Practice Makes Perfect

Practice Makes Perfect ? …………. When should pupils practice? Why should pupils practice? How should pupils practice?

When? Every day Ideally outside of the main learning time

Why? To embed the learning To sustain the learning To connect the learning To develop the learning To utilise variation in order to improve learning.

Purpose of Variation Develop deep learning rather than superficial learning Provide the necessary repetition to embed and sustain learning Make connections between concepts

Should all pupils access the same practice The simple answer is YES Why Yes? All engaged in the same lesson The practice is designed within the context of variation so its not just about answering questions but exploring the concept.

In designing these exercises avoid mechanical repetition, but instead practice the thinking process with increasing creativity. Gu

HOW

Writing Variation (intelligent) Practice The teacher should know… Why they are designing this variation What knowledge they want the pupils to master Which method the pupils may use Where the pupils may fail How they can help pupils to make the connections All the things we do should service the unchangeable things.

Variation not only helps the pupils discover the secrets of maths for themselves but also help them master one concept. To find out what something is, we need to look at it from different angles – then we will know what it really looks like!

An example: Rounding to the nearest 10 What do we want pupils to notice? that when rounding to the nearest multiple 10 we are particularly interested in the units digit (the bit that is not a multiple of 10) what is half way between consecutive multiples of 10 how far a number is from each multiple of 10

Possible variation examples to draw attention to these things Noticing the units digit by keeping it the same how far a number is from each multiple of 10 how far a number is from each multiple of 10

What do you notice What changes and what stays the same? 1 4 + 8 = 2 + 1 = 9 + 1 = 6 + 8 = 4 + 3 = 9 + 3 = 8 + 8 = 6 + 5 = 9 + 5 = 10 + 8 = 8 + 7 = 9 + 7 = 12 + 8 = 10 + 9 = 9 + 9 =   All the things we do should service the unchangeable things

All the things we do should service the unchangeable things

Exploring Zero

The Lesson: When the dividend is zero Generalisation: When the dividend is zero the quotient is zero

The Practice Asked to construct the equation Notice the use of the image s to scaffold and support reasoning

Features of the Practice Consider the practice and connections to be made

Which answer is correct?

Dong Nao Jin

Introducing Algebra 1

Use symbols to express mathematics that you already know What’s the number of each letter on the number line?

Fill in the blanks Use the number sentence with letters to express the laws of arithmetic: Commutative law of addition:( ) Associative law of addition:( ) Commutative law of multiplication:( )Associative law of multiplication:( ) Distributive law of multiplication:( )

2b Use the number sentence with letters to express the operation properties: The properties of subtraction:( ) The properties of division:( ) 2c If the side-length of a square is “a” cm, the perimeter is ( ) cm the area is ( ) cm2.

3 What’s the number of each letter 3 What’s the number of each letter? (1)2,4,6,a,10,12…… a=( ) (2)100,90,b,70,60,50…… b=( ) (3)1,3,6,10,15,x,28,36…… x=( ) (4)1,1,2,3,5,8,13,y,34…… y=( )

4. Match it with straight line 3a b×a x+5 x×1 ba a×a a2 5+x X a×3

Dong Nao Jin What’s the number of each letter in these diagrams? This is dong nao jin, not because its hard, but because its unfamiliar.

True or False ? Why are true/false questions a good form of practice?

Types of Questioning

1. ( ) ( )s added Addition: Multiplication： 2、Right or wrong： Can the number sentence be written as multiplication？ 5+5+5+5+5+5 （ ） 12-3-3-3-3 （ ） 7+7 +9 （ ）

3. Write the multiplication sentence 3+3+3+3+3+3+3=21 ( )×( )=( ) 6+6+6+6=( ) ( )×( )=( ) 4. Challenge Change the number sentence below into multiplication? How many methods do you have? 2+2+2+2+4=12

Key Structures

Use this fact to calculate other facts   43.2 ÷ 6 = 432 ÷ 0.6 = 0.432 ÷ 0.6 = 43.2 ÷ 0.6 =

Identify the missing operation 7.2 0.2 = 1.44 7.2 0.2 = 36 7.2 1.2 = 6 7.2 1.2 = 8.64

Link the two sides of the equation 3.6 ÷ 1.5 = ( ) ÷ 15 4.93 ÷ 8.5 = ( ) ÷ 85 9.8 ÷ 0.07 = ( ) ÷ 7 0.51 ÷ 0.68 = ( ) ÷ 68

Use the pattern to unpack the structure 9 x 0.2 = 9 x 0.2 x 0.2 = 9 x 0.2 x 0.2 x 0.2 = 9 x 0.2 x 0.2 x 0.2 x 0.2 =  

Build the structure   1 ÷ 3 = 2 ÷ 3 = 3 ÷ 3 = 4 ÷ 3 = 5 ÷ 3 = 6 ÷ 3 = 7 ÷ 3 = 8 ÷ 3 = 9 ÷ 3 = 10 ÷ 3 = 11 ÷ 3 = 12 ÷ 3 =

Key Points Variation lies at the heart of practice - this is what makes it intelligent practice There is variation within questions Each question looks at the concept from a different angle, thus supporting extraction of the essence of the concept. The dong nao jin looks at the learning in an unfamiliar context

Updates Numberblocks EYFS Teaching for Mastery Materials

Thankyou for Listening

Dong Nao Jin questions – their purpose