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**L.O.1 To be able to identify factor pairs of small 2-digit numbers**

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**A factor is a number that goes into another exactly.**

36 A factor is a number that goes into another exactly. One factor of 36 is 9, what is its pair? Write the other factor pairs of 36.

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Factor pairs of 36 are: 9 x 4 = 36 3 x 12 = 36 18 x 2 = 36 1 x 36 = 36 6 x 6 = 36 The number 36 is special as one factor pair has two identical numbers x 6. Q. What do we call numbers like 36?

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36 is a square number.

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**In your book write the factor pairs for :**

40 24 64 Two minutes

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L.O.2 To be able to use factors as a strategy for mental multiplication.

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**Q. How would you work this out in your head?**

LOOOOOK! 4 X 3 X 5 Q. How would you work this out in your head?

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**The operation of multiplication is commutative…..**

a sum can be done in different ways. 4 x 3 x 5 e.g. 4 x 3 = 12 x 5 = 60 4 x 5 = 20 x 3 = 60 3 x 5 = 15 x 4 = 60 The answer is the same whichever way you do it.

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**Try doing these in different ways in your books.**

15 x 3 x 2 2 x 3 x 4 x 5 Four minutes

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LOOOOOOK! 17 x 12 This may look hard but isn’t once we find the factors. Q. What factors can we find for 17 and 12

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17 x 12 = 17 x 3 x 2 x 2 Q. How does this make the calculation easier?

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**We can multiply 17 by 3 then double and**

e.g x 17 x x 2 17 x 3 x 2 x 2 = x 2 x 2 = 102 x 2 = 204

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**Work in pairs and use this method to find answers to : 23 x 6 17 x 4 **

Not long

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26 x 6 To help us do this sum we will find factor pairs for each number. 26 x 6 = ( 2 x 13 ) x ( 2 x 3 ) = 3 x 13 x 2 x 2 = 39 x 2 x 2 = 78 x 2 = 156

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Let’s try : 34 x 6

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**Calculations for you to do in the same way :**

Prisms : 14 x 8 ; 23 x 6 ; 24 x 9 ; 18 x 22 16 x 9 ; 27 x 12 Spheres: 15 x 9 ; 11 x 12 ; 14 x 6 ; 16 x 8 Tetrahedrons: 14 x 8 ; 16 x 6 ; 13 x 15

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**Here’s one to do as a class…..**

22 x 18

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

Use factors to carry out multiplication mentally.

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**L.O.1 To be able to order a set of positive and negative integers**

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**Copy this number line into your books:**

-20 +20

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**We need 6 numbers which will fit somewhere on your line.**

The numbers are : Put the numbers in the correct place on your line.

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If we change the sign for each number so that positive numbers become negative and negative numbers become positive we get : Q. How will the numbers change on the number line? A. ……. Draw a new number line and insert the new numbers.

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**The new numbers become a reflection about 0. Loooooook!**

Mirror -6 6 -20 20

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**Draw another number line and put in these numbers:**

-14 ; 8 ; -9 ; 10 ; 3 ; -17 . Now change the signs and insert the new numbers – use a different colour. Check your partner’s! 4 minutes

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L.O.2 To be able to solve simple word problems. To begin to use brackets.

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Fish £2 Chips £1 Q. I have just spent £9. What could I have bought? Q. How many fish could I have bought?

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**A good way to sort all the possibilities is like this:**

Fish Chips You can see there are 5 possible combinations.

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Try this: Cola 50p. Pizza £1:50 Q. If I spend £8 what could I buy? Record your working in the same way as the problem we have just done. Q. How many possible combinations are there?

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**Create a similar problem for the other pairs on your table to answer.**

5 minutes

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**Let’s go back to our first problem**

Fish £2 : Chips £1 A child goes to the chip shop and asks for “Two fish and chips”. The owner asks for £6. but the child expects to be charged only £5. Q. Can you explain why?

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**“ two ( fish and chips)” : “ ( two fish ) and chips” **

Q. What is the difference between the two statements? Using brackets can help us solve the problem. 2 x ( £2 + £1) : ( 2 x £2 ) + £1 The brackets help remove confusion.

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REMEMBER THE STEP IN BRACKETS IS ALWAYS DONE FIRST !

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**Q. How would you work out this calculation?**

compare 6 + 3 – – Q. How would you work out this calculation? Consider these: (6 + 3) – 2 = ( ) = 7 = = 7 compare: 6 – = ? – = ? (6 – 3) = – ( ) = 1 6 - ( 3 + 4) = (6 – 3 ) = 5

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**We will try to get as close to a target number as we can using 3 digits, 5 signs and some brackets.**

Digits are 6 ; 4 ; and 1. (6 x 4)+1= (6-1)x4= (6+1)x4= x (4+1)=30

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**Record your attempts in your book. **

With a partner choose a target number between 20 and 50. Use 3 rolls of the die to give you the digits you need. Get as close to your target number as you can. Record your attempts in your book. Prisms : 4 different target numbers. Circles : 3 different target numbers. Tetrahedra : 2 different target numbers. 5 minutes maximum

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Try these in your book: 4 + 2 x 3 4 x 2 x 3 4 – 2 x 3 You can use brackets anywhere. Q. Which calculation could give the biggest / smallest answer? Why?

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

Use brackets, Solve simple word problems by listing.

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**L.O.1 To be able to use doubling and halving starting from known facts.**

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7 Double this ad infinitum.

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**Now halve the last number!**

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**24 x 4 = 24 x 2 x 2 24 x 4 using the above statement?**

Q. How can we work out the answer to 24 x 4 using the above statement? A. …… 48 X 2

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**To multiply by 4 we use doubling then doubling again.**

As 2 is a factor of 4 this method is really using factors. 560 ÷ 4 Q. How can we work this out?

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(560 ÷ 2) ÷ 2 Dividing by 2 is the same as halving and halving again. Look : 560 ÷ 2 = 280 280 ÷ 2 = 140

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L.O.2 To be able to use all four operations to solve simple word problems. To begin to use brackets.

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1. 48 ÷ – (33 – 18) x 2 5. 23 – (3 + 5) x 2 7. ( 12 ÷ 2 ) x ÷ ( ) Brackets always indicate the first stage of a calculation. Q. In a class of 33 children, 18 had no pets, the others had two pets each. How many pets is that? Which calculation from those shown would you use to solve this problem?

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**Tetrahedra – do at least 3**

÷ – (33 – 18) x 2 5. 23 – (3 + 5) x 2 7. ( 12 ÷ 2 ) x ÷ ( ) With a partner work out some word- based problems for which the other calculations on the board will be the solutions : Prisms – do all 7 Spheres – do at least 5 Tetrahedra – do at least 3 10 minutes

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A. ….. Read problems aloud. Q. Which calculation matches the word problem? How did you decide?

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**Work out a calculation ON YOUR OWN**

using all four operations and develop a word problem from it. Make it as interesting as possible. A. ……

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**The answer to a problem is “ 37 legs”**

The answer to a problem is “ 37 legs”. With a partner make up an interesting word problem which has this answer.

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

Solve “story problems about numbers in real life, choosing the appropriate operation and method of calculation. Explain and record using numbers, signs and symbols how the problem was solved.

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**L. O. 1 To develop calculator skills and use a calculator effectively**

L.O.1 To develop calculator skills and use a calculator effectively. To begin to use brackets

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A class of 37 children were deciding what type of drink they should have when they go on their day out. 15 children said they would like cola, 17 said they would like orange and the remainder said they would like fruit juice. Cola and orange cost 35p. Fruit juice costs 25p. Work in pairs to calculate how much the drinks would cost for the class. Record every calculation you make. We will check your working to see whose strategy was the most efficient .

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**Work out the answer to this problem using your calculators.**

( 37 x 0.35 ) – ( 5 x 0.08 ) Work out the answer to this problem using your calculators. This calculation gives the answer to the problem on the last screen. Q. How does this calculation work?

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L.O.2 To be able to check with the inverse operation when using a calculator. To be able to use all four operations to solve simple word problems.

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**22 children have each received the same number of merits**

22 children have each received the same number of merits. Between them they have 242 merits. How many merits does each child have? Q. What calculation would I carry out to solve this problem.

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**The calculation will be :**

242 ÷ 22 = 11 Q. What calculation would I carry out to check that the answer is 11?

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**The calculation will be :**

22 x 11 = 242 This checks that the calculation is correct by “using the inverse operation”.

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**How much space is left on the shelf?**

A reading book is 14mm wide. There are 36 reading books on the classroom shelf. The shelf is 65 cm wide. How much space is left on the shelf? Q. What calculation would I carry out to solve this problem?

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The calculation is : 650 – ( 36 x 14 )

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**CANS BOXES CHILDREN MONEY TIME WEIGHT**

Work with a partner to make up some word problems. Each word problem must contain at least two of the above words. For each problem you make you should record the calculation needed to solve the problem. 8 minutes

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This screen is blank so some of you can record your problems and the calculations needed to solve them. We may check some of your calculations by using the inverse operation.

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( 18 x 7 ) x ( ) Work in pairs to produce a word problem for each calculation. The 18 must represent children and the 7 must be pounds. Q. What could the 3 represent? Q. Why must the 3 be money if the problem is to make sense?

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

Check an answer by performing the inverse calculation. Solve “story” problems about numbers in real life by choosing the most appropriate operation and method of calculation.

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**L.O.1 To be able to add or subtract any pair of 2-digit numbers, including crossing 100**

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**23 57 Q. What is the sum of these numbers?**

Q. What is the sum of these numbers? Q. What is the difference between these numbers? Write the answers in your books.

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**I am going to choose a number that is greater than 50 and is also a multiple of 5.**

Q. What number might I choose? Before I choose my number you must write in your book a 2-digit number which, when added to mine, will also give a multiple of 5.

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My number is 65. Work out the sum of our two numbers and also the difference between the two.

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**I am going to choose a number below 50 which is a multiple of four.**

Q. Which number might I choose? Before I choose my number you must write in your book a 2-digit number which, when added to mine, makes 100.

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My number is 44. Work out the sum of our numbers and also the difference between the two.

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**I am going to choose a number which is less than 30 but which is a multiple of 6.**

Q. Which number might I choose? Before I choose my number you must write in your book a number which, when multiplied by mine, gets as close to 100 as possible.

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My number is 18. Work out the sum of our two numbers, the difference between the two and their product.

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L.O.2 To be able to solve problems. To be able to choose appropriate methods and operations.

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**What does a large mushroom pizza cost?**

With an extra topping of cheese? NOW DO PART ‘A’

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**Q. For question 1, did you find the cost of toppings first or**

start with the cost of the pizza? Which method is easier? Q. For question 4, did you work out the cost of each pizza and then add them together or list the items and add them? Q. What calculations did you use for Q.2 and Q.3?

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**The calculations are : Question 2 : (2 x £4.65 ) + £4.50 Question 3 :**

£ £ £ £0.40 The only operations used were addition and multiplication and brackets were not always needed.

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**Do part ‘B’. You may use a calculator if you wish.**

Remember to record your calculations.

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A sensible approach is to take away the cost of the toppings which total £ 1.00 so the pizzas must cost £9 or less. Was the calculator helpful in solving the problem in part ‘B’?

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**You are going to find sets of 3 consecutive numbers.**

3 , 4 , 5 You are going to find sets of 3 consecutive numbers. For one of the numbers 3 will be a factor, for another one 4 will be a factor and 5 will be a factor of the other number. One group is 8, 9, 10 because 4 is a factor of 8; 3 is a factor of 9; 5 is a factor of 10. The factors do not have to be in the order 3,4,5.

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**What answers did you find?**

Q. What numbers did you try and why? Q. As 5 is a factor what can you say about one of the consecutive numbers? end in 5 or 0 Q. As 4 is a factor what must one of the other numbers be? even

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**100 Q. What 3 consecutive numbers can we try if 100**

is to be one of them?

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**Q. Which of the other sets of numbers can be discarded? Why?**

Remember one number must end in 5 or 0 and another must be even so they could be 98, 99,100, or 100,101,102 but not 99, 100, 101 as neither 99 nor 101 is even. Q. Which of the other sets of numbers can be discarded? Why?

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**We can discard these: 100,101,102 One number ends in 5 or 0.**

One number is even but not a multiple of 4. Dividing by 4 is the same as halving and halving again. Half of 102 is 51 so 4 will not divide into 102. Q. Does 3 divide into 99?

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**although one number ends in 5 or 0**

3 does divide into 99 but we can discard 98, 99, 100 as although one number ends in 5 or 0 the other even number is not a multiple of 4 since half of 98 is 49 and cannot be halved again so 4 does not divide into 98. So neither set of numbers works.

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Even though you could have used a calculator it may be more efficient to solve a problem by applying what you know about numbers.

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

Solve ‘story’ problems about numbers in real life choosing the appropriate operation and method of calculation. Make and justify decisions.

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Copyright © 2003 Pearson Education, Inc. Slide 1 Computer Systems Organization & Architecture Chapters 8-12 John D. Carpinelli.

Copyright © 2003 Pearson Education, Inc. Slide 1 Computer Systems Organization & Architecture Chapters 8-12 John D. Carpinelli.

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