**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**

- Recap add whole numbers with more than 4 digits (column method)
- Recap subtract whole numbers with more than 4 digits (column method)
- Recap inverse operations (addition and subtraction)
- Recap multi-step addition and subtraction problems
- Add and subtract integers
- Recap multiply 4-digits by 1-digit
- Recap multiply 2-digits (area model)
- Recap multiply 2-digits by 2-digits
- Recap multiply 3-digits by 2-digits
- Multiply up to a 4-digit number by a 2-digit number
- Recap divide 4-digits by 1-digit
- Recap divide with remainders
- Short division
- Division using factors
- Long division (1)
- Long division (2)
- Long division (3)
- Long division (4)
- Recap Factors
- Common factors
- Common multiples
- Primes to 100
- Squares and cubes
- Order of operations
- Mental calculations and estimation
- 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?

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