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Y6 ratio(Spring term) linked to WR small steps

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Y6 ratio(Spring term) linked to WR small steps

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The small steps in this block are identical to the Y2 Spring term Fractions block. The new learning for Y3 will be in the Summer term block.

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Y4 Decimals (Spring term) linked to WR small steps

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Y4 Decimals (Spring term) linked to WR small steps

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Y6 perimeter, area and volume (Spring term) linked to WR small steps

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Y6 perimeter, area and volume (Spring term) linked to WR small steps

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Y6 perimeter, area and volume (Spring term) (1)

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Y2 Fractions (Spring term) linked to small steps

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Y2 Fractions (Spring term) linked to small steps

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Y3 length and perimeter (Spring block) linked to WR small steps

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Y3 length and perimeter (Spring block) linked to WR small steps

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Y1 - length and height linked to WR small steps (Spring block)

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Y1 - length and height linked to WR small steps (Spring block)

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Y5 decimals & percentages (Spring term) - linked to WR small steps

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Y5 decimals & percentages (Spring term) - linked to WR small steps

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Y5 - Decimals & Percentages (Spring block) (1)

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Y3 money (Spring term) linked to WR small steps

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Y3 money (Spring term) linked to WR small steps

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Y4 fractions (Spring term) linked to WR small steps

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Y4 fractions (Spring term) linked to WR small steps

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Y6 measures: converting units (Spring block) linked to WR small steps

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Y6 measures: converting units (Spring block) linked to WR small steps

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Y2 - properties of shape: geometry linked to WR small steps (Spring block)

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Y2 - properties of shape: geometry linked to WR small steps (Spring block)

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Y2 - geometry properties of shape (Spring term)

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Y3 multiplication & division questions (Spring term) linked to WR small steps

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Y3 multiplication & division questions (Spring term) linked to WR small steps

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Y3 multiplication & division (Spring term)

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Y6 Algebra (Spring term) linked to WR small steps

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Y6 Algebra (Spring term) linked to WR small steps

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Hello! The properties of shape PDF will not upload properly on this site. Please email Anna Tapper if you'd like it. Thanks

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Y5 Fractions (Spring term) linked to small steps

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Y5 Fractions (Spring term) linked to small steps

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Y4 - area (Spring term) linked to WR small steps

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Y4 - area (Spring term) linked to WR small steps

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Y5 multiplication & division linked to WR small steps (Spring block)

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Y5 multiplication & division linked to WR small steps (Spring block)

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Y5 multiplication & division (Spring block)

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Y4 - multiplication & division questions (Spring term) linked to WR small steps

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Y4 - multiplication & division questions (Spring term) linked to WR small steps

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Y4 multiplication & division (Spring block)

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Y3 - questions linked to WR small steps (Autumn block)

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Y3 - questions linked to WR small steps (Autumn block)

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Y3 GDS questions - multiplication & division

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Y5 area & perimeter linked to WR small steps (Autumn block)

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Y5 area & perimeter linked to WR small steps (Autumn block)

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Y2 - multiplication & division questions linked to WR small steps (Spring block)

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Y2 - multiplication & division questions linked to WR small steps (Spring block)

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Y4 - multiplication & division questions linked to WR small steps (Autumn block)

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Y4 - multiplication & division questions linked to WR small steps (Autumn block)

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Y4 GDS questions - multiplication & division

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Y6 - Decimals questions linked to WR small steps Spring block)

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Y6 - Decimals questions linked to WR small steps Spring block)

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Y6 - percentages linked to WR small steps (Spring block)

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Y6 - percentages linked to WR small steps (Spring block)

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An oldy but a goody - lots of interesting puzzles and problems linked to the NC and with answers supplied

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An oldy but a goody - lots of interesting puzzles and problems linked to the NC and with answers supplied

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Ring a Ring of Numbers

Here is a picture of four numbers placed in squares on a circle so that each number is joined to two others:

What do you see?
What do you notice?

Choose four numbers from this list: 1, 2, 3, 4, 5, 6, 7, 8, 9 to put in the squares so that the difference between joined squares is odd.
Only one number is allowed in each square. You must use four different numbers.
What can you say about the sum of each pair of joined squares?

What must you do to make the difference even?
What do you notice about the sum of the pairs now?

Here are some sheets for recording your solutions.

This problem is based on an idea taken from "Apex Maths Pupils' Book 2" by Ann Montague-Smith and Paul Harrison, published in 2003 by Cambridge University Press.

This problem provides a context in which children can recognise odd and even numbers, and begin to think about their properties. It also offers practice in addition and subtraction.

It would be good to show the image in the problem to the class and ask what they notice, and whether they have any questions. Give them time to consider on their own, then to talk to a partner. Invite learners to offer their noticings and questions but try not to say anything more than "thank you" as they share their thoughts with everyone. Rather than answering any questions yourself, encourage other members of the group to respond.

Use the ideas that have been offered to build up to introducing the task as stated and give pairs of children chance to find at least one way of making odd differences. They could be using You could invite pairs to record arrangements that work on the board as they find them and invite everyone to check that they are indeed solutions. this sheet of blank circles and/or digit cards.

Once you have several ways on the board, invite learners to comment on what they notice. What do all the arrangements have in common? You can work through the rest of the problem in a similar way, drawing the whole class together as appropriate.

It is important to encourage the children to explain why the arrangements of odd/even numbers produce these results. You could make drawings like these using paired joined squares to help deepen their understanding.

What do you notice about the numbers in the ring when the difference between joined pairs is odd?

What do you notice about the numbers in the ring when the difference between joined pairs is even?

Can you explain why?

Some learners might benefit from having counters or other objects to help with their addition and subtraction.

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Here is a picture of four numbers placed in squares on a circle so that each number is joined to two others: What do you see? What do you notice? Choose four numbers from this list: 1, 2, 3, 4, 5, 6, 7, 8, 9 to put in the squares so that the difference between joined squares is odd.

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Ring a Ring of Numbers

Here is a picture of four numbers placed in squares on a circle so that each number is joined to two others:

What do you see?
What do you notice?

Choose four numbers from this list: 1, 2, 3, 4, 5, 6, 7, 8, 9 to put in the squares so that the difference between joined squares is odd.
Only one number is allowed in each square. You must use four different numbers.
What can you say about the sum of each pair of joined squares?

What must you do to make the difference even?
What do you notice about the sum of the pairs now?

Here are some sheets for recording your solutions.

This problem is based on an idea taken from "Apex Maths Pupils' Book 2" by Ann Montague-Smith and Paul Harrison, published in 2003 by Cambridge University Press.

This problem provides a context in which children can recognise odd and even numbers, and begin to think about their properties. It also offers practice in addition and subtraction.

It would be good to show the image in the problem to the class and ask what they notice, and whether they have any questions. Give them time to consider on their own, then to talk to a partner. Invite learners to offer their noticings and questions but try not to say anything more than "thank you" as they share their thoughts with everyone. Rather than answering any questions yourself, encourage other members of the group to respond.

Use the ideas that have been offered to build up to introducing the task as stated and give pairs of children chance to find at least one way of making odd differences. They could be using You could invite pairs to record arrangements that work on the board as they find them and invite everyone to check that they are indeed solutions. this sheet of blank circles and/or digit cards.

Once you have several ways on the board, invite learners to comment on what they notice. What do all the arrangements have in common? You can work through the rest of the problem in a similar way, drawing the whole class together as appropriate.

It is important to encourage the children to explain why the arrangements of odd/even numbers produce these results. You could make drawings like these using paired joined squares to help deepen their understanding.

What do you notice about the numbers in the ring when the difference between joined pairs is odd?

What do you notice about the numbers in the ring when the difference between joined pairs is even?

Can you explain why?

Some learners might benefit from having counters or other objects to help with their addition and subtraction.

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Here is a picture of four numbers placed in squares on a circle so that each number is joined to two others: What do you see? What do you notice? Choose four numbers from this list: 1, 2, 3, 4, 5, 6, 7, 8, 9 to put in the squares so that the difference between joined squares is odd.

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Y4 & 5 Using rules of multiplication to assign values to shapes.

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These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

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Y5 & 6 - reasoning about efficient methods to multiply and divide

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There are four multiplication calculations hidden below.

Your challenge is to put them in order, from easiest to hardest. Try to do this without actually calculating each answer if you can.

Click on 'Show' to see them.

70 x 40

70 x 57

70 x 21

70 x 100

How did you decide the order?

We would love to hear the reasons for your final order.

You might like to do exactly the same with the set of four division calculations hidden below.

350 $\div$ 7

350 $\div$ 1

350 $\div$ 25

350 $\div$ 3

Create a set of four multiplications or four divisions yourself, which you think could be put in order from easiest to hardest.
Give them to someone else to order.
Do they agree with your final order? Why or why not?

You may find it useful to print off this sheet, which contains the two sets of calculations. You could cut them up into two sets of four cards.

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There are four multiplication calculations hidden below. Your challenge is to put them in order, from easiest to hardest. Try to do this without actually calculating each answer if you can. Click on 'Show' to see them. 70 x 40 70 x 57 70 x 21 70 x 100 How did you decide the order?

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Y5 & 6 - reasoning about products when multiplying

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This activity has been particularly created for very highest attainers. (The pupils that you come across in many classrooms just once every few years.)
On the table in front of you is a grid like this:-

Now imagine that you have another grid, just the same but made of plastic that you can see through.

You place the plastic one over the one on the table so that it covers it completely.

You could have flipped it over and/or turned it around as you put the plastic one down.

Then the numbers that are paired, one above the other, are multiplied together.

Finally, all the results of multiplying together will be added together.

Without doing the $36$ multiplications and then adding them together your challenge is to say which way of flipping over and/or turning the plastic grid will give you the highest total and which way will give the lowest total.

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This activity has been particularly created for very highest attainers. (The pupils that you come across in many classrooms just once every few years.) On the table in front of you is a grid like this:- Now imagine that you have another grid, just the same but made of plastic that you can see through.

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Booklet of ideas for developing mathematical thinking in early years

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Booklet of ideas for developing mathematical thinking in early years

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A booklet full of useful ideas, designed to narrow the gap for those children with less mathematical experience on entry to Nursery and Reception as a result of Covid.

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arithmetic procedures with integers and decimals

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arithmetic procedures with integers and decimals

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Journaling is a fantastic way to develop children's written explanations of their mathematical thinking. It requires them to use specific mathematical vocabulary, to explain their thoughts clearly and often to use representations to aid their explanations. Great practise for those 'how do you know?' or 'explain your answer' questions.
The document below is full of examples about how this can be used from early years to Y6.

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Inspiration for how you could develop journaling in your classroom