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Back through ten

Back-through-ten strategies involve using decades as landmarks to solve harder calculations. For example, 52 – 8 = ? can be solved by calculating 52 – 2 = 50 then 50 – 6 = 44.

Equal differences

Difference problems can be made easier by adjusting both numbers by the same amount. 

Facts and models

In this game, students draw on their knowledge of fact families to generate multiplication and division facts.

Facts within facts

In this activity, students draw on their knowledge of known facts, doubles and partitioning to identify related facts within facts.

How many possible ways?

In this activity, students explore the different arrays that can be formed for a specific number.

Investigating patterns

In this activity, students construct a rectangular array for a given number from which they will generate and record the multiplication facts and the list of factors. 

Parking ones and moving tens

An important understanding of early strategic use of place value is what changes (ones, tens or both) in a given calculation. 'Parking ones' refers to the idea of leaving ones unchanged while working on tens.

Partial arrays

Array structures are ways to represent factors. In this activity, students are given the number of tiles in each row and column and are asked to find the total number of tiles needed to construct the rectangle.

Renaming to add and subtract

Combining 10 ones to form a new 10 or decomposing a 10 into ones are procedures. Automation of these renaming procedures eases the memory load in more complex calculations.

Splitting arrays

In this activity, students construct a rectangular array for a given number which they then partition into areas using known facts. This assists them to derive new facts. 

The power of ten

The place value system was developed as an efficient way to count and record large numbers. Groupings of 10 allow students to efficiently combine, separate or find the difference between two-digit numbers.

Up through ten

Up-through-ten strategies use decades as landmarks to solve harder calculations. For example, 9 + 7 = ? can be solved by calculating 9 + 1 = 10 then 10 + 6 = 16.

Using tens

Students who are in the early stages of learning about place value need to understand the power of grouping ones into sets of 10. They also need to know the way tens and ones groupings are represented in written numerals.

What do I know?

In this activity, students build up a list of facts they can recall automatically. They discuss some possible strategies to deal with those that they do not know or need to use additional thinking to work out. 

What do you see?

The structure of a rectangular array assists students to visualise the multiplicative situation. The group is seen as a composite unit rather than as a collection of individual items.