Multiplication / Division – Step 1 and 2

  • Where are they now?

    Structured and supported spatial patterning or sharing games and activities as well as rhythmic songs or rhymes will help to build this concept.

  • Where to next?

    Multiplication: Makes and distributes small equal groups with support (e.g 2 paste bottles per table, 6 crayons per table) Division: Shares collections equally in supported play

  • Purpose

    The ability to ‘unitise’ – that is, to consider a group of objects as a single, countable unit – is perhaps the most critical of all mathematical ideas. It provides the foundation of all mathematical understanding beyond simple counting and in fact provides the basis for our number system itself. It helps students to become more efficient in adding and subtracting as well as allowing them to understand multiplication, division and beyond.

  • Building Multiplication and Division skills

    The skill of multiplying and dividing draws on all of the skills studied in the whole number, addition and subtraction areas.  A failure to progress here generally indicates that one or more of these earlier skills needs to be revisited. Particularly, part-part-whole skills (or ‘combining and partitioning’) will help pave the way for ‘multiplicative’ thinking – that is, thinking based on treating a group of items as a single, countable item in itself. Multiplicative thinking starts with the ability to make and count equal groups and gradually develops into an ability to derive and apply multiplication and division facts and rules. A word of warning here, trying to get students to memorise ‘times tables’ before they have developed a strong multiplicative concept is likely to do more harm than good for a majority of students.

Activities and Assessments (designed to move students from step 1 and 2 to step 3)

Beehives – 1:1 Correspondence

Adapted from ‘Beehive’, Developing Efficient Numeracy Strategies Stage 1 page 34. NSW Department of Education and Training, Professional Support and Curriculum Directorate 2003 Focus: Matching the results of a count with a numeral, while reinforcing the idea of one count per item. How: See Beehives – 1:1 Correspondence sheet and Video Example below

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    Four Dice Totals Activity sheet

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    Download Bees template

Beehives – Matching with manipulatives (Video Example)

Adapted from ‘Beehive’, Developing Efficient Numeracy Strategies Stage 1 page 34. NSW Department of Education and Training, Professional Support and Curriculum Directorate 2003 Focus: Students determine the number of a collection of counters, checking the count against a numeral How: See Beehives – Counting with manipulatives sheet as well as Video Example below

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    Download Beehives boards

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    Bees template

Spin ‘n’ Cover

Focus: Identifying numerals and matching them wih collections, building the idea that numbers are not just about order, but about quantity. How: For small groups of around 4 students. Each student is given a collection of counters of a unique colour, for example one student will have green counters, another student blue counters and so on. On each turn, a student spins the spinner provided (or throws a 10 sided die) and locates a square on the game board that matches the numeral indicated on the spinner. The student then places one of their counters on to that square, then passes the spinner to the next player. If there are no unoccupied squares matching the number indicated on the spinner, the student misses a turn. The aim is to be the first to place three counters (of the same colour) in a row, either horizontally, vertically or diagonally. Questions to ask students during this activity: “What is that number?”, “Can you find a square with that many dots in it?”, “How many dots in that square?”, “Can you count them?”, “Is that number of dots the same as the number on your spinner?”

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    Download Spin and Cover 1-5 sheet

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    Download Spin and Cover 1-10 sheet

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    Spinner to 5

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    Spinner to 10

Numerals and Collections Memory

Focus: Visualising collections for given numerals helps to consolidate the idea of each numeral representing a specific quantity How: See Numerals and Collections Memory sheet

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    Download dot cards 1-10 (random arrangement)

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    Download numeral cards 1-10

Assessment Points – Counting collections

Place a collection of counters (10 or fewer) in front of a student. Ask them to determine ‘how many counters’ as quickly as possible. Note the method they use (e.g. do they count ones, twos or even make a sub-collection of 5?). If they find the task easy, try with a greater number of counters.

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    Download Assessment Points – Matching 1 sheet