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National Curriculum: Multiplication and Division Year 6 - Making Connections


Created on 15 October 2013 by ncetm_administrator
Updated on 18 December 2013 by ncetm_administrator
 

Making Connections

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, p9)

Connections within Mathematics

Making connections to other topics within this year group

Fractions

  • identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places
  • multiply one-digit numbers with up to two decimal places by whole numbers
  • use written division methods in cases where the answer has up to two decimal places
  • divide proper fractions by whole numbers [e.g. ⅓ ÷ 2 = ⅙]
  • multiply simple pairs of proper fractions, writing the answer in its simplest form

When working on multiplication and division and/or fractions there are opportunities to make connections between them, for example:

Multiply numbers such as:

  • 245.25 by 10, 100 and 1000
  • 1.35 by 8
  • ¼ x ½

Divide numbers such as:

  • 12 578 by 10, 100 and 1000
  • 237 by 5
  • ⅓ ÷ 2

Ratio and proportion

  • solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts

When working on multiplication and division and/or ratio and proportion there are opportunities to make connections between them, for example:

Convert the ingredients in this lasagne recipe for 4 people so that it will serve 12:

  • 350g minced beef
  • 1 onion
  • 1 clove garlic
  • 600g tin of tomatoes
  • 2 tablespoons tomato puree
  • 175g lasagne sheets

Algebra

  • express missing number problems algebraically
  • use simple formulae

When working on multiplication and division and/or algebra there are opportunities to make connections between them, for example:

Solve missing number problems, e.g. 6(a + 12)  =  144
multiply out the equation: 6a + 72  =  144
balance by -72: 6a + 72 – 72  =  144 – 72
  6a  =  72
Use known division facts: a  =  72 ÷ 6
  a  =  12

Find perimeters and areas of rectangles using the appropriate formulae, e.g. a square field has sides of 24.75m. What is its perimeter? What is its area?

Measurement

  • solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate
  • convert between miles and kilometres

When working on multiplication and division and/or measurement there are opportunities to make connections between them by solving problems such as;

  • 1 pint = 0.57 litres, how many litres in 8 pints? How many pints in 12 litres?
  • Dan was driving between two cities in France. The sign said the distance was 185km. He wanted to know what that was in miles. How can he find out? How many miles is it?

Statistics

  • calculate and interpret the mean as an average

When working on multiplication and division and/or statistics there are opportunities to make connections between them, for example:

Solve problems, e.g. find the mean monthly temperature for Reykjavik, Iceland

Monthly temperatures for Reykjavik
Jan Feb March April May June July Aug Sept Oct Nov Dec
-2°C -1°C 3°C 6°C 10°C 13°C 14°C 14°C 11°C 7°C 5°C -2°C

Making connections to this topic in adjacent year groups

Year 5

  • identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers
  • solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes
  • 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
  • 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 numbers mentally drawing upon known facts
  • 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.
 

Key Stage 3

  • use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property
  • use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
  • use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals
  • recognise and use relationships between operations including inverse operations
  • use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations
  • interpret and compare numbers in standard form A x 10n 1≤A<10, where n is a positive or negative integer or zero
  • define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%
  • interpret fractions and percentages as operators
  • use a calculator and other technologies to calculate results accurately and then interpret them appropriately

Cross-curricular and real life connections

Learners will encounter multiplication and division in:

Art & Design

Within the art and design curriculum there are opportunities to connect with multiplication and division, for example in the introduction of the Key Stage 2 Programme of Study it states that pupils should be taught to develop their techniques, including their control and their use of materials, with creativity, experimentation and an increasing awareness of different kinds of art, craft and design. This could include designing and creating life size models of, for example a Barbara Hepworth sculpture or a Van Gogh painting where the children need to find realistic measurements and then scale them down using division.

Geography

Within the geography curriculum there are opportunities to connect with multiplication and division, for example 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. Work on multiplication and division could include converting between miles and kilometres and vice versa when looking at distances between countries or famous locations, making currency converters for pounds stirling and the currency in the country they are investigating.

See, for example:

History

Within the history curriculum, there are opportunities to connect with multiplication and division, for example in the introduction of the Key Stage 2 Programme of Study it states that ‘in planning to ensure the progression described above through teaching the British, local and world history outlined below, teachers should combine overview and depth studies to help pupils understand both the long arc of development and the complexity of specific aspects of the content’. The history curriculum requires that pupils should ‘compare aspects of life in different periods’, suggesting comparisons between Tudor and Victorian periods, for example. Scale models could be one way of learning about life in different periods.

See, for example:

 

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