Mathematics Alignment Lesson
Grade 5 Quarter 4 Day 148
Common Core State Standard(s)
5.MD.1 Convert among different-sized
standard measurement units within
a given measurement system (e.g.,
covert 5 cm to 0.05 m), and use
these conversions in solving
multi-step, real world problems.
Standards for Mathematical Practice
Standard 1 Make sense of problems and
persevere in solving them.
Standard 6 Attend to precision.
Materials Needed:

Transparencies/Blackline Masters –
“Converting Between Units of
Length”, “Length Conversions
Word Problems”
Assessment
Ask students to find a second way to solve the
each question on the “Length Conversions Word
Problems”.
Alignment Lesson
Converting Between Units of Length
1. Display Transparency “Converting Between Units of
Length” and have student volunteers help you fill in
equivalences for each of the units of length given.
2. Display the question (Walking at Recess) at the bottom
of the Transparency and have a student leader read it
aloud. Give students time to solve this problem in small
groups. Call everyone back together and have a student
leader guide the class through solving. Once that student
leader has finished, ask if anyone had a different way of
finding the solution. If so, ask that student leader to guide
the class through solving the problem a second way. (If
necessary, the teacher should show a second way.)
3. Have students turn to Transparency/Blackline
Master- “Length Conversions Word Problems”.
Read the directions with the students and reinforce
that they will need to show all of their work and
explain their solution. Allow students to work in
pairs or small groups to answer the questions. Tell
all students that if they finish answering each
question before the class is ready to check, they
should find a second way to solve each problem.
4. Once students have had time to finish answering the
questions, have the class come back together to
review the answers. Select different student leaders
to share their solutions to each problem and make
sure to show at least 2 different ways of solving each
problem.
5. Have students complete Blackline Master, “Length
Conversions Word Problems” for homework.
Homework
Blackline Master, “Length Conversions Journal
Prompt”
Source: Teacher Created & Math Partners Grant
Vocabulary
Metric measurement
Converting Between Units of Length
Customary measurement
within the Metric and Customary Systems
Conversion/convert
Wake County Public School System, 2012
Transparency/Blackline Master
Grade 5
Day 148
Standard 5.MD.1
Metric Units of Length
1 centimeter
1 meter
1 kilometer
Customary Units of Length
1 inch
1 foot
1 yard
1 mile
Read the information below and answer the question. You can use the conversions you’ve filled
in above to help you answer the question.
Walking At Recess:
Three friends, Madison, Grace and Julia wore special pedometers during recess. They disagree
over who walked the farthest. Madison’s pedometer reported that she walked 440 yards. Grace’s
pedometer reported that she walked 31,680 inches and Julia’s reported that she walked 660 feet.
Madison says that yards are bigger than inches and feet so she went the farthest.
Grace says 31,680 is bigger than 440 and 660, but inches are the smallest unit that their
pedometers reported so she couldn’t have walked the farthest.
Julia says 66 is bigger than 44 and 31 so she walked the farthest.
Who actually walked the farthest? Write an explanation that will prove to each of the girls that
are you correct.
Adapted from Math Partners Grant Activity
Wake County Public School System, 2012
Answer Key Grade 5
Day 148
Standard 5.MD.1
Converting Between Units of Length – Answer Key
within the Metric and Customary Systems
1 centimeter
1 meter
1 kilometer
Metric Units of Length
1/100 meters (0.01 meters)
100 centimeters; 1/1000 kilometers (0.001 kilometers)
1,000 meters
1 inch
1 foot
1 yard
1 mile
Customary Units of Length
1/12 foot; 1/36 yard
12 inches; 1/3 yard
36 inches; 3 feet
1,760 yards; 5,280 feet; 63,360 inches
Walking At Recess:
Three friends, Madison, Grace and Julia wore special pedometers during recess. They disagree
over who walked the farthest. Madison’s pedometer reported that she walked 440 yards. Grace’s
pedometer reported that she walked 31,680 inches and Julia’s reported that she walked 660 feet.
Madison says that yards are bigger than inches and feet so she went the farthest.
Grace says 31,680 is bigger than 440 and 660, but inches are the smallest unit that their
pedometers reported so she couldn’t have walked the farthest.
Julia says 66 is bigger than 44 and 31 so she walked the farthest.
Who actually walked the farthest? Write an explanation that will prove to each of the girls that
are you correct.
Grace actually walked the farthest. One way to see this is to convert each distance to the smallest unit
that the pedometers reported, which is inches. Madison walked 440 yards; that is equal to 15,840 inches.
I know this because there are 36 inches in a yard and she walked 440 yards so 440 x 36 = 15,840. Julia
walked 660 feet; this is equal to 7,920 inches. I know this because there are 12 inches in a yard and she
walked 660 feet so 660 x 12 = 7,920. Grace walked 31,680 inches which is larger than 15,840 inches
(Madison) and 7,920 inches (Julia). You can’t compare the numbers until you are looking at the same
unit (in this case I used inches).
Another strategy would be to determine what fraction of a mile each of these pedometers read. Madison walked
440 yards; there are 1,740 yards in a mile. 1,740 divided by 440 is 4 which means 440 yards is ¼ of a mile. Grace
walked 31,680 inches; there are 63,360 inches in a mile. 63,360 divided by 31,680 is 2 which means 31,680 inches
is ½ of a mile. Julia walked 660 feet; there are 5,280 feet in a mile. 5,280 divided by 660 is 8 which means 660
feet is 1/8 of a mile. So Madison walked ¼ of a mile, Grace walked ½ of a mile and Julia walked 1/8 of mile. All
you have to do is compare the fractions and you will see that Grace walked the farthest (1/2 is greater than ¼ and
1/8).
Adapted from Math Partners Grant Activity
Wake County Public School System, 2012
Blackline Master
Grade 5
Day 148
Standard 5.MD.1
Length Conversion Word Problems
Directions: Answer each conversion question below. Use the conversions table created in class to help
you. Be sure to explain how you solved each question. Show your work and record your answers on
another sheet of paper (or the back of this page) if you need more space.
1. Michael measured the length of his driveway and found that it was 14 yards long. Jordan also
measured the length of his driveway and found his to be 52 feet long. Who has a shorter
driveway, Michael or Jordan? How do you know?
2. Mia and Christine both have very tall dads and were debating whose dad is the tallest. Mia’s dad is 78
inches tall. Christine’s dad is 6 feet 2 inches tall. Whose dad is taller? How do you know?
3. The local zoo has both a hippopotamus and a camel in exhibits this summer. The adult hippopotamus is
about 4 meters long. The camel is about 360 centimeters long. Which animal is longer? How much
longer? How do you know?
4. Each of these animals, the hippo and the camel, needs to have a cage at the zoo for when it is not out in the
exhibit. The area of the cage must be the same for each animal and the zookeeper prefers to give the
animals as much space as possible. The length and width of the cage should be twice the size of the
animal. Which animal should you use to determine the area of the cage? What is the area of each cage?
5. Shaun and Amy are working to make a meter-long paper chain to decorate their classroom for an end of the
year party. Shaun is using strips of paper that are 6 centimeters long. Amy is using strips of paper that are
0.05 meters long. If they should use Shaun’s paper to make more than ½ of the chain and Amy’s for the
remainder of the chain, how many strips of paper do they each need to use? How do you know? Is there
more than one possible answer? Explain how you know.
6. Randy and Hope both drive trucks for Blue Tree Delivery Company. Randy drives a truck that measures 5
1/6 yards long. Hope drives a truck that is 372 inches long. Who drives a longer truck? How much longer
is the truck? Explain how you know.
Wake County Public School System, 2012
Answer Key Grade 5
Day 148
Standard 5.MD.1
Length Conversion Word Problems – Answer Key
1.
Michael measured the length of his driveway and found that it was 14 yards long. Jordan also
measured the length of his driveway and found his to be 52 feet long. Who has a shorter
driveway, Michael or Jordan? How do you know? Michael’s driveway is shorter than Jordan’s
driveway. To figure this out, I converted 14 yards to feet so that I would be comparing the same units. 14
yards is equal to 42 feet (there are 3 feet in a yard and 14 x 3 = 42). Jordan’s driveway is 52 feet long;
therefore Michael’s driveway is shorter (10 feet shorter to be exact). Note: students may convert both to
inches to get their answer as well; they could also convert the length of Michael’s driveway to yards (17
1/3 yards) to get their answer.
2. Mia and Christine both have very tall dads and were debating whose dad is the tallest. Mia’s dad is 78
inches tall. Christine’s dad is 6 feet 2 inches tall. Whose dad is taller? How do you know? Mia’s dad is
taller than Christine’s dad. To figure this out, I converted Christine’s dad’s height to inches since Mia’s
dad’s height was already given in inches. To convert 6 feet to inches, I multiplied 6 by 12 (because there
are 12 inches in a foot) and then added the extra 2 inches. This gave me 74 inches, meaning Christine’s
dad is 74 inches tall. This means Mia’s dad is taller (4 inches taller to be exact). Note: students may
convert Mia’s dad’s height to feet and inches (6 feet 6 inches or 6 ½ feet) to get their answer as well.
3. The local zoo has both a hippopotamus and a camel in exhibits this summer. The adult hippopotamus is
about 4 meters long. The camel is about 360 centimeters long. Which animal is longer? How much
longer? How do you know? The hippopotamus is longer than the camel. To figure this out, I converted
the length of the hippo from meters to centimeters so that both lengths would be in centimeters and could
be compared. 4 meters = 400 centimeters (this is because there are 100 centimeters in a meter). The
hippo is 40 centimeters (or 2/5 meters) longer than the camel. Note: students may convert the camel’s
length to meters (3 3/5 meters) to get their answer as well.
4. Each of these animals, the hippo and the camel, needs to have a cage at the zoo for when it is not out in the
exhibit. The area of the cage must be the same for each animal and the zookeeper prefers to give the
animals as much space as possible. The length and width of the cage should be twice the size of the
animal. Which animal should you use to determine the area of the cage? What is the area of each cage?
To give the animals the largest cage, you should use the length of the hippo since it is longer than the
camel. The length and width of the cage should both be 8 meters long (since that is twice the length of the
hippo). If both the length and width are 8 meters, then the area would be 64 square meters. This means
the area of each cage should be 64 square meters.
5. Shaun and Amy are working to make a meter-long paper chain to decorate their classroom for an end of the
year party. Shaun is using strips of paper that are 6 centimeters long. Amy is using strips of paper that are
0.05 meters long. If they should use Shaun’s paper to make more than ½ of the chain and Amy’s for the
remainder of the chain, how many strips of paper do they each need to use? How do you know? Is there
more than one possible answer? Explain how you know. If Shaun should use his strips to make up more
than half of the meter-long chain, his strips should make up more than 50 centimeters. Since Amy’s strips
are 5 centimeters long, Shaun’s total will need to be something that is a multiple of 5 so that when added to
Amy’s strips, they’d get an even number of centimeters (100). The following combinations would work:
Shaun – 10 strips (60 cm) and Amy 8 strips (40 cm). Shaun 15 strips (90 cm) and Amy 2 strips (10 cm).
6. Randy and Hope both drive trucks for Blue Tree Delivery Company. Randy drives a truck that measures 5
1/6 yards long. Hope drives a truck that is 372 inches long. Who drives a longer truck? How much longer
is the truck? Explain how you know. Hope’s truck is longer and it is twice as long as Randy’s truck. To
figure this out, I converted the length of Randy’s truck to inches. 5 yards is equal to 180 inches and 1/6 of
a yard is 6 inches and 180 + 6 = 186 inches (Randy’s truck). I know Hope’s truck is twice as long as
Randy’s because 186 x 2 = 372 inches. Note: students could convert Hope’s truck to yards (10 1/3 yards)
to compare.
Wake County Public School System, 2012
Answer Key Grade 5
Day 148
Standard 5.MD.1
Name: _________________________________
Date: __________________________________
Length Conversions Journal Prompt
Several students participated in the long jump at First in Fitness. Randall was the first to
go and he jumped 9 feet. Kim was next and jumped 2 ½ yards. Mike as the final jumper
and he reached 60 inches. Who was the winner of the long jump? Explain how you know.
Wake County Public School System, 2012
Answer Key Grade 5
Day 148 Standard 5.MD.1
Name: _________________________________
Date: __________________________________
Length Conversions Journal Prompt – Answer Key
Several students participated in the long jump at First in Fitness. Randall was the first to
go and he jumped 6 feet. Kim was next and jumped 2 ½ yards. Mike as the final jumper
and he reached 84 inches. Who was the winner of the long jump? Who came in second
place? Third? Explain how you know.
Kim is the winner of the long jump because she jumped 7 ½ feet. Mike is in 2nd
place because he jumped 7 feet. To determine his distance, I divided 84 inches by 12
12 since there are 12 inches in a foot. I know that both of these are more than
Randall because he only jumped 6 feet. I knew Kim jumped 2 ½ yards. To convert
this to feet I needed to determine how many feet are in 2 yards and how many feet
are in ½ yard. 2 yards = 6 feet and ½ yard = 1 ½ feet giving a total of 7 ½ feet for
Kim. So, 1st place goes to Kim, 2nd place goes to Mike and 3rd place goes to Randall.
Wake County Public School System, 2012