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Using Formulas Problem Solving

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Using Formulas Problem Solving

Mathematical formulas and calculator illustration

🎯 WALT (We Are Learning To)

Today we are learning to:

  • Recognise and use variables to represent everyday formulas algebraically
  • Substitute numerical values into formulas to solve practical problems
  • Apply formulas to real-world contexts familiar to students

✅ Success Criteria

I will be successful when I can:

  • Accurately recognise variables within a range of formulas
  • Correctly substitute numbers into formulas and calculate the unknown
  • Solve practical problems using formulas independently
  • Explain my working clearly

📚 Part 1: Formula Recognition

1. Look at this formula: A = l × w (Area = length × width)

Circle the variables in this formula:

A

l

w

×

2. Which formula would you use to find the perimeter of a rectangle?

A = l × w

P = 2l + 2w

V = l × w × h

C = πd

3. Match the formula to its purpose:
D = S ÷ T
V = l × w × h
C = 2πr
Volume of a rectangular prism
Circumference of a circle
Density

🧮 Part 2: Substitution and Problem Solving

4. Sarah's rectangular garden bed has a length of 8 metres and width of 5 metres. Use the formula A = l × w to find the area.

Show your substitution: A = _____ × _____

Calculate: A = _______ square metres

5. Tom drives 240 kilometres in 3 hours. Use the formula S = D ÷ T (Speed = Distance ÷ Time) to find his average speed.

Substitute the values: S = _____ ÷ _____

Tom's average speed = _______ kilometres per hour

6. A swimming pool is 25 metres long, 10 metres wide, and 2 metres deep. Use V = l × w × h to find the volume of water it can hold.

Show your working:

The pool can hold _______ cubic metres of water.

7. Jake earns $15 per hour. Use the formula P = R × H (Pay = Rate × Hours) to calculate how much he earns working 6 hours.

Substitute: P = $_____ × _____ hours

Jake earns $_______ for 6 hours of work.

8. Challenge Problem: A circular pizza has a radius of 12 centimetres. Use C = 2πr to find the circumference. (Use π = 3.14)

Show your substitution and calculation:

The circumference is _______ centimetres.

💭 Part 3: Reflection

9. Explain in your own words why formulas are useful for solving everyday problems:
10. Which problem-solving step do you find most challenging when using formulas?

Identifying which formula to use

Substituting the correct values

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