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OUTCOME
A student:
MA1-6NA: uses a range of mental strategies and concrete materials for multiplication and division
TEACHING POINTS | After students have divided a quantity into equal groups (eg they have divided 12 into groups of four), the process can be reversed by combining the groups, thus linking multiplication and division. |
| When sharing a collection of objects into two, four or eight groups, students may describe the number of objects in each group as being one-half, one-quarter or one-eighth, respectively, of the whole collection. | |
| An array is one of several different arrangements that can be used to model multiplicative situations involving whole numbers. It is made by arranging a set of objects, such as counters, into columns and rows. Each column must contain the same number of objects as the other columns, and each row must contain the same number of objects as the other rows. | |
| Formal writing of number sentences for multiplication and division, including the use of the symbols × and ÷, is not introduced until Stage 2. |
STRATEGIES | Sharing (partitive) – How many in each group? eg ‘If 12 marbles are shared between three students, how many does each get?’ |
| Grouping (quotitive) – How many groups are there? eg ‘If I have 12 marbles and each child is to get four, how many children will get marbles?’ This form of division relates to repeated subtraction, 12 – 4 – 4 – 4 = 0, so three children will get four marbles each. |
LANGUAGE | Students should be able to communicate using the following language: add, take away, group, row, column, array, number of rows, number of columns, number in each row, number in each column, total, equal, is the same as, shared between, shared equally, part left over, empty number line, number chart. |
| The term ‘row’ refers to a horizontal grouping, and the term ‘column’ refers to a vertical grouping. | |
| Refer also to language in Stage One 1 Multiplication and Division |
Recognise and represent multiplication as repeated addition, groups and arrays | model multiplication as repeated addition, eg 3 groups of 4 is the same as 4 + 4 + 4 |
| – find the total number of objects by placing them into equal-sized groups and using repeated addition (Problem Solving) | |
– use empty number lines and number charts to record repeated addition, eg (Communicating) | |
| – explore the use of repeated addition to count in practical situations, eg counting stock on a farm (Problem Solving) | |
| recognise when items have been arranged into groups, eg ‘I can see two groups of three pencils’ | |
use concrete materials to model multiplication as equal ‘groups’ and by forming an array of equal ‘rows’ or equal ‘columns’, eg | |
| – describe collections of objects as ‘groups of’, ‘rows of’ and ‘columns of’ (Communicating) | |
| – determine and distinguish between the ‘number of rows/columns’ and the ‘number in each row/column’ when describing collections of objects (Communicating) | |
| – recognise practical examples of arrays, such as seedling trays or vegetable gardens (Reasoning) | |
| model the commutative property of multiplication, eg ‘3 groups of 2 is the same as 2 groups of 3’ |
Represent division as grouping into equal sets and solve simple problems using these representations | model division by sharing a collection of objects equally into a given number of groups, and by sharing equally into a given number of rows or columns in an array, eg determine the number each person receives when 10 objects are shared between two people
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| – describe the part left over when a collection cannot be shared equally into a given number of groups/rows/columns (Communicating, Problem Solving, Reasoning) | |
| model division by sharing a collection of objects into groups of a given size, and by arranging it into rows or columns of a given size in an array, eg determine the number of columns in an array when 20 objects are arranged into rows of four | |
| – describe the part left over when a collection cannot be distributed equally using the given group/row/column size, eg when 14 objects are arranged into rows of five, there are two rows of five and four objects left over (Communicating, Problem Solving, Reasoning) | |
| model division as repeated subtraction | |
| – use an empty number line to record repeated subtraction (Communicating) | |
| – explore the use of repeated subtraction to share in practical situations, eg share 20 stickers between five people (Problem Solving) | |
| solve multiplication and division problems using objects, diagrams, imagery and actions | |
| – support answers by demonstrating how an answer was obtained (Communicating) | |
| – recognise which strategy worked and which did not work and explain why (Communicating, Reasoning) | |
| record answers to multiplication and division problems using drawings, words and numerals, eg ‘two rows of five make ten’, ‘2 rows of 5 is 10’ |
Learning experiences we develop will be added here
