4.1 Small Group · Group 1

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

Understand Percent · Percent · Procedural Fluency · Real-World Applications

Name: Date: Period: Learning Goal:

■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — What a percent really says

1A percent is a ratio comparing a number to 100. The whole is always 100%, so a percent above 100 means MORE than one whole.

Percent means per hundred. Any part-to-whole comparison becomes a percent by rewriting it as an equivalent ratio whose second term is 100. A decimal grid makes that visible: 100 squares, one for each percent. 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 turn a vote into a percent

Students voted on a mascot, and 4 out of every 10 voters chose the tiger. I want to know how many that is out of 100.
"4 out of every 10" is a ratio, so I write an equivalent ratio with 100 as the second term. Multiplying both terms by 10 gives 40 out of 100.
On a decimal grid of 100 squares, I shade 40 squares — one square for each percent.
40 out of 100 is written 40%. So 40% of the students voted for the tiger.

3Mathematical Word Bank

Understand Percent (Comprender el porcentaje) — A percent is a ratio that compares a number to 100, so every percent answers the question “how many out of 100?”
Percent (Porcentaje) — A ratio that compares a number to 100. The word means “per hundred,” and the symbol is %.
Per hundred (Por cada cien) — The meaning hidden inside the word percent: for every group of 100. It is why every percent can be written as a fraction over 100.
Decimal grid (Cuadrícula decimal) — A 10-by-10 grid of 100 squares. Shading squares shows a percent directly, one square per percent.
Part-to-whole (Parte a todo) — A comparison of one part against the whole amount. In a percent, the whole is always 100%.
Greater than 100% (Mayor que 100 %) — More than one whole. A percent above 100 means the amount is larger than the thing it is being compared to.

4Watch out

A common mistake with percent is scaling only one term of the ratio: reading 7 out of 10 as 7%. A percent compares to 100, so BOTH terms must be multiplied by the same factor — 10 × 10 = 100, so 7 × 10 = 70, giving 70%. Reading it as 7% describes seats that are nearly empty when they are nearly full. A second mistake is treating a percent as an amount: 150% of a 200-point goal is 1.5 × 200 = 300 points, not 150 points.

SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]

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