Algebra Year 10, 2016 Day 1

Algebra Puzzles day 1 26 4 3

Algebra What is algebra to you?

Algebra Give some examples of what you remember. What does algebra look like to you? Algebra How do you feel about algebra? When in life would you use algebra? What would you like to know about algebra? Terms used with algebra

Algebra Algebra basics

Building the basics Multiplication can be calculated in any order 2×3×4=6×4=24 2×3×4=2×12=24 2×2×2=2× 2 2 =2 3 =8 In algebra 𝑎×𝑏=𝑏×𝑎=𝑎𝑏 2×𝑎×4=8×𝑎=8𝑎 𝑐×𝑐×𝑐= 𝑐 3 2×𝑎×𝑏×𝑏=2𝑎 𝑏 2 Addition and subtraction 5+5+5+5=4×5 3+3+8+8+8=2×3+3×8 In algebra 𝑎+𝑎+𝑎+𝑎=4𝑎 𝑏+𝑏+𝑡+𝑡+𝑡=2𝑏+3𝑡 5+𝑛+4+𝑛=9+2𝑛 3×𝑠+5=3𝑠+5

Building the basics Multiplication using algebra 4𝑧×2=4×𝑧×2=8𝑧 3𝑝𝑟×2𝑞=3×𝑝×𝑟×2×𝑞 =6𝑝𝑞𝑟 Using integers and variables Positive x positive = positive Negative x negative = positive Positive x negative = negative −4𝑎×3𝑏=−4×𝑎×3×𝑏=−12𝑎𝑏 Exponents in algebra 3𝑏×2𝑏=3×𝑏×2×𝑏=6 𝑏 2 𝑠 𝑡 2 ×4𝑠=𝑠×𝑡×𝑡×4×𝑠=4 𝑠 2 𝑡 2 𝑎 𝑏 2 ×3𝑎=𝑎×𝑏×𝑏×3×𝑎=3 𝑎 2 𝑏 2

Building the basics 5𝑎 𝑎 = 5×𝑎 𝑎 =5 12𝑏 6𝑏 = 2×6×𝑏 6×𝑏 =2 Simplifying Division 24 𝑑𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 2 𝑐𝑎𝑛 𝑏𝑒 𝑤𝑟𝑖𝑡𝑡𝑒𝑛 𝑎𝑠 24÷2 𝑜𝑟 24 2 = 12×2 2 =12 Algebra uses the same skills 5𝑎 𝑎 = 5×𝑎 𝑎 =5 12𝑏 6𝑏 = 2×6×𝑏 6×𝑏 =2 14 𝑐 2 7𝑐 = 2×7×𝑐×𝑐 7×𝑐 =2𝑐 23 𝑦 2 2 𝑦 3 = 23×𝑦×𝑦 2×𝑦×𝑦×𝑦 = 23 2𝑦