What is the GCF of \(4\) and \(6\)?
- A \(2\)
- B \(4\)
- C \(6\)
- D \(24\)
Check answer and explanation
Answer A: \(2\)
List factors: \(4\) has factors \(1, 2, 4\). \(6\) has factors \(1, 2, 3, 6\). The greatest common factor is \(2\).
CH04-04 lesson
Factoring Expressions Learning Activity
A focused Grade 7 learning session for Factoring Expressions using visual models, worked examples, strategy guidance, and a short mastery check.
- 15
- minutes
- 6
- lesson parts
- 11
- practice items
Students will build Grade 7 mastery of factoring expressions using models, equations, and test-style reasoning.
Student goal: I can solve problems involving factoring expressions.
Helpful first:
Expanding Expressions with the Distributive Property
Learn the Idea
Factoring Expressions is part of Grade 7 Expressions. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of factoring expressions using models, equations, and test-style reasoning.
See the Math
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Follow a Worked Example
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Factoring Expressions, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Connect It to a Real Situation
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
Avoid Mistakes and Choose a Strategy
- Underline the exact question before solving.
- Label units, variables, or graph axes when they appear.
- Estimate first so unreasonable answers are easier to catch.
- Review missed questions and write the reason for each mistake.
Remember the Key Idea
I can solve problems involving factoring expressions.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Solve before opening the answer
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
warmup
2 questionsWhich expression shows \(2 \cdot 5 + 2 \cdot 3\) factored?
- A \(2(5+3)\)
- B \((2+5)(2+3)\)
- C \(2 \cdot 15\)
- D \(5+3\)
Check answer and explanation
Answer A: \(2(5+3)\)
Both terms share the common factor \(2\). Factor it out: \(2 \cdot 5 + 2 \cdot 3 = 2(5+3)\).
guided
1 questionFactor the expression: \(6x+18\)
- A \(6(x+3)\)
- B \(3(2x+6)\)
- C \(2(3x+9)\)
- D \(6(x+18)\)
Check answer and explanation
Answer A: \(6(x+3)\)
The GCF of \(6\) and \(18\) is \(6\). \(6x+18=6(x+3)\).
practice
5 questionsFactor: \(5x + 25\)
- A \(5(x+5)\)
- B \(5x(1+5)\)
- C \(5(x+25)\)
- D \(25(x+1)\)
Check answer and explanation
Answer A: \(5(x+5)\)
The GCF of \(5x\) and \(25\) is \(5\). Divide both terms by \(5\) to get \(5(x+5)\).
Which expression is equivalent to \(3(2y+7)\)?
- A \(6y+21\)
- B \(6y+7\)
- C \(3y+10\)
- D \(2y+21\)
Check answer and explanation
Answer A: \(6y+21\)
Distribute: \(3(2y+7) = 3(2y) + 3(7) = 6y+21\). Check: factor back to verify.
Find the GCF of \(8b\) and \(20b\).
- A \(4b\)
- B \(8b\)
- C \(20b\)
- D \(2b\)
Check answer and explanation
Answer A: \(4b\)
Find GCF of \(8\) and \(20\): it is \(4\). Since both terms have \(b\), the GCF is \(4b\).
Factor: \(9m + 12\)
- A \(3(3m+4)\)
- B \(9(m+12)\)
- C \(3m(3+4)\)
- D \(12(0.75m+1)\)
Check answer and explanation
Answer A: \(3(3m+4)\)
The GCF of \(9\) and \(12\) is \(3\). So \(9m+12=3(3m+4)\). (Option B confuses the constant. Option C factors only the variable. Option D uses a decimal.)
Which factorization is correct?
- A \(10x+15=5(2x+3)\)
- B \(10x+15=2(5x+7.5)\)
- C \(10x+15=10(x+1.5)\)
- D \(10x+15=3(3x+5)\)
Check answer and explanation
Answer A: \(10x+15=5(2x+3)\)
The GCF of \(10\) and \(15\) is \(5\). Check: \(5(2x) + 5(3) = 10x + 15\). Correct.
exit
3 questionsFactor: \(7a + 14b\)
- A \(7(a+2b)\)
- B \(7a(1+b)\)
- C \(14(a+b)\)
- D \(a(7+14b)\)
Check answer and explanation
Answer A: \(7(a+2b)\)
The GCF of \(7a\) and \(14b\) is \(7\). Factor out \(7\): \(7(a+2b)\).
What is the GCF of \(6xy\) and \(9y\)?
- A \(3y\)
- B \(6y\)
- C \(9y\)
- D \(3xy\)
Check answer and explanation
Answer A: \(3y\)
GCF of \(6\) and \(9\) is \(3\). Both terms contain \(y\). GCF is \(3y\).
Factor: \(12p - 8\)
- A \(4(3p-2)\)
- B \(2(6p-4)\)
- C \(8(4p-1)\)
- D \(6(2p-1.33)\)
Check answer and explanation
Answer A: \(4(3p-2)\)
The GCF of \(12\) and \(8\) is \(4\). Factor out \(4\): \(12p-8=4(3p-2)\).
