Free Grade 3 Introduction to Function Notation in Context Essentials: Common Mistakes — Reasoning Lesson Plans
Free Grade 3 lesson plans for Introduction to Function Notation in Context Essentials: Common Mistakes — 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.
Free
Higher
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introduction to function notation in context essentials: common mistakes — reasoning
Identify introduction to function notation in context essentials: common mistakes — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introduction to function notation in context essentials: common mistakes — reasoning
Explain introduction to function notation in context essentials: common mistakes — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introduction to function notation in context essentials: common mistakes — reasoning
Calculate introduction to function notation in context essentials: common mistakes — reasoning accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introduction to function notation in context essentials: common mistakes — reasoning
Compare introduction to function notation in context essentials: common mistakes — 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 Function Notation in Context Essentials: Common Mistakes — 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) = 2x + 4. Find f(-4).[1]
- 2.f(x) = 2x − 2. Find f(0).[1]
- 3.f(x) = 2x − 2. Find f(-4).[1]
- 4.f(x) = 4x − 1. Find f(-2).[1]
- 5.f(x) = 4x + 5. Find f(6).[2]
- 6.f(x) = 2x + 1. Find f(-4).[2]
- 7.f(x) = 6x − 5. Find f(1).[2]
- 8.f(x) = 5x + 3. Find f(6).[2]
- 9.f(x) = 2x + 5. Find the inverse f⁻¹(x).[3]
- 10.f(x) = 3x − 1. Find the inverse f⁻¹(x).[3]
- 11.f(x) = 2x − 6. Find the inverse f⁻¹(x).[3]
- 12.f(x) = 6x − 5. Find the inverse f⁻¹(x).[3]
Show answers and working
1. -4
Replace x with -4: 2 × (-4) + 4. = -4
2. -2
Replace x with 0: 2 × 0 − 2. = -2
3. -10
Replace x with -4: 2 × (-4) − 2. = -10
4. -9
Replace x with -2: 4 × (-2) − 1. = -9
5. 29
Replace x with 6: 4 × 6 + 5. = 29
6. -7
Replace x with -4: 2 × (-4) + 1. = -7
7. 1
Replace x with 1: 6 × 1 − 5. = 1
8. 33
Replace x with 6: 5 × 6 + 3. = 33
9. f⁻¹(x) = (x − 5) / 2
Write y = 2x + 5 and swap x and y. Rearrange for y: y = (x − 5) / 2.
10. f⁻¹(x) = (x + 1) / 3
Write y = 3x − 1 and swap x and y. Rearrange for y: y = (x + 1) / 3.
11. f⁻¹(x) = (x + 6) / 2
Write y = 2x − 6 and swap x and y. Rearrange for y: y = (x + 6) / 2.
12. f⁻¹(x) = (x + 5) / 6
Write y = 6x − 5 and swap x and y. Rearrange for y: y = (x + 5) / 6.
Worked examples
f(x) = 6x − 7. Find f(4).
- Replace x with 4: 6 × 4 − 7.
- = 17
- Answer: 17
f(x) = 5x − 5. Find f(-4).
- Replace x with -4: 5 × (-4) − 5.
- = -25
- Answer: -25
f(x) = 6x − 3. Find the inverse f⁻¹(x).
- Write y = 6x − 3 and swap x and y.
- Rearrange for y: y = (x + 3) / 6.
- Answer: f⁻¹(x) = (x + 3) / 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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- Start with Introduction to Function Notation in Context Essentials: Common Mistakes — Application, Introduction to Function Notation in Context Essentials: Common Mistakes — Understanding, Introduction to Function Notation in Context Essentials: Visual Models. Each one has its own free lesson, worksheet and quiz.
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