Mathematics and English progression

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Step 6 Objective

Use standard column procedures for multiplication and division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations.

Examples of what pupils should know and be able to do

1.89 × 23 is approximately 2 × 20 = 40, and is equivalent to 1.89 × 100 × 23 ÷ 100 or 189 × 23 ÷ 100

428 ÷ 3.4 is approximately 400 ÷ 4 = 100 and is equivalent to 4280 ÷ 34

• FTM(S)Y789 pp. 104 - 107 - Acrobat pdf document (47Kb)

• Photos question - Rtf (rich text format) document (204Kb)
• Calculators question - Rtf (rich text format) document (84Kb)

Probing questions

37 × 64 = 2368. Explain how you can use this fact to devise calculations with answers 23.68, 2.368, 0.2368.

2368 ÷ 64 = 37. Explain how you can use this fact to devise calculations with answers 3.7, 3700, 0.37?

3.2 × 23 = 73.6. Explain how you can use this fact to devise other calculations with the same answer.

73.6 ÷ 3.2 = 23. Explain how you can use this fact to devise other calculations with the same answer.

What if pupils find this a barrier?

If pupils have difficulty with numbers involving decimals, explore sets of related facts. For example: 137 × 29 = 3973, what is:

13.7 × 29
137 × 2.9
13.7 × 2.9?

Given that 3.5 × 3.2 = 11.2, make up some other questions with the answer 11.2.

Make up questions with answer 112, 1.12, etc.

The FTM(S)Y789 pp. 104-107 - Acrobat pdf document (47Kb) gives an outline of progression. It is important to identify the stage that pupils have currently reached, then look for the next appropriate step for each individual.