1. Learning Objectives; Use letter symbols to represent unknown variables; Simplify expressions by collecting like terms. Keywords; Expression; Variable; simplify Mental and Aural Starter – (10 mins) Introduce the ‘amazing’ triangle company that we are hoping to get up and running in PCS. Throughout this module we will be working through all the processes that a company would go through if starting up a new company. Everything that the company does must be mathematical, including the logo… Main activity – (40 mins). We are going to use tactiles to produce the mathematical logo, will spend the first lesson explaining how tactiles work; Introduce idea that x represents the unknown area of a square and get students to create as many pentominoes as they can in 5 minutes. Discuss what the area of these shapes is, and then of a shape with 6, 17 squares etc. Introduce y quadrant, and show that a square plus a quadrant can be written as x + y. Give 5 expressions and get students to write them down and draw 2 different shapes with that area. The last 2 can include x-y as extension. Plenary – (10 mins). Discuss how the x-y shape can be drawn. Get students to come up to board with suggestions.

2. R/A/GLearning Objective Key Words Are you ready to learn? Planner on green Correct equipment Key objective written down. Use letter symbols to represent unknown variables Simplify, Variable

3. The Situation It is 2020. Companies rule the world. There are good companies, bad companies, and just alright companies. And they make everything: window handles; blue cars; on/off buttons; and horses. Well almost everything. To this day there has still never been a company that makes, yes you’ve guessed it: Triangles! Your Job You can’t believe it. No one else has noticed. It came to you in a dream one hot night. Make triangles, lots and lots of triangles. Create a super company that makes triangles. How will you do it? What will your company be called? Do you have a cool LOGO? What type of triangles do people want? How much can you sell them for? So much to do.. so little time.

4. We are going to design a mathematical logo for the company. You have decided that the only way to design a truly mathematical design is to use TACTILES. But first you need to investigate what tactiles are…

5. x This is Taktile 1. We don’t know it’s area, so we represent it’s area with… How would we represent the combined area of this shape? Yes, it’s 5x Well done! Now, how many ‘pentominoes’ can you make from 5 ‘x’- shapes?

6. y TakTiles This is Taktile 2. We don’t know it’s area, so we represent it’s area with… How would we represent the combined area of this shape? Yes, it’s 2y Well done!

7. Now, let’s try some more difficult combined shapes.

8. And more difficult…

9. Can you make and draw two different shapes with the following areas? 1. 3x 2. 2x + y 3. x + 3y 4. 4x + 2y 5. x - y

10. Learning Objectives; Simplify linear algebraic expressions by collecting like terms Keywords; Expression, simplify. Mental and Aural Starter – (10 mins) 10 questions found on t-share drive. Main activity – (40 mins). Re-enforce idea of unknown area implies giving a letter to the shape. Re-engage by showing groups of tactiles on the board (using following ppts) and get students to show how to work out the area using a few different methods; i.e. using the different values of each known tactile; counting the number of squares and quadrants…they can ‘show me’ answers on whiteboards to gauge understanding. Introduce tactiles and using sheet B1 (tactiles A-E), students are to identify which tactile is which letter. Draw around each tactile on plain paper and calculate what the value is of all of them to use as a crib sheet for next lesson. Make sure this is stuck in books! If there is time, can start to create own picture using a number of tactiles and work out the expression of the area. Plenary – (10 mins). Resources Taktiles, whiteboards, white paper

11. Are you ready to learn? Planner on green Correct equipment Key objective written down. To find the areas of taktiles using algebra unknown, simplify, variable05/06/2016

12. 1.Multiply 11 x 40 2.Simplify 2x + 6y + 6x + 9y 3.How many degrees are in a circle? 4.Find the mean of: 3, 7, 5 5.Divide 220 by 11 6.If 8b = 64, find b 7.Name this shape 8.Find P (throwing an even number with a die) 9.What is ¼ of 440? 10.What is the formula for the area of a rectangle?

13. Now, lets introduce the final Taktile. Look at the square below. What would happen if you took a big ‘y’-shaped bite out of it? [3 clicks] Now try and work out this tough combo. [5 clicks] End

14. Shape 1

15. Shape 2

16. Shape 3

17. Shape 4

18. Shape 5

19. Tak A

20. Tak B

21. Tak C

22. Tak D

23. Tak E

24. Learning Objectives; Simplify linear algebraic expressions by collecting like terms Keywords; Expression, simplify. Mental and Aural Starter – (10 mins) Algebra pyramids; put x y 2x at the bottom of a pyramid and students are to add up the adjacent bricks. Main activity – (40 mins). Put a tactile shape on the board without any squares on the background. How can we find the expression that represents this shape? What smaller tactiles are used to create this? We are going to create the logo for our triangle company that we are starting up this module. In your pairs you must create a design that has a maximum area of 4x + 3y. The most interesting design will be used for our class’ company logo. Extension; Introduce the fact that y is equivalent to a circle by placing 4 y’s together which gives an area of 4y and then reducing it to 1/4. Students can now add tactiles F-H to crib sheet from last lesson. Plenary – (10 mins). As a class show the different logo’s that have been designed. Decide which one is the groups favourite and use this as the class logo for the triangle company

25. R/A/GLearning Objective Key Words Are you ready to learn? Planner on green Correct equipment Key objective written down. To use our taktiles to find more difficult areas Simplify, Variable 05/06/2016

26. What expression is at the top of the pyramid? x y2x4y 2x6y

29. Back to front Shape 5

30. What happens if you put 4 y’s together? How about if I made it 4 times smaller?

32. x y 2x 4y 2x 6y x y 2x 4y 2x 6y x y 2x 4y 2x 6y x y 2x 4y 2x 6y

33. 16/09/05 collect like terms To produce our logo with a given area 7b

34. What expression is at the top of the pyramid? x +y x-2y3x3x +y x-y 2x +y Even harder Than last Time!!

35. We are going to design a mathematical logo for the company. You have decided that the only way to design a truly mathematical design is to use TACTILES. You only have enough money for materials to make a logo with an area of 4x + 3y.

36. x +y x-2y 3x 3x +y x-y 2x+y x +y x-2y 3x 3x +y x-y 2x+y