Free Grade 3 Working with Introducing Function Notation Techniques: Common Mistakes — Mastery Lesson Plans
Free Grade 3 lesson plans for Working with Introducing Function Notation Techniques: Common Mistakes — Mastery: 12 real questions with a full answer key and worked solutions. A function is a rule that turns an input into an output. The inverse function reverses it.
Free
Foundation
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with introducing function notation techniques: common mistakes — mastery
Identify working with introducing function notation techniques: common mistakes — mastery accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with introducing function notation techniques: common mistakes — mastery
Explain working with introducing function notation techniques: common mistakes — mastery accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with introducing function notation techniques: common mistakes — mastery
Calculate working with introducing function notation techniques: common mistakes — mastery accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with introducing function notation techniques: common mistakes — mastery
Compare working with introducing function notation techniques: common mistakes — mastery accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Working with Introducing Function Notation Techniques: Common Mistakes — Mastery works
A function is a rule that turns an input into an output. The inverse function reverses it.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.f(x) = 4x − 5. Find f(-4).[1]
- 2.f(x) = 6x + 2. Find f(-3).[1]
- 3.f(x) = 4x + 4. Find f(1).[1]
- 4.f(x) = 6x + 5. Find f(3).[1]
- 5.f(x) = 4x + 6. Find f(2).[2]
- 6.f(x) = 4x − 1. Find f(-1).[2]
- 7.f(x) = 4x − 4. Find f(-3).[2]
- 8.f(x) = 3x + 4. Find f(1).[2]
- 9.f(x) = 5x + 3. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 6x − 4. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 6x − 7. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 3x − 3. Find the inverse f⁻¹(x).[3]
Show answers and working
1. -21
Replace x with -4: 4 × (-4) − 5. = -21
2. -16
Replace x with -3: 6 × (-3) + 2. = -16
3. 8
Replace x with 1: 4 × 1 + 4. = 8
4. 23
Replace x with 3: 6 × 3 + 5. = 23
5. 14
Replace x with 2: 4 × 2 + 6. = 14
6. -5
Replace x with -1: 4 × (-1) − 1. = -5
7. -16
Replace x with -3: 4 × (-3) − 4. = -16
8. 7
Replace x with 1: 3 × 1 + 4. = 7
9. f⁻¹(x) = (x − 3) / 5
Write y = 5x + 3 and swap x and y. Rearrange for y: y = (x − 3) / 5.
10. f⁻¹(x) = (x + 4) / 6
Write y = 6x − 4 and swap x and y. Rearrange for y: y = (x + 4) / 6.
11. f⁻¹(x) = (x + 7) / 6
Write y = 6x − 7 and swap x and y. Rearrange for y: y = (x + 7) / 6.
12. f⁻¹(x) = (x + 3) / 3
Write y = 3x − 3 and swap x and y. Rearrange for y: y = (x + 3) / 3.
Worked examples
f(x) = 5x + 0. Find f(4).
- Replace x with 4: 5 × 4 + 0.
- = 20
- Answer: 20
f(x) = 2x − 7. Find f(-4).
- Replace x with -4: 2 × (-4) − 7.
- = -15
- Answer: -15
f(x) = 4x + 1. Find the inverse f⁻¹(x).
- Write y = 4x + 1 and swap x and y.
- Rearrange for y: y = (x − 1) / 4.
- Answer: f⁻¹(x) = (x − 1) / 4
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Reads f(3) as f × 3.
Correction: f(3) means 'put 3 into the rule'.
Reverses operations in the wrong order for the inverse.
Correction: Undo the last step first.
Teacher tips
- · Use function machines before notation.
Parent tips
- · Play 'guess my rule' with numbers.
Real-life applications
- · Converting temperatures, phone-plan costs.
Assessment objectives
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