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Number pupils 1
to 30 (for a class of 30). Draw 2 giant circles
with a sizeable overlap on board (or floor if space).
Label one 24 and the other 30.
Ask pupils with factors of 24 and 30 to stand in
front of correct circle.
Are
all possible factors present? How can we tell? (Place
pupils in ordered pairs.) What’s special about
the factors in the overlap? (Common factors.)
Which is HCF?
Repeat for other numbers - or add 3rd number (e.g.
13,18, 30).
Which
numbers will only need 2 pupils? (Prime numbers.)
Which pupil will make
the most appearances? (1) |
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- To be able to
recognise and use multiples (including LCM), factors
(including HCF) and prime numbers.
- To use tests of divisibility.
- To be able to rapidly recall multiplication facts,
and use to derive related division facts. |
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multiple,
common multiple
LCM, factor common factor HCF
divisor, divisible divisibility prime
prime factor
factorise |
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Use Eratosthenes Sieve or 1-100 grid
to solve a problem involving multiples and prime
numbers.
Eg:
In Selly Oak Young Runners
Club, all runners in training stop for a breather
on a regular basis. Neil, the new boy, stops every
third lamp-post; Sukhvinder stops every 5 lamp-post;
and Manjit, the most seasoned runner only stops
every 10 lamp-posts.
Q: - If there are 200 lamp-posts during their 5km
training run:
- Which lamp-posts are visited the most?
- Which ones do both Neil and Sukhvinder stop at?
- Neil and Manjit?
- All 3runners?
- Which is the last lamp-post all 3 stop at? (HCF). |
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1. Range of activities
involving factors, multiples and prime numbers.
Include tests of divisibility to identify factors.
Eg 1: Factors of 16: 1
2 4 8 16
Factors of 12: 1 2 3 4 6 12
Eg 2: Eratosthenes Sieve.
2. Link to simplification of fractions.
HCF of 8 and 12?
CFs: 1, 2, 4
HCF: 4
8 = 2
12 3
That is, divide numerator & denominator by HCF
simplest equivalent fraction
3. Extend to problems.
ALSO USEFUL:
Alien
Tables
- find the correct multiples and hyperblast the
rest! |
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HCF
of 32 and 42?
LCM of 32 and 42?
Use to review strategies used in lesson to find
factors and multiples faster, more easily, without
omissions.
Eg:
- rapid recall of tables
- divisibility tests
- find factors in pairs
- simplify word problems |
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OHS
N5a/1: Related Facts
Use starting fact to derive as many other facts
as possible.
(Useful exercise to quickly assess range of established
strategies.)
OR
BGfL's
Mental Gym
- ever popular . Mental strategies against the clock! |
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- To be able to
use strategies for mental addition & subtraction,
including complements to 100.
- To be able to use strategies for mental multiplication
& division (with jottings), extending
to decimals.
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To be able to check a result by considering order
of magnitude. |
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1. Discuss Starter
and draw up list of strategies to for efficient
mental calculations.
Eg: If times both numbers
in 5.6 ÷ 7 by the same factor (2, 10, 1000
…), the answer stays the same.
2. Compare standard written methods.
3. Review checking by approximating: 5.28
x 7 ˜ 5 X 7 ˜ 35.
4. Highlight common misconceptions,
Eg: 0.6 x 0.02 = 0.012
not 0.12 Prevent by approximating 1st. (see
Starter). |
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Activities requiring
range of mental strategies using all 4 operations,
including:
- associated division facts;
Eg: 8 x 9 = 72
72 ÷ 8 = 9
- partition:
Eg: 3.2 x 9 = 3.2 x 10 – 3.2 x 1 = 28.8
- breaking down into factors:
Eg: 288 ÷ 12 = 288 ÷ 3 ÷ 4
- divisibility tests for larger numbers;
Eg: 288: (sum of digits are divisible by 3)
so 288 is divisible by 3.
- deriving known facts from unknown facts.
Eg: 0.7 x 0.6 = 7 x 6 ÷ 10 ÷ 10 =
0.42
- doubling & halving.
Eg: 4.5 x 14 = 9 x 7= 63
ALSO USEFUL:
Make
a Million – Multifacts!
- rapid fire interactive multiplication game. |
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Review range of
teaching methods used.
Eg: 18 X 7.5 =
18 X 15 ÷ 2
9 X 15
18 X 7 + 18 X 0.5
18 X 5 + 18 X 2.5
10 X 7.5 + 8 X 7.5
20 X 7.5 – 2 X 7.5
(and X 8 = X 2 X 2 X 2) |
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