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-
multiply 3-digit by 2-digit
numbers; extend to multiplying decimals (1d.p. &
2 d.p.) by 1-digit whole numbers
(p 104)
- make and justify estimates & approximations
of calculations
(p102)
- check a result by considering
whether it is of the correct order of magnitude
and by working the problem backwards
(p110) |
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multiply
multiplication
divide
division
subtract
subtraction
add, addition
guess, estimate
approximate approximately not enough approximately
equal to (& symbol)
roughly
nearly
too many
too few
enough |
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Introduce
problem leading up to X of two nos with at least
2-digit; ask pupils to explain how they solved it.
Eg: 5 minibuses with 19 pupils in each one. Total?
15 buses? 26 buses? 243 buses?
Review understanding that X is repeated addition
and highlight one efficient method, eg: grid method. |
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Activities
involving long multiplication.
- Focus on grid method for a number of problems.
(Eg: see p 104) (Rough estimate by approximating
before each calculation.)
- Explain distributive law and link to grid method
Eg: 26 x 19? Estimate: 25 x 20 = 500 Calculation:
26 x 19 = 20 x 19 + 6 x 19 OR 26 x 20 - 26 x 1 =
494
- Discuss other informal methods of multiplication
as appropriate.
- Check results from order of magnitude & by
working backwards
For practice in speed multiplication of two 2-digit
numbers, play:
Batter's Up Baseball |
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| What is 239 x 41? Grid method?
Other methods? |
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- divide
3-digit by 2-digit numbers; extend to dividing decimals
(1d.p. & 2 d.p.) by 1-digit whole numbers
(p106)
- make and justify estimates & approximations
of calculations
(p102)
- check a result by considering
whether it is of the correct order of magnitude
and by working the problem backwards
(p110) |
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Introduce problem
for ÷ of two 2-digit numbers. Share different
pupils' methods. Review understanding that division
is repeated subtraction and highlight one efficient
method, eg: chunking method.
Eg: 19 pupils per minibus, how many buses for all
of Y7 (95 pupils)?
Lower School (285)? Whole school (500)?(last one
has a Remainder
Discuss rounding up/down issue. Plenary? |
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Activities involving
long division
1) Focus on chunking method using a range of problems.
- Carry out rough estimate by approximating first.
- (Chunking links division to repeated subtraction,
in this method, in chunks) Eg: 494 ÷ 19 ?
19 I 494 Estimate: 494 ÷ 19 is approximately
500 ÷ 20 = 50 ÷ 2 = 25 - 380 (19 x 10
= 190, so 19 x 20 = 380, subtract 20 x19) = 114
- 114 ( 6 x 19 = 114, so subtract 6 x 19) = 0 Ans:
20+6 =26
2) Focus on Listing method to solve a range of problems.
- (Listing links division to repeated subtraction).
Eg: 285 ÷ 19? 19, 38, 57, 76, 95, 114, 133,
152, 171, 190, ...List too long so…
0 1 5 19's in 2? 0 19 I 2 8 5 19's in 28? Look at
list: 1x19=19 Rem 9 - 1 9 bring down 5 0 9 5. 19's
in 95? Look at list: 5x19=95 - 9 5 0 0 no Rem: stop.
Ans: 15
- Discuss other informal methods of division s appropriate.
- Check results from order of magnitude & by
working backwards. |
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1) Return to Minibus
problem :500 ÷ 19=26 Remainder 6. Is this
26 or 27 minibuses?Should you always round up? Why?
OR
2) Discuss informal methods of division for decimals,
eg: 2.4 x 1.2. |
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