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Grade 6 · Mathematics · 30 minutes

Unit 1 · Number relationships and rates · Lesson 2 of 3

Fraction Servings and Decimal Costs

Connect fraction division to a serving model, then check a decimal purchase.

Mr. S Teaches · Original starter mini-lesson · MS6-MATH-02

Learning objective

Represent a fraction-division situation and calculate a decimal total with a reasonableness check.

Before you begin

  • Equivalent fractions
  • Decimal place value

Gather your materials

  • Paper and pencil
  • Ruler and graph paper

Language to know

quotient
The result of division.
reciprocal
A number that multiplies with another to make one.
estimate
A nearby value used to check reasonableness.

Understand the concept

Fraction division can ask how many groups of a given size fit in an amount. Express both fractions in equal-sized pieces to see the number of groups. Multiplying by the divisor’s reciprocal is a reliable calculation because it changes division by that amount into multiplication by its inverse. Decimal calculations still follow place value; an estimate helps detect misplaced decimal points.

Teach it step by step

  1. Draw a bar representing 3/4 liter and partition a whole liter into eighths.
  2. Mark each 1/8-liter serving and count how many fit inside 3/4 liter.
  3. Write 3/4 ÷ 1/8 = 3/4 × 8 and check by multiplying the number of servings by 1/8.
  4. Set out a separate decimal-cost example and align place values when adding the amounts.
  5. Have the learner state what a fractional number of servings would mean rather than rounding automatically.

Make the thinking visible

Worked example or model response

3/4 liter contains six eighth-liters: 3/4 ÷ 1/8 = 6 servings. Six × 1/8 = 3/4 verifies it. Buying 3 containers at $2.35 each costs $7.05; an estimate of 3 × $2.40 = $7.20 supports the size of the result.

Guided practice

Model 2/3 meter of ribbon cut into 1/6-meter pieces. Then calculate the cost of 4 rolls priced at $1.75 each.

Independent practice

1. How many 1/4-cup portions are in 5/8 cup? Interpret the remainder as part of a portion. 2. Find $10.00 − $6.47 and check by addition.

Quick assessment

Explain why 1/2 ÷ 1/4 is 2 rather than 1/8.

Answer key & assessment criteria

Answers and teaching guidance

  1. Guided: 4 ribbon pieces; four $1.75 rolls cost $7.00.
  2. Independent 1: 5/8 ÷ 1/4 = 5/2 = 2.5 portions: two full portions and half of another. 2: $3.53; $6.47 + $3.53 = $10.00.
  3. Quick check: Two quarters fit in one half, so the quotient is 2. Multiplying the fractions answers a different question.

Look for: Look for an explanation of the choices, not only a final answer. Require units and a check against the context.

Make it work for your learner

More support

Use paper fraction strips with common denominators and money place-value columns.

Extension challenge

Create a fraction division problem whose answer is less than one and explain why.

Selected contributions · Official sources

Standards connections

Contributes to Common Core standard

6.NS.A.1

Common Core · Grade 6

Interpret and calculate division of fractions using a serving model.

Read the official standard ↗

This lesson contributes selected skills; it does not fully address the standard.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.

Contributes to Common Core standard

6.NS.B.3

Common Core · Grade 6

Use decimal multiplication, addition and subtraction in a purchase calculation.

Read the official standard ↗

A few calculations contribute practice; they do not demonstrate fluency in all four decimal operations.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.