Introduction week 9 Hi all First of all

Introduction- week 9 Hi all First of all I hope you are all still keeping safe, healthy and looking after yourselves. Now to the boring bit…. Work… My expectation…. I will be expecting you to be doing 5 hours of maths a week. This is no more than what you do in school so it should be relatively straight forward. Now this can be completed by doing an hour a day or spending a few hours on 2 or 3 days completing the entirety of the work, the choice is yours, however, I will be expecting the work to be completed. There will be 4 lessons of NEW CONTENT a week with the 5 th lesson having to complete questions on everything you’ve just learnt (Each lesson 1 hr long). There will be an instruction of how I expect these questions to be completed when you go to lesson 5. I will be providing you with lessons to go through and will be expecting each of you to take notes and answer any questions which are within the slides to help develop your understanding. The week will be topic based so lesson 1 will help with lesson 2 and 3 and so on, so PLEASE DO NOT skip slides. All the lessons will provide you with material on topics that we were yet to cover during your first year at LEEP. If you feel you get stuck or are confused please do not hesitate to contact me. I will be allocating every Wednesday for you to contact with any questions or concerns and will respond to them as soon as I can on the day. However if you have any questions outside of that day I will get back to you as soon as I possibly can. Email: s. rivera@leep. org. uk Please continue to look after yourselves and work hard to ensure we are not having to play catch up when we are back. Mr Rivera

Timetable: Monday – Lesson 1 material Tuesday – Lesson 2 material Wednesday – Lesson 3 material Thursday – Lesson 4 material Friday – Exam questions

Please look at these slides in full screen so you get all the content material. There a lot of slides but please take your time reading through them. Some slides are just additional bits of information for the previous slides so do not be daunted. Remember, if you have any questions you will be able to send an email to me. I will respond as soon as possible. Email: s. rivera@leep. org. uk

Lesson 1

Inequalities • Show inequalities on a number line • Write down whole numbers that satisfy an inequality • Solve simple linear inequalities in one variable and represent the solution on a number line

Inequality Signs < means “is less than” means “is less than or equal to” > means “is greater than” means ”is greater than or equal to” Reading Inequalities 6 < 8 or equivalently 8 > 6 1. 3 < n < 9 n is greater than 3 but less than 9. 2. 4 n < 7 n is greater than or equal to 4 but less than 7. 3. -2 n 1 n is greater than or equal to -2 but less than or equal to 1.

Starter: MWB Write a sentence for the following inequalities 1. 0 < n < 3 n is greater than 0 but less than 3. 2. -5 n < 2 n is greater than or equal to -5 but less than 2. 3. -7 n -1 n is greater than or equal to -7 but less than or equal to -1. 4. x > 9 x is greater than 9 5. x > -1 x is greater than -1 6. p 6 p is greater than or equal to 6 7. a - 4 a is greater than or equal to - 4

Displaying Inequalities on a Number Line x 1 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 x -2 -6 -5 x>4 -6 -5 x>0 -6 -5

Displaying Inequalities on a Number Line x 1 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 x -2 -6 -5 x<4 -6 -5 x<0 -6 -5

Displaying Inequalities on a Number Line -5 n 5 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -1 < n 4 -6 -5 -4 -5 < n < 0 -6 -5 -4 -3 n < 6 -6 -5 -4

MWB: State the inequalities displayed on each number line below. 0 n 5 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 < n 4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 0<n<5 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 n < -3 -6 -5 -4 1 2 3 4 -3 -2 -1 0 1 2 3 4 5 6

X < 2 Show Me!

X ≥ -3 Show Me!

X ≤ 0 Show Me!

X > -8 Show Me!

-1< X < 2 Show Me!

-7≤X ≤ -1 Show Me!

0≤ X < 6 Show Me!

-4 < X > 2 Show Me!

One last thing:

MWB List the integer values that satisfy the inequalities below: -2, -1, 0, 1, 2 2, 3, 4, 5

How do you solve inequalities?

Try solving these inequalities:

Method 1 Method 2 Both methods give the same answer!

Have a go at solving these:

An example: Get the letter onto one side Get the numbers on the other side

Another example: Get the letter onto one side Get the numbers on the other side

Solve these inequalities:

Plenary: Solve .

Solve these inequalities and write all the integer values that satisfy them:

Lesson 2

CW Solve inequalities 28/11/2020 Solve two linear inequalities in x find solution sets and compare them to see which x satisfies

Starter: Plot these inequalities x < 5 ‘x is less than 5’ x ≤ 5 ‘x is less than or equal to 5’ 5 5 x > 7 ‘x is greater than 7’ 7 x ≥ 7 ‘x is greater than or equal to 7’ 7

Inequalities Solve the inequality below, and show the answer on a number line… ÷ 8 1 8 x ≤ 32 x ≤ 4 2 3 4 ÷ 8 5

Inequalities Solve the inequality below, and show the answer on a number line… ÷ 3 11 3 x > 39 x > 13 1 2 1 3 1 4 ÷ 3 1 5

Inequalities are very similar to Equations The only difference is that you will end up with a range of values for ‘x’, rather than 1 specific value They are solved in the same way as we did equations…

Inequalities Solve the inequality below, and show the answer on a number line… +5 3 x - 5 > 19 3 x > 24 ÷ 3 x 6 7 > 8 8 9 +5 ÷ 1 0 3

Inequalities Solve the inequality below, and show the answer on a number line… 6 x + 6 6 x -6 ÷ 6 x 3 4 ≤ 36 ≤ 30 ≤ 5 5 6 -6 ÷ 7 6

Inequalities Solve the inequality below, and show the answer on a number line… + 2 x -3 5 x + 3 7 x + 3 ≥ 10 - 2 x ≥ 10 7 x ≥ 7 ≥ 1 ÷ 7 x -1 0 1 2 + 2 x -3 ÷ 7 3

Inequalities Write down the integers that satisfy this inequality… < < 3 +1 4 2 4 x-1 x 6 < < 8 8 +1 9 1 0 Integers (whole numbers) that satisfy this inequality are: 5, 6, 7, 8,

Task: Now try these questions… 1) Solve the following Inequalities and display the answers on a number line: a) Add 5 4 b) Divide by 2 5 6 7 Subtrac t 3 y 8 0 1 c) Add 3 3 4 Divide by 4 Multiply by -1 (swap the sign) Divide by 3 2 Subtrac t 7 0 1 2 3 4 2) Write down the integers that satisfy both the Inequalities below: Add 4 2 3 4 5 6 7 8 Subtract 2 x Subtract 2 Divide by 3 The integers are 5 and 6!

Inequalities Solve the inequality below, and show the answer on a number line… x by -1 6 5 -x > x < -4 4 4 3 x by -1 2 When you multiply/divide an inequality by a negative, you must reverse the sign…

Inequalities Solve the inequality below, and show the answer on a number line… + 2 x 6 - 2 x ≤ 6 ≤ ÷ 3 -2 4 3 ≥ 2 5 x 3 x x -1 + 2 x ÷ 0 -3 When you multiply/divide an inequality by a negative, you must reverse the sign…

Card matching activity. How confident do you feel with this topic? Write Red, Amber or Green in your book Complete the corresponding activity Challenge work: CGP Book: Page 110 Exercise 1: Q-5, 6, 7

Plenary What values of x satisfy both of these inequalities? Give your answer as a single inequality (draw a number line to show both – this will help!) 3 x – 15 > 9 – 5 x and 5 x – 3 ≤ 25 + x

Summary We have learnt how to solve inequalities We have seen that inequalities give us a range of answers We have seen how to show these answers on a number line

Lesson 3

Starter : Writing inequalities and drawing number lines You need to be able to sketch equalities and strict inequalities on a number line. x>3 This is known as a ‘strict’ inequality. Means: x is (strictly) greater than 3. ? 0 1 2 3 4 5 ? x≥ 4 x < -1 Means: x is (strictly) less than -1. ? -3 -2 -1 0 1 2 ? x≤ 5 Means: x is greater than or equal to 4. ? Means: x is less than or equal to 5. ? 2 3 4 5 6 7 ? ?

Deal or No Deal? We can manipulate inequalities in various ways, but which of these are allowed and not allowed? Can we add or subtract to both sides? Click to Deal Click to No Deal

Deal or No Deal? We can manipulate inequalities in various ways, but which of these are allowed and not allowed? Can we divide both sides by a positive number? Click to Deal Click to No Deal

Deal or No Deal? We can manipulate inequalities in various ways, but which of these are allowed and not allowed? Can we multiply both sides by a positive number? Click to Deal Click to No Deal

Deal or No Deal? We can manipulate inequalities in various ways, but which of these are allowed and not allowed? Can we multiply both sides by a negative number? Click to Deal Click to No Deal

Task 1 Hint: Do the addition/subtraction before you do the multiplication/division. Solve Solve ? ? ?

Dealing with multiple inequalities Hint: Do the addition/subtraction before you do the multiplication/division. 8 < 5 x 5 x -- 22 ≤ 23 and 2 < x and x ≤ 5 Click to start bromanimation

More Examples Hint: Do the addition/subtraction before you do the multiplication/division. Solve ? ?

Test Your Understanding – MWB’s Solve ? ?

Task 2 Solve the following inequalities, and illustrate each on a number line: 1 2 3 4 ? ? 5 ? 6 ? ? ? 7 8 9 1 0 1 1 Extensio n ? N Extensio n 2 ? ? ? ?

Combining inequalities It’s absolutely crucial that you distinguish between the words ‘and’ and ‘or’ when constraining the values of a variable. AND How would we express “x is greater than or equal to 2, and less than 4”? ? x<4 x ≥ 2 and x ≥ 2, ? x < 4 2 ≤ x? < 4 This last one emphasises the fact that x is between 2 and 4. OR How would we express “x is less than -1, or greater than 3”? ? x>3 x < -1 or This is the only way you would write this – you must use the word ‘or’.

Combining inequalities It’s absolutely crucial that you distinguish between the words ‘and’ and ‘or’ when constraining the values of a variable. 2≤x<4 x < -1 or x > 4 0 1 2 3 4 5 -1 0 1 2 3 4 ? ?

Combining inequalities It’s absolutely crucial that you distinguish between the words ‘and’ and ‘or’ when constraining the values of a variable. To illustrate the difference, what happens when we switch them? o x ≥ 2 and x<4 r x < -1 or x > 4 0 1 2 3 4 5 -1 0 1 2 3 4 ? and ?

Misconceptions This is technically equivalent to: ? x < 4 This is technically equivalent to: ? x > 7 The least offensive of the three, but should be written: 4 < x < 7 ?

Combining Inequalities In general, we can combine inequalities either by common sense, or using number lines. . . 2 5 Where are you on both lines? 4 Combined ? 2 5 4 Combined ?

Test Your Understanding ? -1 1 st condition 2 nd condition Combined -3 ? ? 5

Exercise 2 By sketching the number lines or otherwise, combine the following inequalities. 1 2 3 4 5 6 7 8 9 1 0 1 1 2 1 3 1 4 1 5 ? ? 1 ? ? ? ?

t s e o i s i v e R u Q n s n io

Questions You must now go through all the questions that are in the lessons and ensure you complete all of them. You should be doing the questions as you go through each lesson, so if they are already completed you don’t have much to do other than go through them and check answers.