A focused Grade 6 learning session for Equivalent Expressions using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving equivalent expressions.
Equivalent Expressions means choosing a model, naming what each number means, and explaining the strategy.
Question: The area model shows \(4(3x+12)\) split into two rectangles. Which expression is equivalent?
Why it works: Area model: left rectangle is \(4 \times 3x=12x\); right rectangle is \(4 \times 12=48\). Total: \(12x+48\).
Answer: \(12x+48\)
Question: Which expression is equivalent to \(4(2x+3)\)?
Answer: \(8x+12\)
Question: Which expression is equivalent to \(3(x+5)\)?
Answer: \(3x+15\)
Question: A store sells packs of pencils. Using the expression \(4(5n+2)\), where \(n\) is the number of packs, what is an equivalent expression?
Why it works: Distribute: \(4(5n+2)=4 \cdot 5n+4 \cdot 2=20n+8\).
Answer: \(20n+8\)
Equivalent Expressions becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
Which expression is equivalent to \(4(2x+3)\)?
Answer C: \(8x+12\)
Apply the distributive property: \(4(2x+3)=4\cdot2x+4\cdot3=8x+12\).
Which expression is equivalent to \(3(x+5)\)?
Answer A: \(3x+15\)
Distribute: \(3(x+5)=3\cdot x+3\cdot5=3x+15\).
Simplify \(5x+2x\).
Answer C: \(7x\)
Combine like terms: \(5x+2x=(5+2)x=7x\).
Which expression is equivalent to \(6(3y-2)\)?
Answer A: \(18y-12\)
Distribute: \(6(3y-2)=6\cdot3y-6\cdot2=18y-12\).
Simplify \(4a+3b+2a-b\).
Answer A: \(6a+2b\)
Combine like terms: \((4a+2a)+(3b-b)=6a+2b\).
Which expression is equivalent to \(2(4x+1)\)?
Answer A: \(8x+2\)
Distribute: \(2(4x+1)=2\cdot4x+2\cdot1=8x+2\).
Simplify \(7m-3m+5m\).
Answer B: \(9m\)
Combine like terms: \((7-3+5)m=9m\).
Which expression is equivalent to \(5(2y+4)\)?
Answer C: \(10y+20\)
Distribute: \(5(2y+4)=5\cdot2y+5\cdot4=10y+20\).
Simplify \(6c+4d-2c+3d\).
Answer C: \(4c+7d\)
Combine like terms: \((6c-2c)+(4d+3d)=4c+7d\).
Which expression is equivalent to \(3(x+2)+2x\)?
Answer A: \(5x+6\)
Distribute then combine: \(3x+6+2x=5x+6\).
Simplify \(9p-4q+p+2q\).
Answer D: \(10p-2q\)
Combine like terms: \((9p+p)+(-4q+2q)=10p-2q\).
