Week 3 - 7 Addition, subtraction, multiplication and division

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

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

1.3 1.5 1.7 1.9

Convince me

Making links

How can you use this fact to solve these calculations?

0.7 x 0.08 =

0.56 ÷ 8 =

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?

Cotmanhay Junior School