Ratio & Rate Review Mission

Grade 6 • Everything we have covered so far
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Family homework · Review

Everything we have learned, in one mission.

This is a review of every skill we have covered so far — writing ratios, equivalent ratios and scale factor, rates, unit rates, and choosing the better buy. Nothing here is new. Start with the Family Note, then work through the six review parts. You get two tries on most questions, and hints are always available.

RatiosPart-to-Part & Part-to-WholeEquivalent RatiosRatesUnit RatesBetter Buy
What this review covers
  • Lesson 3-1 · Understand Ratios
  • Lesson 3-1 · Equivalent Ratios & Scale Factor
  • Lesson 3-2 · Understand Rates and Unit Rates
  • Lesson 3-2 · Comparing Unit Prices
  • Lesson 3-2 · Comparing Unit Rates (Best Value)
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Choose tonight's path

The math stays the same. Pick a path that fits your family's time, and switch any time.

Core path · about 20 minutes

A note for families

Read this first. It explains what this homework reviews and how to help without doing the math for your student.

5 minutes to read

This homework reviews everything we have covered so far.

Up to this point, your student has learned five connected skills: how to write a ratio, how to make equivalent ratios using a scale factor, what a rate is, how to find a unit rate, and how to use unit rates to decide which option is the better buy. Nothing in this review is new. Every question comes from a lesson we have already done in class.

Because it is a review, your student may move faster through some parts than others. That is useful information: the part that feels hard is the part worth going back over together. The My Results tab lists exactly which sections still need work.

Para las familias: esta tarea repasa todo lo que hemos cubierto hasta ahora — escribir razones, razones equivalentes y el factor de escala, las tasas, las tasas unitarias y cómo elegir la mejor compra. Nada es nuevo. La pestaña My Results muestra qué secciones necesitan más práctica.

Lesson 3-1Writing ratiosA ratio compares two amounts, and the order matters. 3 cups of apple juice to 2 cups of sparkling water is 3:2 — part to part. Apple juice to the whole drink is 3:5 — part to whole.
Lesson 3-1 · Part 2Equivalent ratios & scale factorMultiply both quantities by the same number and the comparison does not change. 1:3 scaled by ×4 is 4:12 — the recipe still tastes the same.
Lesson 3-2RatesA rate compares two amounts with different units, like miles and hours. "150 miles per hour" means 150 miles for every 1 hour.
Lesson 3-2 · Parts 2 & 3Unit rates & better buysPut the cost on top and the amount on the bottom, divide Top ÷ Bottom, drop the 1, and compare. The lower unit rate is the better value — even when its total price is higher.
👀 What to listen for
  • "Which amount is named first?" — the order of a ratio is part of the answer.
  • Scaling multiplies. Adding the same number to both parts is the most common slip: from 1:3, adding 3 to each gives 4:6, but the answer is 4:12.
  • "Per" means "for each one." A rate always names two different units.
  • The cost goes on top. Flipping the fraction gives items per dollar instead of dollars per item.
  • The smaller total price is not automatically the better buy.
🤝 How to help
  • Let your student write the ratio or set up the fraction first, before you say anything.
  • Ask them to explain why a step works, not just what the answer is.
  • If they are stuck, press the ? or Hint button on the question rather than giving the answer.
  • You do not need to know the math. Asking "how did you get that?" is the whole job.
  • Ten focused minutes beats an hour of frustration. Stop and tell me what was hard.
💬 Sentence starters

The ratio of ___ to ___ is ___ because ___.

I multiplied both parts by ___, so ___.

This is a rate because it compares ___ and ___.

First, I ___. Then, I ___.

___ is the better buy because ___ per 1 is less than ___ per 1.

Try this together · 5 minutes
Find a real ratio and a real unit price in your kitchen.

Pick any two things you can count — forks and spoons, apples and oranges, cans and boxes. Have your student write the ratio out loud in both directions ("4 to 6" and "6 to 4") and say which is which. Then pick up any package with a price and a count on it, and ask: what does one of these cost? That single question is the whole unit-rate lesson.

Sin costo: puede hacer esta actividad en español. Lo importante es que su estudiante explique su razonamiento en voz alta, en el idioma que prefiera.
Kitchen mission ready · complete it together when you can.
RatioA comparison of two amounts, like 3 to 2.Razón — una comparación de dos cantidades.
Equivalent ratiosRatios that make the same comparison with bigger or smaller numbers.Razones equivalentes.
Scale factorThe number you multiply both parts of a ratio by.Factor de escala.
RateA comparison of two amounts with different units.Tasa.
Unit rateThe amount for exactly 1 of something.Tasa unitaria.
Unit priceA unit rate in money — the cost of exactly 1 item.Precio unitario.
Part-to-wholeComparing one group to the total.Parte a todo.
Better buyThe option with the lower unit price.Mejor compra.

Part 1 · Writing Ratios

A ratio compares two amounts, and the order you write them in matters. Comparing one part to another part is part-to-part. Comparing a part to the total is part-to-whole.

6 ratios • two tries each
Remember how
Chef Reyes's drink uses 3 cups of apple juice for every 2 cups of sparkling water.
Part to part
3 : 2apple juice to sparkling water
→
Part to whole
3 : 5apple juice to the whole drink (3 + 2 = 5)
Order matters: water to apple juice is 2:3 — a different ratio. Always write the amount that is named first first.

Part 2 · Equivalent Ratios & Scale Factor

Find what the first quantity was multiplied by — that number is the scale factor — then multiply the second quantity by the same number.

5 builders • find the scale factor first
Remember how
Tahira's salad dressing uses 1 spoon of vinegar for every 3 spoons of olive oil. She wants to use 4 spoons of vinegar.
Find the scale factor
1 × 4 = 4the vinegar went from 1 to 4
→
Use the same factor
3 × 4 = 121 : 3 becomes 4 : 12
Watch out: scaling multiplies — it never adds. From 1 : 3, adding 3 to each part gives 4 : 6, but the correct equivalent ratio is 4 : 12. Check your answer by dividing back: 4 : 12 ÷ 4 = 1 : 3. ✓

Part 3 · Rates

A rate compares two amounts with different units, like miles and hours. Build a model by counting up by the rate, keeping the units lined up.

4 models • fill the table, then answer
Remember how
A high-speed train travels 150 miles per hour. The trip from Boston to Washington, D.C. is 450 miles. How long does the trip take?
Worked example: miles travelled after each hour at 150 miles per hour
Miles150300450
Hours123
The model lands on 450 miles at 3 hours, so the trip takes 3 hours. Division says the same thing: put the total distance on TOP (450) and the rate on the BOTTOM (150). 450 ÷ 150 = 3 hours.

Part 4 · Unit Rates

Set up the ratio yourself: cost on top, amount on the bottom. Divide both parts by the bottom number so the bottom becomes 1. Then drop the 1 and say the unit rate.

5 problems • build it, then solve it
Remember how
Theater A charges $15 for 3 tickets. What is the cost per ticket?
1 · Set up the ratio
$153 tickets
→
2 · Divide both parts by 3
$51 ticket
3 · Drop the 1. The division gives 5/1, but we do not keep the 1 — we write $5 per ticket. Careful: if you flip the fraction to 3/15, you get tickets per dollar instead of dollars per ticket.

Part 5 · Best Value

You cannot compare two packages by their total price, because they hold different amounts. Find each unit price first, then compare.

5 matchups • type both unit prices
Remember how
Bag A holds 4 lb for $7.00. Bag B holds 6 lb for $9.60. Which is the better buy?
Bag A · 7 ÷ 4
$1.75per pound
vs
Bag B · 9.60 ÷ 6
$1.60per pound
$1.60 is less, so Bag B is the better buy — even though $9.60 is the bigger total price. The lower unit price always wins when the products are the same.

Part 6 · Mixed Review

All five skills, shuffled together. This is the closest thing to what a quiz looks like — the question does not tell you which skill to use.

8 questions • two tries each

My Results

Your work saves automatically on this device. Finish any incomplete section, then print this page for your family and your teacher.

Aim for 80%+ mastery
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Review score
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Complete the review sections to build your score.
⚖️Ratios
✖️Equivalent
⏱️Rates
➗Unit Rates
🏷️Best Value
🧠Mixed Review
📌 What to go back over
  • Finish a section to see your review list.
✍️ Family sign-off · Firma de la familia

We talked about this review together, and here is what was hardest.

Family member
Hardest part
Stop 1 of 7 · Family Note