7aut1lesson71.pptx simplification of like terms
- 1. Simplifying Expressions: Discuss: Which of these expressions contain a pair of like terms? How do you know? 𝟐 𝞫+𝟐𝜶 𝟓 𝒚𝟐 +𝟐 𝒚𝟐 𝟓√𝟑+𝟑√𝟓
- 2. 5 𝑦2 − 2 𝑦 5 𝑦2 − 2 𝑦2 5 𝑦 −2 𝑦 3𝑝 −2 𝑦 3𝑝 −2𝑝 3𝑝 −3𝑝 3𝑝+3𝑝 5 𝑦 2 +2 𝑦2 −5 𝑦2 +2 𝑦2 Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike In pairs: Decide which expressions contain ONLY like terms
- 3. 5 𝑦 −4 .7 +2 𝑦− 4 .7 − 𝑦− 4 .7 5 𝑦 4 7 +2 𝑦 4 7 − 𝑦 4 7 5 𝑦 −4 +2 𝑦− 4 − 𝑦− 4 5 𝑦 −2 +2 𝑦− 3 − 𝑦 5 𝑦 −2 +2 𝑦− 3 5 𝑦 −2 +2 𝑦− 2 5 𝑦 −2 +2 𝑦2 5 𝑥 4 7 +2 𝑦 4 7 − 𝑧 4 7 Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike 5 𝑦 −2 +2 𝑧− 2 Like / Unlike
- 4. 5 𝑥+2√𝑥 − 𝑥2 5 𝑥+2√𝑥− √𝑥 5√𝑥+2√𝑥− √𝑥 5√𝑥+2√𝑦− √𝑧 Like / Unlike Like / Unlike Like / Unlike Like / Unlike
- 5. 5 𝑦2 − 2 𝑦 5 𝑦2 − 2 𝑦2 5 𝑦 −2 𝑦 3𝑝 −2 𝑦 3𝑝 −2𝑝 3𝑝 −3𝑝 3𝑝+3𝑝 5 𝑦 2 +2 𝑦2 −5 𝑦2 +2 𝑦2 Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike
- 6. 5 𝑦 −4 .7 +2 𝑦− 4 .7 − 𝑦− 4 .7 5 𝑦 4 7 +2 𝑦 4 7 − 𝑦 4 7 5 𝑦 −4 +2 𝑦− 4 − 𝑦− 4 5 𝑦 −2 +2 𝑦− 3 − 𝑦 5 𝑦 −2 +2 𝑦− 3 5 𝑦 −2 +2 𝑦− 2 5 𝑦 −2 +2 𝑦2 5 𝑥 4 7 +2 𝑦 4 7 − 𝑧 4 7 Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike 5 𝑦 −2 +2 𝑧− 2 Like / Unlike
- 7. 5 𝑥+2√𝑥 − 𝑥2 5 𝑥+2√𝑥− √𝑥 5√𝑥+2√𝑥− √𝑥 5√𝑥+2√𝑦− √𝑧 Like / Unlike Like / Unlike Like / Unlike Like / Unlike
- 8. 6 𝑎+6 𝑏 13𝑎−27𝑎 13𝑎2 − 27𝑎 13𝑎2 − 27𝑎−2 13√𝑎−27√𝑎 Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike Your Turn: In your books copy and complete the following:
- 9. Mark your work 6 𝑎+6 𝑏 13𝑎−27𝑎 13𝑎2 − 27𝑎 13𝑎2 − 27𝑎−2 13√𝑎−27√𝑎 Like / Unlike Like / Unlike Like / Unlike Like / Unlike Like / Unlike
- 10. Collecting ‘like’ terms Algebraic expressions can be simplified by collecting like terms "Like terms" are terms whose variables (and their powers such as the 2 in x2 ) are the same. The coefficients may be different.
- 11. Simplify a a a a a a + a + a + a + a = 5a 5a
- 12. And another… 3c + 2c + c = 6c 3c 2c c 6c
- 13. And another… 5d 4d d 5c 4d + d + d – d = d -d
- 15. And another… 3b b 2a + 3b + 4a + b = 6a + 4b 2a 4a 2a 4a 3b b 3b b 2a 4a 6a + 4b
- 16. And another… -3b b -2a - 3b + 4a + b = 2a – 2b -2a 4a
- 17. On your whiteboards… Simplify the following expressions by collecting like terms.
- 18. 4d + d + 3d 8d
- 19. 5d -2d + 3d 6d
- 20. 5p + 4q – 2p + q 3p + 5q
- 21. 5s - t +s + t 6s
- 23. 3pq - 4 + 5pq 8pq - 4
- 24. Worked Example Your Turn TITLE: Collecting Like Terms 3p 2p 4 𝑧 − 𝑧 Working out: Answer:
- 25. In your books, fully simplify each expression 10.
- 26. Mark your work 1. 1
- 27. Algebra Pyramids
Editor's Notes
- #2: Print out sides 2, 3, 4
- #11: Example
- #24: Explicit Instruction Try modelling the worked example in silence, without talking it through. This reduces “cognitive overload”. Then ask students to describe each step or explain each step yourself after your silent demonstration Students can use whiteboards to attempt “their turn” first, ask students to model their working out as you have. Students to then record at least one of the examples in their Maths books.
- #27: Print out sheets for students Acknowledgements: Craig Barton www.variationtheory.com, East Midlands East Maths hub and NES Maths Department