Week 3 Understanding and using numbers MATHS Week 3 Understanding and using numbers

To warm up……. Can you answer all 10 questions on this weeks number?

Today’s plan: Understand, use and calculate using number Calculate using +, -, x and ÷ Rounding Negative numbers Part 2 of your diagnostic (Measure, shape and space section)

What did we do last week?

Why are they misleading? Misleading graphs Why are they misleading?

1. Which is the better graph – and why. 2 1. Which is the better graph – and why? 2. Where is the spelling mistake – and why?

Although the vertical scale starts at 0, it does not go up in even steps. This distorts the graph, and makes it look as though the biggest jump is between 1 and 2, rather than 3 and 4. Also, there are no labels on the axes, so we have no idea what this graph represents!

On this pictogram, there is no category for people who do not own a pet. The pictures are different sizes, and it appears that more people own a horse than any other animal. An improvement would be to redraw the pictogram, with each of the animals the same size and aligned with one another.

True or False: Twice as many people like Thrillers than Romance films. 150 120 100 60 Number of People 40 25 The scale on the vertical axis is not linear, so even though the green bar is twice as big as the purple bar, it does not represent twice as many people. 20 5 Horror Comedy Action Romance Thriller Favourite Films

Summary of points Scale doesn’t start at zero Scale made very small to make graph look very big Scale values or labels missing from the graph Incorrect scale placed on the graph Size of images used in pictograms are different for the different categories

Understand and use very large numbers Give me a number….let’s look at the place value

Here are some annual salaries Here are some annual salaries. Write them out in order from largest to smallest. Can you say the figures in words? (talk about place value) £25,740,030 £51,931,640 £40,100,000 £51,750,000 £34,621,093 £9,600,000 £149,440 £143,789 £25,216,800 £27,847,401 £0 £43,500,000

The order should look like this: £51,931,640 £51,750,000 £43,500,00 £40,100,000 £34,621,093 £27,847,401 £25,740,030 £25,216,800 £9,600,000 £149,440 £143,789 £0

Who am I? Write down the name of the celebrity next to the amount of money you think they earn in a year. Good luck! (Source: www.wageindicator.co.uk)

Who am I? How much money do I earn per year? Usain Bolt

Who am I? How much money do I earn per year? Theresa May

Who am I? How much money do I earn per year? Boris Johnson

Who am I? How much money do I earn per year? Lewis Hamilton

Who am I? How much money do I earn per year? Adele

Who am I? How much money do I earn per year? Jeremy Clarkson

Who am I? How much money do I earn per year? Daniel Radcliffe

Who am I? How much money do I earn per year? Pope Francis

Who am I? How much money do I earn per year? Queen Elizabeth II

Who am I? How much money do I earn per year? Jose Mourinho

Who am I? How much money do I earn per year? Ed Sheeran

Who am I? How much money do I earn per year? Simon Cowell

The wealthiest is…. correct them as you go

The wealthiest is…. £51,931,640

Next wealthiest is…. £51,750,000

Next wealthiest is…. £43,500,000

Next wealthiest is…. £40,100,000

Next wealthiest is…. £34,621,093

Next wealthiest is….. £27,847,401

Next wealthiest is…. £25,740,030

Next wealthiest is…. £25,216,800

Next wealthiest is…. £9,600,000

Next wealthiest is…. £149,440

Next wealthiest is…. £143,789

And the least wealthy is…. £0

The order should look like this: Adele £51,931,640 Daniel Radcliffe £51,750,000 Simon Cowell £43,500,00 The Queen £40,100,000 Lewis Hamilton £34,621,093 Ed Sheeran £27,847,401 Usain Bolt £25,740,030 Jose Mourinho £25,216,800 Jeremy Clarkson £9,600,000 Theresa May £149,440 Boris Johnson £143,789 The Pope £0

Addition and Subtraction problems Sum Total Add Plus Increase Subtract Take Away Minus Less Decrease

Addition and subtraction problems

Addition and subtraction problems 1099 – 875 = £224

Multiplication and division problems 159 ÷ 30 = 5.3 So they would need 6 coaches 1079 ÷ 8 = 134.875 So Jarred would need 135 boxes

Multiplication and division problems 5 x 9 = 45 chips 45 ÷ 7 = 6.428 So 6 chips each as you can’t divide the rest up equally 24 x 19 = 456 456 ÷ 8 = 57 carrots for each rabbit

Rounding Nearest 10, 100, 1000

DISCUSS!!! What is ROUNDING? What do we mean by ‘round up’ and ‘round down’? Can you think of some examples of when you have seen rounding before?

We do not need to know the exact number for everything. Why do we use rounding? THINK! We do not need to know the exact number for everything. Can you think of any other examples of numbers from everyday that have probably been rounded? Why not just 7 billion… There are exactly 6,970,442,289 people on planet Earth Teacher Notes: Class discussion – pupils may have more ideas but key point here is that rounded values are easier to work with in practical contexts.

What sorts of things do we round? Teacher Notes: The globe with the people represents population. This slide can be used as a brainstorming activity, using the triggers after students have come up with their own ideas.

50 40 43 Rounding to the nearest 10 43 is closer to 40 than to 50. Which two TENS does the number 43 lie between? Where would you place 43 on the washing line? Teacher Notes: Discuss rounding UP and DOWN as rounding to the ten, hundred or thousand closest to the original number. Language of ROUNDING DOWN can be confusing – what does this actually mean? So, 43 rounded to the nearest 10 is 40.

Rounding to the nearest 10 180 190 186 186 is closer to 190 than to 180. Teacher Notes: Even though our number now includes place value column of HUNDREDS, we are only rounding to nearest TEN. Which two TENS does the number 186 lie between? Where would you place 186 on the washing line? So, 186 rounded to the nearest 10 is 190.

But the rule is… 5 or more, round up Rounding to the nearest 10 10 20 15 15 is exactly halfway! But the rule is… 5 or more, round up Teacher Notes: Discuss convention of rounding – even though 5 represents half-way, we round UP. Which two TENS does the number 15 lie between? Where would you place 15 on the washing line? So, 15 rounded to the nearest 10 is 20.

APPLY 81 Round

APPLY 75 Round

APPLY 51 Round

APPLY 23 Round Use this slide to discuss the fact that 23 to the nearest 100 is 0!

APPLY 97 Round Use this slide to discuss the fact that 97 to the nearest 10 is 100.

APPLY 412 Round

APPLY 673 Round

APPLY 845 Round

APPLY 312 Round

APPLY 755 Round

Which of these numbers round to 60 to the nearest 10? ANALYSE Which of these numbers round to 60 to the nearest 10? 157, 56, 61, 66, 55

Which of these numbers round to 90 to the nearest 10? ANALYSE Which of these numbers round to 90 to the nearest 10? 98, 92, 87, 84, 95

Rounding to the nearest 100 600 700 629 629 is closer to 600 than to 700. Which two HUNDREDS does the number 629 lie between? Where would you place 629 on the washing line? So, 629 rounded to the nearest 100 is 600.

9000 8000 8711 Rounding to the nearest 1000 8711 is closer to 9000 than to 8000. Which two THOUSANDS does the number 8711 lie between? Where would you place 8711 on the washing line? So, 8711 rounded to the nearest 1000 is 9000.

Split your scrap paper into three columns. nearest 1000 nearest 100 nearest 10 Split your scrap paper into three columns. Round each number to… Nearest 10 Nearest 100 Nearest 1000 APPLY

APPLY 342 Round

APPLY 864 Round

APPLY 192 Round

APPLY 196 Round Use this slide to discuss the fact that 196 to the nearest 10 is 200.

APPLY 107 Round

APPLY Round 4629

APPLY Round 1811

APPLY Round 3815

APPLY Round 7489

APPLY Round 9615 Use this slide to discuss the fact that 9615 to the nearest 1000 is 10 000.

Positive and negative numbers

Positive and negative numbers

Positive and negative numbers The Number Line

Positive and negative numbers

Positive and negative numbers Look at the number line on the wall if you want a clue!

Positive and negative numbers Extension Questions… What is the highest / lowest temperature? What is 100C cooler than 30C? It is -150C in Moscow (Russia) and 230C in Florida. What is the difference in temperatures?

Diagnostic Please complete the second part of the diagnostic (Measure, shape and space section) You will have 30 minutes to complete as much as you can