Maths lesson 1 - ipsleyacademy.co.uk · Maths lesson 2. Hello Y6. Complete to warm yourself up. I expect A and B, with C if you want to challenge yourself ... Spider = 16 2 Superman

Maths lesson 1

Hello Y6. Complete to warm yourself up. I expect A and B, with C if you want to challenge yourself

1) 800 x 120 =

2) 1,148 ÷ 4 =

3)42 – 7.85 =

4)𝟒

𝟔x

𝟑

𝟓

5) 22% of 480 =

A B C

Starter answers

1) 800 x 120 = 96000

2) 1,148 ÷ 4 = 287

3) 42 – 7.85 = 34.15

4)𝟒

𝟔x

𝟑

𝟓= 𝟏𝟐

𝟑𝟎or

𝟐

𝟓

5) 22% of 480 = 105.6

A B C

Product means the answer of two numbers multiplied together: 6 x ? = 762.Do the inverse: 762 ÷ 6 = 127

Squares have right angles (90°)Bottom right of triangle = 65° (90-25)Internal angles of triangle add up to 180°77° + 65° = 145°180 - 145 = 35 b = 35°

LO: To solve number picture puzzles

Can you solve the puzzle and find out the value of the dog, cat and rabbit?

What do we know?

Which line on the grid are you going start with?

If you are not sure what to do there are hints on the next slide.

Each picture is worth a number. The total for the pictures is written at the end of some of the rows and columns. Can you find the value of each picture and work at the missing totals?

LO: To solve number picture puzzlesStep by step instruction to how to solve the puzzle What do we know?

Which line on the grid are you going start with?Look at rows across and down.There is row down of 3 dogs = 27 (each dog is the same value) so 3 x ? = 27 9

So now we know a dog =9 go back and look at the rows across and down.There is a row across dog + cat + cat = 19We now know dog = 9 so 9 + cat + cat =19cat + cat = 19 – 9(dog)cat + cat = 10 so a cat = 5

Look back at the grid: cat + cat + rabbit =21 we know a cat = 5rabbit = 21 - 10 = 11

Now use this to fill in the other total

Answers – the key thing to do is start with the row or column that has 3 the same. Once you know one picture, you can use it to solve the others

9 115

25

31

27

Here’s another one to try. Remember, you start with the row or column that has the same pictures.

Can solve the puzzle and find out the value of the hammer, spanner and screwdriver?

What do we know?


Think what we did on the last one.

Each symbol has a numerical value. The total for the symbols is written at the end of some of the rows and columns. Can you find the value of each symbol and work at the missing totals?

Answers – once you know the hammer, you can use this to find what the other pictures are worth

Can solve the puzzle and find out the value of the hammer, spanner and screw driver?

What do we know?Which line on the grid are you going start with?3 hammer = 18 so 1 hammer = 6

Now I know a hammer is 6 I can work out the spanner28 – (3 x6) = 28 – 18 = 10

From this you can work out the rest

6

261912

22

10 3

Silver – solve these puzzles in your books. You don’t have to draw them, just write down: Cake = ___, Milkshake=___ and Sundae=___ as your answer

Can solve the puzzle and find out the value of the cake, milkshake and ice cream?

What do we know?



1)


Answers – you should start by finding the value of the cake by solving 36 ÷ 3 = 12. You can then use this to work out the milkshake and sundae

12 2

1621

16

7

Silver – there are no rows/columns with all the same, so you need to look at what’s the same and what’s different

2)Can solve the puzzle and find out the value of the fries, burger and cola?

What do we know?




Hint: there’s only one fries difference!

Answers – Fries + Burger +Burger = 18 and Fries + Fries + Burger + Burger = 30. That means one Fries is the difference between 30 and 18. So Fries = 12. Then use this to solve the rest!

12

36 17 22

29

3 7

Silver

+ + = 12

+ + = 18

+ + = 26

+ x =

= = =

Don’t forget

BIDMAS

3)

Each symbol has a numerical value. Can you find the value of each symbol and work at the missing totals?

Hint: look carefully, not all the operations are addition!

Answers – start with the first line to find that the Pig is 4. Then use this to solve the rest.

+ + = 12

+ + = 18

+ + = 26

+ x = 34

= 4 = 6 = 10

BIDMAS means you do the multiplication before the addition!

Silver –look carefully here, sometimes there are two symbols together to try and trick you!

+ + = 15

x + = 59

+ X = 32

+ X = ____

= ___ =_____ =___

4)Each symbol has a numerical value. Can you find the value of each symbol and work at the missing totals?

Hint: start with the tennis ball first.

Remember BIDMAS!

Answers - once you know the tennis ball is 5, then you can use this to find the American football. Remember that you need to multiply before you add!

+ + = 15

x + = 59

+ X = 32

+ X = 148

= 5 =7 = 4

10

8 10 14

Well done, you have completed Silver. I hope you have started to get the hang of these, because they get a little trickier in Gold…

Gold – solve in your books. Use the same method as before as before: look for a row or column that is all the same.

= ___ = ____ = ____

1)Each symbol is added together to give the totals at the end of each row and column.

Find the value of each symbol and complete the table.

Gold – answers. Start with the triangle: 3 triangles = 45, so one triangle = 15. Use this to then solve the rest

= 15 = 6 = 9

Gold – These kind of questions can come up in SATs papers too – you just solve them in exactly the same way

total100

total 96

Find the value of and

2)

Hint: this triangle is in a row AND a column.

Answers – 3 triangles add to make 96, so one triangle is 32. You can then use this to find the value of the two circles, then half your answer to find one circle.

total100

total 96

Find the value of and 32 18

Gold – This includes some negative numbers, but that doesn’t change the way you should solve it. Start with the footballs!

3) Each symbol is added together to give the totals at the end of each row and column.


Answers – for the football do -6 ÷ 3 = -2. You can then use this to find the other pictures

-2 105

20

13

18

Gold – There is no row or column that is all the same, so you should look for two that are very similar to each other…

4)Each symbol is added together to give the totals at the end of each row and column.


Hint: what’s the same and what is different between this row and column?

8 1

25

6

-3

-117

Answers

The only difference between this row and column is one bike. Therefore one bike = -3. You can then use this to solve the other pictures.

Platinum challenge – if you’ve solved Gold and have time, then push yourself to try this!

Amina is making designs with two different shapes. She gives each shape a value.

Total value is 147 total value is 111

Calculate the value of each shape

Hint: what’s the same and what is different?

Platinum answers

Amina is making designs with two different shapes. She gives each shape a value.

Total value is 147 total value is 111

Calculate the value of each shape

First shape is made up of 2 hexagons and 3 wedges= 147 The second shape is made up of 1 hexagon and 3 wedges = 111

The difference in shapes in 1 hexagon so find difference between 147 and 111 – hexagon = 36

Now I can use this work out the value of the wedges

111 – 36 = 75 75 ÷ 3 = 25

I am going to double check this on the first shape

147 – (2 X36) = 147 - 72 = 75 75 ÷ 3 = 25

36 25

Maths lesson 2


1) 6² - 3³ =

2) 529 x 6 =

3)39.2 + 16.912 =

4) 5𝟏

𝟑÷ 4 =

5) 4925 x 37 =

A B C

Starter answers

1) 6² - 3³ = (36–27) = 9

2) 529 x 6 = 3,174

3) 39.2 + 16.912 =

56.112

4) 5𝟏

𝟑÷ 4 = 1 𝟒

𝟏𝟐or 1

𝟏

𝟑or

𝟏𝟔

𝟏𝟐

5) 4925 x 37 = 182,225

A B C

Step 1: 67 x 10 = 670Step 2: 67 x 3 = 201

Step 3: 670 + 201 = 871

Train : Rocket3 : 1 = 4 total parts = £52

4 parts = £52. 52 ÷ 4 = 13

13 x 3 = £39 Train = £32

LO To express rules using algebraWhat can you remember from yesterday?

Have a go at solving this algebra puzzle!

Hint: look verycarefully at the spiders!

Work step by step, finding the value of each symbol (or to use a fancy maths word – variable). You need to work in order

2 spiders= 32Spider = 16

2 Superman – Spider = 42 Superman – 16 = 42 Superman = 20Superman = 10

2 Shields = 6Shield = 3

2 Wonder woman + Superman = 122 Wonder woman + 10 = 122 Wonder woman = 2Wonder woman = 1

Now you can solve the last step but look carefully at the spider!

Spider = 16

Superman = 10

Shield = 3

Wonder woman = 1

A spider with 8 legs = 16So each leg = 2This spider only has 6 legs!That means this spider = 6 x 2 = 12

So this final equation is:12 + 3 + 1 = 16

What is algebra? Hopefully, you can remember some of this from the last lesson. Make notes in your books if it helps.

• Another way of saying something we don’t know…yet

• Is useful because it can help us to find lots of different solutions for one problem, rather than having to do lots of different ones

• It also prepares us for more complex maths as we get older

• Generally uses letters instead of numbers

• 𝑥 and 𝑦 are the most commonly used letters, but you can use any letter!

A function machine takes a number, does something to it and gives you an answer on the other side.

What could have happened to 12 to turn it into 4?

Mr Byrom says you have divided it by 3.

Mr McNidder says you have subtracted 8.

They could both be correct!

When we have more examples of the function machine, we can work out exactly what has been done to it – we call this a rule

Mr Byrom says the rule is that you half the first number

Mr McNidder says he is incorrect. Who do you agree with? Why?

For a rule to be correct, it must work for all the examples given

So Mr Byrom is incorrect, because his rule of halve the first number only works for the first example.

It doesn’t work for the second!

The correct rule is that you subtract 3 from the first number.

What has happened to each of the inputs to turn them into their outputs?

We call the first numbers inputs because they are what you put into the number machine.We call the second numbers outputs because they are what you get out of the number machine.

I’m sure you spotted that the rule is that you subtract 3 from the input to get the output. Now we can start to use algebra to show the rule in a simpler way

Let’s call the input a letter rather than a number. I’m going to use 𝑥.So our rule becomes 𝑥 – 3This rule works for all of these function machines!

-3

-3

-3

-3

This is important to know when you use algebra to explain different rules. You might want to make notes in your book.

Multiplying

You don’t write 2 x 𝑥

Instead you write 2𝑥

So, if 𝑥 = 7, 2𝑥 = 14

Dividing

You don’t write 𝑥 ÷ 2

Instead you write 𝑥

2or

1

2𝑥

So, if 𝑥 = 20, 𝑥

2= 10

Guided practice - find the same rule that fits both function machines using algebra.

Let’s use y as the letter for the input

What has happened to y each time to turn it into the output?

How do I write this properly? Look at the last slide if you need.

Guided practice - answers

Let’s use y as the letter for the input

y has been multiplied by 3 to make the output

We write that as 3y

Guided practice - find the same rule that fits both function machines using algebra.

Let’s use t as the letter for the input

What has happened to t each time to turn it into the output?

Remember to write your rule using algebra


Remember, it must be the same rule for both function machines.

If you just look at the first machine the rule could bet+ 7 or 2t

But when you look at the second machine as well, you can see the answer must bet + 7

X 3

36

Guided practice - if you need to work backwards, you use the inverse (opposite)

The inverse of x is ÷.

So, 36 ÷ 3 = 12.

But if you read the question carefully, it says the number was put through the machine twice, so we need to do it again.

12 ÷ 3 = 4. Lucy started with 4.

I can check it by putting this into the machine

Guided practice - once we’ve completed the table, think about what the algebraic rule would be – use the last two boxes to help

When working backwards, remember to use the inverse!


10 10.8 15 2 -3

4 164 -5

a + 5 y + 5

Silver– complete in your books. Remember your neat presentation!

Let’s call the number you put in for each question y.

So, what has happened to the first number in each machine to turn it into the second number?

Remember, it must be the same function for all three machines in the question.

Silver– complete in your books.

5

If the input value is 𝑥, write down

the two possible algebraic

expressions for the equation

Hint: both expressions do not use the same operation (+ - x ÷)

Silver– answers

1) y + 32) y – 23) 3y

4) y ÷ 2 or 𝑦

2

Silver– answers

5

If the input value is 𝑥, write down

the two possible algebraic

expressions for the equation

Hint: both expressions do not use the same operation (+ - x ÷)

The two answers are:3𝑥

𝑥 + 12

Gold – complete in your books. Don’t worry if you can’t solve them all. Try your best and remember you can check your answers later

1 2

3

Hint: think about the inverse for 1) b) and 2) b)

a)

b)

c)

a)

b)

c)

Use 𝑥 to represent the input for c)


4 5

Is David correct? Prove it using

examples

Hint: a stands for the input number

Think about the inverse for finding the outputs

Gold – answers

1

2

3

a) The difference between each answer is 3b) Use the inverse: 20 + 4 = 24

24 ÷ 3 = 8c) 3𝑥 - 4

a)

b)

c)

a)

b)

c)

a) 5 x 2 =10 10 + 5 = 15

b) 19- 5 = 14 14 ÷ 2 = 7

c) 2a + 5 or 2x + 5

-1 2 5 8 11

Use the inverse:2.5 x 2 = 5

It says Lucy put it through the machine twice, so you need to do it again:

5 x 2 = 10, so the answer is 10

Gold – answers

4 5

Is David correct? Prove it using

examples

David is incorrect

Prove using examples:

e.g. if the input is 1

1 + 5 = 6 6 x 2 = 121 x 2 = 2 2 + 5 = 7


2 + 5 = 7 7 x 2 = 142 x 2 = 4 4 + 5 = 11


3 + 5 = 8 8 x 2 = 163 x 2 = 6 6 + 5 = 11

15 19

35 12.5

Platinum challenge – if you’ve solved Gold and have time, then push yourself to try these!

Here’s a link to the problem:https://nrich.maths.org/1053

https://nrich.maths.org/1053

Platinum challenge – answers

Here’s a link to the solution. There are lots of different ways of solving:https://nrich.maths.org/whatsitworth/solution

Once you’ve done, check the puzzle works with the numbers you’ve found. The answers should be:

Triangle – 6Square – 8Hexagon – 7 Circle – 4

So ? = 21

https://nrich.maths.org/whatsitworth/solution

Maths lesson 3


1) 42 + 6 ÷ 3 =

2) 15% of 160 =

3) 429 x 1 =

4) 3𝟏

𝟑+ 1

𝟐

𝟔=

5) 5886 ÷ 18 =

A B C

Starter answers

1) 42 + 6 ÷ 3 = BIDMAS = 44

2) 15% of 160 = 24

3) 429 x 1 = 429

4) 3𝟏

𝟑+ 1

𝟐

𝟔= 𝟏𝟎

𝟑+𝟖

𝟔=

𝟐𝟖

𝟔or 𝟒

𝟒

𝟔or 𝟒

𝟐

𝟑

5) 5886 ÷ 18 = 327

A B C

Step 1: 126 x 5 = £630Step 2: 195 x 10 = £1,950Step 3: 38 x 7 = £266

Step 4: 630 + 1950 + 266 = £2,846

Triangle + Star must = 50 as it is half of the shapes used in the first equation.2 x heart must therefore = 28

28 ÷ 2 = 14 Heart = 14

LO To solve problems using algebraI bet you can already do it!

Find the value of a.

a + 5 = 9

Find the value of b.

20 - b = 12

Remember, algebra is just another way of showing a ? in a question. It represents something we don’t know…yet!

You probably solved these in your head but think of the maths you used to do it. This will help you with more complicated problems.


a + 5 = 9

a = 4

-5 -5

a = 4 and b = 8

The equals sign is like a seesaw. It means that everything on one side is worth exactly the same as everything on the other.

If you do something to one side, then you must do the same to the other to keep it balanced.

To solve algebra problems, you must get the letter on its own.

We’re taking away 5 from one side to get the letter on its own. So, we must also subtract 5 from the other side

Guided practice. You should set your working out line by line. Just do one step at a time



2a + 6 = 30

2a = 24

a = 12

1) Get the letters on their own by -6 (remember you just do the same to both sides)

2) We know 2a = 24, and we want to find a. That means we need to divide by a 2, so we must also do 24 ÷ 2

3) We have our answer, a = 12

-6 -6

÷ 2 ÷ 2

Guided practice. We use the same rules every time – step by step, setting out line by line. It’s all about the inverse

𝑎

3- 6 = 54

𝑎

3= 60

a = 60 x 3

a = 180

1) We want to get 𝑎

3on its own, so what do we

do with ‘-6 ‘?

2) 𝑎

3means a ÷ 3, so what is the inverse of ÷?

3) We have our final answer by solving 60 x 3

+6 +6

x3 x3


Guided practice. Sometimes we might have more than one letter (term). We must collect them first, then solve as normal

Find the value of 𝑥.

3𝑥 + 6 = 40 – 𝑥

4𝑥 + 6 = 40

4𝑥 = 36

𝑥 = 9

1) We want all the 𝑥 on one side. If we have -𝑥on one side, we must use the inverse to get rid of it. That means we add 𝑥 to each side.

2) To get the 𝑥 on its own, we must subtract 6 from each side

3) Now we know 4𝑥 = 36, we must ÷ by 4 to get 𝑥

+ 𝑥

-6

+ 𝑥

-6

÷ 4 ÷ 4

Guided practice. Follow our rules to solve this yourself. You can look back at the previous slides to help you

5p + 7 = 2p + 25


5p + 7 = 2p + 25

3p + 7 = 25

3p = 18

p = 6

Silver – complete in your books. Remember to solve these equations line by line, doing one step at a time (and you ‘ll be just fine!)

1) 7t + 3 = 45

2) 12d – 8 = 100

3) 3p – 0.6 = 3.9

4) 30 + 𝒙 = 4𝒙 + 𝟑

5) 6c - 40 = 2c + 12

Silver – answers. If you didn’t get them all right don’t worry. Use the answers to try and correct your working

1) 7t + 3 = 45

2) 12d – 8 = 100

3) 3p – 0.6 = 3.9

4) 30 + 𝒙 = 4𝒙 + 𝟑

5) 6c - 40 = 2c + 12

t = 6

d = 9

p = 1.5

x = 9

c = 13


1 2 3The rule for making scones is use

4 times as much flour (f) as butter (b).

If not, what is the answer?

a)

b)


4

Gold – answers

1 2 3The rule for making scones is use

4 times as much flour (f) as butter (b).

If not, what is the answer?When a =10, p = 25

That means c = 10 - 25

c = -15

a) Joe is incorrect – the letter can equal anything. It is not linked to the order it comes in the alphabet!

b) Derek is incorrect. When c = 5, x = 16

a)

b)

The correct formula is B because you one flour needs to be 4 lots of butter

Gold – answers. If you didn’t get them all right don’t worry. Use the answers to try and correct your working

4

w + 10 = 13w + x = 8y – w = -0.5

w + x + y = 10.5w – x – y = -4.5y + y + y = 7.5

Platinum challenge – if you’ve solved Gold and have time, then push yourself to try this!

Hint: the best way to check is to substitute your numbers into each equation.

Each letter is a differentnumber (including a zero!)

If:

A+C=AF×D=FB−G=GA+H=EB ÷ H=GE−G=F

and A-H represent the numbers from 0 to 7

Find the values of A,B,C,D,E,F,G and H.

Platinum challenge – answers

A = 5B = 6C = 0D = 1E = 7F = 4G = 3H = 2

If:

A+C=AF×D=FB−G=GA+H=EB ÷ H=GE−G=F

and A-H represent the numbers from 0 to 7

Find the values of A,B,C,D,E,F,G and H.

Maths lesson 4


1) 3,000,000 – 12,599 =

2) 829 x 5 =

3) 14.885 + 56.522 =

4) 4𝟏

𝟐− 2

𝟑

𝟓=

5) 1248 ÷ 26 =

A B C1) What are the missing numbers?

2)

Warm up answers

1) 3,000,000 – 12,599 =

2,987,401

2) 829 x 5 = 4,145

3) 14.885 + 56.522 =

71.407

4) 4𝟏

𝟐− 2

𝟑

𝟓= 1

𝟗

𝟏𝟎or

𝟏𝟗

𝟏𝟎

5) 1248 ÷ 26 = 48

A B C1) What are the missing numbers?

2)

3.1 3𝟏

𝟒(3.25)

𝟏𝟖

𝟓(3.6)

4.2

420

250g = 𝟏

𝟒of 1kg.

£1.80 ÷ 4 = 45p

300g = 𝟑

𝟏𝟎of 1kg.

£2.60 ÷ 10 = 26p (100g)

26p x 3 = 78p

• 4 operations, including decimals

• 4 operations with fractions

• Fractions of amounts

• percentages

• X and ÷ by powers of 10

• Using x table knowledge for larger numbers

• Square (²) and cube (³) numbers

• BIDMAS

• Trick question (x 1 or ÷ 1)

• Negative numbermaybe

This is going to help you keep your amazing arithmetic skills fresh – these are the topics it will cover

• Remember to use your maths methods

• Make your decimal points clear

• Check you have written the correct answer in the box

• Write your numbers neat and clear so the marker can read them

Time to practice your skills with an arithmetic paper. Look back in your book to see what your score was last time – can you improve/maintain it?

Write your answers in your books and show your working. Use the squared paper to set out your calculations carefully.

1) 3844 + 100

2) 237 ÷ 1

3) 2 x 214

4) 774 – 7

5) 125 ÷ 5

6) ______ = 2954 – 763

7) 2 x 9 x 5

8) ______ = 33 361 + 2978

9) 9.9 – 0.3

10) 83 x 7

11) 560 ÷ 7

12) 427 ÷ 100

13) 19.1 + 0.007

14) 200 x 400

15) 8547 x 9

16) 8800 ÷ 11

17) 1

5+ 2

5

18) 43.682 – 8.72

You have 30 - 40mins, make a note of the time to help you pace yourself.

If you finish, then please check!

Keep going – you can do it!

19) 176 951 – 17 572

20) 8² + 12

21) 1000 x 0.522

22) 6516 ÷ 4

23) 5

6of 120

24) 45 – 2.13

25) 40% x 120

26) 608 ÷ 19

27) 25 x 9.8

28) 276 x 82

29) 72% of 70

30) 1

6+

7

18

31) 4653 x 64

32) 5

6÷ 5

33) 1624 ÷ 28

34) 1 1

4-5

9

35) 13 x 1 1

3

36) 108 – 81 ÷ 9

Remember that long multiplication and long division are worth 2 marks. Everything else is one mark, so don’t get stuck on one question for too long!

Before you look at the answers, remember…

Answers – mark your work. If you didn’t get it right first time, see if you can see where you went wrong and correct it.

1) 3844 + 100 = 3944

2) 237 ÷ 1 = 237

3) 2 x 214 = 428

4) 774 – 7 = 767

5) 125 ÷ 5 = 25

6) 2191 = 2954 – 763

7) 2 x 9 x 5 = 90

8) 36 339 = 33 361 + 2978

9) 9.9 – 0.3 = 9.6

10) 83 x 7 = 581

11) 560 ÷ 7 = 80

12) 427 ÷ 100 = 4.27

13) 19.1 + 0.007 = 19.107

14) 200 x 400 = 80 000

15) 8547 x 9 = 76 923

16) 8800 ÷ 11 = 800

17) 1

5+ 2

5= 3

5

18) 43.682 – 8.72 = 34.962

Answers – mark your work. If you didn’t get it right first time, see if you can see where you went wrong and correct it.

19) 176 951 – 17 572 = 159 379

20) 8² + 12 = 76

21) 1000 x 0.522 = 522

22) 6516 ÷ 4 = 1629

23) 5

6of 120 = 100

24) 45 – 2.13 = 42.87

25) 40% x 120 = 48

26) 608 ÷ 19 = 32 (2 marks)

27) 25 x 9.8 = 245

28) 276 x 82 = 22 632 (2 marks)

29) 72% of 70 = 50.4

30) 1

6+

7

18= 10

18or

5

9

31) 4653 x 64 = 297 792 (2 marks)

32) 5

6÷ 5 =

5

30or

1

6

33) 1624 ÷ 28 = 58 (2 marks)

34) 1 1

4-5

9= 25

36

35) 13 x 1 1

3= 52

3or 17

1

3

36) 108 – 81 ÷ 9 = 99

Make a note of your score in your books out of 40.

Did you beat your score from last time?

See if you can do even better next time!

This is the end of the Maths lessons for this week. Well done on completing your work – see you again next week☺

Remember, you’ve also got the pixl app, Mathswatch and tt rockstars if you can’t wait until your next set of lessons. In fact…

Keep battling to try and make Ipsley come out on top!

We’re playing against Church Hill and Sutton Park. Prove that we’re the best!

You can access it through ‘Top of the Rocks’ in the tournament section.

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Maths lesson 1 - ipsleyacademy.co.uk · Maths lesson 2. Hello Y6. Complete to warm yourself up. I expect A and B, with C if you want to challenge yourself ... Spider = 16 2 Superman