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The Learning Framework In Number: Multiplication & Division

The Learning Framework In Number: Multiplication & Division. Chris Francis. The Multiplication and division aspect of the learning framework underpins:. Count Me In Too Counting On Taking Off With Numeracy. Structure.

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The Learning Framework In Number: Multiplication & Division

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

  2. 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.

  4. Typical progression Not intended to be aligned

  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

  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

  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

  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

  10. 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.

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