Divide by 10 and 100 Learners should know that: • dividing by 10 changes thousands into hundreds: hundreds into tens: tens into units:
• dividing by 100 changes thousands into tens: hundreds into units:
4 000 ÷ 10 = 400 400 ÷ 10 = 40 40 ÷ 10 = 4
which means that a nought is removed from the end of the whole number.
4 000 ÷ 100 = 40 400 ÷ 10 = 4
which means that two noughts are removed from the end of the whole number.
Round off to the nearest 10, 100 or 1 000 and compensate Rounding off plays a role in two different ways: • On its own it is used to estimate answers:
81 × 79 ≈ 80 × 80 ≈ 8 × 10 × 8 × 10 ≈ (8 × 8) × (10 × 10) ≈ 64 × 100 ≈ 6 400
• In problem solving, it is used in combination with compensation, which means that whatever gets added, needs to be subtracted again so that the relevant statement remains equivalent: 47 + 34 = (47 + 3) + (34 – 3) = 50 + 31 = 81
Build up and break down numbers Learners should be able to use place value to: • expand any 4-digit number into thousands, hundreds, tens and units: 4 321 = 4 000 + 300 + 20 + 1
• build any 4-digit number using thousands, hundreds, tens and units: 7 000 + 20 + 1 = 7 021 This skill is very important in addition, subtraction, multiplication and division problems.
Add and subtract units to/from any 4-digit whole number • Since units must be added and subtracted, focus on the number of units. Strategies that could be used:
• adding/subtracting units:
4 864 + 8 = 4 860 + (4 + 8) = 4 860 + 12 = 4 872 4 864 – 8 = 4 860 + (4 – 8) = 4 850 + (14 – 8) = 4 850 + 6 = 4 856 • filling up tens:
4 864 + 8 = (4 864 + 6) + 2 = 4 870 + 2 = 4 872 (from 4 864, count 8 forwards) 4 864 – 8 = (4 864 – 4) – 4 = 4 860 – 4 = 4 856 (from 4 864, count 8 backwards) Rule: If units are added or subtracted, focus on only units.
Add and subtract multiples of 10 and of 100 to/from any 3- or 4-digit number Learners should understand that 3- and 4-digit numbers can be interpreted in different ways, e.g.: • 234 = 2 hundreds + 3 tens + 4 units = 20 tens + 3 tens + 4 units = 23 tens + 4 units
28 Section 3: Teaching and learning Mathematics
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