Year 6 key objective Carry out long multiplication of a three-digit by a two-digit integer and short multiplication and division of whole numbers Associated knowledge Errors and Questions to identify errors and Teaching to address errors and Next steps and skills misconceptions misconceptions misconceptions Multiply and divide one-, Misuses rules about Can you tell me a quick way of Multiplication by ten, one hundred.. using What's the best way you can think two- and three-digit multiplying and dividing multiplying a number by one a calculator and recording numbers before of to find: numbers by ten and one by powers of ten and thousand? and after multiplication in HTU columns. 71 x 20? hundred. the associative law, for 202 x 6? example: I have thirty-seven on my Repeat for division. 82 x 300? Apply the associative law 145 x 30 = 145 000. calculator. What single (but not by name) to multiplication should I key in to Ask the child to describe patterns observed multiply up to three-digit change it to three thousand and suggest a generalisation. Ask the child numbers by multiples of seven hundred? to illustrate with further examples. ten and hundred, for example: What is 3 ÷ 1? ... 30 ÷ 10? ... 300 ÷ Demonstrate that 42 x 12 is the same as 42 147 x 20 = 147 x 2 x 10. 100? x 6 x 2. What other ways can we multiply 1 Y6 x/÷ Tell me about this pattern. forty-two by twelve? If I had four thousand eight hundred on my calculator, what single division could I key in to change the display to forty-eight? 47 x 10 = 470 What do you think 47 x 20 equals? Present the remainder in a quotient as a whole number or fraction. 2 Y6 x/÷
Has difficulty, when appropriate, interpreting a remainder as a fraction, for example: 17 ÷ 4 = 4¼.
There are twenty-six apples for four horses, so they can have six and a half each. How do I know this?
Repeat with other numbers. Use factor 'tree' to support this, for example: 12= 4x3 3x4 2x6 6x2 12x1 1x12 What is a sensible answer for each of the following division calculations? 1. Divide twenty-eight eggs by six. 2. Divide twenty-seven bars of chocolate into four. 3. Divide £47 by four. 4. Divide sixty-two children into teams of ten.
Write a division question for your partner which you know will have a fraction as part of the answer. How do you know it will have a fraction as part of the answer?
Dividing by numbers smaller than one, for example: 12 ÷ ½ = 24 5 ÷ ¼ = 20
Interprets division as sharing but not as grouping (repeated subtraction) so is unable to interpret a calculation such as 12 ÷ ½.
How many half tomatoes can you get from three whole tomatoes?
Model with practical contexts and equipment, calculations such as:
How many quarters of pizza can you get from four pizzas?
How many halves in six? ... quarters in eight? Demonstrate associated recording.
Is not confident in making reasonable estimates for multiplication or division calculations.
600 ÷ 30 = 2 Can this calculation be correct? How do you know?
3 Y6 x/÷ Judge whether the answer to a multiplication or division calculation is reasonable. 4 Y6 x/÷
Explain how to work out 5 x ½, 5 ÷ ½
Try some more, such as: 540 ÷ 20 = 52 24 x 20 = 4800 15 ÷ ½ = 30 24 ÷ ¼ = 96
Use a variety of images and contexts to illustrate, for example, jumps on a number line, chocolate bars, etc. Use examples of calculations to model making estimates, for example: We know thirty-five divided by seven equals five. Is thirty-three divided by seven more or less than this? How can we decide?
When I divide my mystery number by half the answer is ten. What's my mystery number? Make up some more questions with mystery numbers.
If the question is fifty-four divided by seven, what number<br>facts could you use to help you estimate an answer? Explain how each of the facts you suggest would be useful to help you make an estimate.
Repeat using calculations such as: 44 ÷ 10 207 ÷ 20
What about the question five hundred and four divided by six?
Ask the child to justify the estimates they suggest.
Choose some more questions to use.