Workshop 3 Multiplication and Division

CENTRE FOR

EDUCATIONAL DEVELOPMENT

Workshop 3Multiplication and Division

CENTRE FOR


CENTRE FOR EDUCATIONAL DEVELOPMENT

Nā te hiahia kia titiro, ā, ka kite ai tātou te mutunga.

You must understand the beginning if you wish to see the end.

CENTRE FOR



Sharing TimeFocusing Questions – What has been working well? What are the difficulties? What is your next step?

Place difficulties on stickers and place them on chart at front of the room.

Homework1) Shifts in development: Journey1) Shifts in development: Journey

2) Use Planning Sheets for Add & Sub2) Use Planning Sheets for Add & Sub

CENTRE FOR



Loopy

Teacher Multiplication and Division Loopy – what are they learning at each stage?

Discussion time -What underpins multiplication and division development?1. Repeated addition / subtraction2. Sets of …3. Division as halves4. Two ways of dividing5. Patterns for times tables6. Estimation

CENTRE FOR



Mult and Div Scenarios

In a small group discuss the scenarios and stage

CENTRE FOR



Two students are solving this problem:

A family has $96.00 to spend at the adventure park.

Each ride costs $4.00.

How many rides can the family go on?

CENTRE FOR



I need to find out how many times I can take

$4.00 away from $96.00

96-492-488-484etc.

…Frank

They think They record

There are 25 lots of $4.00 in $100, $96.00

is $4.00 less, so…

25 x 4 = 100100 – 4 = 96

So24 x 4 = 100

…

Awhina

Discuss each student’s strategy. Are they both thinking multiplicatively?

CENTRE FOR



There was a qualitative difference in the way these two students solved the problem.

Frank’s strategy was additive (rather strange when he was subtracting).

Awhina’s strategy was multiplicative (rather strange since the problem was about division).

CENTRE FOR



Discuss what strategies you use to solve this problem:Each carton holds

36 cans of spaghetti.

There are 5 cartons.

How many cans

of spaghetti is that?

How would this be solved using the commutative property

From: GloSS Form C

CENTRE FOR



Here is a strategy that you might have used along with an equipment representation:

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

5 x 36 = 5 x 30 + 5 x 6

150

= 150

30

+ 30

180

= 180

CENTRE FOR



The first strategy involved the distributive property. This meant that one of the factors was split additively.

5 x 36 = 5 x 30 + 5 x 6

The 36 was split (distributed) into 30 + 6.

CENTRE FOR



Another strategy you may have used on the spaghetti can problem used the commutative property in conjunction with the associative property.

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

5 x 36 = = 18 x 1036 x 5 = 180

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

ten

180

CENTRE FOR



The associative property is about regrouping the factors.

So in 36 x 5 the 36 was split multiplicatively:

36 x 5 = (18 x 2) x 5

= 18 x (2 x 5)

= 18 x 10

= 180

CENTRE FOR



Here’s another example of the associative property:How many small cubes make up this model?

Any way in which you group the factors multiplicatively leaves the product invariant (unchanged).

CENTRE FOR



What if the question changed to this?Give the dimensions of another cuboid with the same volume as this one?

3

5

4

CENTRE FOR



Example 1: What equation could be used to represent this model of division?(There are twelve containers)

CENTRE FOR



Example 2: What equation could be used to represent this model of division?

CENTRE FOR



Both of the stories you made up for the animations can be recorded as 12 ÷ 3 = 4, but the numbers refer to quite different things.The first animation showed 12 ÷ 3 as “twelve shared among three.”

In this case the answer, four, tells how many are in each share.

This is called partitive division (sharing).

CENTRE FOR



There are two kinds of division partitive and quotitive.

The second animation showed 12 ÷ 3 as “twelve separated (measured) into sets of three.”

In this case the answer four tells the number of sets that could be made.

This is called quotitive division (measurement).

CENTRE FOR



Equipment Animations – NZmaths

Happy HundredIce Cream ContainersMultiplication arrays 2Multilink cubes

CENTRE FOR



Lesson ModellingFun with Five

pg 28 Book 6 (book structure)

Powerful Numbers

pg 73 Book 6 (book structure)

CENTRE FOR



Play and Stage1) Play the activity

2) Stage the activity (use book 1 to help)

3) Think about possible adaptations for other stages

CENTRE FOR



Follow up tasks

Check which Basic Facts your students know and target the ones they do not know.

Read the start of Bk 6

Workshop 3 Multiplication and Division

Documents

Transcript of Workshop 3 Multiplication and Division