Math lesson plan · 12th grade (Year 13 in England) · 60 minutes
Read amplitude, period and midline from y = a sin(bx) + d
Trigonometry
CCSS HSF.TF.B.5CCSS HSF.IF.C.7.EEngland: A-level Pure Mathematics
Objective and success criteria
Students will: Read amplitude, period and midline from y = a sin(bx) + d.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Graphs of sine and cosine: amplitude and period
Leads to: the next skill in this area.
Materials: Scientific calculators, Protractors and rulers, Right-triangle diagrams, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Graphs of sine and cosine: amplitude and period). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What is the amplitude of y = 4 sin(6x)? → 4Prompt: The amplitude is the number multiplying sin or cos.
- What is the maximum value of y = 1 sin x + 5? → 6Prompt: sin x goes between −1 and 1.
- What is the amplitude of y = 3 cos(3x)? → 3Prompt: The amplitude is the number multiplying sin or cos.
Hook · 6 min
- Show a ramp or a ladder against a wall and ask how steep it is.
- Share the objective: Read amplitude, period and midline from y = a sin(bx) + d. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: For y = 5cos(3x) − 3 (x in degrees), what is the midline value (y = ?)?
- Step 1: y = −3
- Answer: -3
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- For y = −5cos(4x) + 4 (x in degrees), what is the period, in degrees? → 90Prompt: Amplitude is |a|, the period is 360° divided by b, and the midline is y = d.
- What is the period of y = 2cos(8x), with x in radians? Give it in terms of π. → pi/4Prompt: In radians, one full cycle of cos x takes 2π.
You do: independent practice · 17 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- For y = −5sin(x) + 5 (x in degrees), what is the midline value (y = ?)? → 5Prompt: Amplitude is |a|, the period is 360° divided by b, and the midline is y = d.
- What is the period of y = 5cos(8x), with x in radians? Give it in terms of π. → pi/4Prompt: In radians, one full cycle of cos x takes 2π.
Watch out for
- Mixing up opposite and adjacent sides.
- Calculator in radians instead of degrees.
Support and stretch
Support
- Review first: Graphs of sine and cosine: amplitude and period.
- Use concrete materials: scientific calculators.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-12.
Free lesson plan from eurekami.com/lesson-plan-builder