Free Grade 3 Introduction to Introducing Function Notation Techniques: Step-by-step Method — Reasoning Lesson Plans
Free Grade 3 lesson plans for Introduction to Introducing Function Notation Techniques: Step-by-step Method — Reasoning: 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.
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20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introduction to introducing function notation techniques: step-by-step method — reasoning
Explain introduction to introducing function notation techniques: step-by-step method — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introduction to introducing function notation techniques: step-by-step method — reasoning
Calculate introduction to introducing function notation techniques: step-by-step method — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introduction to introducing function notation techniques: step-by-step method — reasoning
Compare introduction to introducing function notation techniques: step-by-step method — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introduction to introducing function notation techniques: step-by-step method — reasoning
Justify introduction to introducing function notation techniques: step-by-step method — reasoning 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 Introduction to Introducing Function Notation Techniques: Step-by-step Method — Reasoning 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 + 4. Find f(0).[1]
- 2.f(x) = 4x + 3. Find f(1).[1]
- 3.f(x) = 6x + 3. Find f(-3).[1]
- 4.f(x) = 2x + 3. Find f(5).[1]
- 5.f(x) = 5x − 8. Find f(-3).[2]
- 6.f(x) = 2x + 1. Find f(-3).[2]
- 7.f(x) = 5x − 8. Find f(3).[2]
- 8.f(x) = 4x − 6. Find f(6).[2]
- 9.f(x) = 6x − 3. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 4x − 8. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 3x − 6. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 3x − 2. Find the inverse f⁻¹(x).[3]
Show answers and working
1. 4
Replace x with 0: 4 × 0 + 4. = 4
2. 7
Replace x with 1: 4 × 1 + 3. = 7
3. -15
Replace x with -3: 6 × (-3) + 3. = -15
4. 13
Replace x with 5: 2 × 5 + 3. = 13
5. -23
Replace x with -3: 5 × (-3) − 8. = -23
6. -5
Replace x with -3: 2 × (-3) + 1. = -5
7. 7
Replace x with 3: 5 × 3 − 8. = 7
8. 18
Replace x with 6: 4 × 6 − 6. = 18
9. f⁻¹(x) = (x + 3) / 6
Write y = 6x − 3 and swap x and y. Rearrange for y: y = (x + 3) / 6.
10. f⁻¹(x) = (x + 8) / 4
Write y = 4x − 8 and swap x and y. Rearrange for y: y = (x + 8) / 4.
11. f⁻¹(x) = (x + 6) / 3
Write y = 3x − 6 and swap x and y. Rearrange for y: y = (x + 6) / 3.
12. f⁻¹(x) = (x + 2) / 3
Write y = 3x − 2 and swap x and y. Rearrange for y: y = (x + 2) / 3.
Worked examples
f(x) = 2x + 4. Find f(1).
- Replace x with 1: 2 × 1 + 4.
- = 6
- Answer: 6
f(x) = 3x + 4. Find f(1).
- Replace x with 1: 3 × 1 + 4.
- = 7
- Answer: 7
f(x) = 6x − 7. Find the inverse f⁻¹(x).
- Write y = 6x − 7 and swap x and y.
- Rearrange for y: y = (x + 7) / 6.
- Answer: f⁻¹(x) = (x + 7) / 6
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
How mastery is evidenced, and which standards it maps to.
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