Number & Algebra
Chapter 5 | Multiplication
Teacher Resource Sheets
Getting Started
The possum babies (Getting started 5)
(You could use this sheet before starting the chapter to check whether students are familiar with the concept of multiplication as repeated addition.)
This displays the Getting started on page 103 of the Student Resource Book.
- Using materials, and drawing diagrams of equal groups or arrays all support the development of multiplicative thinking. Asking students to show what 5 x 4 looks like before beginning the Getting started activity may provide useful information about student’s prior understanding.
- You could ask students to draw what 4 x 5 looks like and review ‘turn-abouts’ (commutative property) with students. Students should notice that although the different equations have a different meaning, the total number of baby possums is the same.
- It is worthwhile to make time for some discussion, so that students can listen and learn from the perspective of others as they explain the diagrams they have drawn.
Adding and subtracting by choosing a strategy
Using a 10 x 10 array (Teacher Resource Sheet 14)
(You could use this sheet in conjunction with the discussion on page 106 of the Student Resource Book.)
This displays a 10 x 10 array and shows students how they can mask a part of the array to show 4 x 5.
- It is helpful to laminate arrays so that students can use a whiteboard marker to partition or extend an array, for example, by doubling, to solve facts (also shown). This makes it easier to transition students to arrays that can help them explore strategies to solve problems with larger numbers.
- Once students know how to use the cards on the array you can give them other problems to solve to practice this.
Multiplying by tens and fives
Multiplying 5s and 10s - number lines (Teacher Resource Sheet 15)
(You could use this sheet in conjunction with the array practical on page 109 or in conjunction with Activity 2 on page 119 Student Resource Book.)
This displays a sheet with number lines that show the relationship between multiples of 5 and 10. A problem is given that could be investigated in pairs or small groups and followed by whole class discussion.
- It is important to introduce students to rate problems that can be solved using multiplication and division. One way to do this is on a number line.
- Number lines are also frequently used to represent repeated addition, but students often have misconceptions about what they show. For example, some students may suggest that both boys ate the same number of biscuits because this is the number of jumps on each number line.
- It is probably helpful to discuss what the number line shows before giving students’ opportunity to solve, explain and justify the strategies they used for solving the biscuit problems.
- Ask students what they notice about the biscuits both boys ate and the relationships between the number lines. Students may notice for example, that Hamish ate twice as many biscuits as Ari each day, so It took Ari two days to eat the same number of biscuits that Ari ate in one day.
- Students could use other materials, for example, a Slavonic abacus, blocks, pictures or arrays, alongside this number line to model the problems and support interpretation. It is important to keep referring to the context, ensuring that the students are checking that their responses make sense.
Multiplying by threes
A little bit more or less (Teacher Resource Sheet 16)
(You could use this sheet after the teaching section on page 112 Student Resource Book.)
This displays a 6 x 2 and a 6 x 1 array and asks students which fact these two arrays could combine to solve.
- Teachers could use this array to explain how arrays can be joined or partitioned to solve facts students do not yet know.
Multiplying by adding some on or taking some off
On or off? (Teacher Resource Sheet 17)
(You could use this sheet after the teaching section on page 114 Student Resource Book.)
This displays a 3 x 9 and a 3 x 10 array and asks students how 3 x 10 could be used to solve 3 x 9.
- Teachers could use this array to talk about other ways the array could be partitioned to calculate the answer, e.g. (3 x 5) + (3 x 4) or (2 x 9) + (1 x 9). Students should be encouraged to think flexibly about the way they could combine facts they know to work out other multiplication problems.
x 2, x 3, x 5 and x 10 multiplication practice
What do I know? What can I do? (Teacher Resource Sheet 18)
(You could use this sheet prior to the games and puzzles on page 114 or the Rich Task on page 105 of the Student Resource Book to revise the strategies students could use to derive multiplication facts.)
This displays a multiplication grid and asks students to fill in facts that they already know and then use these to fill in the rest.
- The shaded section of the grid represents the x 0, x 1 x 2, x 5, and x 10 multiplication facts which students are expected to know by the end of Level 2. The remaining 18 facts can be derived from these.
- Teachers may like to use this table for discussion. Students could use their own copy to highlight any of the shaded squares that they do not know yet for focused practise.
- Some prompts are given to remind students of appropriate strategies they have learned, but students may use others, for example, rather than doubling 3 groups to solve 6 groups they could combine 5 groups and 1 group. It is important to encourage students to use known facts rather than resorting to skip counting at this level.
