Multiplication & Division Workshop

Multiplication & Division Workshop Teacher: Who can tell me what 7 x 6 is? Pupil: 42! Teacher: Very good. Now who can tell me what 6 x 7 is? Pupil: 24!

Learning Facts are Easy“According to Jim”

Purpose of this session… • Understand strategies for multiplication and division • Know how to plan and teach multiplication and division • Develop an independent number knowledge programme in the classroom

Overview • Introduce Strategy Stages for Mult/Div • Stage 5 and Stage 6 • Morning tea • Modelling Session (Stage 6-7) • Content higher stages

Multiplication Grid Game e.g. Roll a three and a four: 3 x 4 or 4 x 3

Show 6 x 5 on your Happy Hundreds Board The convention in New Zealand is to regard 6 x 5 as 6 groups of 5 How many cups in each row? How many rows of cups? How many cups are there altogether?

Counting All From One (Stage2-3)

5 10 15 20 25 30 Skip Counting AC (Stage 4)

5 + 5 =10 10 10 Repeated Addition EA (Stage 5) 10 + 10 + 10 = 30

Where were most of your class?

8 x 5 = 40 8 x 1 = 8 So 40 + 8 =48 Derived Multiplication AA (Stage 6)for 8 x 6

Derived Multiplication AA (Stage 6) 8 x 6 10 x 6 = 60 60- (2x6) =48 2 x 6 = 12

Knowledge Strategies Focusing on Stage 5 and Stage 6 Basic Facts can be effectively taught with understanding through using strategies. Knowledge of Basic Facts to 10x10 are then useful for using advanced strategies for harder problems. How you solve a mult/div problem.

Using Basic Fact Data IKAN? Basic Fact Tests? • Which facts do they know already?, • What needs to be taught and then practiced next? • What assessment information do/can you use for basic facts? • How is it used summatively / formatively?

Assessing Analysing data Planning Teaching Practicing / Applying Teaching Multiplication Basic Facts Efficiently

Multiplication Counter Game Teaching Practising Assessing Which of the basic facts activities in your classroom are focusing on teaching?

Teaching to develop understanding and application of basic facts rather than just fact recalling Early Additive: Stage 5 • Establish link between multiplication and repeated addition. E.g. 3 x 6 = 6 + 6 + 6 Advanced Additive: Stage 6 • Deriving unknown facts from known facts and apply deriving strategies to larger numbers x0 x1 x2 x5 x10 x9 x3 x4 x6 x7 x8

Stage 6Deriving unknown facts through using strategies x9, x3 x4 x6, x7 x8 (and apply these strategies to larger numbers) How can we solve the 18x table?

What else do I know? 3 x 5 =15

Stage 6: Multiplying by 10 How do you describe what happens? Not just “add a zero” The numbers move one place value along 2 3 0

Division Share a division story problem for the following: 8 ÷ 2 = 4

Different Types of Division 8 ÷ 2 = 4 • Division by Sharing: 8 lollies shared between 2 people. How many lollies does each person have? • Division by Grouping: John has 8 lollies, he puts 2 lollies into each bag. How many bags of lollies will he have?

Play “Is it divisible?” Dice: 2,3,4,5,6 choice

Existing Knowledge & Strategies Using Imaging • Using Number Properties Using Materials New Knowledge & Strategies Stage 6 Advanced Additive (NC Level 3)Book 6 A Little Bit More a Little Bit Less. The Royal Cooking Lesson What diagnostic snapshot would you ask?

Modelling Session

How does each person benefit? StudentsTeacher Modelling Book Thinking Groups Diagnostic Snapshot at start of lesson

+ 7 - 4 x ÷ “6 - 3 = 3, and 7 - 4 = 3” Arithmefacts + 6 - 3 x ÷ 6 + 3 = 9 6 - 3 = 3 6 x 3 = 18 6 ÷ 3 = 2

What is Multiplicative Thinking? Multiplicative thinking is not about the type of problems you solve but how you solve it. Although 3 x 18 is a multiplication problem, if it is solved by adding 18 + 18 + 18 then you are not thinking multiplicatively but are using an additive strategy. Similarly an addition problem e.g. 27 + 54 can be solved multiplicatively by doing; (3 x 9) + (6 x 9) = 9 x 9

Stage 7 AM (NC Level 4)book 6 Page 41 • Take a moment to read….. • Required Knowledge? • Knowledge being developed? • Key Ideas?

3 x 18 There were 3 minivans each with 18 children on them going on a school trip. How many children were there altogether?

3 x 18 Compensation with tidy numbers (rounding) (3 x 20) - (3 x 2) Place Value Partitioning (splitting) (3 x 10) + (3 x 8) Proportional Adjustment 6 x 9 Splitting Factors 3 x (3 x 3 x2) Standard Written Forms How would you use the teaching model to teach these strategies? Book 6 p.52 onwards

3 x 10 = 30 3 x 8 = 24 10 10 10 Place Value Partitioning 3 x 18 30 + 24 = 54

3 x 20 = 60 60 - (3 x 2) = 54 10 10 10 10 10 10 Tidy Numbers 3 x 18

6 x 4 = 3 x 8

Using Imaging for 3 x 18

3 x 9 3 x 9 3 x 18

3 x 18 6 x 9 x 2 ÷ 2 3 x 18 = 6 x 9

Generalise using number properties: Proportional Adjustment is about re-arranging the factors to create a simpler problem (Associative Property) 12 x 33 (2 x 6) x 33 2 x 2 x 3 x 33 4 x 99 6482 x 5 12 x 33

Using Number Lines to show 3 x 18 Proportional Adjustment Place value Tidy Numbers 54 A 30 54 B 54 60 C

28 42 13 59 34 17 48 51 Multiplication Roundabout (MM6-6) Start

28 42 13 59 34 17 48 51 Multiplication Roundabout (MM6-6) E.g. Roll a 3. Move 3 places then multiply the number by 3

59 x 3 = 180 - 3 = 177 (place counter between 150 & 200) 28 42 13 59 34 17 48 51 Multiplication Roundabout (MM6-6)

Let’s look at Stage 7 Division… Tidy Numbers Place Value 72 ÷ 4 Proportional Adjustment Reversing

72 ÷ 4 Compensation with tidy numbers (rounding) Place Value Partitioning (splitting) Proportional Adjustment Splitting Factors Standard Written Forms

Which strategy will you choose?3680 ÷ 8 = A sheep station has eight paddocks and 3,680 sheep. How many sheep are there in each paddock?

3680 ÷ 8 Compensation with tidy numbers (rounding) Place Value Partitioning (splitting) Proportional Adjustment Splitting Factors Standard Written Forms

Multiplication & Division Workshop