1. 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
Introduction of that the session is about, what you are going to gain from the session, what you will take away

2. Why is a deeper understanding of the basics so important
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
Why is regular application important, how often do we and our colleagues become frustrated because our students cant remember the rule for…. The explanation for…..
We are going to cover a principle of establishing the basics, and applying them to a range of mathematical situations, but regularly doing so in a way that relies on the basic knowledge of number manipulation

3. Expanding Factorising Standard Form Fractions Surds Indices
Factorising
Standard Form
   
Fractions
Surds   
Indices
In pairs/small groups take 5 minutes to review the 6 headings, note down the key words you use to remind your students of how to tackle these types of questions, what words do you use to explain

4. 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
Move away from any “rules” or tricks apart from the basic number rules
Be really confident with these, present opportunities to practice them and always keep referring back to them

5. Basic Laws of number manipulation
Associative
Commutative
Distributive
Brief discussion about the 3 laws of number

6. Which laws are these “rules, explanations” based on
Expanding
Factorising
Standard Form
   
Fractions
Surds   
Indices
Which laws are these “rules, explanations” based on
Relook at the table, which of these rely on which number law
Give a number example for each,

7. Supporting division
Factorising
18 x 18 = (18 x 3) +(18 x 6) 324 ÷ ÷ 3 = 108 , 108 ÷ 6 = 18 9 x 6 = (9 x 2) + (9 x 3) 54 ÷ 6 54 ÷ 2 = ÷ 9
What is 816 ÷ 24

9. Factorising 54 + 72 = 9(6 + 8) could you write this in any other way?
8 x x 5
8 (7 + 5)
ab + ac
a x b + a x c
a(b + c)

10. (3 x 4) ÷ (6 x 4) = (3 ÷ 6) x (4 ÷ 4) Explain why this works
The Star Ship Enterprise travelled 3× km at a speed of 1.5× km/s. How long did the journey take?
𝑡𝑖𝑚𝑒= 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑠𝑝𝑒𝑒𝑑
𝑡𝑖𝑚𝑒= 3× × 10 3
First rearrange the sum to make it easier.
You now have two easy sums to do.
These give you your answer in standard form.
𝑡𝑖𝑚𝑒=(3× )÷(1.5× 10 3 )
𝑡𝑖𝑚𝑒=3÷1.5 × ÷ 10 3
𝑡𝑖𝑚𝑒=2× s

11. Ed Southall – Teaching for deeper Understanding