6.15 Small Group · Group 1

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

Simplify Algebraic Expressions · Like Terms · Procedural Fluency · Reasoning & Critique

Name: Date: Period: Learning Goal:

■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do we simplify by combining like terms?

1Only combine terms that have the same variable part; numbers without a variable combine with each other.

Like terms are terms with the same variable, like 2x and 5x. To simplify an expression, you add or subtract the like terms to make it shorter. 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

The rooms need microphones and stands: (4 + 2 + 6) microphones and (3 + 5 + 1) stands.
Microphones are like items, so I add: 4 + 2 + 6 = 12 microphones.
Stands are like items, so I add: 3 + 5 + 1 = 9 stands.
In algebra this is the same as 4m + 2m + 6m + 3s + 5s + 1s = 12m + 9s.

3Mathematical Word Bank

Simplify Algebraic Expressions (Simplificar expresiones algebraicas) — Rewrite an expression in a shorter equivalent form by combining like terms and using properties.
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.
Simplify (Simplificar) — To rewrite an expression in a shorter form that is still equal to the original.
Coefficient (Coeficiente) — The number in front of a letter, like the 3 in 3x.
Term (Término) — A single number, variable, or product of them, separated by + or − signs.

4Watch out

A common mistake in Simplify Algebraic Expressions is sweeping a constant into the variable terms — for example, simplifying 6x + 4 + 2x as 12x by adding all three numbers (6 + 4 + 2 = 12) instead of recognizing that 4 has no variable and cannot combine with 6x and 2x. The correct simplified expression is 8x + 4 (combine 6x + 2x = 8x, and let the 4 stay on its own). Before you submit, check that every term you combined has the exact same variable part.

SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]

1 DRAG SORT
Sort each pair of terms by whether they are like terms (can be combined) or not.

Target Categories: Like Terms Not Like Terms
2 FILL TABLE

Simplify each expression by combining like terms.

Expression Like Terms Combined Simplified
3a + 5a + 2
6x + 4 + 2x + 7
10m − 3m + 5
4y + 3 + y + 9

✏️ Scratchpad / Reasoning

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