reduce numerical demands (initially)

One of a number of tried and tested technique for teaching work that students find hard to learn found in teaching tricks and tips

The plan for this page is to build up examples as above and include links to "teaching Higher work to Foundation students" videos and more easy on the eye student "remind-me" videos. For now though here is a list of situations where we have found it helps students to learn when teachers reduce the numerical demands initially.

product of prime factors

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 write down, as a product of powers of its prime factors, (i) the highest common factor (HCF) of E and F (ii) the lowest common multiple (LCM) 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. Each lap Naoko runs takes her 30 minutes. Each lap Irina runs takes her 35 minutes. ... when they are next ... together.
strand 10	Word problems like: Habiba is going to make some cheese and pineapple sticks for a party. She buys some packets of cheese and some tins of pineapple. There is enough for 20 cheese cubes in each packet of cheese. There is enough for 24 pineapple chunks in each tin of pineapples. ....
strand 11	Students ALSO need to be able to divide by other primes e.g. 7 and 11 and 13 etc. AND students need to reason about which primes to try to divide by.

factorPRIME FACTORproductOFprime does it divide by ... tricks

factorPRIME FACTORproductOFprime 80

factorPRIME FACTORproductOFprime 63

factorPRIME FACTORproductOFprime divide by 9 trick

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

Start with situations where one continues a sequence to fill in the table of values - see algebraGraphs1.pdf - or below for a quick peak.

calculator skills - don't ask students to write their answer correct to ... until students have built up their skills