Lesson+17+by+Milos+and+Jack

__We stared the lesson by doing a think of a number problem__. Think of a number The number must be between 0-10 Then multiply it by ten Think of a second number between 0-10 and multiply it by ten Then add it to the result of the first number. When we are told the answer itis easy to calculate what the two different numbers were. For example Emma 's final answer was 65.So the first number she thought of was 6 and the second 5

__Algebraic and Addition Pyramids__ + + + + 16x 14 7x 7x + x² 8x 8x 8 6 5x 2x 4x 3x + x² 3x 5x 3x 4 4 2 2x 3x -x x 3x x² -x 4x x 2x

__simplify like " like terms "__ 3 x 3 + 4 x 3 3 x 4 + 4 x 4 3 x 5 + 4 x 5 ↑ + ↑ = 7 x 3 ← __simplifying__ ↑ + ↑ = 7 x 4 ← __simplifying__ ↑ + ↑ =7 x 5 ← __simplifying__ ==21= 28 =35= jacob sais 3 x 3 is 9 then add 7 x 3 which is 12

__generalise__ this What have i done in each case? its straight forward or am i just a genius. What i have done is that if you get 3 x a number and 4 x a number + them together it is equal to 7 x a number. __How do we write this in algebra__ Jacob sais 3n + 4n = 7n

__once more__ 5 x 2 - 3 x 2 + 6 5 x 3 - 3 x 3 + 6 5 x 4 - 3 x 4 + 6 5 x 7 - 3 x 7 + 6 ↑ - ↑ + 6 = 2 x 2 + 6 ↑ - ↑ = 2 x 3 + 6 ↑ - ↑ = 2 x 4 + 6 ↑ - ↑ = 2 x 7 + 6 __simplifed by Beth__ __simplified by Shayan__ __simplified by Kishan__ __simplified by Milos__ ↓ __Generalise__, 5 x × - 3 x × + 6 = __2x + 6__ ↓ ↓ 5× and 3× are like terms (they can be added and subtracted) this 6 is not a like term unlike 3×or 5×

__once more__ !!!! 2 x 3 + 4 x 3 + 3² 2 x 4 + 4 x 4 + 4² 2 x 5 + 4 x 5 + 5²

↑ + ↑ = 6 x 3 + 3² ←__simplified__ ↑ + ↑ = 6 x 4 + 4² ←__simplified__ ↑ + ↑ = 6 x 5 + 5² ←__simplified__ ↓ __Generalise__ __6x + x²__

__DON'T FORGET__ " 6 " and " 2 " __ARE__ like terms " 2x " and " 3x " __ARE__ like terms " x² " and " 2x " __ARE NOT__ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!