1. Inequalities in Real Life
L.O.
All pupils can use inequalities to solve some realistic problems
Most pupils can relate inequalities requiring logic

2. When inequalities are used in real life
Starter:
When inequalities are used in real life

3. Starter:

4. Inequalities in Real Life
L.O.
All pupils can use inequalities to solve some realistic problems
Most pupils can relate inequalities requiring logic

5. First of all think of the following…
What don’t you know? Represent it with a variable (a letter) and what do you know?
Is there more than 1 possible solution?
What type of inequality sign will you need?

6. E.g. 1 Main 1: Consider this problem:
use inequalities to solve some realistic problems
Consider this problem:
An 18-wheel truck stops at a weigh station before passing over a bridge.
The weight limit on the bridge is 65,000kg.
The cab (front) of the truck weighs 20,000kg, and the trailer (back) of the truck weighs 12,000kg when empty. In pounds, how much cargo can the truck carry and still be allowed to cross the bridge?

7. First of all think of the following…
What don’t you know? Represent it with a variable (a letter) and what do you know?
Is there more than 1 possible solution?
What type of inequality sign will you need?

8. Main 1:
E.g. 1
use inequalities to solve some realistic problems
This problem offers us an upper limit — — but we are interested in finding out the full range of possibilities for the weight of the truck’s cargo.
We can represent the situation using the following inequality, where c is the weight (in kg) of the truck’s cargo:
65,000kg
cab weight +
trailer weight
cargo weight ≤
allowable weight
20,000 +
12,000 c ≤
65,000

9. Main 1:
E.g. 1
use inequalities to solve some realistic problems
cab weight +
trailer weight
cargo weight ≤
allowable weight
20,000
12,000 c
65,000
Solving this inequality for c, we find that c ≤ 33,000. This means that the weight of the cargo in the truck can be anywhere between 0 kg and 33,000 kg and the truck will be allowed to cross the bridge.
20, ,000 + c ≤
65,000
20, ,000 + c – 32,000
65,000 – 32,000 c
33,000

10. E.g. 2 Main 1: Consider this problem:
use inequalities to solve some realistic problems
Consider this problem:
Erykah has found three pairs of running trainers that she likes, costing $150, $159, and $179.
She has saved $31 already, and she has a job where she earns $8.50 per hour.
How many hours will she have to work in order to afford any of these trainers?

11. First of all think of the following…
What don’t you know? Represent it with a variable (a letter) and what do you know?
Is there more than 1 possible solution?
What type of inequality sign will you need?

12. Main 1:
E.g. 2
use inequalities to solve some realistic problems
Erykah has found three pairs of running trainers that she likes, costing $150, $159, and $179. She has saved $31 already, and she has a job where she earns $8.50 per hour. How many hours will she have to work in order to afford any of these trainers?
Notice that this problem is not asking us to find out the number of hours Erykah will have to work to afford a specific trainers—it is asking about any of these trainers.

13. Main 1:
E.g. 2
use inequalities to solve some realistic problems
Erykah has found three pairs of running trainers that she likes, costing $150, $159, and $179. She has saved $31 already, and she has a job where she earns $8.50 per hour. How many hours will she have to work in order to afford any of these trainers?
Since the least expensive trainers are $150, we need to create an inequality that shows how much she needs to work in order to have “at least $150”—or, in math symbols, “≥ $150”.
We will use the variable h to represent the number of hours she works.

14. Number of hours she works Price of the least expensive sneakers
Main 1:
E.g. 2
use inequalities to solve some realistic problems
Erykah has found three pairs of running triners that she likes, costing $150, $159, and $179. She has saved $31 already, and she has a job where she earns $8.50 per hour. How many hours will she have to work in order to afford any of these trainers?
We can solve this inequality like this:
Hourly wage •
Number of hours she works +
Money she has saved ≥
Price of the least expensive sneakers
($8.50 h)
$31
$150.00

15. Number of hours she works Price of the least expensive sneakers
Main 1:
E.g. 2
use inequalities to solve some realistic problems
Erykah has found three pairs of running triners that she likes, costing $150, $159, and $179. She has saved $31 already, and she has a job where she earns $8.50 per hour. How many hours will she have to work in order to afford any of these trainers?
Hourly wage •
Number of hours she works +
Money she has saved ≥
Price of the least expensive sneakers
($8.50 h)
$31
$150.00
Example
Problem
8.5h + 31 ≥
150
8.5h 
150 – 31
8.5h
119
Answer h 14

16. Main 1:
E.g. 2
use inequalities to solve some realistic problems
Erykah has found three pairs of running sneakers that she likes, costing $150, $159, and $179. She has saved $31 already, and she has a job where she earns $8.50 per hour. How many hours will she have to work in order to afford any of these sneakers?   
Erykah needs to work at least 14 hours to afford any of the running sneakers. If she works more hours, she’ll be able afford the more expensive models.
Example
Problem
8.5h + 31 ≥
150
8.5h 
150 – 31
8.5h
119
Answer h 14

17. “Sam has more than twice the number of books as Gerard?”
Main 1:
use inequalities to solve some realistic problems
If s represents the number of books that Sam has, and g represents the number of books that Gerard has, which inequality models the situation:
“Sam has more than twice the number of books as Gerard?”
A) s > 2g
B) s < 2g
C) g < 2s
D) g > 2s

18. First of all think of the following…
Main 1:
use inequalities to solve some realistic problems
First of all think of the following…
What don’t you know?
Represent it with a variable (a letter)
What do you know?
2. Is there more than one possible solution?
3. What type of inequality sign will you need?

19. Main 1: Write an equality to represent the following situation:
use inequalities to solve some realistic problems
Write an equality to represent the following situation:
Debbie has at most £60 to spend on clothes.
She wants to buy a pair of jeans for £22 and spend the rest on t-shirts.
Each t-shirt cost £8.

20. Main 1: Think of the following…
use inequalities to solve some realistic problems
Think of the following…
What don’t you know?
Represent it with a variable (a letter)
What do you know?
2. Is there more than one possible solution?
3. What type of inequality sign will you need?
We don’t know how many t-shirts can be bought … let this be “x” We know that jeans cost £22 – this will be a constant in the equation
Yes!
Because she could spend ALL of the £60 or just some of it.
If she bought just 1 t-shirt and the jeans, she would have money left to buy more t-shirts!
We know that the jeans and t-shirt COULD BE £60 or could be LESS THAN £60… so we will be using the sign ≤

21. Main 1: In words: £22 pair of jeans + £8 PER t-shirt ≤ £60
use inequalities to solve some realistic problems
Debbie has at most £60 to spend on clothes. She wants to buy a pair of jeans for £22 and spend the rest on t-shirts. Each t-shirt cost £8.
In words:
£22 pair of jeans + £8 PER t-shirt ≤ £60
Remember that we said t-shirts would be represented by “x” so…
22 + 8x ≤ 60
£22 + £8x ≤ £60 OR…

22. Main 1:
use inequalities to solve some realistic problems
Julia has £80. She wants to purchase a nail paint set for £16 and earrings. She spends the rest of the money on earrings. Each pair of earrings costs £8. Write an inequality for the number of pairs of earrings she can purchase.
Christina goes to the market with £50. She buys one papaya for £20 and spends the rest of the money on bananas. Each banana costs £6. Write an inequality for the number of bananas she can purchase.
Billy goes to the store. He has £90. He wants to purchase a leather jacket for £45, a hat for £10, and the rest on jeans. Each pair of jeans costs £35. Write an inequality for the number of jeans he can purchase.
Rebecca bought one gold fish (£32) and one star fish (£12). She spends the rest of her money on guppy fish. She starts with £80. Each guppy costs £6. Write an inequality for the number of guppies she can purchase.

23. Main 1:
use inequalities to solve some realistic problems
Julia has £80. She wants to purchase a nail paint set for £16 and earrings. She spends the rest of the money on earrings. Each pair of earrings costs £8. Write an inequality for the number of pairs of earrings she can purchase.
Christina goes to the market with £50. She buys one papaya for £20 and spends the rest of the money on bananas. Each banana costs £6. Write an inequality for the number of bananas she can purchase.
Billy goes to the store. He has £90. He wants to purchase a leather jacket for £45, a hat for £10, and the rest on jeans. Each pair of jeans costs £35. Write an inequality for the number of jeans he can purchase.
Rebecca bought one gold fish (£32) and one star fish (£12). She spends the rest of her money on guppy fish. She starts with £80. Each guppy costs £6. Write an inequality for the number of guppies she can purchase.
x ≤ 8
16 + 8x ≤ 80
x ≤ 5
20 + 6x ≤ 50
x ≤ 1
x ≤ 90
x ≤ 6
x ≤ 80

24. Inequalities in Real Life
L.O.
All pupils can use inequalities to solve some realistic problems
Most pupils can relate inequalities requiring logic

25. Using Logic with Inequalities
Main 2:
relate inequalities requiring logic
Using Logic with Inequalities
Page 168

26. Inequalities in Real Life
L.O.
All pupils can use inequalities to solve some realistic problems
Most pupils can relate inequalities requiring logic

27. Plenary:

28. Plenary:

29. Plenary:

30. Inequalities in Real Life
L.O.
All pupils can use inequalities to solve some realistic problems
Most pupils can relate inequalities requiring logic
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