1. The Learning Framework In Number: Multiplication & Division
Chris Francis

2. Count Me In Too Counting On Taking Off With Numeracy
The Multiplication and division aspect of the learning framework underpins:
Count Me In Too
Counting On
Taking Off With Numeracy

3. Structure
Early multiplication and division strategies focus on the structure and use of groups of things.
A composite unit is formed when a student takes a group of items and treats it as a unit.
Recognising units is not sufficient. It is necessary to develop ways of coordinating the groups that are formed.
Rather than emphasising individual items in a group students develop strategies for understanding and using composite units.
Seeing both the parts and the whole in a group of things contributes to the development of composite units.

4. Not intended to be aligned
Typical progression
Unable to see the structure of the composite unit
Use the structure of the composite unit when items are visible
Coordinate units of units when the items are not present
Not intended to be aligned
Counting individual items
Skip counting
Counting in multiples
Keeping track of multiples

5. Level 1: Forming equal groups
The student:
uses perceptual counting and sharing to form equal groups
finds the total of the groups, counting by ones
does not take notice of the structure of the groups when finding the total.
NES1.3
PAES1.1
There will be some students who will be unable to operate at level 1
For these students, teaching will need to focus in on forming equal groups of specified sizes.

6. Level 2: Perceptual multiples
The student :
uses items to form equal groups
finds the total of the groups through rhythmic, skip or double counting, only when the items are visible
cannot deal with concealed items.
NS1.3
PAS1.1

7. Level 3: Figurative units
The student:
does not rely on items being visible
counts forwards or backwards using multiples (or a combination of multiples and rhythmic counting )
uses perceptual markers (e.g. fingers) to keep track of the groups
reconstructs the groups before counting.
NS1.3
PAS1.1
VDO Scruffy: 5:44 – 6:10

8. Level 4: Repeated abstract composite unit
The student:
uses repeated addition or subtraction to find the total
does not need perceptual markers to represent the groups
might use fingers to keep track as they count
might use skip counting or a double count.
NS1.3, NS2.3
PAS1.1, PAS2.1
VDO: Cutie girl 7:10-7:50

9. Level 5: Multiplication & division as operations
The student:
recalls a wide range of multiplication and division facts
uses multiplication and division as inverse operations to solve problems
explains the composite structure in a range of contexts; not simply recalling facts.
PAS2.1
NS2.3

11. Observations
Students are usually confident with some multiples over others.
Strategy use is strongly dependent on knowledge of multiples.
Students may use a combination of strategies.
Students typically appear more confident with multiplication than division.
Modeling of strategies is needed.
The use of arrays is useful in developing visualisation.
To support the teaching of M&D, I would not group according to levels. Grouping may be based around prior to framework level 1, those needing material, those able to visualise – working as a whole class, sharing strategies.