Unit Rates With Fractions

Grade 7 · Proportion · Page 1 of 2

Name Date
DIRECTIONS: Find each rate for ONE — divide by the amount after “per”.
Example: 34 of a mile in 14 of an hour: 34 ÷ 14 = 34 × 41 = 3 miles per hour.
Part A — Find the unit rate.
1.
Dev jogs 513 miles in 23 of an hour.
Work
miles per hour
2.
34 inch of snow fell in 14 of an hour.
Work
inches per hour
3.
A pipe puts 223 gallons into a tank in 13 of a minute.
Work
gallons per minute
4.
Mom used 118 cups of sugar making 34 of a batch of granola.
Work
cups per batch
5.
A mower covers 34 acre in 12 of an hour.
Work
acres per hour
6.
A wedge of cheese weighing 14 pound costs $1.00.
Work
dollars per pound

Unit Rates With Fractions — continued

Grade 7 · Proportion · Page 2 of 2

Part B — Which is the better buy? Write both rates.
  1. Cheddar is sold two ways: 12 pound for $6.00, or 134 pounds for $17.50. Which is the better buy?
    Show your work
  2. A 112-pound bag of coffee costs $12.00. A 3-pound bag costs $30.00. Which bag is the better buy?
    Show your work
  3. Ribbon comes in a 34-yard roll for $8.25 and a 112-yard roll for $15.00. Which roll is the better buy?
    Show your work
Part C — Explain it.
  1. A recipe uses 23 of a cup of oats for 12 of a serving. Jordan works out 12 ÷ 23 = 34 and writes “3/4 cups per serving.” His division is correct. His answer is not. Which words in the question decide which number goes underneath, and what is the right rate?
  2. In Part A, every answer came out BIGGER than the amount you started with. Priya says at least one of them must be wrong, because dividing makes numbers smaller. Explain why every one of them is right.

Daily Language Review — Set 1

Grade 7  ·  Mixed Review  ·  Page 1 of 2

Name Date
DIRECTIONS: Fix every mistake and write the sentence right on the lines. Number 1 is done.
Remember CUPS: Capital letters  ·  Usage (right word)  ·  Punctuation  ·  Spelling
  1. Due to the fact that my bike had a flat tire. I walked all the way to practice.Done for you
    Fixed:Because my bike had a flat tire, I walked all the way to practice.
  2. The bus was late again, everybody in my class were standing outside in the rain.
  3. My little brother only eats cereal for breakfast, he wont touch anything else.
  4. Running late for school, my backpack was left on the kitchen table and I had no calculater all day.
  5. It was a cold wet morning and the big red bus, was twenty minutes late.

Set 1, continued

Grade 7  ·  Mixed Review  ·  Page 2 of 2

  1. We won the game. We was down by ten at halftime. Nobody thought we could do it.
  2. In my personal opinion I think that the new lunch menu is worse then last year.
  3. My uncle sold his truck to a guy from work with a broken tailgate, the guy fixed it in one weekend.
  4. My mom signed me up for the early bus. Which means getting up at six on a school day, even fridays.
  5. The reason why I was late is because there was a really long line at the office, I got to class at 8:15.

Why Anything Bigger Needs Plumbing

Grade 7 · Building a body · Page 1 of 3

Name Date
DIRECTIONS: As a living thing grows, its surface cannot keep up with its insides. Read, then answer.
Diffusion is quick across a hundredth of an inch and hopeless across an inch. So a living thing can stay tiny, stay thin, or build something to carry supplies to the middle.
#Living thingStay tiny, stay thin, or build plumbing? And how?
Done for youan amoeba, one cell acrossStay tiny. Every part of it is already at the surface, so diffusion is enough on its own.
1.a flatworm, wide but paper-thin
2.a jellyfish, big but mostly water with thin walls
3.an insect, with air tubes running to every part inside
4.you
  1. A flatworm can be an inch wide and is never thick. Say why being flat solves the same problem that your blood solves.

Five Words, In Order

Grade 7 · Building a body · Page 2 of 3

DIRECTIONS: Put the five words in order. Each step can do something the one below cannot.
celltissueorgan…systemorgansorganismyoueach box is made of the one before it, and does something none of them could
#This thingWhich level is it?
6.one muscle cell
7.a sheet of muscle cells all pulling the same way
8.the heart
9.the heart, the blood and every vessel, working together
10.you
  1. A heart is made of muscle tissue, which is made of muscle cells. Say what the heart can do that a bag of loose muscle cells could not — and what that says about the word "organ".

Four Problems, Four Systems

Grade 7 · Building a body · Page 3 of 3

DIRECTIONS: Being big creates problems a single cell never had. Name the system that solves each.
#The problem a big body hasWhich system solves it, and roughly how
12.food arrives in lumps far too big to cross any membrane
13.the cells in the middle are nowhere near the outside world
14.oxygen has to come in and carbon dioxide has to go out, constantly
15.waste builds up everywhere at once
  1. Every one of those systems ends by bringing something close to a cell and letting go. Say why "close" is the word that matters, and what happens in the last fraction of an inch.

Younger Than America

The map is younger than you think · Page 1 of 2

Name Date
DIRECTIONS: How old is each country? Take the year from 2026. Then read the box.
The countrySinceWhat happened that yearHow old
1. The United States1776independence declared
2. Italy1861the separate states joined into one kingdom
3. Germany1871the same, twenty-odd states into one — and see page 2
4. India and Pakistan1947one colony became two countries in a night
5. Ghana1957the first colony in sub-Saharan Africa to become independent
6. Nigeria1960one of seventeen African countries independent in that year alone
7. Bangladesh1971split from Pakistan after a war
8. Kazakhstan, Ukraine and 13 others1991the Soviet Union ended and fifteen countries existed
9. South Sudan2011the newest member of the United Nations
Now compare the top three. Italy is 165 and Germany is 155. The United States is 250.

Two of the oldest-feeling countries in Europe are younger than America by the better part of a century, and Germany is younger than the American Civil War. That is not a trick of wording. Before those dates the places existed and the countries did not: what was there was dozens of separate states that happened to share a language.

Younger Than America — The Date Argues Back

The map is younger than you think · Page 2 of 2

Ask how old Germany is and you get at least three answers.

1871 — the states joined into one country.
1949 — after the Second World War it was divided, and two separate German countries were founded.
1990 — those two joined again, which is when the Germany on today's map began.

All three are defensible. Which one you pick depends on what you think a country is — a people, a government, or a shape on a map — and there is no way to settle that by looking anything up.
  1. Which of the three dates would you use, and why? There is no right answer and there is a right kind of reason.
  2. Say why "how old is this country" is a harder question than "how old is this mountain range".
  3. Somebody says a country is ancient because people have lived there for thousands of years. Say what is right about that and what is wrong with it.

Seven Guesses

How long does it take? · Page 1 of 2

Name Date
DIRECTIONS: Play higher-or-lower, 1 to 100, with someone. Write down your guesses.
Always guess the middle of what is left.
GameThe guesses I made, in orderHow many
Done for you
they picked 61		50 (higher) → 75 (lower) → 62 (lower) → 56 (higher) → 59 (higher) → 60 (higher) → 61 (got it!)7
1
2
3
4
Every guess halves what is left: 100, 50, 25, 13, 7, 4, 2, 1. That is 7 guesses, whatever they picked. One at a time could take 100.
Fill in: how many halvings to get down to one?
Numbers to searchGuesses, one at a time (worst case)Guesses, halving
1. 1 to 1010
2. 1 to 100100
3. 1 to 1,0001,000
4. 1 to 10,00010,000
5. 1 to 1,000,0001,000,000

Seven Guesses — What the Column Does

How long does it take? · Page 2 of 2

Look down your last column. The first column grows ten times each row. Yours grows by about three.
  1. A hundred takes 7 guesses and a million takes 20. Say how a task ten thousand times bigger costs only 13 more guesses.
  2. Halving only works if the numbers are in order. Say what "higher or lower" is doing for you that a shuffled pile could not.
  3. You have 20 guesses and want the biggest range you could still win on. Work out roughly what it is, and say how you got there.