Download deeper understanding

Objectives of this session
Explore why deeper understanding is important
Look at what it is and what it isn’t
Give you - CPD session to take back to school
Look at tasks to develop deeper understanding
Give you – a range of tasks to try in school
Why is a deeper understanding of the basics so
important?
“Why cant they remember how to do this?”
“Why cant they do this its really simple?”
Really broad – just going to focus on multiplication principles can be applied to all areas
Very topical – see article
Expanding
Factorising
Standard Form
Fractions
Surds
Indices
What it is, what it isn’t
• What is deeper understanding
• Not more of the same
• Knowing and being really confident with the basics
• Challenging thinking to apply the basics in a range of situations
• Making the links
• Always refer back to the basics
What are the basics
Basic Laws of number manipulation
• Associative
• Commutative
• Distributive
Expanding
Factorising
Standard Form
Fractions
Surds
Indices
Which laws are these “rules,
explanations” based on
Supporting division
Factorising
18 x 18 = (18 x 3) +(18 x 6)
324 ÷ 18
324 ÷ 3 = 108 , 108 ÷ 6 = 18
9 x 6 = (9 x 2) + (9 x 3)
54 ÷ 6
54 ÷ 2 = 27
27 ÷ 9
What is 816 ÷ 24
Factorising
• 54 + 72 = 9(6 + 8) could you write this in any other way?
•8x7+8x5
• 8 (7 + 5)
• ab + ac
•axb+axc
• a(b + c)
(3 x 4) ÷ (6 x 4) = (3 ÷ 6) x (4 ÷ 4)
Explain why this works
(4 x 8) ÷ ( 2 x 4 ) = (4 ÷ 2) x (8 ÷ 4)
The Star Ship Enterprise travelled 3 × 1015 km at a speed of 1.5 × 103 km/s. How long did
the journey take?
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑡𝑖𝑚𝑒 =
𝑠𝑝𝑒𝑒𝑑
3 × 1015
𝑡𝑖𝑚𝑒 =
1.5 × 103
𝑡𝑖𝑚𝑒 = (3 × 1015 ) ÷ (1.5 × 103 )
𝑡𝑖𝑚𝑒 = 3 ÷ 1.5 × 1015 ÷ 103
𝑡𝑖𝑚𝑒 = 2 × 1012 s
1. First rearrange the sum to make it
easier.
2. You now have two easy sums to do.
3. These give you your answer in
standard form.
Ed Southall – Teaching for deeper
Understanding