11022022 Substitution MATHSWATCH CLIP 95 GRADE 3 L

11/02/2022 Substitution MATHSWATCH CLIP 95 GRADE 3 L. O. To be able to § Substitute values into a given algebraic expression and evaluate Key Words substitute, calculate, evaluate Starter

11/02/2022 Substitution MATHSWATCH CLIP 95 GRADE 3 L. O. To be able to § Substitute values into a given algebraic expression and evaluate Key Words substitute, calculate, evaluate Starter answers

11/02/2022 Substitution MATHSWATCH CLIP 95 GRADE 3 Substitution into Expressions Video – Corbettmaths www. corbettmaths. com/2012/08/20/substitution-into-expressions

11/02/2022 Substitution MATHSWATCH CLIP 95 GRADE 3 Discussion What does substitution mean?

11/02/2022 Substitution MATHSWATCH CLIP 95 GRADE 3 Substitution § Remember the letters in algebra are put there to represent Ø numbers that we don’t know, or Ø numbers that can change while the relationship between them stays the same § Substitution is when we are given values for these letters, and need to switch the letters for numbers METHOD § Re-write the expression, equation or formula § Make it exactly the same EXCEPT where you see a letter you can switch, change it into the given number instead, but with a little set of brackets around it § Then use BIDMAS to work out the value of the expression, or use inverse operations to rearrange and solve the equation

11/02/2022 Substitution Examples – Find the value of the following… a) 5 a when a = 10 MATHSWATCH CLIP 95 GRADE 3 REMEMBER to get rid of brackets we MULTIPLY them out b) 8 c when c = 4 c) 3 c when c = 2 • Re-write, but… • Switch letters for numbers (with d) 4 p when p = 20 brackets around) • Calculate, using BIDMAS

11/02/2022 Substitution MATHSWATCH CLIP 95 GRADE 3 Examples – Use substitution to work out the value of the following expressions a) 3 a + 2 c when a=5 and c=4 b) 6 s + 3 c when s=8 and c=5 • Re-write, but… c) 8 t + 4 u + 15 when t=2 and u=7 • Switch letters for numbers (with brackets around) • Calculate, using BIDMAS

Difficulty */** Substitution MATHSWATCH CLIP 95 GRADE 3 Task – work out the values of the following expressions 1) 3 a when a = 4 2) 5 b when b = 6 3) 6 t when t = 2 4) 2 x when x = 8 5) 7 e when e = 1 6) 4 y when y = 4 7) 12 h when h = 2 8) 10 g when g = 5 9) 9 j when j = 10 10) 8 k when k = 1 1) 2) 3) 4) 5) 6) 7) 8) 2 a + 4 b when a = 3 and b = 2 3 r + 7 e when r = 4 and e = 2 2 x + 5 y when x = 1 and y = 6 5 m + 3 f when m = 5 and f = 3 8 h + n + 3 when h = 2 and n = 4 7 u + 4 c + 6 when u = 1 and c = 1 8 t + 2 w + 4 f when t = 10, w = 5 and f = 3 3 g + k + 2 r + 1 when g = 0, k = 1 and r = 5

11/02/2022 Substitution MATHSWATCH CLIP 95 GRADE 3 Task – work out the values of the following expressions 1) 3 a when a = 4 2) 5 b when b = 6 3 × 4 = 12 3) 6 t when t = 2 4) 2 x when x = 8 6 × 2 = 12 5) 7 e when e = 1 6) 4 y when y = 4 7× 1=7 7) 12 h when h = 2 8) 10 g when g = 5 12 × 2 = 24 9) 9 j when j = 10 10) 8 k when k = 1 9 × 10 = 90 1) 2) 3) 4) 5) 6) 7) 8) 2 a + 4 b when a = 3 and b = 2 3 r + 7 e when r = 4 and e = 2 2 x + 5 y when x = 1 and y = 6 5 m + 3 f when m = 5 and f = 3 8 h + n + 3 when h = 2 and n = 4 7 u + 4 c + 6 when u = 1 and c = 1 8 t + 2 w + 4 f when t = 10, w = 5 and f = 3 3 g + k + 2 r + 1 when g = 0, k = 1 and r = 5 5 × 6 = 30 2 × 8 = 16 4 × 4 = 16 10 × 5 = 50 8× 1=8 14 26 32 34 23 17 102 12

11/02/2022 MATHSWATCH CLIP 95 GRADE 3 Substitution Task – For each group, spot the odd one out! 6(x– 2) 4(x– 1) 4 x - 3 When x = 4 3 x 2 x + 4 CLICK for solution 1 2(x– 2) When x = 7 2 x + 4 10 ( x – 6 ) x+3 3 x- 11 CLICK for solution 2

Difficulty ** Substitution MATHSWATCH CLIP 95 GRADE 3 Task - Look at the sums below, each of the letters A, B, C, …. . J represents 0, 1, 2, 3, …. . 9 but not in that order. Work them out. A C E A D D B E E F B A D + C A F E + D A D 1 7 5 8 6 4 6 6 4 + H I G H J A G G E D + G A G G E D 7 8 9 0 9 4 0 1 2 8 6 D E A D + H E A D B A G G A G E H E D G E 6 5 5 2 9 1

11/02/2022 Substitution MATHSWATCH CLIP 95 GRADE 3 Task - Look at the sums below, each of the letters A, B, C, …. . J represents 0, 1, 2, 3, …. . 9 but not in that order. Work them out. A C E A D D B E E F B A D + C A F E + D A D 1 7 5 8 6 4 6 6 4 + G A G G E D 7 8 9 0 9 4 0 1 2 8 6 H I G H D E A D + H E A D B A G G A G E J A G G E D + H E D G E 6 5 5 2 9 1 Answers A=3 B=7 C=9 D=2 E=8 F=0 G=5 H=1 I =4 J =6

11/02/2022 Substitution MATHSWATCH CLIP 95 GRADE 3 • Re-write, but… • Switch letters for numbers (with brackets around) • Calculate, using BIDMAS

11/02/2022 Substitution MATHSWATCH CLIP 95 GRADE 3 SUBSTITUTION TRUE OR FALSE?

Difficulty * Substitution True or false If x=3 5 x = 53 MATHSWATCH CLIP 95 GRADE 3

Difficulty * Substitution True or false If x=3 4 x = 43 MATHSWATCH CLIP 95 GRADE 3

Difficulty * Substitution True or false If x=3 4 x = 12 MATHSWATCH CLIP 95 GRADE 3

Difficulty * Substitution True or false If x=3 2 x= 6 MATHSWATCH CLIP 95 GRADE 3

Difficulty * Substitution True or false If x=3 x-2=1 MATHSWATCH CLIP 95 GRADE 3

Difficulty * Substitution True or false If x=3 and y=4 x-y=-1 MATHSWATCH CLIP 95 GRADE 3

11/02/2022 Substitution SUBSTITUTION SKILLS CHECK! MATHSWATCH CLIP 95 GRADE 3

Difficulty ** Substitution 4+3× ===– 17 133 5. 8 28 19 0. 6 43 – 7 8 5 MATHSWATCH CLIP 95 GRADE 3

Difficulty ** Substitution 7 × 0. 4 22 – 3 6 9 2 ====– 10. 5 31. 5 1. 4 21 77 MATHSWATCH CLIP 95 GRADE 3

Difficulty ** Substitution 0. 2 12 – 4 3 9 2 +6 ===6. 04 150 15 22 87 MATHSWATCH CLIP 95 GRADE 3

Difficulty ** Substitution 2( – 13 3. 6 18 69 7 + 8) ===23. 2 154 – 10 30 52 MATHSWATCH CLIP 95 GRADE 3

11/02/2022 Substitution MATHSWATCH CLIP 95 GRADE 3 Examples – Evaluate these expressions when a = 5, b = 2 and c = – 1 a) 3 a + 2 c b) a(b + c) • Re-write, but… c) abc • Switch letters for numbers (with brackets around) • Calculate, using BIDMAS

Difficulty */**/*** Substitution MATHSWATCH CLIP 95 GRADE 3 Task – Evaluate the following expressions 1) 4 x when x = - 2 2) 2 w when w = - 3 3) - 3 y when y = 6 4) - 4 h when h = - 2 5) 3 e when e = 4 6) -g when g = - 1 7) 2 x + 3 when x = - 1 8) 3 h – 10 when h = - 2 9) 2 e – 5 when e = 1 10) - 2 f + 4 when f = - 3 11) 6 – 2 m when m = - 3 13) 2 a + 3 b when a = 2 & b = - 1 12) g – 1 when g = - 1 14) 4 m – 2 n when m = - 3 & n = 4 15) e – 2 f 16) 6 a – b when e = 10 & f = 3 17) 4 ab + a when a = - 2 & b = 3 when a = 1 & b = - 2 18) - a - b when a = - 1, b = - 2 19) 2 a – 3 b + c when a = 5, b = - 1 & c = - 3

Difficulty */**/*** Substitution MATHSWATCH CLIP 95 GRADE 3 Task – Evaluate the following expressions - 8 2) 1) 4 x when x = - 2 2 w when w = - 3 -6 3) - 3 y when y = 6 - 18 4) - 4 h when h = - 2 8 5) 3 e when e = 4 12 6) -g when g = - 1 1 7) 2 x + 3 when x = - 1 1 8) 3 h – 10 when h = - 2 - 16 9) 2 e – 5 when e = 1 -3 10) - 2 f + 4 when f = - 3 10 -2 12 12) 11) 6 – 2 m when m = - 3 g – 1 when g = - 1 13) 2 a + 3 b when a = 2 & b = - 1 1 14) 4 m – 2 n when m = - 3 & n =- 20 4 15) e – 2 f when e = 10 & f = 3 4 16) 6 a – b when a = 1 & b = - 28 17) 4 ab + a when a = - 2 & b = 3 - 26 18) - a - b when a = - 1, b = - 2 19) 2 a – 3 b + c when a = 5, b = - 1 & c = - 3 10 3

11/02/2022 Substitution MATHSWATCH CLIP 95 GRADE 3 Example - Evaluate this expression when a = 5, b = 2 and c = – 1 • Re-write, but… • Switch letters for numbers (with brackets around) • Calculate, using BIDMAS

Difficulty **/*** Substitution Task – Evaluate the following expressions 1) m ( m – n ) when m = 4 & n = 3 2) f + g ( f + g ) when f = 2 & g = - 3 3) 2 a 2 – b 4) 4 m 2 – 3 am when m = - 3 & a = 2 5) f 2 g – fg 6) when a = 3 & b = - 2 when f = 3 & g = - 1 2 a 3 – 3 b 2 + ab when a = - 1 & b = - 2 MATHSWATCH CLIP 95 GRADE 3

Difficulty **/*** Substitution MATHSWATCH CLIP 95 GRADE 3 Task – Evaluate the following expressions 1) m ( m – n ) when m = 4 & n = 3 4 2) f + g ( f + g ) when f = 2 & g = - 3 5 3) 2 a 2 – b 4) 4 m 2 – 3 am when m = - 3 & a = 2 54 5) f 2 g – fg -6 6) when a = 3 & b = - 2 when f = 3 & g = - 1 2 a 3 – 3 b 2 + ab when a = - 1 & b = - 2 20 - 12

Difficulty */**/*** Substitution MATHSWATCH CLIP 95 GRADE 3 Task – Evaluate these expressions 1. 4 k + 3 (k = 7) 2. 9 p + 15 (p = 3) 3. 5 x - 3 (x = 0) 4. 7 x - 30 (x = 2) 5. 9 - 2 z (z = -3) 6. 8 - 6 k (k = 2) 7. -6 q + 2 (q = 7 ) 8. 8 r - 7 (r = - ¼ ) 1. 2 k 2 + 3 (k = 3) 2. p 3 + 12 (p = 2) 3. 5 x 2 - 3 (x = 3) 4. x 2 + 30 (x = -5) 5. 9 - 2 z 2 (z = -3) 6. 4 k 3 - 9 (k = 1) 7. 8 q 2 + 2 (q = -2 ) 8. 8 r 2 - 7 (r = - ½ )

Difficulty */**/*** Substitution MATHSWATCH CLIP 95 GRADE 3 Task – Evaluate these expressions 1. 4 k + 3 (k = 7) 2. 9 p + 15 (p = 3) 3. 5 x - 3 (x = 0) 4. 7 x - 30 (x = 2) 5. 9 - 2 z (z = -3) 6. 8 - 6 k (k = 2) 7. -6 q + 2 (q = 7 ) 8. 8 r - 7 (r = - ¼ ) 31 42 -3 -16 15 -4 -40 -9 1. 2 k 2 + 3 (k = 3) 2. p 3 + 12 (p = 2) 3. 5 x 2 - 3 (x = 3) 4. x 2 + 30 (x = -5) 5. 9 - 2 z 2 (z = -3) 6. 4 k 3 - 9 (k = 1) 7. 8 q 2 + 2 (q = -2 ) 8. 8 r 2 - 7 (r = - ½ ) 21 20 42 55 -9 -5 34 -5

11/02/2022 MATHSWATCH CLIP 95 GRADE 3 Substitution Task – For each group, spot the odd one out! x 2 + 2 3 x + 12 3 x When x = -2 10 + 2 x x+8 CLICK for solution 1 x 3 + 1 When x = -1 x 2 - 1 x+x 2(x+1) x 3 + x 2 CLICK for solution 2

Difficulty */**/*** Substitution MATHSWATCH CLIP 95 GRADE 3 Task – Work out the value of the missing variable in each formula 1. P = 4 k + 3 (k = 7) 1. P = 2 k 2 + 3 (k = 3) 2. S = 9 p + 15 (p = 3) 2. S = p 3 + 12 (p = 2) 3. y = 5 x - 3 (x = 0) 3. y = 5 x 2 - 3 (x = 3) 4. y = 7 x - 30 (x = 2) 4. y = x 2 - 30 (x = 5) 5. P = -2 z - 9 (z = -3) 5. P = -2 z 2 + 9 (z = 1) 6. L = 8 - 6 k (k = -2) 6. L = 4 k 3 + 5 (k = 5) 7. M = -6 q + 2 (q = ½ ) 7. M = -8 q 3 + 2 (q = 2 ) 8. V = 8 r - 7 (r = - ¼ ) 8. V = 8 r 2 - 7 (r = - ½ )

11/02/2022 Substitution MATHSWATCH CLIP 95 GRADE 3 Task – Work out the value of the missing variable in each formula 1. P = 4 k + 3 (k = 7) P = 31 1. P = 2 k 2 + 3 (k = 3) P = 21 2. S = 9 p + 15 (p = 3) S = 42 2. S = p 3 + 12 (p = 2) S = 20 3. y = 5 x - 3 (x = 0) y = -3 3. y = 5 x 2 - 3 (x = 3) y = 42 4. y = 7 x - 30 (x = 2) y = -16 4. y = x 2 - 30 (x = 5) y = -5 5. P = -2 z - 9 (z = -3) P = -3 5. P = -2 z 2 + 9 (z = 1) P=7 6. L = 8 - 6 k (k = -2) L = 20 6. L = 4 k 3 + 5 (k = 5) L = 505 7. M = -6 q + 2 (q = ½ ) M = -1 8. V = 8 r - 7 (r = - ¼ ) V = -9 7. M = -8 q 3 + 2 (q = 2 ) M = -62 8. V = 8 r 2 - 7 (r = - ½ ) V = -5