Math lesson plan · 6th grade (Year 7 in England) · 45 minutes
Substitute into everyday formulas
Algebra
CCSS 6.EE.A.2.CEngland: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Substitute into everyday formulas.
- 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: Evaluate expressions
Leads to: the next skill in this area.
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Evaluate expressions). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find the value of 7x − 9 when x = 6. → 33Prompt: Replace x with 6.
- Evaluate x² + 4y when x = 3 and y = 6. → 33Prompt: Substitute each letter, using brackets around negative numbers.
- Use v = u + at to find v when u = 6, a = 10 and t = 2. → 26Prompt: at means a × t.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Substitute into everyday formulas. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: The perimeter of a rectangle is P = 2(l + w). Find P when l = 15 cm and w = 3 cm.
- Step 1: P = 2(15 + 3) = 2 × 18 = 36 cm
- Answer: 36
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Distance = speed × time (d = st). A train travels at 70 km/h for 3 hours. How far does it go, in km? → 210Prompt: Substitute the speed and the time.
- To change °C to °F, use F = 1.8C + 32. What is 0 °C in °F? → 32Prompt: Multiply the Celsius temperature by 1.8 first.
You do: independent practice · 10 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 · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A taxi fare is C = 3 + 2m (in dollars), where m is the number of miles. Find C for a 15-mile trip. → 33Prompt: Replace m with the number of miles.
- The volume of a cube is V = s³. Find V when s = 4 cm. → 64Prompt: Substitute the side length.
Watch out for
- Doing an operation to one side of an equation but not the other.
- Reading 3x as 3 + x, or thinking x always stands for one particular number.
Support and stretch
Support
- Review first: Evaluate expressions.
- Use concrete materials: balance scales or a balance drawing.
- 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-6.
Free lesson plan from eurekami.com/lesson-plan-builder