6.6 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

Equivalent Expressions · Equivalent · Procedural Fluency · Reasoning & Critique

Name: Date: Period: Learning Goal:

■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — When are two expressions equivalent?

1Equivalent expressions give the same answer for every value of the variable.

Two expressions are equivalent when they always give the same value, no matter what number you put in for the variable. They can look different but mean the same thing. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.

2Worked Example — Watch me

Producer A wrote 3x + 2x + 10 and Producer B wrote 5x + 10. Are they equivalent?
I test x = 4. For A: 3(4) + 2(4) + 10 = 12 + 8 + 10 = 30.
For B: 5(4) + 10 = 20 + 10 = 30.
Both give 30, and 3x + 2x is just 5x, so they are equivalent.

3Mathematical Word Bank

Equivalent Expressions (Expresiones equivalentes) — Expressions that look different but have the same value for every allowed variable value.
Equivalent (Equivalente) — Expressions that always have the same value.
Simplify (Simplificar) — To rewrite an expression in a shorter form that is still equal to the original.
Like Terms (Términos semejantes) — Terms with the same letter raised to the same power, like 2x and 5x.
Combine (Combinar) — To add or subtract terms with the same letter into one.
Coefficient (Coeficiente) — The number in front of a letter, like the 3 in 3x.

4Watch out

A common mistake in Equivalent Expressions is adding the exponents instead of the coefficients when combining like terms — writing 3x + 2x as 5x² instead of 5x. Remember: 3x means 3 groups of x and 2x means 2 more groups of x, so you add the coefficients (3 + 2 = 5) and keep the variable's power the same (x¹, not x²).

SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]

1 MULTIPLE CHOICE
Which expression is equivalent to 4x + 3x?
1. A7x
2. B12x
3. C7x²
4. D43x
✏️ Workspace & Solution Steps
2 MULTIPLE CHOICE
Which expression is equivalent to 2(m + 5)?
1. A2m + 10
2. B2m + 5
3. Cm + 10
4. D7m
✏️ Workspace & Solution Steps
3 DRAG SORT
Sort each pair of expressions by whether they are equivalent or not.

Target Categories: Equivalent Not Equivalent
4 DRAG SORT
Match each expression with its simplified form.

Target Categories: Correctly Matched

SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]

🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

Group Discussion Prompt: How does your visual model justify your mathematical solution?

🗣️ Partner A:
Partner A: "I modeled this by identifying the relationship and..."

👂 Partner B:
Partner B: "I agree with your step because the standard mathematical rule states..."

✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE The ratio remains equivalent because both quantities are scaled by the exact same multiplicative factor.

BUT Two ratios may look similar, but inverting the order of terms fundamentally changes the comparison.

SO The recipe requires 3 parts flour to 2 parts water, so the unit rate is 1.5 cups of flour per cup of water.

📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim

Starter: My mathematical claim is that the solution is...

E Evidence

Starter: The evidence from the model/table demonstrates that...

R Reasoning

Starter: This proves my answer because the standard mathematical definition of...

Student Mastery Self-Assessment:

1 · Need More Support

2 · Getting Closer

3 · Got It / Solid

4 · Master / Can Teach It