National curriculum content

• Multiply numbers up to 4 digits by a one or two-digit number using a formal written method, including long multiplication for two-digit numbers
• Multiply and divide numbers mentally drawing upon known facts
• Divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context

Lesson objectives

1. Multiply up to a 4-digit number by a 1-digit number
2. Multiply a 2-digit number by a 2-digit number (area model)
3. Multiply a 2-digit number by a 2-digit number
4. Multiply a 3-digit number by a 2-digit number
5. Multiply a 4-digit number by a 2-digit number
6. Solve problems with multiplication
7. Short division
8. Divide a 4-digit number by a 1-digit number
9. Divide with remainders
10. Efficient division
11. Solve problems with multiplication and division

What we want children to know

• Recognise the importance of fluency in multiplication tables for calculation
• Use previous place value knowledge to multiply numbers
• Consolidate multiplication and division from an expanded method to a standard written method
• Recognise efficient methods for calculation
• Understand how remainders impact on problem solving

What skills we want children to develop

Use knowledge to solve reasoning and problem solving questions such as:

Always, sometimes, never

•When multiplying a two-digit number by a one-digit number, the product has 3 digits.

•When multiplying a two-digit number by 8 the product is odd.

•When multiplying a two-digit number by 7 you need to exchange.

Explain your answer

Eva says: To multiply 23 by 57, I just need to calculate 20 x 50 and 3 x 7 and find the total.

What mistake has Eva made?

37 sweets are shared between 4 friends. How many sweets are left over?

Four children attempt to solve this problem.

•Alex says it’s 1

•Mo says it’s 9

•Eva says it’s 9 r 1

•Jack says it’s 8 r 5

Can you explain who is correct and the mistakes other people have made?

Vocabulary/Mathematical Talk

• How are these methods the same? How are they different?
• Why is the zero important? What numbers are being multiplied in the first line and the second line?

When do we need to make an exchange?

What happens if there is an exchange in the last step of the calculation?

• If we know what 38 × 12 is equal to, how else could we work out 39 ×12?
• If we are dividing by 3, what is the highest remainder we can have?

If we are dividing by 4, what is the highest remainder we can have?

Can we make a general rule comparing our divisor (the number we are dividing by) to our remainder?

• Can we partition a number in more than one way to support dividing it more efficiently?
• When would we round the remainder up or down?