📐 Neft Teacher · Grade 6 · Unit 4 HyperDoc

Rates, Percents & Measurement Conversion

A rate is a comparison that hides inside almost everything you buy, build, and travel. In this HyperDoc you will turn messy real-world numbers into clean unit rates, find percents the way smart shoppers do, and convert measurements like an engineer.

6.RP.3 · Ratio & rate reasoning 6.RP.3b · Unit rate 6.RP.3c · Percent of a quantity 6.RP.3d · Measurement conversion
  1. 1 Engage
  2. 2 Explore
  3. 3 Explain
  4. 4 Apply
  5. 5 Reflect

Engage

Two stores, one juice. Which is the better deal — and how do you prove it?

The 30-second deal-off

Mega-Mart sells a 6-pack of mango juice for $9.00. The corner store sells a 4-pack for $5.60. Your job is not to guess — it is to compare them fairly. The only fair comparison is the price for one bottle.

Mega-Mart 6 bottles · $9.00 Corner Store 4 bottles · $5.60

Predict first (no calculator needed yet): Which one do you think is cheaper per bottle? Jot your guess — you will check it for real in the Apply section.

Explore

Pick up the tools. Each link builds one piece of Unit 4 — open them in a new tab and come back.

Explain

Three big ideas in Unit 4 — each one is just a ratio wearing a different hat.

1 · Unit rate = the "per one" price

A rate compares two different units (dollars and bottles). A unit rate shrinks that comparison down to one of something. To find it, divide the top number by the bottom number.

Mega-Mart: $9.00 ÷ 6 bottles = $1.50 per bottle
Corner Store: $5.60 ÷ 4 bottles = $1.40 per bottle

The corner store wins by 10¢ a bottle. Same juice — you only see it once you reach the "per one" price.

2 · Percent = a rate out of 100

Percent means "per 100." To find a percent of a number, turn the percent into a decimal (move the dot two places left) and multiply.

Find 25% of $48 sneakers.
25% = 0.25  →  0.25 × 48 = $12 off  →  you pay $36.

Percent: 25% As a decimal: 0.25 Discount on $48: $12.00

3 · Converting units = multiply by a clever "1"

Any conversion fact (like 1 ft = 12 in) can be written as a fraction equal to 1. Multiply so the unit you don't want cancels, leaving the unit you do want. A ratio table keeps it organized.

Feet → inches (×12 each step)
Feet 1 2 3 4
Inches 12 24 36 48

So 3 ft = 36 in. The same trick converts cups↔fluid ounces, km↔m, and grams↔kilograms.

Level 1 Extra support

Always label your numbers with their units before you divide. Reading "$9 for 6" out loud helps you set up 9 ÷ 6, not 6 ÷ 9.

Apoyo: escribe siempre la unidad (dólares, botellas) junto a cada número. "Tasa unitaria" = precio por una cosa.

Level 2 Stretch your thinking

If 25% off $48 is $12, what single decimal could you multiply $48 by once to get the final price of $36 directly? Explain why it works.

Apply

Six problems, increasing challenge. Type or choose, then press Check my work. You can fix and recheck.

1 Back to the juice from Engage. What is the corner store's unit rate ($5.60 for a 4-pack), in dollars per bottle? Type the number only, like 1.25
$ per bottle

2 Using both unit rates ($1.50 vs $1.40), which is the better buy and why?

3 A train travels 165 miles in 3 hours at a steady speed. What is its speed in miles per hour?
mph

4 A $60 jacket is marked 25% off. How many dollars do you save?
$ saved

5 A recipe needs 40 fluid ounces of milk. There are 16 fl oz in 1 pint. How many pints is that?
pints

6 Stretch: A car uses 4 gallons to drive 120 miles. At the same rate, how far can it drive on a full 12-gallon tank?

Teacher Notes & Answer Key (not printed)

Stage-by-Stage Notes (Engage → Explore → Explain → Apply → Reflect)

  • Engage: which bottle pack is the better buy? Sets up unit-rate comparison.
  • Explore: interactive converters for $/bottle, mph, and percent off.
  • Explain: define unit rate, percent of a number, and conversion via ratio reasoning.
  • Apply: answer key below.
  • Reflect: students explain why a true "per 1" rate makes comparison fair.

Apply — Answer Key

  • Q1 — Unit price: $5.60 ÷ 4 = $1.40 per bottle.
  • Q2 — Better buy (MC): $1.40 < $1.50 → answer b (each bottle costs less).
  • Q3 — Speed: 165 mi ÷ 3 h = 55 mph.
  • Q4 — Percent off: 25% of $60 = 0.25 × 60 = $15 saved.
  • Q5 — Rate/convert: 2.5.
  • Q6 (MC): answer c.

Standard

CCSS 6.RP.A.3b–d.

Reflect

Your thinking is part of the grade. Write in full sentences — these save with your name when you download.

1. Why does finding the "per one" price make two deals fair to compare?

2. Describe one place outside of class where YOU could use a unit rate, percent, or conversion this week.

3. What is one thing in Unit 4 that felt tricky, and what helped it click?

Neft Teacher · Grade 6 Reveal Math · Unit 4 — Rates, Percents & Measurement Conversion (6.RP.3). Enter your name at the top, finish every section, then save your HyperDoc to turn it in.