6.9 Small Group · Group 1

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

Visual Models · Divide Whole Numbers by Fractions · Whole Number · Procedural Fluency

Name: Date: Period: Learning Goal:

■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — How do I divide a whole number by a fraction?

1Dividing by a fraction is the same as multiplying by its reciprocal (the fraction flipped over).

To divide a whole number by a fraction, you can use Keep, Change, Flip: keep the first number, change divide to multiply, and flip the fraction upside down (its reciprocal). Then multiply. 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 Park has 4 pounds of powder and each bag holds 1/2 pound. I want 4 ÷ 1/2.
Keep the 4. Change ÷ to ×. Flip 1/2 to make 2/1, which is just 2.
Now I multiply: 4 × 2 = 8.
So 4 ÷ 1/2 = 8. He can fill 8 bags. That makes sense: each pound fills 2 bags, and 4 pounds × 2 = 8.

3Mathematical Word Bank

Divide Whole Numbers by Fractions (Dividir números enteros entre fracciones) — Find how many fractional groups fit in a whole number by multiplying by the reciprocal.
Whole Number (Número entero) — A counting number with no fraction or decimal, like 0, 1, 2, 3.
Fraction (Fracción) — A number that shows part of a whole, like 3/4.
Reciprocal (Recíproco) — A fraction turned upside down.
Keep, Change, Flip (Mantener, cambiar, invertir) — A way to divide fractions: keep the first, change ÷ to ×, flip the second.
Quotient (Cociente) — The answer when you divide.

4Watch out

A common mistake in Divide Whole Numbers by Fractions is doing 'Keep, Change' but skipping the 'Flip' — students multiply by the divisor as it is instead of by its reciprocal. For example, for 6 ÷ 3/4, a student might write 6 × 3/4 = 4 1/2 and stop there, but the divisor 3/4 must be flipped to 4/3 first: 6 × 4/3 = 24/3 = 8. Before you submit, check: did I flip the second fraction (the divisor) upside down before multiplying?

SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]

1 NUMBER LINE

How many jumps of 1/4 does it take to get from 0 to 2?
✏️ Workspace & Solution Steps
2 FILL TABLE

Complete the table: Whole Number ÷ Fraction. Use Keep, Change, Flip.

Expression Rewrite as Multiplication Quotient
5 ÷ 1/4
8 ÷ 1/2
3 ÷ 1/6
7 ÷ 1/3

✏️ Scratchpad / Reasoning

SECTION 2 COMPUTATION & PROCEDURAL FLUENCY [Show Every Step]

🗣️ 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