Planning tool

Students:

• understand that multiplication and division are inverse operations
• describe and use the properties of multiplicative operations
• develop fact families
• solve multiplicative numerical equations.

Some students may:

• not be proficient at recalling multiplication facts. Arrays can be used for building multiplication facts in a meaningful way. Before drilling and memorising tables, it is helpful for students to understand how these facts are developed. Some students do not yet make connections between number facts in the same table and instead rely on memorising each of the facts. Supporting students to understand and apply the commutative property of multiplication may help these students.
• find division is the most challenging of the four operations to master. Typically, full understanding of division tends to occur much later than the other operations. Often students have fewer opportunities to use physical materials to develop their conceptual knowledge and instead jump into solving formal equations too early. These students typically have problems with explaining the inverse relationship between division and multiplication. To address this, use arrays to show the relationship using multiple examples. Use arrays as part of a number talk. For example, 3 × 5 = 15, or that 3 rows of 5 make 15, as can be represented by an array. Prompt students to look at the array in different ways to reveal the inverse, that is 15 ÷ 3 = 5 or 15 put into 3 rows makes 5 columns, or 5 in each row. Be mindful of the language used to describe arrays. Language plays an important role in being able to express the mathematical relationships. As students develop their conceptual knowledge, extend to large numbers and explore calculations such as 13 x 5 where the array can be split into useful chunks such as 10 and 3. This encourages students to use their known number facts to work out calculations. For example, 13 x 5 = (10 x 5) + (3 x 5). Use blank arrays for students to explore and represent calculations. The blank array helps students use other strategies, such as compensating, when carrying out multiplication. For example, 37 x 9, the student could choose to do 37 x 10 and then subtract the 37 x 1.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

• We are learning to recognise the connection between multiplication and division.

Why are we learning about this?

• Knowing this relationship helps us to solve larger number problems.

What to do

Use your knowledge of fact families to complete the multiplication and division facts, filling in the missing numbers.

Success criteria

I can:

• develop fact families
• describe the relationship between multiplication and division.