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Grade 6 · Mathematics · 30 minutes

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

Unit Rates at the Notebook Shop

Compare prices and travel speeds by finding a quantity per one unit.

Mr. S Teaches · Original starter mini-lesson · MS6-MATH-01

Learning objective

Calculate two unit prices, justify the better value and use a constant rate to predict a new quantity.

Before you begin

  • Divide whole numbers
  • Equivalent ratios

Gather your materials

  • Paper and pencil
  • Ruler and graph paper

Language to know

ratio
An ordered comparison of two quantities.
unit rate
An amount for one unit of another quantity.
equivalent ratios
Comparisons made by scaling both quantities equally.

Understand the concept

A ratio keeps quantities in a stated order. A unit price divides total cost by the number of items, so dollars per notebook can be compared fairly. Equal total prices do not imply equal value when package sizes differ. A prediction using a unit rate assumes that the price or speed stays constant.

Teach it step by step

  1. Write a two-column table for 4 notebooks costing $10: notebooks 1, 4 and 8. Label the money column in dollars.
  2. Divide $10 by 4 to find the price for one notebook. Scale that rate to complete the table.
  3. Compare a second offer: 6 notebooks for $14.40. Ask why comparing $10 with $14.40 alone is misleading.
  4. Model an average-speed calculation and ask learners to attach miles per hour to the quotient.
  5. Let the learner justify a buying choice in a complete sentence and state the constant-price assumption.

Make the thinking visible

Worked example or model response

Offer A: $10 ÷ 4 = $2.50 per notebook. Offer B: $14.40 ÷ 6 = $2.40 per notebook. B is cheaper per notebook by $0.10. At A’s price, 8 notebooks cost $20.

Guided practice

Together compare 3 pens for $5.40 with 5 pens for $8.50. Build a ratio table for the better offer showing 1, 5 and 10 pens.

Independent practice

1. A cyclist travels 24 miles in 2 hours at a constant speed. Predict the distance in 3.5 hours. 2. Explain one reason a real store might not charge exactly twice as much for twice as many items.

Quick assessment

Which has the lower unit price: 8 folders for $12 or 10 folders for $16? Show both rates.

Answer key & assessment criteria

Answers and teaching guidance

  1. Guided: $1.80/pen versus $1.70/pen; the second offer is better. Its table is 1→$1.70, 5→$8.50, 10→$17.
  2. Independent 1: 12 miles/hour × 3.5 hours = 42 miles. 2: Bulk discounts, a fixed fee or a changing price can break the constant-rate assumption.
  3. Quick check: $1.50/folder versus $1.60/folder; 8 for $12 is cheaper per folder.

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 whole-dollar packages first and draw equal groups before dividing.

Extension challenge

Create a third offer that is cheaper per item but costs more in total; explain why both statements can be true.

Selected contributions · Official sources

Standards connections

Contributes to Common Core standard

6.RP.A.3.b

Common Core · Grade 6

Compare unit prices and use constant speed to solve a rate problem.

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.