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First students meet cases where only dividing by 2 and 10 is required. Once the method is fully mastered then more numerical difficulties can be added. In this case the next stage is needing to divide by 9 (when the 9's fingers trick can be used but the students must also remember to write 9 as a product of its factors); the next where dividing by 3 and 5 are required and finally only for those students who master HCF and LCM would students meet problems where they had to systematically try other prime numbers to find all the prime factors.
| strand 1 | Students also need to be able to divide by 2 and 10 |
| strand 2 | Students also need to be able to divide by 9 (up to 81) |
| strand 3 | e.g. Write down all the factors of 20 |
| strand 4 | Students also need to be able to divide by 3 and 5 |
| strand 5 | e.g. Find the Highest Common Factor (HCF) of 60 and 75 |
| strand 6 | e.g. Find the Lowest Common Multiple (LCM) of 16 and 40 |
| strand 7 | Given that E = 23 x 35 x 5 and F = 24 x3 x 52 (i) the highest common factor (HCF) of E and F |
| strand 8 | Find the Lowest Common Multiple (LCM) of 5, 6 and 9 |
| strand 9 | Word problems like: Naoko and Irina run around a cross-country circuit. |
| strand 10 | Word problems like: Habiba is going to make some cheese and pineapple sticks for a party. |
| strand 11 | Students ALSO need to be able to divide by other primes e.g. 7 and 11 and 13 etc. |
factorPRIME FACTORproductOFprime does it divide by ... tricks
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Here is a list of more situations where the strands reduce the numerical demands, whilst other skills are built up (see also scaffolding)
percent of a number
| percent NC | |
|---|---|
strand 1: 50% of ONLY even digits | (a) Work out 50% of £ 840 (b) Work out 50% of £ 46 (c) Work out 50% of £ 0.64 |
strand 2: 50% of includes odd digits | (a) Work out 50% of £ 87 (b) Work out 50% of £ 520 (c) Work out 50% of £ 15.60 |
strand 3: 10% of | (a) Work out 10% of £ 54 200 (b) Work out 10% of £ 18 (c) Work out 10% of £ 17.40 (d) Work out 10% of £ 234 |
strand 4: 50% or 10% ÷ by 2 or 10 or 10% x by 2 1% or 5% or 25% or 20% | (a) Work out 1% of £ 34 (b) Work out 5% of £ 35 (c) Work out 20% of £ 35 (d) Work out 25% of £ 34 |
strand 5: adding two % from strand 1 - 4 together | (a) Work out 75% of £ 160 (b) Work out 30% of £ 4200 (c) Work out 15% of £ 82.00 |
strand6: 50% or 10% ÷ by 2 or 10 or 10% x by 2 or 10 more than once | (a) Work out 40% of £ 520 (b) Work out 80% of £ 520 (c) Work out 2% of £ 520 (d) Work out 2.5% of £ 520 |
strand 7: % of word problems with calculations from strand 1 to 6 | The headteacher asks 240 students Year 9 students about their GCSE options. 20% of the students chose to study Chinese. Calculate how many students chose to study Chinese. |
strand 8: % increase or decrease word problems with calculations from strand 1 to 6 | (a) Izzy earns £18 000 per year. She will have a pay rise of 2.5% next year. How much will her new salary be? (b) A fridge-freezer costs £260 Hettie gets 5% off the price of the fridge-freezer. Work out how much she has to pay for the fridge-freezer |
plot algebra graphs
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Start with situations where one continues a sequence to fill in the table of values - see algebraGraphs1.pdf - or below for a quick peak.
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- calculator skills - don't ask students to write their answer correct to ... until students have built up their skills
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