01 · DISCOVER
Using Properties to Rewrite Expressions: before you begin
Build your understanding of properties to rewrite expressions through examples and practice. Explain each step and check whether your answer makes sense. For related lessons, return to the math pathway collection. When your teacher allows it, use the Desmos graphing calculator to check coordinates, equations, or calculations.
Enter your name and school email to save your learning. You’ll explore using properties to rewrite expressions and then practice 12 questions with feedback.
Success criteria
- I can explain the main math idea in my own words.
- I can use a model, calculation, or example to solve a related problem.
- I can check my answers and explain why a solution makes sense.
Essential question: How can we use using properties to rewrite expressions to solve problems?
02 · LEARN & EXPLORE
Where this matters
Properties of operations help students calculate efficiently and show why steps preserve the same value.
03 · LEARN & EXPLORE
Understand the mathematics
Use the distributive property: 3(x + 4) = 3x + 12. Combine like terms: 2x + 5x = 7x. Check equivalence by substituting the same number into both expressions.
Trace each operation and verify the result by checking the original problem.
The expression 3(x + 4) is equivalent to 3x + 12.
04 · LEARN & EXPLORE
Model the first situation
Use the distributive property on 4(x + 3): 4 × x + 4 × 3 = 4x + 12. You can show this using four matching groups.
Think: Which operation or representation best shows this situation?
05 · LEARN & EXPLORE
Why this concept matters
Properties of operations help students calculate efficiently and show why steps preserve the same value.
Use diagrams, number lines, tables, or algebraic representations where appropriate to explain why a procedure works.
06 · LEARN & EXPLORE
Understand a second strategy
Combine like terms: 5x + 2x − 3 = 7x − 3. You cannot combine 7x with −3 because they represent different types of terms.
Try it: Check the reasoning with your own numbers or a visual model.
07 · LEARN & EXPLORE
Apply your learning
Compare 2(3x − 4) and 6x − 8 by testing x = 2. Both expressions equal 4, confirming the rewrite for this value.
Strategy reminder: Preserve equivalence. Every rewrite must produce the same result for any allowed value of x.
08 · LEARN & EXPLORE
Connect the idea
Equivalent expressions can look different while having the same value. Use the distributive property and combine like terms carefully.
Explain the idea in your own words and identify when you would use it.
INDEPENDENT PRACTICE · 1 OF 12
Which is equivalent to 5(2x – 3)?
Choose the best answer, then study the feedback.
Distribute 5 to both terms.
INDEPENDENT PRACTICE · 2 OF 12
Simplify 4x + 7 – x + 2.
Work independently and check that your answer makes sense.
Combine x-terms and constants separately.
INDEPENDENT PRACTICE · 3 OF 12
Expand 2(x + 3).
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 4 OF 12
Simplify 4x + 3x.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 5 OF 12
Expand -3(x – 2).
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 6 OF 12
Simplify 5 + 2 + x.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 7 OF 12
Expand 4(2x + 1).
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 8 OF 12
Simplify 6y – 2y.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 9 OF 12
Expand (a + 5) + 3.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 10 OF 12
Simplify 2(x + 5) + x.
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 11 OF 12
Which property lets you write 2+3 as 3+2?
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 12 OF 12
Which equals 7(x – 1)?
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
RESULTS · REFLECT
Your Learning Pathway Results
Check your work and submit your first-attempt score to your teacher.