6.10 Small Group · Group 1

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

Divide Mixed Numbers · Mixed Number · Procedural Fluency · Real-World Applications

Name: Date: Period: Learning Goal:

■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do I divide with mixed numbers?

1Always convert a mixed number to an improper fraction first, then divide using Keep, Change, Flip.

A mixed number, like 3 1/2, has a whole part and a fraction part. Before you can divide, you change each mixed number into an improper fraction (top heavier than bottom). Then you use Keep, Change, Flip. 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

Agent Chen has a 3 1/2-mile route cut into 1/4-mile segments. I want 3 1/2 ÷ 1/4.
First I convert 3 1/2. Multiply the whole by the bottom: 3 × 2 = 6. Add the top: 6 + 1 = 7. So 3 1/2 = 7/2.
Now Keep, Change, Flip: keep 7/2, change ÷ to ×, flip 1/4 to 4/1.
Multiply: 7/2 × 4/1 = 28/2.
Simplify: 28/2 = 14. So 3 1/2 ÷ 1/4 = 14 segments.

3Mathematical Word Bank

Divide Mixed Numbers (Dividir números mixtos) — Change mixed numbers to improper fractions, then multiply by the reciprocal.
Mixed Number (Número mixto) — A whole number plus a fraction, like 2 1/3.
Improper Fraction (Fracción impropia) — A fraction where the top is bigger than or equal to the bottom, like 7/4.
Convert (Convertir) — To change a number to a new form but keep the same value.
Simplify (Simplificar) — To write a fraction with smaller numbers that names the same amount, like 2/4 = 1/2.
Reciprocal (Recíproco) — A fraction turned upside down. You use it in keep-change-flip.

4Watch out

A common mistake in Divide Mixed Numbers is dividing the whole-number parts and fraction parts separately instead of converting first — for example, treating 4 1/2 ÷ 1 1/2 as (4 ÷ 1) + (1/2 ÷ 1/2) = 5. Always convert each mixed number to one improper fraction first, then divide using Keep, Change, Flip: 4 1/2 ÷ 1 1/2 = 9/2 ÷ 3/2 = 9/2 × 2/3 = 3.

SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]

SECTION 2 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]

SECTION 3 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 mathematical model proves the solution because each step preserves quantitative equivalence.

BUT An estimate provides a quick benchmark, but an exact proof is required for precision.

SO The quantities follow the standard rule, so the final result is verified with certainty.

📐 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