The Learning Framework In Number: Multiplication & Division Chris Francis

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

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.

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

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.

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

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

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

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

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.