Stage 1 multiplication and division

Strategies

Students can:

  • use skip counting to solve multiplication and division problems
  • build arrays to solve problems
  • link multiplication and addition facts

Activities to support the strategies

Activity 1 – skip counting

Display a hundreds chart. Students use the hundreds chart to skip count by 2s, 5s and 10s.

Students colour their own hundreds chart following these steps:

  • Colour all the numbers counting by twos in blue.
  • Colour all the numbers counting by fives in red.
  • Colour all the numbers counting by tens in green.

Students discuss:

  • What patterns can you see in your hundreds chart?
  • What numbers did you colour twice?
  • What numbers did you colour three times?

Activity 2 – grouping and skip counting

  • Students use a collection of counters to make equal groups, e.g. using 30 counters, make as many groups of 5 as they can.
  • Students use skip counting to determine the number of counters.

equal groups illustration

Repeat using numbers.

Activity 3 – skip counting

Students use rhythmic or skip counting to find the total number of items that are arranged in the octopus. Students illustrate and write number stories about their combinations using words and symbols.

Octopus has 8 legs illustration

Skip counting illustration

Activity 4 – combining numbers

Students use arrays to make a combination of numbers. They can use items such as counters or marbles to form equal groups, e.g. make four rows of three counters.

Array to make combination of number illustration

Students look at each array of objects. They count the number of objects in each row and then count the number of rows to determine the total number.

Ask students:

  • to explain how they worked out the total number in each array.
  • how their representations to assist  in identifying the relationship between multiplying and dividing groups of numbers.

The teacher writes the language used as students explain the processes, highlighting actions such as:

  • puts together
  • pulls apart
  • groups
  • divided into
  • quarters, halves, thirds.

Students can use the arrays they have made to link multiplication and addition facts, example below:

The teacher uses narrative to bring alive the concepts being explored. Students can demonstrate their understanding by structuring their own experiences or newly acquired knowledge in a narrative form.

Activity 5 – grouping

Display this array from the 2007 Basic Skills Test, Year 3, question 25.

View and print (PDF 964.21KB)

The students look at the array. The teacher says:

Tell me a story about the picture? What might it be?

Example

  • a set of cards
  • a block of chocolate
  • a page of stamps.
  • how many are there altogether?

Encourage students to focus on the strategies used to get to 18 rather than the actual answer by asking probing questions such as:

  • how many ways can you group the chocolates or stamps to get to a total of 18?
  • are there any others?

Make a list of the different ways on a chart

  • Students draw the arrays to match each of these
  • Display the whole BST question

Look at the array below

Ask questions about the whole question.

  • What does ‘colour ALL the ___ mean'?

Students need to know there can be more than one answer.

  • Do you use both the question and the picture of the array to answer the question? Reinforce that students always check all the possible answers.
  • How do you know you have all the correct answers?

Reinforce the need for students to develop sound checking strategies.

References

Australian curriculum reference: ACMNA031

Recognise and represent multiplication as repeated addition, groups and arrays

NSW Syllabus Reference: MA1-6NA

Uses a range of mental strategies and concrete materials for multiplication and division

NSW Numeracy Continuum Reference

Aspect 5: Multiplication & Division; Repeated abstract units; Multiplication and division as operations.

Teacher resources

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