Section 1.2 Multiplication and division with decimals Learning objectives
Resources and homework
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Multiply a decimal number by another decimal number Divide by a decimal by changing the calculation to division by an integer
Student Book 1.2: pages 12–15 Practice Book 1.2: pages 6–7
Making mathematical connections
Making cross-curricular connections
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Place value manipulation Standard form
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Science – calculating with decimal numbers Relevance – basic mathematical fluency with decimals
Prior learning • •
Students must be able to multiply three-digit integers by two-digit integers. They should also be able to multiply decimal numbers by 10, 100, 1000 and so on. Students should be able to use pencil and paper methods for division of integers.
Working mathematically • •
Encourage students to estimate the answer before calculating in order to check that their answers are sensible. Structure tasks so students can work out the methods for themselves, either by increasing the difficulty incrementally or through one straightforward and one complex example.
Common misconceptions and remediation • • •
Multiplication: Students may forget to insert the decimal point or put it in the wrong position. Division: Students may change both numbers into integers, and then have the decimal point in the wrong place. Students should be able to reduce these errors with repeated emphasis on the rules for multiplying and dividing with decimals.
Probing questions •
Use this calculation to write down more questions with the same answer: 108.8 ÷ 3.4 = 32.
Literacy focus • •
Key terms: decimal place (dp), decimal point Ask students to describe their method for multiplying and dividing with decimals.
Part 1 •
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Ask students quickfire, linked, mental multiplication questions, gradually increasing the level of difficulty, e.g. 6 × 7 (42) followed by 12 × 7 (84). Ask how they obtained the second answer. Students may know the 12 times table, or realise it is double the previous answer. Now use other numbers, e.g. 9 × 8 (72), then 90 × 80 (7200). Again ask how they obtained the second answer. Next give several division questions with integer values and answers, e.g. 342 ÷ 3 (114), 8561 ÷ 7 (1223), 2784 ÷ 12 (232). Discuss the methods used: chunking, short division and long division.
AQA GCSE Maths Higher Teacher Pack – Chapter 1
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