Mathematics • Year 7 • Unit 2 • Lesson 3

Substitution

Build the basics: replace every variable with a given number using brackets, follow BODMAS, and evaluate expressions safely, including expressions with negative numbers and powers.

Build · I Do / We Do / You Do

1. I do, fully worked example

Read every line. Each step has a short reason on the right so you can see why, not just what.

Problem. Evaluate 3x² − 2x + 4 when x = −2.

Step 1, Write the expression.

3x² − 2x + 4

Reason: start from the original, don't change anything until you substitute.

Step 2, Replace every x with (−2), keeping brackets.

= 3(−2)² − 2(−2) + 4

Reason: brackets are essential when substituting a negative number. (−2)² is positive 4, but −2² without brackets is −4. The brackets protect the sign.

Step 3, Apply the power (BODMAS: Orders first).

= 3(4) − 2(−2) + 4

Reason: (−2)² = (−2) × (−2) = +4. A negative squared is positive.

Step 4, Multiply (BODMAS: Multiplication before Add/Sub).

= 12 − (−4) + 4

Reason: 3 × 4 = 12, and 2 × (−2) = −4.

Step 5, Subtract a negative → add.

= 12 + 4 + 4 = 20

Reason: − (−4) becomes + 4. Two negatives make a positive.

Answer: 20.

Stuck? Revisit lesson § "Substituting Negative Numbers", brackets around every substituted value, then BODMAS.

2. We do, fill in the missing steps

Fill in each blank line. 4 marks

Problem. Evaluate 5a + 2b − 1 when a = 3 and b = −4.

Step 1, Write the expression:

5a + 2b − 1

Step 2, Substitute (use brackets):

= 5(____) + 2(____) − 1

Step 3, Multiply each term:

= ______ + ______ − 1

Step 4, Combine left to right:

= ______ Final answer: ______

Stuck? Always wrap the substituted number in brackets, especially when it's negative. 2 × (−4) is −8, not +8.

3. You do, independent practice

Show working under each problem. Read carefully, negative numbers and powers need brackets!

Foundation, single step

3.1 If x = 4, find the value of 3x + 2. 1 mark

3.2 If n = 7, find the value of 2n − 5. 1 mark

3.3 If a = 6, find the value of a ⁄ 2 + 3. 1 mark

3.4 If y = 5, find the value of y². 1 mark

Standard, combine two ideas

3.5 If x = 3 and y = 2, find the value of 4x + 5y − 7. 2 marks

3.6 If m = −3, find the value of 2m + 11. (Watch the signs!) 2 marks

Extension, push your thinking

3.7 If x = −4, find the value of x² + 2x − 5. (Don't forget the brackets around the −4 when squaring!) 3 marks

3.8 If a = 6 and b = 2, find the value of (a + b) ⁄ (a − b). 2 marks

Stuck on 3.8? Calculate the top first, then the bottom, then divide. The fraction bar groups each one.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers, Do not peek before attempting

Section 2, We do (5a + 2b − 1, a = 3, b = −4)

Step 2: = 5(3) + 2(−4) − 1.
Step 3: = 15 + (−8) − 1.
Step 4: = 15 − 8 − 1 = 6. Final answer: 6.

3.1-3x + 2 at x = 4

= 3(4) + 2 = 12 + 2 = 14.

3.2-2n − 5 at n = 7

= 2(7) − 5 = 14 − 5 = 9.

3.3, a ⁄ 2 + 3 at a = 6

= 6 ⁄ 2 + 3 = 3 + 3 = 6.

3.4, y² at y = 5

= (5)² = 5 × 5 = 25.

3.5-4x + 5y − 7 at x = 3, y = 2

= 4(3) + 5(2) − 7 = 12 + 10 − 7 = 15.

3.6-2m + 11 at m = −3

= 2(−3) + 11 = −6 + 11 = 5. (Notice: 2 × (−3) = −6, a positive times a negative gives a negative.)

3.7, x² + 2x − 5 at x = −4

= (−4)² + 2(−4) − 5 = 16 + (−8) − 5 = 16 − 8 − 5 = 3. (Brackets matter: (−4)² = 16, NOT −16.)

3.8, (a + b) ⁄ (a − b) at a = 6, b = 2

Top: a + b = 6 + 2 = 8. Bottom: a − b = 6 − 2 = 4. Then 8 ÷ 4 = 2.