Download Why everyone should learn the number laws

Why everyone should learn the number laws
• Starter questions on board
• What are the number laws?
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What do you know? Name that law
Jo Boaler film – go through how these link to the number laws
• Why teach them?
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Importance of number fluency – example of Y13 resit student
Use of generalisation early on – introduces algebra
Using proper mathematical language from early age
• How did we teach them?
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Family pairs
How we structured the lessons: one key concept; variation; concept / non-concept; Dong Nao Jing
Worked examples on board
Worksheet to try
Go through answers
• Benefits and links to other topics
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5 min think
they appear EVERYWHERE
• What staff and kids think
• Recap question from start
Mastery Maths
Please have a go at these
questions…
9999 + 999 + 99 + 9 + 5 =
0.62 x 37.5 + 3.75 x 3.8 =
What Shanghai has taught us
Why everyone should learn the number laws
• What are the number laws?
• Why teach them?
• How did we teach them?
• Benefits and links to other topics
Name that law!
a+b=b+a
a×b=b×a
(a + b) + c = a + (b + c)
(a × b) × c = a × (b × c)
a - b - c = a - (b + c)
a-b-c=a–c–b
a ÷ b ÷ c = a ÷ (b x c)
(a + b) × c = a × c + b × c
1. Commutative law of addition and multiplication
a + b = b + a; a x b = b x a
2. Associative law of addition and multiplication
(a+b) + c = a + (b + c);
(a x b) x c = a x (b x c)
3. Distributive law a x b + a x c = a x (b+c)
4. Laws of subtraction
a – b – c = a – (b + c);
5. Law of division
a ÷ b ÷ c = a ÷ (b x c)
a–b–c=a–c–b
Why explicitly teach the Number Laws?
• https://www.youcubed.org/what-is-number-sense/
How did we teach the Number Laws?
5 big ideas
Family pairs
• One key concept
• Proper vocabulary
• True / false
• Dong Nao Jin
2 x 5 = 10
4 x 25 = 100
8 x 125 = 1000
Need to learn these!!!!
Warming-up:
Can you find the same factor?
(1) 35×23 + 65×23
=(35 + 65)×23
(2) 52×16 + 48×16
=(52+ 48)×16
(3) 55×12 － 45×12
=(55 － 45)×12
(4) 19×64 － 9×64
=(19 － 9)×64
Which law of subtraction would make these easier?
(Don’t calculate!)
(1) 100-35-45=
(2) 447-190-47=
(3) 189-28-72=
(4) 321-45-121=
100-(35+45)
447-47-190
189-(28+72)
321-121-45
Which one is easier to calculate?
(1) 3200÷25÷4
3200÷（25×4）
(2) 7000÷125÷8
7000÷（125×8）
(3) 800÷8÷20
800÷（8×20）
(4) 140÷7÷4
140÷（7×4）
a÷b ÷ c = a ÷ ( b × c )
• Have a go yourselves
• Pay attention to:
• The questions themselves
• The nature of the task
Make these commutative
What goes in the
missing box?
Complete the following:
A) 17×4 + 17×6
B) 63×34 - 63×24
C) (8+10) X 125
D) 99×12
E) 999×99 + 99
True or false?
(22 – 17) × 35 = 22 × 35 – 22 × 17
78 × 91 + 91 × 25 = 78 + 25 × 91
2 × (3 × 4) = 2 × 3 × 2 × 4
Now try these:
Use different laws to calculate
84 x 25
1000 ÷ 40
Dong Naojin: choose the right answer
The boy was solving the number sentence:
（ 25 +50）×4 , he calculated like this, 25×4+50
What’s difference between the wrong answer and
the right answer?
（25 +50）×4
= 25 ×4+50×4
25×4+50
A. 50
B. 100
C. 150
D.200
1. Rewrite each of these in a way that makes them easier to do
2. Find the answer, writing your workings mathematically
(1) 25＋34＋66 =
(2) 25×40×78 =
(3) 56＋72＋44 =
(4) 75×8×2×125 =
•In each pair of calculations, which one would you prefer to work out? Explain
your choices.
A
35 × 0.3 + 3.5 × 7
or B
3.5 × 0.3 + 35 × 7
C
6.4 × 1.27 – 64 × 0.1
or D
6.4 × 1.27 – 64 × 0.027
E
52.4 ÷ 0.7 + 524 ÷ 7
or F
52.4 ÷ 0.7 – 524 ÷ 7
G
31.2 ÷ 3 – 2.4 ÷ 6
or H
31.2 ÷ 3 – 1.2 ÷ 0.3
• Go through the answers
Dong Naojin:
solve in easier way
25×28
(2) 25×28
(1) 25×28
=（20+5）×28
=25×（20+8）
=20 × 28+5 × 28
=25 × 20+25 × 8
=560+140
=500+200
=700
=700
(3) 25×28
=25×（4×7）
=（25×4）×7
=100×7
=700
Benefits and links to other topics
• Number calculations and fluency
• Collecting like terms
• No more BODMAS!
• Factorising
• Area of trapezium
• Angle calculations
Tick and cross: Are they like terms or
not in each group?
TWO SAMEs
 variables
 power of each variable
 TWO DOESN'T MATTERs
 order
 coefficient
①2ab、2b
②2. 3a、- 4. 5a
③2a b 、- 3b a
2 2
2 2
④3x y、2y x
2
2
Steps of Collecting like terms
③9a b  4a b
2
2
=  9- 4  a b
2
 5a b
2
① Combine the
coefficient of like terms
② write down the result of
coefficient, and maintain the
common factor of both terms
Commutative can be very useful
Family Pairs!
20m
9.5m
What staff / pupils think
Mastery Maths
Would you now do them
differently?
9999 + 999 + 99 + 9 + 5 =
0.62 x 37.5 + 3.75 x 3.8 =
What Shanghai has taught us
Sharing of resources
• Link to all lessons: http://tinyurl.com/shanghaigoogledrive
PLEASE look, add, comment – this link gives editing rights
http://tinyurl.com/sussexshanghaicpd
Contains: all resources from our CPD sessions
all lessons that are on Google drive above