The Interior — MathGrades K–2

Unit 4 · Measuring, Time and Money

A unit of the course: the story, then chapter by chapter — sections, numbered lessons, a source or the numbers to read, three checks each — a review per chapter, and the wrap-up at the end.

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Drawn scene: a classroom wall with a chalkboard, a big analog clock, a ruler taped up and a rainy window with a rain gauge, and a bake-sale table with a cash box and coins
4Unit

Measuring, Time and Money

Measurement

How long is your desk? What time is lunch? How much is in your pocket? Every day you measure things. This unit shows you how. You will lay units end to end. You will read a ruler in inches and centimeters. You will make a graph of what you find.

Then you will learn the clock. The short hand tells the hour. The long hand counts minutes by fives. You will know when it is 3:00 and when it is 3:30. You will know the difference between a.m. and p.m.

Last, you will count coins. Pennies, nickels, dimes and quarters each have a value. You will add them up, buy things and give change. By the end, you can run a bake sale table all by yourself.

How we figured it out
7:00 a.m.

Wake up. The short hand is on the 7, the long hand on the 12.

8:30 a.m.

School starts. The long hand points to the 6: half past 8.

9:00 a.m.

Measure the hallway in shoes, then in feet with a tape.

10:15 a.m.

Make a bar graph of everyone's shoe lengths.

12:00 noon

Lunch. The clock hands both point straight up.

1:30 p.m.

Sort the bake sale coins: quarters, dimes, nickels, pennies.

2:00 p.m.

Count the coins. Big coins first: 25, 35, 45, 50.

2:45 p.m.

A cookie costs 35¢. Count up to make change from 50¢.

3:00 p.m.

The bell rings. School is over for the day.

6:00 p.m.

Dinner. Tell someone at home what time it is.

Chapter

Length and Data

Measurement and Data
Big questionHow can we measure how long something is and show what we found?
The story

The Hallway in Shoes

A class measures the same hallway two ways and gets two very different numbers.

Ms. Ruiz's class had a question. How long is the hallway outside the room? Nobody knew. Amir had an idea. He took off one shoe. He set it on the floor by the wall. Then he set his other shoe in front of it, heel to toe.

Amir walked the hallway shoe by shoe. His friends counted with him. At the far wall he stopped. The count was 40 shoes. Then Nia tried it with her shoes. Her shoes were smaller. Her count was 50 shoes. The class was puzzled.

Ms. Ruiz brought out a long tape measure. It had numbers on it. Two students held the ends. They read the number at the far wall. The hallway was 30 feet long. Every student got 30 feet, no matter who held the tape.

Amir looked at the two numbers. Forty shoes. Fifty shoes. Thirty feet. The hallway had not changed at all. Only the unit had changed. That afternoon the class made a graph of everyone's shoe lengths.

Talk about itWhy did Amir and Nia get different numbers for the same hallway?
Section 1

Comparing Lengths

7.1

Longer and Shorter

Main ideaTo compare two lengths, line up one end, then look at the other end.

Maya has a red crayon and a blue crayon. Which one is ? She puts them side by side. She lines up the left ends. Now she looks at the right ends. The red crayon sticks out more. So the red crayon is longer. The blue crayon is .

Lining up the ends matters. If one crayon starts ahead, you get fooled. A short crayon can look long. Always start both objects at the same line. Then compare the other ends.

Try it with a pencil and a marker. Line up the ends. Which one sticks out? That one is longer. If neither one sticks out, they are the same length.

Words to know
longer
reaching farther than the other object when the ends are lined up
shorter
not reaching as far as the other object when the ends are lined up
Check yourself

1. Two ribbons start at the same line. The blue ribbon sticks out past the red one. Which ribbon is longer?

2. Why do you line up the ends before you compare?

3. A pencil is longer than a crayon. The crayon is longer than an eraser. Which is shortest?

7.2

Putting Three in Order

Main ideaOrder lengths from shortest to longest by comparing two at a time.

Leo has three sticks. The brown stick is 5 cubes long. The gray stick is 8 cubes long. The white stick is 3 cubes long. He wants to line them up from shortest to longest.

Compare two at a time. 3 is less than 5, so white goes before brown. 5 is less than 8, so brown goes before gray. The is white, brown, gray. Shortest to longest: 3, 5, 8.

You can also order without numbers. Line up the ends. Find the shortest one. Set it first. Then find the next shortest. Keep going until all of them are in a row.

Words to know
order
a line-up that goes from shortest to longest, or longest to shortest
Check yourself

1. Three ropes are 4 feet, 9 feet and 6 feet long. Which order is shortest to longest?

2. A jump rope is 7 feet. A scarf is 3 feet. A ladder is 10 feet. Which is longest?

3. Sam's pencil is longer than Ana's. Ana's pencil is longer than Kim's. Whose pencil is in the middle?

Section 2

Measuring with Units

7.3

Units End to End

Main ideaMeasure by laying same-size units end to end with no gaps and no overlaps.

How long is the book? Rosa uses paper clips. She lays them in a line along the edge. Each clip touches the next. No . No overlap. She counts 6 clips. The book is 6 paper clips long.

The clips must all be the same size. Big and small clips mixed give a wrong count. Gaps make the count too small. Overlaps make it too big. Start at one end. Stop at the other end.

A different gives a different number. The same book is 6 big clips long. It is 9 small clips long. The book did not change. The unit changed. A smaller unit means more units.

Words to know
unit
the one thing you use over and over to measure, like a paper clip or a cube
gap
an empty space between two units that should be touching
Check yourself

1. Tia measures a shelf with cubes. She leaves gaps between the cubes. What happens to her count?

2. A desk is 5 long shoes long. You measure it again with short shoes. What happens?

3. Which rule is a good rule for measuring?

7.4

Inches and Feet

Main ideaAn inch is a small unit. A foot is 12 inches. Use a ruler to measure.

A has marks. Each mark is one . Put the 0 end at one end of the object. Read the number at the other end. A marker ends at the 7. The marker is 7 inches long.

A is 12 inches. Your math book is about 1 foot long. A door is about 7 feet tall. Use inches for small things. Use feet for big things, like a rug or a room.

Do not start at the 1 mark. Start at 0. If you start at 1, your number is one too big. A crayon that ends at 5 looks like 5 inches. But it is only 4 inches.

Words to know
inch
a small unit of length; a paper clip is about 1 inch long
foot
a unit of length equal to 12 inches; a math book is about 1 foot
ruler
a flat stick with marks for measuring inches or centimeters
Check yourself

1. A pencil starts at 0 on a ruler and ends at the 6. How long is it?

2. How many inches are in 1 foot?

3. Which is best measured in feet?

7.5

Centimeters and Meters

Main ideaA centimeter is smaller than an inch. A meter is 100 centimeters.

A is a small unit. It is about the width of your pinky finger. Many rulers show centimeters on one side. A paper clip is about 3 centimeters long.

A is 100 centimeters. A baseball bat is about 1 meter long. A door is about 2 meters tall. Use a meter stick for big things. Use a centimeter ruler for small things.

Measure a pencil twice. In inches it is 6. In centimeters it is 15. Centimeters are smaller, so you need more of them. Both numbers are right. They just use different units.

Words to know
centimeter
a small unit of length, about the width of a pinky finger
meter
a unit of length equal to 100 centimeters, about one big step
Check yourself

1. How many centimeters are in 1 meter?

2. A ribbon is 4 inches long. You measure it again in centimeters. What happens to the number?

3. Which tool is best for measuring a hallway?

7.6

Estimate, Then Measure

Main ideaAn estimate is a careful guess. Use something you know as a guide.

An is a careful guess. You know a paper clip is about 1 inch. A crayon looks about 4 clips long. So your estimate is about 4 inches. Then you measure. It is 4 inches. Good estimate!

Big things need a bigger guide. Your math book is about 1 foot. A desk looks like 2 books. Estimate: about 2 feet. Then measure it. If it is 2 feet, your guess was close.

Estimates do not have to be exact. Close is good. If you guess 20 feet and it is 3 feet, think again. Pick a better guide. Then guess again.

Words to know
estimate
a careful guess about a size or amount, made before you measure
Check yourself

1. A paper clip is about 1 inch. A marker looks like 5 clips long. About how long is the marker?

2. What is an estimate?

3. A rug looks like 6 math books long. A math book is about 1 foot. About how long is the rug?

Section 3

Showing Data

7.7

Picture Graphs and Bar Graphs

Main ideaA graph shows counts with pictures or bars so you can compare fast.

The class votes on a favorite pet. Dog gets 6 votes. Cat gets 4. Fish gets 2. A shows one picture for each vote. The dog row has 6 pictures. The cat row has 4.

A uses bars instead of pictures. A taller bar means more. The dog bar goes up to 6. The fish bar goes up to 2. You can see the winner fast. Dog wins.

Graphs answer questions. How many more dogs than cats? 6 − 4 = 2. How many votes in all? 6 + 4 + 2 = 12. Read the numbers off the graph. Then add or subtract.

Words to know
picture graph
a graph that uses one small picture for each thing counted
bar graph
a graph that uses bars; a taller or longer bar means a bigger count
Check yourself

1. A graph shows dog 6, cat 4, fish 2. How many more dogs than cats?

2. Dog 6, cat 4, fish 2. How many votes in all?

3. In a bar graph, which bar shows the biggest count?

7.8

Line Plots

Main ideaA line plot puts an X above each measurement on a number line.

The class measures pencils in inches. The lengths are 5, 6, 6, 7, 6, 5. A shows them. Draw a number line from 5 to 7. Put an X above the number for each pencil.

Above 5 there are 2 X’s. Above 6 there are 3 X’s. Above 7 there is 1 X. The tallest stack shows the most common length. That is 6 inches.

Count all the X’s to find how many pencils. 2 + 3 + 1 = 6 pencils. How many pencils are longer than 5 inches? Count the X’s above 6 and 7. 3 + 1 = 4.

Words to know
line plot
a number line with an X above a number for each measurement
Check yourself

1. A line plot has 2 X's above 5, 3 above 6 and 1 above 7. Which length is most common?

2. Same plot: 2 X's above 5, 3 above 6, 1 above 7. How many pencils in all?

3. Same plot. How many pencils are longer than 5 inches?

Chapter review

Length and Data

0 / 6

1. Two straws start at the same line. The green straw sticks out past the pink one. Which straw is shorter?

2. Ivan measures a table with cubes. He leaves gaps between them. What is his count?

3. How many inches are in 1 foot?

4. A pencil is 6 inches long. You measure it in centimeters. The new number is...

5. A bar graph shows red 5, blue 3, green 4. How many votes in all?

6. A line plot has 1 X above 4, 4 X's above 5 and 2 X's above 6. Which length is most common?

Chapter

Time and Money

Measurement
Big questionHow do clocks and coins help us know what time it is and how much we have?
The story

The Clock and the Cash Box

One clock on the wall and one box of coins run the whole day in Room 12.

Every morning in Room 12, Dev looks at the clock over the door. The short hand points at the 9. The long hand points at the 12. It is 9:00. That means lunch count time. Dev counts hands. Twelve kids want hot lunch. He writes 12 on the slip.

The clock keeps going. At 9:30 the long hand points down at the 6. Reading time. At 10:15 the long hand is on the 3. Math time. Dev likes to say the times out loud. His teacher says the clock is a map of the day.

On Friday the class holds a bake sale. Cookies cost 25 cents. Juice costs 50 cents. Dev sits by the cash box. A girl hands him three dimes for a cookie. He counts: 10, 20, 30. That is more than 25. He counts up from 25 to 30. He gives her back a nickel.

At 3:00 p.m. the bell rings. Dev counts the cash box. Quarters first, then dimes, then nickels, then pennies. The class made $6.75. The clock said the day was over. The coins said the sale was a success.

Talk about itWhy did Dev count the quarters before the pennies?
Section 1

Telling Time

8.1

Hour and Half Hour

Main ideaThe short hand tells the hour. Long hand on 12 means o'clock; long hand on 6 means half past.

A clock has two hands. The short hand is the . The long hand is the . When the long hand points to 12, it is o’clock. Short hand on 3, long hand on 12: 3 o’clock. We write 3:00.

When the long hand points to 6, it is . The short hand sits between two numbers. It is between 3 and 4, so it is half past 3. We write 3:30. Thirty minutes is half an hour.

A digital clock shows only numbers. 3:00 means 3 o’clock. 3:30 means half past 3. Watch out: at 3:30 the short hand is past the 3, not on it. Use the number it just passed.

Words to know
hour hand
the short hand on a clock; it points to the hour
minute hand
the long hand on a clock; it shows the minutes
half past
30 minutes after the hour; the long hand points to the 6
Check yourself

1. The short hand is on 5. The long hand is on 12. What time is it?

2. The short hand is between 8 and 9. The long hand is on 6. What time is it?

3. How many minutes are in half an hour?

8.2

Five Minutes at a Time

Main ideaEach number on the clock is 5 minutes. Count by fives from the 12.

The long hand moves around the clock. Each number it passes is 5 . Count by fives from the 12. At the 1 it is 5 minutes. At the 2 it is 10. At the 3 it is 15. At the 6 it is 30.

Short hand just past 2, long hand on the 4. Count: 5, 10, 15, 20. It is 2:20. Short hand near 10, long hand on the 9. Count: 5, 10, 15, 20, 25, 30, 35, 40, 45. It is 9:45.

Read the short hand first. Use the number it passed. Then count the long hand by fives. A common mistake is reading the long hand as 4 instead of 20. The number is a helper, not the minutes.

Words to know
minute
a short bit of time; 60 minutes make one hour
Check yourself

1. The long hand points to the 8. How many minutes past the hour is it?

2. The short hand is just past 4. The long hand is on the 2. What time is it?

3. The short hand is near 6. The long hand is on the 11. What time is it?

8.3

Morning, Noon and Night

Main ideaA.M. is morning, before noon. P.M. is afternoon and evening, after noon.

A day has 24 hours. The clock goes around twice. means the hours from midnight to noon. means the hours from noon to midnight. 7:00 a.m. is breakfast time. 7:00 p.m. is close to bedtime.

Look at a school day. School starts at 8:30 a.m. Lunch is at 12:00. That is . Recess is at 1:15 p.m. School ends at 3:00 p.m. Dinner is at 6:00 p.m.

A schedule is a list of times. It tells what comes next. Reading is at 9:00 a.m. Math is at 10:00 a.m. Math comes after reading. The earlier time always comes first.

Words to know
a.m.
the hours from midnight to noon; the morning
p.m.
the hours from noon to midnight; afternoon, evening and night
noon
12:00 in the middle of the day, when a.m. changes to p.m.
Check yourself

1. You eat breakfast at 7:00. Is it a.m. or p.m.?

2. What do we call 12:00 in the middle of the day?

3. Music is at 1:00 p.m. Art is at 10:00 a.m. Which comes first?

Section 2

Coins

8.4

What Each Coin Is Worth

Main ideaA penny is 1 cent, a nickel 5 cents, a dime 10 cents, a quarter 25 cents.

A penny is worth 1 . A nickel is worth 5 cents. A dime is worth 10 cents. A quarter is worth 25 cents. We write cents with a ¢ sign. 5¢ means 5 cents.

Size can fool you. A dime is the smallest . But it is worth more than a penny or a nickel. A nickel is bigger than a dime but worth less. Look at the coin, not its size.

Two nickels make 10 cents, the same as one dime. 5 + 5 = 10. Five pennies make one nickel. Two dimes and a nickel make 25 cents. 10 + 10 + 5 = 25. That is the same as one quarter.

Words to know
cent
the smallest amount of U.S. money; a penny is one cent
coin
a small round piece of metal money, like a penny or a dime
Check yourself

1. Which coin is worth 10 cents?

2. How many pennies equal one nickel?

3. Which is worth more, a dime or a nickel?

8.5

Counting Mixed Coins

Main ideaStart with the biggest coins. Count on by 25, 10, 5, then 1.

Jamal has a quarter, a dime and two pennies. Start with the biggest coin. Quarter: 25. with the dime: 35. Add a penny: 36. Add a penny: 37. He has 37 cents.

Sort first. Put quarters, then dimes, then nickels, then pennies. Two dimes and three nickels: 10, 20, then 25, 30, 35. That is 35 cents. Big coins first keeps the numbers easy.

Check by counting a different way. Three nickels are 15. Two dimes are 20. 15 + 20 = 35. Same answer. If your two counts do not match, count again.

Words to know
count on
start at one number and keep counting up from there
Check yourself

1. One quarter and one dime. How many cents?

2. Two dimes and one nickel. How many cents?

3. One quarter, one nickel and two pennies. How many cents?

Section 3

Dollars and Cents

8.6

Money Word Problems

Main idea100 cents make 1 dollar. Add or subtract cents to solve money problems.

A is 100 cents. Four quarters make a dollar: 25 + 25 + 25 + 25 = 100. We write one dollar as $1.00. We write 45 cents as 45¢ or as $0.45.

Mia buys a pencil for 30¢ and an eraser for 15¢. How much in all? 30 + 15 = 45. She pays 45¢. Kai has 50¢ and spends 20¢. How much is left? 50 − 20 = 30. He has 30¢ left.

Read the question twice. In all means add. Left means subtract. Draw the coins if it helps. Then check your work: 30 + 15 = 45, and 45 − 15 = 30. It matches.

Words to know
dollar
100 cents; four quarters or ten dimes make one dollar
Check yourself

1. A sticker costs 40¢. A pencil costs 35¢. How much for both?

2. Lily has 80¢. She spends 30¢. How much is left?

3. How many quarters make one dollar?

8.7

Making Change by Counting Up

Main ideaTo make change, count up from the price to the money paid.

A cookie costs 35¢. Tom pays with two quarters, 50¢. How much does he get? Count up from 35. From 35 to 40 is a nickel. From 40 to 50 is a dime. 5 + 10 = 15. Tom gets 15¢ back.

Check with subtraction. 50 − 35 = 15. Same answer. Counting up is like climbing stairs. Start at the price. Stop at the money paid. The steps you took are the change.

Try another one. Juice is 60¢. Ana pays $1.00. Count up: 60 to 70 is 10. 70 to 100 is 30. 10 + 30 = 40. The change is 40¢. Check: 100 − 60 = 40. Yes.

Words to know
change
the money you get back when you pay more than the price
Check yourself

1. A pencil costs 20¢. You pay with a quarter. How much change do you get?

2. Gum costs 70¢. You pay with $1.00. How much change do you get?

3. Why do we count up from the price?

Chapter review

Time and Money

0 / 6

1. The short hand is on 9. The long hand is on 12. What time is it?

2. The long hand points to the 3. How many minutes past the hour is it?

3. Bedtime is 8:00 at night. Is that a.m. or p.m.?

4. One dime and three pennies. How many cents?

5. A toy costs 60¢. A ball costs 25¢. How much for both?

6. Bread costs 40¢. You pay 50¢. What is your change?

Unit wrap-up

Measuring, Time and Money

Twelve words, twelve meanings

0 / 8

Tap a word, then tap its meaning. A right pair locks in green.

Words
Meanings
Unit test

Fifteen questions across the unit

0 / 10

1. Two sticks start at the same line. The blue stick sticks out past the other one. Which is longer?

2. You measure a table with cubes. The cubes overlap. What happens to your count?

3. How many inches are in one foot?

4. How many centimeters are in one meter?

5. A picture graph shows 5 apples and 3 bananas. How many more apples than bananas?

6. The short hand is between 2 and 3. The long hand is on the 6. What time is it?

7. The long hand points to the 10. How many minutes past the hour is it?

8. One quarter and two dimes. How many cents?

9. A pencil costs 30¢. A pen costs 45¢. How much for both?

10. A snack costs 65¢. You pay with three quarters, 75¢. How much change do you get?

Spiral review

Five questions from earlier units

0 / 5

1. (Unit 3) What is 623 + 245?

2. (Unit 2) What is 9 − 5?

3. (Unit 1) Which has fewer: 6 cats or 8 dogs?

4. (Unit 3) What is 275 in expanded form?

5. (Unit 2) What is 7 + 7?

Write it

You have one quarter, two dimes and one nickel. You buy a cookie for 35¢. How much money do you have? How much is left after you buy the cookie? Explain each step.

  • Say your answer first.
  • Count the coins big to small: 25, 35, 45, 50.
  • Show the subtraction: 50 − 35.
  • Check by counting up from 35 to 50.
  • Say why your answer makes sense.
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Practice rooms

Rooms already on the site that belong to this unit — cards, quizzes, a lab.

For the teacher

Every lesson keeps its own three checks; a lesson is ticked when all three are right. Chapter reviews, the unit test and its spiral review (five questions from earlier units in this band) score on the page. When the site is connected to your sheet, or the link carries ?dest=, each one also has a Send box: the first-try score, the standards, the supports used, the attempt number and the minutes go to your sheet as an IEP data point.

Print this page for a paper copy of the readings, the sources, the words and the questions; the answers print as dashed boxes under each question.

Fact-check notes for this course live in the handoff: quotes marked (paraphrased) were set that way on purpose.