Neft Teacher · Grade 6 Math · HyperDoc

Unit 1

Smoothie Stand: Ratios & Unit Rates

Standard 6.RP.A.1–3 · Engage → Explore → Explain → Apply → Reflect

Learning Target

I can write a ratio to compare two quantities using words, a colon, or a fraction.
I can find a unit rate by dividing to get a rate per 1.
I can use equivalent ratios to solve real-world problems.

Standard: 6.RP.A.1–3 Time: ~50 minutes Materials: pencil, this page, scratch paper

Teacher Notes (click to expand) — not for students

Pacing Guide

Engage (5 min) — Think-pair-share the smoothie doubling question.
Explore (10 min) — Independent or partner: 3D game or linked resources.
Explain (10 min) — Vocabulary choral read; teacher models worked example on board.
Apply (15 min) — Individual self-check; debrief incorrect items whole-class.
Reflect (10 min) — Written response; share-out optional.

Grouping

Engage: pairs or triads. Explore: individual with partner talk. Apply: individual. Reflect: individual, then optional share.

Differentiation — Support

Provide a fraction bar / ratio table graphic organizer.
Allow calculators for computation; focus on the concept.
Pre-teach "compare" and "per" with a picture card.
Pair with a stronger partner during Explore.

Differentiation — Challenge

Ask students to write their own unit-rate scenario and solve it.
Extend: compare unit rates across three options (best-buy task).
Introduce a double number line for equivalent ratios.

ESOL / Language Supports

Post key terms (ratio, rate, unit rate) with picture examples on a word wall or vocabulary card.
Use sentence frames: "The ratio of ___ to ___ is ___." / "The unit rate is ___ per ___."
Allow answers in L1 for reflection; accept drawings for ratio models.
Read question stems aloud; allow extended time on Apply.

1 Engage

You run a smoothie stand. A recipe uses 2 cups of mango for every 3 cups of ice.

Think: If you double the recipe, how much mango and ice do you need? Share your answer with a partner.

A ratio compares two amounts. Today you will use ratios and unit rates to run your stand smartly!

2 Explore

Open one link. Play and look for ratios. Then come back to this page.

Play the 3D Smoothie Stand game Math Hub Math Graphic Novels

After you explore, write one ratio you noticed below (optional):

Quick note: One ratio I saw or noticed was …

3 Explain

Ratio: a comparison of two amounts. Example: 2 to 3, written 2:3 or 2/3.

Rate: a ratio that compares two different units. Example: 60 miles in 2 hours.

Unit rate: the rate for exactly 1 of something. Example: 30 miles per 1 hour.

Equivalent ratios: different ratios that name the same comparison. Example: 2:3 = 4:6 = 6:9.

Worked example. A pack has 12 cups for $4.

Unit rate (price per 1 cup) = $4 ÷ 12 cups = $0.33 per cup.

Unit rate (cups per $1) = 12 ÷ 4 = 3 cups per dollar.

Equivalent ratio check: 2:3 is the same as 4:6 — multiply both parts by 2.

To find a unit rate: divide the top number by the bottom number (get 1 on the bottom).

4 Apply — Show What You Know

Answer each question. Type a number or pick a choice. Then press Check My Work to see instant feedback.

Q1. A recipe uses 2 cups of mango and 3 cups of ice. Write the ratio of mango to ice (use a colon, like 2:3).

Q2. 8 strawberries make 4 smoothies. How many strawberries are needed for 1 smoothie? (unit rate)

Q3. 6 cups cost $12. What is the price for 1 cup? (write like 2 or $2)

Q4. The mango:ice ratio is 2:3. If you use 4 cups of mango, how many cups of ice do you need?

4 5 6 8

Q5. A blender makes 10 cups in 5 minutes. What is the unit rate (cups per 1 minute)?

1 cup/min 2 cups/min 5 cups/min 10 cups/min

Q6. A store sells 15 oranges for $3. What is the unit rate in dollars per orange? (write like 0.20)

Teacher Answer Key (click to reveal)

Q1. 2:3 — also accepted: 2 to 3 or 2/3 as a ratio.
Q2. 2 — 8 ÷ 4 = 2 strawberries per smoothie.
Q3. $2 — $12 ÷ 6 cups = $2 per cup.
Q4. 6 — 2:3 = 4:6; multiply both by 2.
Q5. 2 cups/min — 10 ÷ 5 = 2.
Q6. 0.20 — $3 ÷ 15 = $0.20 per orange.

Sample reflection — R1: "A unit rate tells you the amount for exactly 1 of something, like cost per 1 item or miles per 1 hour." R2: Accept any real-world context: grocery shopping, cooking, speed, etc.

★ Rubric — Ratios & Unit Rates

Level	Score	What it looks like
Exceeds (4)	6/6	All answers correct; reflection uses precise vocabulary (ratio, rate, unit rate, equivalent); real-life example is detailed and accurate.
Meets (3)	4–5/6	Most answers correct; minor errors in notation or arithmetic; reflection clearly explains the concept in own words.
Approaching (2)	2–3/6	Some correct answers; confuses ratio with rate or struggles with equivalent ratios; reflection is brief or partially accurate.
Beginning (1)	0–1/6	Most answers missing or incorrect; little or no reflection; needs reteaching of ratio concept and unit rate procedure.

5 Reflect

Write 1–2 complete sentences for each prompt. Think carefully — use the vocabulary words.

R1. In your own words, what is a unit rate? Give one example from today.

R2. Where could you use a ratio or unit rate in real life outside of school? Explain why it is useful.

Deliverable: When you finish, press Check My Work in the Apply section, then use the Save as PDF or Save as DOC button above to turn in your completed HyperDoc. Your teacher will use the rubric above to score it.

Your reflection is saved with your work when you save as PDF or DOC.