National curriculum content

• Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
• Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
• Divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context
• Perform mental calculations, including with mixed operations and large numbers
• Identify common factors, common multiples and prime numbers
• Use their knowledge of the order of operations to carry out calculations involving the four operations
• Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

Lesson objectives

1. Recap add whole numbers with more than 4 digits (column method)
2. Recap subtract whole numbers with more than 4 digits (column method)
3. Recap inverse operations (addition and subtraction)
4. Recap multi-step addition and subtraction problems
5. Add and subtract integers
6. Recap multiply 4-digits by 1-digit
7. Recap multiply 2-digits (area model)
8. Recap multiply 2-digits by 2-digits
9. Recap multiply 3-digits by 2-digits
10. Multiply up to a 4-digit number by a 2-digit number
11. Recap divide 4-digits by 1-digit
12. Recap divide with remainders
13. Short division
14. Division using factors
15. Long division (1)
16. Long division (2)
17. Long division (3)
18. Long division (4)
19. Recap Factors
20. Common factors
21. Common multiples
22. Primes to 100
23. Squares and cubes
24. Order of operations
25. Mental calculations and estimation
26. Reason from known facts

What we want children to know

• How to divide up to 4-digits by up to 2-digits
• The short division and long division method
• Use knowledge of factors to see relationships between the dividend and the divisor
• When to choose a mental strategy or a standard method
• How to use their place value knowledge to confidently exchange in addition and subtraction calculations
• How to check calculations using rounding and estimating
• That calculations can be checked for accuracy using inverse operations
• Fluently recall their multiplication table facts
• Draw upon known multiplication table facts to mentally multiply and divide numbers
• Develop strategies to prove a number is a prime number
• Explore relationships between square and cube numbers
• Use strategies to identify multiples and factors
• Use strategies to identify the common factors of two numbers
• The order of operations

What skills we want children to develop

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

Always, sometimes, never?

• Is it always, sometimes or never true that when you square an even number, the result is divisible by 4?
• Is it always, sometimes or never true that multiples of 7 are 1 more or 1 less than prime numbers?

Making an estimate

• Circle the number that is the best estimate  to 932.6  - 931.05

1.3     1.5    1.7   1.9

Convince me

• Three four-digit numbers total 12435. What could they be? Convince me.

Making links

• 0.7 x 8 = 5.6  

How can you use this fact to solve these calculations? 

0.7 x 0.08 =        

0.56 ÷ 8 =

• 12 x 1.1 = 13.2

Use this fact to work out

15.4 ÷ 1.1 =

27.5 ÷ 1.1 =

Mathematical Talk

• What happens when there is more than 9 in a place value column?
• Can you make an exchange between columns?
• How can we find the missing digits? Can we use the inverse?
• When should we use mental methods
• Why is it important to set out multiplication using columns?
• Explain the value of each digit in your calculation.
• How do we show there is nothing in a place value column?
• Which part of the multiplication is the product?
• What is the same and what is different between the three representations (Base 10, place value counters, grid)?
• Why is the zero important?
• When do we need to make an exchange?
• What can we exchange if the product is 42 ones?
• How would you draw the calculation?
• Can the inverse operation be used?
• When would we round the remainder up or down?
• Do you notice any patterns?
• Does using factor pairs always work?
• How can we use multiples to help us divide by a 2-digit number?
• How can we use multiples to help us divide?
• How can you work in systematic way to prove you have found all the factors?
• Do factors always come in pairs?
• What is a prime number?
• Why is 1 not a prime number?
• Why is 2 a prime number?
• How does knowing the approximate answer help with the calculation?
• When do you use the inverse?