Rich tasks
- This is an open-ended activity that requires students to investigate multiples of 2, 5 and 10 up to 20. The task can be given at the start of a topic and done as the students gain enough understanding to complete it or given as a homework task.
- Sausage dinner
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1. Sausage dinner
- Encourage students to explore the patterns made by adding equal sized groups and to be creative in their presentations to justify their answers.
- The use of number lines to show skip counting and 100 charts to show multiples will help students identify patterns that exist between the multiples of 2, 5 and 10.
- Encourage students to notice the commutative property for multiplication and the relationship between multiplying by 5 and multiplying by 10.
Understanding Multiplication page 110
- Understand the connection between multiplication and repeated addition.
- Use an array to demonstrate commutative property and solve multiplication problems.
- Understand how doubles and the two times table are related.
- Solve 2s multiplication through repeated addition and doubling.
- Solve 10s multiplication through repeated addition and connection to place value.
- Solve 5s multiplication through repeated addition and understanding of doubling and halving of 10s.
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Teacher notes
- Arrays are an area model of multiplication and are helpful for understanding the commutative property of multiplication and for later connecting to strategies for calculating area.
- This series adopts New Zealand conventions for interpretation of multiplication written as equations. The first number (multiplier) indicates the number of groups, and the second number (multiplicand) indicates the size of each group. So, 3 x 5 should be read as “3 groups of 5”, with an answer (product) of 15.
- Teachers should be aware that students with a background in Māori immersion classes, as well as students from some other countries, may reverse this convention, so 3 x 5 is read as “5, three times”. It is probably helpful if students (especially in these early stages) are encouraged to adopt the NZ convention so that meaning is shared between students in the same classroom.
- It is also helpful if students are encouraged to draw and interpret arrays in the same way. In the student book, each group is drawn horizontally with subsequent groups added below.
- Many students find it easier to align rows and columns by using grid paper. This ensures that groups contain the same number of objects. Keeping a skip count down the right-hand side of the array reinforces students’ recall of the skip count and an understanding that each row increases by the same quantity so that the final count gives the total number in the group.
- Knowing that x 2 problems can be ‘turned around’ to create doubles that can be solved with known addition facts supports understanding of the commutative property and aids recall of x 2 facts.
- Making the connection between multiplying by ten and place value supports recall of x 10 facts.
- Making the connection between multiplying by 5 and 10 supports recall of x 5 facts.
Multiplying twos, fives and tens page 115
- Solve 2s, 5s and 10s multiplication using repeated addition, understanding of doubling and halving, and the commutative property for multiplication.
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Teacher notes
- This section gives practice at solving 2s, 5s and 10s multiplication. Encourage students to practise and achieve fluent recall of their 2s, 5s and 10s multiplication tables while tackling this section if they have not already done so.
- Students who do not have instant recall of the 2s, 5s and 10s tables will need to use a strategy they have learned to solve each problem. This may lead them to the conclusion that learning their tables is more efficient.
