- 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.
Cross-curricular and real life connections
Learners will encounter multiplication and division in:
Counting – Calculating totals by counting small amounts or a proportion and then scaling up e.g. standing against a tree and using your known height to work out ‘How many of me are equal to the height of the tree?’ or counting people on one part of a stadium and multiplying to calculate the total number of spectators.
Money – shopping: adding multiple products of the same price, adding coins of same value, working out fraction/percentage discounts and special offers, sharing bills.
Measurement – Scaling quantities (e.g. recipes) to cater for more and less people, reading scales and unlabelled increments on measuring apparatus, calculating area for carpets, decorating etc., scaling shapes to scale geometric artwork e.g. How would you make this triangle three times its size/half its size? Comparing river lengths/building heights e.g. the River Nile is x times longer than the River X. The height of Snowdon is (fraction) of the height of Everest.
Statistics – Reading scales and determining appropriate scales for different types of graph relating to weather, temperature, sound etc., Working with proportion, fractions and percentages using pie charts, comparing data using ratio, fractions and scaling such as proportion of children missing breakfast or 1 in 7 children under 10 now has a mobile phone etc.