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**L.O.1 To be able to count in steps of equal size.**

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**We are going to count in even time.**

We’ll do 2’s, 20’s, 3’s, 30’s, 5’s, 50’s, and 0.5’s

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L.O.2 To be able to use closely related facts: multiplying by multiples of ten and adjusting.

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**Mr. Buttons has 20 children in his class**

Mr. Buttons has 20 children in his class. He orders reward stickers for the term. He estimates that each child will earn 14 stickers – one each week. How many stickers does he need to order? Q. What calculation do we need to carry out to answer this question?

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The calculation is 14 x 20 Remember…..14 x 2 = 28 so x 20 = 280 The 20 from the 28 has become 200 and the 8 has become 80. so 14 x 20 = 280 stickers!

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**Q. How could we work out a similar problem if there were 21 children in the class?**

Q. Should we start all over again or can we use any information we already have?

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**We can use the answer to 14 x 20 and record :**

14 x 21 = ( 14 x 20 ) + ( 14 x 1 ) = = stickers.

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**Q. What if there were only 19 children present?**

Q. How could we use the information we have to help us?

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**We could use the answer to 14 x 20 and record:**

14 x 19 = ( 14 x 20 ) – ( 14 x 1 ) = = stickers.

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**Do the sums from the accompanying sheets in your book.**

Set out your work properly and neatly.

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= X 41 is the same as ( X 40 ) + You are going to insert some numbers in this equation and use calculators to see if it is true. Q. Do you think both calculations will always be the same for any number you choose.

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= X 41 is the same as ( X 40 ) + With your partner write a word problem for which the above would be a solution.

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**By the end of the lesson children should be able to:**

Understand how to calculate in multiples of 10 and how to adjust for numbers close to multiples of 10: Multiply a number by 19 or 21, multiply it by 20 and add or subtract the number.

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**L.O.1 To be able to count on in steps of equal sizes**

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**We are going to count in even time.**

We’ll do 4’s, 5’s, 6’s, and 7’s

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**Q. How does counting in 4’s help us count in 8’s?**

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**How does counting in 3’s help us count in 6’s?**

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L.O.2 To be able to use closely related facts for deriving multiplication and division facts

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12 x 3 = 36 Q. Which number sentences can we derive from this one?

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12 x 6 = x 3 = 360 36 ÷ 12 = ÷ 3 = 12 120 x 3 = x 3 = 72 12 x 3 = 36 120 x 3 = 360 13 x 3 = 39 1.2 x 3 = ÷ 30 = 12

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**With a partner draw a web map for this number sentence. Use a ruler!**

Find as many associated facts as you can. 9 x 5 = 45

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**Now try these with a partner: Prisms : 14 x 4, 16 x 5, 19 x 9, 23 x 7. **

Spheres: 12 x 6, 14 x 7, 15 x 9. Tetrahedra: 12 x 5, 13 x 8, 11 x 7. When you have finished check other pairs’ work. 10 minutes

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**Now is the time to review the number strategies we have used over the last two days.**

11 x 4 = 44 What closely related facts can you tell me?

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**Q. Can you explain what you did to get the new facts? **

Write the following neatly in your books: 1. Adding and subtracting… 12 x 4 = 48, 11 x 4 = 44, 11 x 5 = 55 2. Making multiples of 10 11 x 40 = 440, 110 x 40 = 440, 110 x 40 = 4400. 3. Doubling 11 x 8 = 88, 22 x 4 = 88, 11 x 16 = 176 4. Making decimals 1.1 x 4 = 4.4, 11 x 0.4 = 4.4. 5. Finding inverses 44 ÷ 4 = 11, 44 ÷ 11 = 4, 176 ÷ 16 = 11

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For homework write four closely related facts to the number sum 13 x 6 = 78 for each of the 5 headings.

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**By the end of the lesson children should be able to:**

Use related facts Halve an even number in the calculation, find the product, then double it Answer questions like: given that 14 x 11 = 154 what is 11 x 14, 154 ÷ 11 or 140 x 11

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**To be able to count on and back in steps of equal size**

L.O.1 To be able to count on and back in steps of equal size To be able to identify related number facts and calculate differences

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**We are going to count from 0 in steps of 7 using a pendulum.**

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We know ÷ 7 = 8 Write down what other multiplication and division facts we know.

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We know that x 8 = 56 8 x 7 = 56 56 ÷ 8 = 7 Let’s count on….

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**Now let’s count back from 36 in 3’s**

If we stop at 0 write down what the next number will be?

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It should be - 3 Q. How far away from 6 is ?

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**The difference between -12 and 6 is 18.**

Copy into your books: The difference between and 6 is 18.

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**We are going to count on and back in 4’s.**

As we do we shall stop to generate and write down facts and identify differences.

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L.O.2 To be able to use closely related facts (partitioning) and factors – when completing a mental multiplication.

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**Work with your table to find two methods to solve this problem.**

15 x 12 Work with your table to find two methods to solve this problem. 3 minutes

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Q. Can we rewrite 15 x 12 as (15 x 10) + (15 x 2) ? Here we have partitioned the 12. Q. Can we rewrite it in another way?

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**so we could partition the 15 and write :**

Loooook….. 15 x = x 15 so we could partition the 15 and write : 12 x 15 = (12 x 10) + (12 x 5)

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**We can use factors to multiply.**

Write in your book the factor pairs for 15 and 12. 15 = = 12 =

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**15 x 12 Q. How can I write the calculation**

using the information we had on the board?

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15 x 12 = 1 x 15 x 3 x 4 = 15 x 12 = 1 x 15 x 2 x 6 = Are there any more ways? With your table write as many as you can think of. Is the answer always the same?

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Let’s try again: 35 x 8 Write the factor pairs for 35 and for 8 35 = 8 =

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**35 x 8 = 5 x 7 x 4 x 2 Q. Can we rearrange the numbers to make the**

calculation easier ? How?

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35 x 8 = 5 x 2 x 4 x 7 = 10 x 28 = 280 Replacing each number in a multiplication calculation with its factors can often make a calculation easier.

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**14 x 15 Q. How can we write this calculation**

using the factors of 14 and 15?

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**Q. How does this help us carry out the**

14 X 15 Can be written as: 2 x 7 x 3 x 5 Q. How does this help us carry out the calculation mentally? Q. What are the important factors to look for? Why?

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**14 x 15 Can be written as 2 x 5 x 3 x 7 = 10 x 21 = 210 Notice…….**

we have put the factors 2 and 5 first in our calculation!

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**Work with a partner to answer these multiplications by using factors**

Work with a partner to answer these multiplications by using factors. Set them out sensibly. Tetrahedra: 15 x 16; 15 x 24; 15 x 26; 45 x 6 Spheres: (also) 45 x 12; 45 x 18; 35 x 12 Prisms: (also) 35 x 16; 35 x 18; 35 x 48 10 minutes

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**Q. How could we work out this calculation using:**

25 x 32 Q. How could we work out this calculation using: a) partitioning and b) factorising. Q. Which method do you prefer? Q. Would you use the same method every time?

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Remember: Partitioning is reliable and works for any pairs of numbers. Factorising works best when one of the numbers is a multiple of 5

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**By the end of the lesson children**

should be able to: Use factors, for example: 15 x 6 15 x 3 = x 2 = 90 15 x 6 = 90

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L.O.1 To be able to round numbers, including decimals taking account of the context

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**Write answers in your book:**

1. What is £ 3.85 to the nearest pound? 2. What is m. to the nearest metre? 3. What is l. to the nearest litre? 4. What is 0.38 kg. to the nearest kilogram? 5. What is 2501 to the nearest thousand? 6. What is 642.7cm to the nearest metre?

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**The bill for a meal was £ 81. 13 for twelve people**

The bill for a meal was £ for twelve people. They agree to share the cost equally. How much should each one contribute to the cost? Q. What calculation should we carry out?

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**We should do a division sum.**

£ ÷ = Q. What does this answer mean? Q. How much should each person pay?

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**Each person ought to pay £ 6.76**

Q. If each person pays that amount will it cover the bill?

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**If each person pays that amount the total will be £ 6. 76 x 12 = £ 81**

Oh dear. They will be 1p. short! Tragedy!

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**Q. If they round £ 6.76 up to the nearest pound how much is the tip?**

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Do these in your book: A car has travelled 343 miles. If it travels 9 miles on one litre of petrol work out how much petrol it has used to the nearest litre. This year John’s trawler has caught 589 tonnes of fish. He has made 23 journeys to sea. What is his average catch? How many tonnes, to the nearest tonne, could he expect to get on his next journey? Sue’s stall at the fair took £ She had to sell 27 jumpers to achieve this. How much was each jumper? If she had rounded up her price to the next pound how much extra would she have made?

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L.O.2 To be able to use all four operations to solve simple word problems involving numbers and quantities. To be able to explain methods orally and in writing.

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**Look at Resource Sheet 3:1**

Read the Initial Information and the One-step questions. Q. What information will you use to answer the three one-step questions? With a partner write the answers to the one-step questions in your book.

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**Now look at questions 4,5 and 6. **

Q. Can you answer these questions using only the Initial Information? Q. Is further information needed? Q. Where is the information? Q. How are questions 4,5 and 6 different from 1,2 and 3? Answer nos. 4,5 and 6 in your book with a partner.

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**Q. Are these one-step or two-step questions?**

2.5 kg of potatoes cost £1.35 3 litres of milk cost £1.38 How much would 5kg of potatoes cost? 2. How much would 5 litres of milk cost? Q. Are these one-step or two-step questions?

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For question No.1……… As 5 kg is double 2.5kg only ONE calculation is needed. 5 kg of potatoes cost 2 x £1.35 = £ 2.70

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For question No. 2…….. 5 is not a multiple of 3. In this case we need to find the cost of 1 litre, then 5 litres. TWO calculations are needed. 1 litre of milk costs £ ÷ 3 = 5 litres of milk cost x 5 = Use calculators to find the answers.

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**Q. Are these one-step or two-step questions?**

2.5 kg of potatoes cost £1.35 3 litres of milk cost £1.38 3. How much would 9kg of potatoes cost? 4. How much would 9 litres of milk cost? Q. Are these one-step or two-step questions?

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**TWO calculations are needed.**

For question No.3….… 9 is not a multiple of 5. In this case we need to find the cost of 0.5kg. of potatoes and multiply by 18. TWO calculations are needed. 0.5kg of potatoes cost £1.35 ÷ 5 = 9 kg of potatoes costs x 18 =

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For question No. 4……. As 9 litres is 3 x 3 litres only ONE calculation is needed. 9 litres of milk cost 3 x £1.38 = £4.14

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**You don’t believe it? LOOOOK**

When numbers are factors we can find an answer by scaling up OR down using ONE calculation. When numbers are not factors we scale down then up using TWO calculations. You don’t believe it? LOOOOK If 10 buns cost 60p. it is easy to find how much 5 buns or 20 buns will cost – ONE step problems. It is harder to find how much 15 buns will cost – TWO step problem.

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**Q. Is this a one-step question? Try it in your books and see.**

2.5 kg of potatoes cost £1.35 3 litres of milk cost £1.38 5. How much would 10kg of potatoes and 6 litres of milk cost altogether ? Q. Is this a one-step question? Try it in your books and see.

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**Question No. 5 is a THREE step question. **

10 kg. of potatoes cost 4 x £1.35 = 6 litres of milk cost 2 x £1.38 = Altogether they cost =

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**By the end of the lesson children should be able to:**

Solve “story” problems about numbers in real life; Explain and record using signs and symbols how the problem was solved.

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L.O.1 To be able to recall multiplication and division facts and to find remainders after division

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**Complete the sum in your books.**

24 ÷ 6 = Complete the sum in your books. Write any related multiplication and division facts you know.

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**How do we write the answer to this division?**

26 ÷ 4 = How do we write the answer to this division? We know that 24 ÷ 4 = 6 from the previous calculation facts. This time there are 2 remaining.

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**- 26 = 4 x 6 + 2 We can write: 26 ÷ 4 = 6 R2 We also know that :**

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**derive the three associated facts and record these in your book.**

33 ÷ 5 = Work in pairs to do this calculation and to derive the three associated facts and record these in your book.

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**33 ÷ 6 = 5 R3 33 = 6 x 5 +3 33 = 5 x 6 +3 You should have:**

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**Work with a partner to answer these and find all the associated facts:**

÷ 5 = ÷ 7 = ÷ 5 =

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L.O.2 To be able to use all four operations to solve simple problems involving numbers and quantities. To be able to explain methods and reasoning orally and in writing.

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**Q. How can we help the children?**

Look at Activity Sheet 3.1 Two year 5 children are going to cook a special birthday meal for their family of 8. There are three courses. Eight people want soup and six want the macaroni cheese. Everyone wants the pudding. Notice how many people each recipe serves. The two children need to buy the right amount of ingredients to make enough food for everyone. Q. How can we help the children?

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**You will work in a small group to find the answers.**

You may need to scale some recipes up or down. In the space provided on the Activity sheet record your calculations and answers with the units of measure. You may use a calculator but must still record the calculations.

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**Q. Did you use a calculator. Did you use it**

Q. Did you use a calculator? Did you use it for any of the soup calculations ? If you are merely doubling numbers you should not need a calculator. We are going to record the answers on OHT 3.2.

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**Q. How else could we write 600g of potatoes?**

Q. How much flour is needed to cook the meal? Q. How much butter will be used ? Q. How much milk will be needed?

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**Q. If we can buy flour and potatoes in kilogram**

Q. If we can buy flour and potatoes in kilogram packs only how much of each must be bought? How much will be left over? Q. Stock cubes come in packs of 10. How many are needed and how many are left over? Q. Butter comes in 450g. packs. How many are needed and how much is wasted? Q. Eggs come in dozens. How many are left after the pudding has been made?

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**“Can I do this calculation in my head?” **

A packet of crisps costs 55p. A bag of 6 oranges costs £1.25 This week you have been calculating with and without calculators. The first question you should always ask yourself should be “Can I do this calculation in my head?” I shall ask you some questions. In pairs write down quickly how you would do the calculation without a calculator then do it.

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**A packet of crisps costs 55p.**

A bag of 6 oranges costs £1.25 Q. What would 10 packets of crisps cost?

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**A packet of crisps costs 55p.**

A bag of 6 oranges costs £1.25 The answer is £5.50 and can be done mentally. Q. What would 9 packets of crisps cost?

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**A packet of crisps costs 55p. A bag of 6 oranges costs £1.25 **

As 9 is one less than 10 we subtract 55p from £5.50 mentally or with some information recorded to help. Q. What would 18 packets of crisps cost?

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**A bag of 6 oranges costs £1.25 A packet of crisps costs 55p.**

We can do this in different ways: Using factors … 18 x 55p = 2 x 9 x 5 x 11 = 2 x 5 x 9 x 11 = ….. Adjusting … 18 x 55p = (20 x 55p) – (2 x 55p) = ……. or Partitioning … 18 x 55p = (10 x 55p) = (8 x 55p) = …… Do this sum using a calculator but you must write down the calculation as you do it.

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**A packet of crisps costs 55p.**

A bag of 6 oranges costs £1.25 Q. What would 12 oranges cost?

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**. A packet of crisps costs 55p. A bag of 6 oranges costs £1.25**

This is a mental calculation ; double £1.25… Q. What would 15 oranges cost?

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**. A packet of crisps costs 55p. A bag of 6 oranges costs £1.25**

15 oranges would cost….. This is a three-step sum. We’ll work it out together.

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**By the end of the lesson children should be able to:**

Solve “story” problems involving quantities and units of measure, Use a mental, written or calculator method to solve problems.

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