Algebra Problem Solving

Name:

Date:

📚 Part 1: Guided Problem Solving

WALT: Use algebra to solve multi-step problems.

Success criteria: I can: (1) translate words into an algebraic expression, (2) simplify and solve linear equations, and (3) show step-by-step workings and justify each step.

1. Lucy has twice as many marbles as Tom. Tom has x marbles. Together they have 30 marbles.

Write an equation, show your steps in the box, and give the value of x.

2. A rectangle has length (2x + 3) cm and width (x − 1) cm. Its area is 60 cm².

Form an equation using brackets, solve for x and state the length and width.

3. The sum of three consecutive integers is 48. Let the first integer be n.

Write an expression, solve for n and list the three integers.

4. A toy's sale price is 80% of its original price. If the sale price is $28 and original price is (x + 15) dollars, find x and the original price.

Show algebraic steps and final answers.

✏️ Part 2: Extension & Reflection

Differentiation & dyslexia-friendly options: Read the questions aloud, use a coloured overlay if helpful, and break steps into small parts. For extra support, work with a partner or use algebra tiles. For an extension, try harder coefficients or include negative solutions.

5. Create your own two-step algebra problem that uses brackets. Write the problem clearly below, then solve it showing steps.

6. Swap problems with a classmate. Solve their created problem here and give the answer.

7. Self-assess: Tick the boxes that describe your work today.

I translated each word problem into an expression.

I showed clear step-by-step working.

I could explain how I used brackets or the distributive law.

I would like more practice with fractions or decimals in algebra.