Unit 7 Measurement and Data:
Measuring Length in Metric Units
Introduction
In this unit, students will learn about measuring length, width, height, and distance.
Materials
Students will need a large number of 1 cm and 2 cm connecting cubes (also called snap cubes
or linking cubes) and paper clips of two sizes, 3 cm and 5 cm. If you need to buy connecting
cubes, be sure to get cubes that can link in different directions.
In many lessons, you will need to draw images of specific length on the board or demonstrate
working with a centimeter ruler. If you work in a setting that does not allow all students to clearly
see regular-sized manipulatives (1 cm connecting cubes, centimeter rulers, or concrete rulers),
use enlarged versions produced by photocopying. Alternatively, use an overhead or virtual
manipulatives on an interactive whiteboard.
Estimating
Students will often be asked to estimate and then measure length. If you use the questions in
the AP Book for assessment, make sure students estimate before they measure. When
introducing concepts and solving problems as a class, encourage students to estimate the
lengths of different objects and check by measuring. Comparing an estimate with the actual
measurement of an object helps students develop knowledge of the length of a quantity, such
as 1 m, and helps them improve their estimates.
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
H-1
MD2-1
Length, Width, and Height
Pages 175–176
Standards: preparation for 2.MD.A.1
Goals:
Students will compare the lengths of straight objects directly by lining up the ends.
Students will identify and compare widths and heights of objects that have an obvious front.
Vocabulary: height, length, longer, longest, narrower, opposite, shorter, shortest, taller,
wider, width
Materials:
colored pencils of different lengths (5 for each student, 10 for the teacher)
a colored marker or a crayon
3 objects (e.g., index card, playing card, story book) for each student
a toy car
BLM Rectangles (p. H-31; see Extension 2)
Introduce length. Explain that the distance from one end to the other end of an object is called
the length. Demonstrate by showing the length of a pencil. Then, hold two colored pencils in one
hand so that the bottoms are concealed in your fist. Stagger the pencils so that the longer pencil
appears shorter. ASK: Which color of pencil looks longer? Reveal the bottoms of the two pencils
and then align them. ASK: Now which color looks longer? Why did we get different answers?
Which pencil is really longer?
Have several colored pencils available. Align pencils two at a time and ask students to identify
which pencil is longer. Then align the writing end of one pencil with the non-writing end of the
other one and ask which one is longer.
Introduce shorter. Align the end of a long red pencil with the end of a short blue pencil and
SAY: The red pencil is longer than the blue pencil. We say the blue pencil is shorter than the red
pencil. Shorter means “not as long as.” Longer and shorter are opposites. Write “longer” and
“shorter” on the board. Show different pairs of properly aligned colored pencils. ASK: Which
pencil is shorter? To see all students’ answers at the same time, ask them to hold up crayons or
colored pencils of the correct color.
Introduce longest and shortest. Using groups of three or more colored pencils, demonstrate
the meanings of the words longest and shortest. Write “longest” and “shortest” on the board.
Show different triples of properly aligned colored pencils and have students identify the color of
the longest or the shortest pencil.
H-2
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
Compare objects when the ends are not lined up. Show or draw the arrangement shown
below:
ASK: Which pencil is longer? (red) How can you tell even though the ends are not lined up?
(The red pencil is longer because there is extra red at both ends.) Repeat with more
arrangements.
(MP.3) Show or draw the arrangement shown below:
ASK: Which pencil will be longer when I line them up correctly? Explain how you know. ASK: Is
there more extra red at one end or extra blue at the other end? (more extra blue at one end than
extra red at the other end) Line up the pencils correctly to check the prediction. Repeat with
pencils that gradually become more similar in length.
Use folding to compare lengths. Give student pairs a rectangular sheet of paper. SAY: Let’s
find out which side is longer, the top or the side. Have students discuss in pairs how to compare
the lengths of the two sides. SAY: So far, we checked which pencil is longer by lining pencils up.
We cannot line up sides of a sheet of paper, but we can place them one on top of the other.
ASK: How can we place the top of the paper onto the side? (fold the sheet to bring the sides
together) Demonstrate folding the sheet upward diagonally. Mark on the longer side where the
shorter side ends as shown below:
folded edge
Activity 1
Which side is longer? Give students several different precut rectangles, such as those from
BLM Rectangles, or ask students to cut out the rectangles from the BLM. Challenge them to
predict which side is longer. Ask students to fold the rectangles to compare sides and use a
colored marker or crayon to make a mark on the longer side, as shown above.
(end of activity)
(MP.2) Transitivity of length. Give three volunteers 1 pencil each, all of different lengths,
without showing the pencils to the whole class. Ask the volunteer with the middle-sized pencil
(Jin, for example) to demonstrate comparing the pencils first with one of the other two
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
H-3
volunteers (Ava and Kim, for example), then with the other. SAY: Jin’s pencil is longer than
Ava’s pencil, and Kim’s pencil is longer than Jin’s pencil. Who has a longer pencil, Kim or Ava?
(Kim) How do you know? (Kim’s pencil is longer than Jin’s, and Jin’s pencil is longer than Ava’s,
so Kim’s pencil is longer than Ava’s and the longest of the three.) Have the other two volunteers
compare the pencils to check.
Introduce width. Explain that the distance across an object from side to side is called the width.
Illustrate with a JUMP Math AP book: hold up the workbook and run your fingers along the front,
first up and down, then side to side. ASK: Which way is the width? Is it this way (show from side
to side)? Or is it this way (show from top to bottom)? Write “width” on the board.
Explain that when you look at a book so that you can read it, the width is the distance across
from side to side. Ask volunteers to show the width of various objects, such as the blackboard, a
window, a door, a bookshelf, and so on.
Compare widths. Place a JUMP Math AP book on the blackboard ledge. Explain that the
workbook is not as wide as the blackboard. We say the blackboard is wider than the workbook.
Write “wider” on the board, and explain that the word “wider” is used when comparing two
widths. Ask students to find other objects in the classroom that are wider than their workbook,
using their workbooks to check directly.
Introduce narrower. ASK: What is the opposite of longer? (shorter) Explain that narrower is the
opposite of wider. Write “narrower” on the board. Give each student three objects to compare,
for example, an index card, a playing card, and a storybook. ASK: Is the book wider or narrower
than the index card? (wider) Is the playing card wider or narrower than the index card?
(narrower)
Introduce height. Explain that the distance up and down an object is called the height. Write
“height” on the board. Ask a volunteer to stand up, choosing a student who is of average height.
ASK: Who thinks they are taller than (use the volunteer’s name)? How can we check? After
students share their ideas, ask a second volunteer to stand back to back with the first volunteer.
Repeat the exercise with volunteers who think they are shorter.
Finding the width of three-dimensional objects. Show students a toy car and ask them to
identify the front of the car. Have volunteers trace a finger along the car from front to back, side
to side, and top to bottom. ASK: Which way is the width of the car—from front to back, side to
side, or top to bottom? (from side to side)
Draw a car on the board viewed from the side, so that the front is visible as shown below:
H-4
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
ASK: Are we facing the front of the car or one of the sides? (one of the sides) Where is the front
of the car? (the part on the right) Trace your finger along the car on the board from top to
bottom, front to back, and side to side. Ask students to tell you (using thumbs up or down) if a
distance you are tracing represents the width. Add lines to identify each dimension on the
drawing (similar to those on AP Book 2.1 p. 176). Trace or color the line that represents the
width. Repeat with other drawings of concrete objects, such as a toy train, a book, a chair, a
bench, and so on. Have students also identify the height of each drawn object.
Activity 2
“I Spy.” Play a few rounds of “I Spy” with students using the length, width, and height of
classroom objects. Example: I spy something that is narrower than this sheet of paper. You
might invite volunteers to lead a round of the game.
(end of activity)
Extensions
1. Obtain a red and a blue pencil that are close in length (the red pencil should be longer by less
than 1 cm). SAY: I am going to show you something magical that we call an “optical illusion.”
Hold the shorter blue pencil vertically and the longer red one horizontally. Ask students to
predict which pencil is longer, then check their predictions. Explain that objects that sit vertically
(from top to bottom) often look longer than objects that sit horizontally (from side to side).
2. Draw a rectangle on the board. Explain that geometric shapes, such as rectangles, do not
have a front, so it is not clear which distance across is the width. Mathematicians have defined
the width of rectangles to be the shorter side and the length to be the longer side.
width
length
Give students some rectangles from BLM Rectangles. Ask them to trace the rectangles so that
the width, the shorter side, goes from side to side (not up and down). Model an example (see
below).
D
E
F
C
B
A
Sample answers:
3. As a class, read Super, Super, Superwords by Bruce McMillan. The book has numerous
illustrated examples of comparatives and superlatives.
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
H-5
MD2-2
Measuring Length
Pages 177–178
Standards: 2.MD.A.1
Goals:
Students will identify how to correctly measure the length of an object by lining up identical units
in the same position, with no gaps or overlaps.
Prior Knowledge Required:
Count beyond 20
Compare lengths directly by placing objects side by side and aligning properly
Vocabulary: length, longer, measure, unit, unit of measurement
Materials:
1 cm connecting cubes (at least 21 for each student)
pencil that is an exact number of centimeters long
3 cm and 5 cm paper clips (at least 5 small and 8 large for each student)
strips of paper
scissors
masking tape
variety of items to serve as units of measurement (e.g., pattern blocks, play coins, 2 cm
connecting cubes)
finger paint
precut cardboard rectangles
several same-size elastics (see Extension 1)
newspapers and cardstock paper or construction paper (see Extension 2)
(MP.5) Why we need measurement. Hold up a pencil and and ask a volunteer to hold up a
pencil, too. SAY: I want to know whose pencil is longer. How can we check? (line up the
pencils) Invite the volunteer to check. Then explain that you want to check which pencil is
longer, the one you have in your hand or the one you have at home. ASK: How can I check?
(bring the pencil to school and check) Can you check which pencil is longer without bringing it to
school? Can you check which is longer, your pencil, or the pencil of a friend in China? How
might you check? Students may suggest measuring both pencils and comparing the
measurements.
Introduce measure. SAY: When we use a number to show how long a pencil is, we are
measuring its length. Measuring is different from comparing a pencil’s length to the length of
another pencil. We can say that a ruler is longer than a book, but that is not very helpful since
lots of things are longer than a book. (You might brainstorm a list together to illustrate the point.)
When we say that a ruler is 6 inches long, we are giving more information.
H-6
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
Introduce unit of measurement. Write “unit of measurement” on the board. Explain that a unit
of measurement is something that we can use over and over again to measure with. Obtain a
pencil that is an exact number of centimeters long. Place a row of connecting cubes below the
pencil as shown, or show the picture below:
SAY: For example, if we place connecting cubes in a row below a pencil, we can count the
cubes. ASK: How many cubes are in the row? (8) SAY: This pencil is as long as 8 cubes, so we
say that it is 8 cubes long. We can measure the length of other objects in cubes. Using the
same unit to measure different objects allows us to compare objects, even when we can’t place
the objects side by side.
Explain that many objects can be used as a unit of measurement. An example is connecting
cubes. Give each student at least 21 small connecting cubes and ask them to make a chain of
cubes that is as long as their AP book is wide. ASK: How many cubes wide is the book? (21)
Measuring using centimeter cubes. Remind students that to compare lengths properly, they
need to align the ends of the objects. Use a pencil that is an exact number of centimeters long
and a chain of connecting cubes to demonstrate properly aligning the end of the pencil with one
end of the chain.
Have students make a chain of cubes for each pencil or crayon in Questions 1–8 on AP Book
2.1 p. 177.
Exercises: Make a chain of cubes that is as long as each pencil or crayon. How many cubes
long is each pencil?
Answers: 1. 5 cubes, 2. 5 cubes, 3. 7 cubes, 4. 6 cubes, 5. 4 cubes, 6. 5 cubes, 7. 6 cubes, 8.
7 cubes
Units of measurement need to be placed the same way. Have a volunteer use cubes to
measure a pencil that is an exact number of centimeters long. Write on the board:
The pencil is 8 cubes long.
Demonstrate measuring the same pencil incorrectly by arranging connecting cubes as shown
below):
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
H-7
(MP.6) SAY: I think this pencil is 7 cubes long. Is that correct? (no; thumbs down) Have
students show thumbs up or down to represent yes or no, respectively. How is this different
from the way we measured earlier? (the cubes are not in a chain; some cubes are turned so
they take more space) Emphasize that the units need to be placed exactly the same way for
measuring.
Explain that you can also use paper clips to measure length. Show measuring the pencil
incorrectly in another way by arranging paper clips as shown below:
ASK: Is this a good way to measure with paper clips? (no; thumbs down) Why not? (some units
are lying down and some are standing up) Have a volunteer place the paper clips correctly. If
the pencil is not an exact number of paper clips long, point that out and say that the pencil is a
little more (or a little less) than 4 paper clips long.
Units of measurement must be the same length. Give students a variety of small and large
paper clips. Show them how to make a chain of paper clips and how to keep the chain straight.
Demonstrate marking the length of a sample chain of 3 paper clips on a strip of paper, and cut
the strip along the mark. Tell students to make their own chain using any 5 paper clips and then
cut a strip of paper that is as long as their chain. Make sure that at least one student uses only
small paper clips and another uses only large paper clips for their chains. Invite many
volunteers to tape their paper strips on the board. Compare the length of the strips directly,
particularly those made using only one size of paper clip. SAY: All these strips are 5 paper clips
long, but they are not all the same length. Why not? (everyone used different paper clips)
Show or draw a pencil that is 4 large paper clips long and a pencil that is 5 small paper clips
long. Tape or place the paper clips alongside each pencil as shown:
(MP.3) ASK: Which pencil is longer? How can you tell? (the one that measures 4 large paper
clips; because that pencil extends beyond the other one) Should 5 paper clips be longer than 4
paper clips? Explain. (only if the paper clips are the same size)
H-8
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
Next show pencils that are both 8 paper clips long, but use paper clips of different sizes as
shown below:
SAY: Both pencils are 8 paper clips long, but they are not the same length. Explain that when
we measure, we need to use units that are the same length.
There must be no gaps or overlaps between units of measurement. Show another incorrect
way to measure a pencil by leaving gaps as shown below:
ASK: Is this pencil 3 paper clips long? (no, thumbs down) What is wrong with the
measurement? (the paper clips are spread out) Explain that there should be no spaces between
the units. Add 2 more paper clips that cover the gaps but create overlaps as shown below:
ASK: Is this pencil 5 paper clips long? (no, thumbs down) What is wrong with the
measurement? (the paper clips overlap each other) Invite a volunteer to place the paper clips
correctly. Have students show thumbs up if the paper clips are arranged correctly.
(MP.6) Identifying correct measurements. Show different correct and incorrect ways to
measure items, such as paper clips, cubes (1 cm and 2 cm), pattern blocks, and play coins.
Have students show you thumbs up or down to represent arrangements that are correct or
incorrect, respectively. Invite volunteers to correct the arrangements.
Activity
Using fingerprints as units of measurement. Distribute paint and cardboard rectangles of
various lengths. Have students use fingerprints (from the same finger) to measure the length of
the rectangles. Make the rectangles wide enough so that students can write or finger-paint the
number of fingerprints as well.
(end of activity)
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
H-9
Extensions
1. Features of good units of measurement. Explain to students that paper clips are good
units of measurement because it is easy to find many that are the same size. SAY: You can use
many small paper clips or many big paper clips to measure. SAY: Each small paper clip is the
same length. Units of measurement also need to stay the same length. Paper clips stay the
same length because they are rigid. Let’s find out if elastics are good units of measurement.
Use many elastics of the same size to demonstrate how their length changes when you stretch
them. ASK: Are elastics good units of measurement? Why do you think so? (no, they stretch to
different lengths).
Invite students to identify classroom objects that would make good units of measurement. As a
class, discuss the units students found as well as any good units that they may have missed.
Have each student draw and label an appropriate measuring unit and add it to a class poster
titled “Good Measuring Units.”
(MP.6) 2. The need for standard units. SAY: A long time ago, people did not use paper clips
or cubes or even centimeters to measure lengths. They used other things. For example, in
ancient Egypt, they used cubits. A cubit is the length from the tip of your middle finger to the
outside of your elbow. Show this length on your arm. Have students do the following to illustrate
the disadvantages of non-standard units of measurement and the need for standard units.
Have students work in groups of 4 to make a table. Have each student use their own cubit to
make one leg that is 2 cubits long. Students can roll old newspapers to make the legs and use
cardstock paper or construction paper to make the tabletop. (Rolling newspapers diagonally
works well; the ends are thinner and easier to cut off.) Then have students lay a pencil on their
table. ASK: Does the pencil roll off? Why? (yes, the table is not level) Are the legs the same
height? Why not? (no, the length of each cubit is different)
Explain that the ancient Egyptians recognized the need for everyone to use the same, or a
standard, cubit. ASK: Whose arm do you think they used to determine the length of a standard
cubit? The king’s! Discuss how people recorded and shared the king’s cubit so that everyone
would know what it was. (They used a wooden stick with lines scratched in it to show the length
of the king’s cubit, just as we use rulers.)
H-10
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
MD2-3
Measuring in Centimeters
Pages 179–181
Standards: 2.MD.A.1
Goals:
Students will measure pictures of objects in centimeters using centimeter cubes and then a
centimeter ruler.
Prior Knowledge Required:
Count beyond 20
Compare lengths directly by placing objects side by side and aligning properly
Measure length using non-standard units
Vocabulary: centimeter (cm), length, longer, measure, ruler, unit of measurement
Materials:
1 cm connecting cubes (at least 30 for each student)
30 cm rulers
BLM Measuring in Centimeters (p. H-32)
BLM Concrete Rulers (p. H-33)
BLM Measuring with a Ruler (p. H-34)
Measuring by counting cubes in a long chain. Give each student at least 15 small
connecting cubes, and tell them to make a chain using the cubes. Explain to students that they
will use the chain to measure pictures. Help students recall how to measure correctly—one end
of the picture should align with one end of the chain. Tell students to note the place on the chain
where the picture ends and then count the cubes from the end of the chain to the place they
noted. Demonstrate by using a picture on the board or an object that is an exact number of
centimeters long. Have students use their chains to measure the pictures on BLM Measuring
in Centimeters and then write the measurements in cubes. (1. 13 cubes, 2. 11 cubes, 3. 7
cubes, 4. 5 cubes, 5. 6 cubes)
Using a concrete ruler. Tell students that it is often inconvenient to use a chain of cubes to
take measurements. SAY: I want to try using a picture of cubes instead. Show students a
concrete ruler from BLM Concrete Rulers and then distribute concrete rulers to them. ASK: Are
the units placed correctly on the ruler? Are the units placed so there are no spaces or overlaps?
Are the units the same size? (yes, thumbs up to all) Have students check that the units on the
concrete ruler and the connecting cubes are exactly the same size. ASK: How is the picture of
the row of cubes different from an actual row of cubes? (e.g., picture is bendable, picture is flat,
cubes have color) Make sure students notice that the picture of the row of cubes does not start
at the end of the strip.
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
H-11
(MP.3, MP.6) Demonstrate measuring an object incorrectly by aligning the end of the object with
the end of the strip (instead of aligning it with the end of the picture of the cubes), as shown
below. ASK: Is this a good way to measure? (no, thumbs down) Ask students to explain your
mistake.
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
(MP.3) Letting rulers do the counting. Show students a concrete ruler. Discuss the meaning
of the numbers above the cubes on the ruler. ASK: What is drawn above the picture of cubes?
(a number line) What number do you see on the tick that matches the beginning of the row of
cubes? (0)
Draw a line 5 cm long on the board and show how to measure the line using the cubes on the
ruler. Write “5 cubes long” beside the line. Then place the number line side of the ruler below
the line you drew, as shown.
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
SAY: Look, this way the line is 6 units long! Is that correct? (no) Have students explain your
mistake. Emphasize that the line is 5 spaces between the tick marks long. ASK: How should I
place the number line so that I do not need to count spaces? (align with 0) Demonstrate doing
so and show how the number line does the counting.
(MP.6) Have students measure the pictures on BLM Measuring in Centimeters again, this
time using the number line. Emphasize the importance of starting at 0. Point out that since the
distance between each pair of marks on the number line is exactly one cube long, it is like
measuring the pictures in cubes. Beside each measurement in cubes, have students put a
check mark if the answer is the same. Afterward, discuss if students got the same answers
using the number line and the cubes. If not, ask why. PROMPT: Did you forget to line up one
end of the object with 0? Did you count the cubes correctly? Were there so many cubes that you
got lost in the counting? Which way of measuring was easier? Which way was less work? (using
the number line) Why? (because the number line does the counting for us)
Relating the length of small connecting cubes to spaces on a standard ruler. ASK: Do
people usually use pictures of cubes to measure length? (no) What do they use? (rulers)
Explain that a ruler is a tool to measure small lengths. Write “ruler” on the board.
H-12
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
Hand out a standard centimeter ruler and at least 30 small connecting cubes to each student.
Have students look at the ruler. ASK: How is a ruler like a number line? (both have numbers in
counting order; there are equal spaces between the markings) Have students line up the cubes
on the ruler so that they fit in the markings. ASK: What do you notice? (the spaces between the
markings are the same length as the cubes; the cubes fit exactly between the markings) Explain
that the length of each small cube is called a centimeter. People often use centimeters to make
rulers. Write “centimeter” on the board.
Centimeter and cm. Have a volunteer find and circle the letters “c” and “m” in the word
“centimeter.” Tell students that people often write just “cm” for centimeter. Write “cm” on the
board. Have students find the label “cm” on their ruler.
Have students practice measuring by completing BLM Measuring with a Ruler. (1. 4 cm, 2. 5
cm, 3. 6 cm, 4. 3 cm, 5. 7 cm, 6. 2 cm, 7. 2 cm, 8. 3 cm)
Activity
Have students find classroom objects that are about 1 cm long, wide, or high.
(end of activity)
Extension
Have students use a 30 cm ruler to measure objects that are between 20 cm and 30 cm long,
such as a sheet of paper. Have students work in pairs, with each partner measuring the same
objects, one at a time, and then comparing their results. Have them look for any discrepancies.
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
H-13
MD2-4
Length and Subtraction
Pages 182–184
Standards: 2.MD.A.1
Goals:
Students will measure pictures of lines and objects in centimeters using centimeter cubes and a
centimeter ruler.
Prior Knowledge Required:
Count beyond 20
Subtract using a number line
Measure lines and objects that are exact numbers of centimeters long
Compare lengths directly by placing objects side by side and aligning properly
Measure length using non-standard units
Vocabulary: centimeter (cm), length, measure, ruler, unit of measurement
Materials:
a ruler from BLM Concrete Rulers (p. H-33)
1 cm connecting cubes (at least 10)
measuring tape
BLM Subtraction Using a Measuring Tape (p. H-35; see Extension)
Review rulers and centimeters. Remind students that a ruler is a tool to measure length.
Although we can measure length using different units, some units are very common—people
use them in many countries. One of the most common units is the centimeter, which is the same
length as a small connecting cube. When we count units on a centimeter ruler, we count
centimeters.
Counting centimeters as jumps to find the distance on a ruler. Draw a centimeter ruler on
the board and add two arrows as shown below:
0
cm
1
2
3
4
5
SAY: To find how far apart the arrows are, we can jump from one number on the ruler to the
next number, and so on, and count the jumps. Draw the jumps as done on AP book 2.1 p. 182.
Trace the arrows with a finger. ASK: How long is each jump? (1 cm) How many jumps do you
need to make from 0 to 3? (3 jumps) How far apart are the arrows? (3 cm)
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Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
Draw the arrows in several different positions on the ruler, including situations when the first
arrow is not at zero. Have students show the number of fingers equal to the number of jumps
needed to get from one arrow to the other. Record the answer on the board: “The arrows are
___ cm apart.” Have a volunteer fill in the number for each pair of arrows. Progress to a longer
ruler and longer distances.
Point out that when students count jumps on the centimeter ruler, they are actually counting
centimeters. Show the concrete ruler from BLM Concrete Rulers and emphasize that each
jump on a number line is exactly the same as a small cube, so it is exactly 1 centimeter.
Measuring length of lines and objects by counting centimeters. Draw a line 5 cm long and
place a concrete ruler above it as shown:
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15
ASK: How many cubes long is this line? (5 cubes) How many centimeters long is this line? (5
cm) SAY: Instead of counting cubes, we can just count jumps (or centimeters) on the ruler.
Move the ruler below the line so that the line starts at 2 and ends at 7. Show how to count
centimeters on the ruler to find the length.
Draw several different lines (not starting at zero) above the ruler and have students find each
length by counting centimeters. Use lines that are shorter than 10 cm so that students can
signal the answer by holding up the correct number of fingers. Write on the board:
The line is ____ cm long.
Have a volunteer fill in the answer. Repeat the exercise using pictures of objects instead of
lines.
(MP.4) Counting jumps and subtracting on a number line. Help students recall counting
jumps when subtracting on a number line. For example, for 8 – 5, have students sketch a
number line between 5 and 8, and count the jumps as shown. Have a volunteer write the
subtraction.
8–5=3
5
6
7
8
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
H-15
SAY: We can use subtraction to find how far apart arrows are or how long an object is. Above a
ruler, draw a line that starts at 5 and ends at 8, as shown below. ASK: How long is the line? (3
cm)
0
cm
1
2
3
4
5
6
7
8
9
Above the ruler, draw another line that starts at 2 and ends at 6. SAY: Write the subtraction to
find the length of the line. (6 – 2 = 4; the line is 4 cm long) Repeat with other lines. Include lines
that start at zero and longer lines.
Distance from zero. Draw two arrows, one at 0 and another at 7, as shown below:
0
cm
1
2
3
4
5
6
7
8
9
ASK: How far apart are the arrows? (7 cm) SAY: The second arrow is 7 cm away from 0. Draw
an arrow at 5. ASK: How far from 0 is the arrow? (5 cm) ASK: Do you need to count jumps or
subtract to find how far away from zero an arrow is? (no) How else can you do it? (just look at
the ruler) How do you know? (the second arrow points at the answer) SAY: We can count jumps
to find a distance or we can let the ruler do the counting for us.
Extension
Explain that a measuring tape is like a very long ruler, rolled into a tight roll. Show students a
measuring tape. Have students use BLM Subtraction Using a Measuring Tape to subtract
two-digit numbers to find the length.
Answers: 2. 41 – 36 = 5, 5 cm; 3. 67 – 61 = 6, 6 cm; 4. 88 – 84 = 4, 4 cm; 5. 73 – 69 = 4, 4 cm;
6. 95 – 88 = 7 cm, 7 cm; 7. 71 – 59 = 12 cm, 12 cm; 8. 92 – 77 = 15, 15 cm
H-16
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
MD2-5
Measuring to the Closest Centimeter
Pages 185–187
Standards: 2.MD.A.1
Goals:
Students will measure length to the closest centimeter.
Prior Knowledge Required:
Count numbers beyond 20 in order
Subtract using a number line
Measure lines and objects that are exact numbers of centimeters long
Compare lengths directly
Measure length using non-standard units
Vocabulary: about, centimeter (cm), closer to, closest, exactly, length, measure, ruler, unit of
measurement
Materials
2 cm connecting cubes or 5 cm paper clips (10–15 for each student)
a pencil, a marker, a pencil case, and an eraser for each student
30 cm rulers
10 pattern block squares for each student
measuring tape
several small curved objects (e.g., cup, water bottle)
Review measuring in different units. Help students recall what they know about units of
measurement. ASK: What different units have you used to measure the length of objects?
(connecting cubes, paper clips, centimeters) How do you measure objects correctly? (use units
that are the same length; place units in the same position; leave no gaps or overlaps between
units) Give each student 10–15 large connecting cubes or paper clips and ask them to make a
chain. Remind students how to measure length using a chain, before having them find a
classroom object that is an exact number of units long. ASK: How long is the object?
Length and “closer to.” Draw two rows of connecting cubes separated by a line that is
between 5 and 6 connecting cubes long, as shown:
ASK: How long is the line? Is it longer or shorter than 5 cubes? (longer) Is it longer or shorter
than 6 cubes? (shorter) SAY: We can see that the line is not exactly 5 cubes long and not
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
H-17
exactly 6 cubes long—the line is between 5 and 6 cubes long. I would like to know if the line is
closer to 5 cubes long or closer to 6 cubes long. Write the words “closer to” on the board.
Highlight the distance between the end of the line and the last cube above and below it, as
shown below:
Explain that the line is closer to 5 cubes, so we say the line is about 5 cubes long. Write “about”
on the board. Repeat with lines of different lengths. Record the length each time on the board:
“The line is about ___ cubes long.” Have a volunteer fill in the number.
Measuring to the closest unit. Pick an object that is not an exact number of connecting cubes
(or paper clips, depending on the units that students are using) long and demonstrate
measuring it with large cubes.
ASK: Which measurement is the length closest to, 4 cubes or 5 cubes? (4 cubes) ASK: Which
cube is the pencil closest to? Show what you mean by tracing the horizontal distance from the
end of the fourth cube to the end of the pencil; then trace the distance from the end of the pencil
to the end of the fifth cube.
For the exercise, provide students with large connecting cubes to measure a variety of objects.
Have them work in pairs to check each other’s answers by measuring the same objects and
checking that the answers are the same.
(MP.6) Exercises: Use cubes to measure the object. About how many cubes long is the object?
a) pencil
b) marker
c) pencil case
d) eraser
Sample answers: a) 7 cubes, b) 5 cubes, c) 10 cubes, d) 1 cube
Review using a ruler to measure. ASK: What do people often use to measure an object?
(ruler) Hold up a centimeter rule and ASK: What are the units on this ruler? (centimeters)
Remind students to align the zero mark on a ruler with the end of the object they are measuring.
ASK: How does the ruler count the centimeters for you? (the end of the object points to the
answer on the ruler)
Measuring to the closest centimeter. Draw a ruler on the board and draw a line that ends
between two centimeter marks. ASK: How many centimeters long is the line? Have students
signal the answer by raising the correct number of fingers. Repeat several times by drawing
H-18
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
lines slightly shorter and slightly longer than an exact number of centimeters. Then SAY: When
a line is exactly halfway between two units, we use the longer measurement.
Draw or show the pictures below and then SAY: The line is about 6 cm long.
0
cm
1
2
3
4
5
6
Have students use a centimeter ruler to measure the objects in the exercise. Have them work in
pairs to check each other’s answers.
(MP.6) Exercises: Use a ruler to measure the object. About how many centimeters long is the
object?
a) pencil
b) marker
c) pencil case
d) eraser
Sample answers: a) about 14 cm, b) about 10 cm, c) about 21 cm, d) about 2 cm
Extensions
1. Have students make a row of 10 pattern block squares and measure its length to the closest
centimeter.
Answer: 10 pattern block squares are about 25 cm long.
2. Teach students to measure round or curved objects, such as a cup or a water bottle, using a
measuring tape.
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
H-19
MD2-6
Estimating in Centimeters
Page 188
Standards: 2.MD.A.1, 2.MD.A.3
Goals:
Students will use finger width to estimate length in centimeters. They will compare their
estimates to measurements made using a centimeter ruler.
Prior Knowledge Required:
Count numbers beyond 20 in order
Measure length to the closest centimeter using a ruler
Vocabulary: about, centimeter (cm), closer to, estimate, exactly, length, measure, predict,
ruler, unit of measurement
Materials
30 cm rulers
small objects (e.g., small paper clips, play coins)
finger paint
cardboard rectangles
a pencil case
a pencil, a lunch bag, an eraser, and an index card
a stick or meter stick
1 m sparkly gift wrap ribbon for each student
BLM Table Template (p. H-36)
BLM Lights (p. H-37; see Extension)
NOTE: If you plan to do Activity 1, divide it into two parts. Have students complete the first part
before recess, lunch, or another break in the day to allow time for fingerprints to dry.
Using finger width as a benchmark for 1 cm. Give each student a ruler. Have them place
each finger in turn, including the thumb, between the grid marks on the ruler. ASK: Which finger
is closest to 1 cm wide? Which finger is farthest from 1 cm wide? Students will need this
information for Activity 1. SAY: One of your fingers is not exactly 1 cm wide but it is pretty close.
So, you can use that finger to measure in centimeters when you need an answer that is close to
an exact answer.
Measuring short objects using finger widths. SAY: We cannot use many copies of the same
finger to measure something because we have only two copies of the finger we need. Your
pointer, middle finger, and ring finger are all about the same width, so for small objects that are
about 3 fingers long or less, you can use 2 or 3 fingers placed close beside each other. Have
students use 2 or 3 fingers placed close beside each other to estimate the length of a small
object, such as a small paper clip or a penny.
H-20
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
Using only one unit to measure. Draw a line 10 cm long on the board. ASK: Are 3 fingers
enough to measure this? (no) Explain that a different technique is needed. Measure the line
using both index fingers by placing one index finger on the line and alternating with the other
one, as shown below (put chalk or ink on your finger to make fingerprints). Record the length.
Then have a volunteer measure the line using his or her index fingers.
Explain that when you think and then guess about something, you predict. Predict means to
guess based on what you know. Have the class predict which measurement will be closer to the
measurement in centimeters (a student’s finger is closer to 1 cm in width, so the estimate using
a student finger is better). Measure the line using a ruler. Then place your index finger and the
volunteer’s index finger between the markings on a ruler to see whose finger is closer to 1 cm
wide.
Activity 1
Using fingerprints to measure. Distribute paint and cardboard rectangles of various lengths.
Have students use fingerprints (from the same finger) to measure the length of the rectangles.
Make the rectangles wide enough so that students can write or finger-paint the number of
fingerprints as well. Have students measure each length twice: using the finger closest to 1 cm
wide and then using the finger farthest from 1 cm wide.
8
6
Wait until the fingerprints have dried to continue the activity.
Have students circle the measurement that they think will be closest to the actual measurement
in centimeters. Then have them measure the length of the rectangle using a ruler. ASK: Was
your prediction correct? How close was that fingerprint measurement to the actual centimeter
measurement?
(end of activity)
Introduce estimate. SAY: A guess based on what you know is called an estimate. The more
you know, the closer an estimate will be to the correct answer. Write “estimate” on the board.
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
H-21
Emphasize that an estimate is not just a guess; it is a guess based on information. To estimate
means to think and then guess.
Explain that students can use finger width as an estimate for 1 cm. Have students estimate the
length of their pencil cases.
Recording information in a table. Explain that when we need to record a lot of information that
is similar, such as lengths of objects, it makes sense to use a table. Draw a table as shown.
SAY: This table has 2 columns (trace down each column with your finger).
Object
Estimate
Provide students with BLM Table Template. Have them write the labels in the first 2 columns of
the top row. Explain to students that they will learn how to fill in the table. SAY: In the first
column, you will write the name (or draw a picture) of an object you will measure (trace down
the column with your finger). In the second column, you will write your estimate of its length.
SAY: This is a row (trace across the row with your finger). Demonstrate how to fill in the first row
for a pencil case. In the first column, write “pencil case.” Have students do the same. Ask a
volunteer to use his or her finger width to measure the pencil case. In the second column, write
“about ___ cm.” Ask the volunteer to fill in the missing number. Have students do the same
using their estimate of its length.
Fill in the first column of the table with the names of the objects in the exercises, and have
students do the same in their table. Then point to a cell in the second column of the table. ASK:
For which object will you write the length here? Repeat by pointing to each cell in the second
column. Tell students to place the eraser on the cell that shows its length.
For the exercise, have students use the BLM to record their answers.
Exercises: Measure the longest side of the object. Use the finger that is closest to 1 cm wide.
a) pencil
b) lunch bag
c) JUMP Math AP book
d) eraser
e) index card
Sample answers: a) about 18 cm, b) about 24 cm, c) about 28 cm, d) about 4 cm, e) about 12
cm
Measuring to check the estimate. Explain to students that they will check their estimate for
each object and record the information. Point out that the table on the BLM has 3 columns. Add
a column to the table on the board, and label it “Measurement.”
Object
Estimate
Measurement
Have students label the third column on their copy of the BLM. Point to a cell in the third column
of the table. ASK: For which object will you write the length here? Repeat by pointing to each
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Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
cell in the third column. Tell students to place a paper clip in the cell that should show the actual
length of their lunch bag. Demonstrate how to fill in the third column for the pencil case. Ask a
volunteer to measure the pencil case. In the third column, write “___ cm.” Ask the volunteer to
fill in the missing number. Have students do the same.
Have students use a centimeter ruler to measure each object from the exercise and record the
measurement in the table. Then have volunteers fill in the measurements in the table on the
board. Point to different cells in the second and third columns of the table and have students
identify what each cell shows (for example, estimate for the length of a pencil case,
measurement for the length of a pencil).
Estimating centimeters without using fingers. Have students estimate how many
centimeters long, tall, or wide objects are and then check using a ruler. Choose objects that are
less than 30 cm long. To estimate, students should make educated guesses based on their
experiences with centimeters thus far. Have students record their work on BLM Table
Template.
Activity 2
(MP.2) On a stick or on the back of a meter stick make markings of 10 cm, 20 cm, 30 cm, and
so on from the end of the stick. Label the marks clearly. Explain that the markings show the
distance from the end of the stick. Use the stick to play an estimation game with students. Ask
them to tell you to stop when your finger has reached 15 cm from the end of the stick. Slide a
finger slowly along the stick and then mark the place where students tell you to stop. Have a
volunteer measure the distance and check the guess. Repeat with other distances. Students
can play the game in pairs with one partner sliding a finger along the stick and the partner telling
when to stop. Have partners measure the distance from the end. Have partners switch roles
after each round.
(end of activity)
Extension
(MP.1) Give students BLM Lights. Tell students that they will decorate a picture of a house with
ribbon. The ribbon will represent the outdoor lights that people use to decorate their house for a
holiday. Explain that they will glue the ribbon on the thick lines of the house (and the door and
window) but that you are not sure how much ribbon will be needed. To find the length needed
for each feature, have students estimate the length of each thick line and then measure it. Have
them add the lengths. Then give students a length of gift wrap ribbon and have them measure
and cut the length needed for each feature.
Answer: 77 cm of ribbon
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
H-23
MD2-7
Estimating in Meters
Page 189
Standards: 2.MD.A.1, 2.MD.A.3
Goals:
Students will estimate measurements in meters. They will compare their estimates to
measurements made using a meter stick.
Prior Knowledge Required:
Count numbers in order
Measure length to the closest centimeter using a ruler
Measure length to the closest unit
Know that length can be measured in different units
Vocabulary: about, centimeter (cm), closer to, estimate, exactly, length, measure, meter (m),
meter stick, predict, ruler, unit of measurement
Materials
meter sticks
several objects close to 1 m in length, including a baseball bat and a scarf or a piece of yarn
1 m length of string for each student
newspapers
masking tape
scissors
Introduce meters. SAY: I would like to measure the length of the classroom. Do you think it
would make sense to use connecting cubes? Why? Do you think we have enough cubes? How
else could I measure the length in a faster and easier way? Explain that measuring a long
distance, such as the classroom, requires hundreds of cubes, paper clips, or centimeters. SAY:
We use meters to measure long distances. A meter is about the same length as a meter stick.
Write “meter” on the board.
(MP.2) Show students a meter stick and ask them to think of other objects that are about the
same length or height as a meter (e.g., a baseball bat, a child’s golf club, a 4-year-old child, a
bus wheel). If available, show students some of these objects, including a baseball bat and a
piece of yarn or a scarf 1 m long. If the meter stick has a small space between the end and the
start of the number line, point that out, and explain that a meter is slightly shorter than the meter
stick.
Meter and m. Have students recall the short form for centimeter (cm). SAY: You know that
people often write just “cm” for centimeter. They also often write just “m” for meter.
H-24
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
Explain that 1 m is 100 cm long. Write on the board:
1 meter = 100 centimeters
1 m = 100 cm
Invite a volunteer to circle the common letter(s) in the whole word and the abbreviation for each
unit (m and cm, respectively).
(MP.2) Activity 1
Finding benchmarks for a meter. Demonstrate how to check that a length of string is 1 m long
(line up the string with a meter stick and check that the string starts at 0 and ends at 100 cm).
Give each student a 1 m length of string. Have them verify that the string is 1 m long. Then have
students use the string to find classroom objects that are about 1 m in length, width, or height,
and objects that are more than and less than 1 m in length, width, or height. Suggest that
students include distances, such as the distance around the seat of a chair or the distance from
the floor to a door knob. Afterward, have students share the objects that are about 1 m long.
(end of activity)
Using meters to measure. SAY: Predict how many meters long the blackboard is.
Demonstrate how to measure the blackboard correctly using a meter stick. If the meter stick is
slightly longer than 1 m, show making a mark at exactly 100 cm (not at the end of the stick).
SAY: You make a mark at exactly 100 cm because that is how long a meter is. Then
demonstrate measuring incorrectly by holding the stick diagonally and making a mark at 100
cm. Have a volunteer make the mark correctly by holding the stick straight along the board.
(One way to ensure the stick is straight is to align it with the blackboard ledge.)
Review measuring to the closest unit. Point out that the blackboard is longer than, say, 3 m,
but shorter than, say, 4 m. Compare the distance from the last marking. ASK: Is the leftover
distance close to 1 m or much smaller than 1 m? Is the blackboard about 3 m long or about 4 m
long?
Activity 2
Making a meter stick. Have students roll up a newspaper tightly and tape it with masking tape.
Model rolling up newspaper diagonally so that the ends are only one layer thick and easier to
cut. Help students cut the newspaper roll so that it is exactly 1 m long by lining up the roll with
the 0 and 100 cm marks on a meter stick. As a class, use multiple meter sticks to determine
how many meter sticks long the classroom is from side to side and from front to back.
At the point when an additional whole meter stick will not fit in the remaining space, show
students how to estimate the remaining distance by placing another meter stick so that the last
stick in the row and the additional stick overlap as shown.
gap
overlap
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
H-25
Which is larger, the gap or the overlap? If the gap is larger than the overlap, the total distance is
closer to, say, 7 m. If the overlap is larger than the gap, the total distance is closer to 6 m.
(end of activity)
Measuring with only one meter stick. ASK: Is the hallway wider than the classroom? Is it
wider than the classroom is long? Ask students to predict the width of the hallway. Then have
students use their meter sticks to measure the width of the hallway. Have them use small pieces
of masking tape to mark the end of each stick measurement. Students can verify their
measurements by using multiple meter sticks to measure.
(MP.2) Using a benchmark to predict and then check. On the board, list the lengths of items
that students have already measured (for example, blackboard: about 3 m wide). Pick an item
not on the list (for example, a window). ASK: What item on the list is closest to the width of the
window? Is the item larger or smaller than the window? SAY: The window is smaller than the
blackboard, but larger than the door. The door is about 1 m wide and the board is about 3 m
wide. What is a good estimate for the window? (about 2 m) Have students check the prediction.
Repeat with several more items.
Use units that are about the same size to find approximate measurements. SAY: Remind
me about what makes a good unit of measurement. (It is easy to find many units the same size.)
SAY: I want to tell a friend how long the school hallway is. She does not need to know exactly
how big it is; she just wants an idea. I plan to take big steps all the way down the hall to see how
many steps it takes. Do you think my steps are good units? Can I take many steps that are all
the same size? Will my steps be at least close to the same size? Even though steps are not all
exactly the same size, they will all be close to the same size if I try to take big steps all the time.
This will not tell me exactly how long the hallway is, but it will give me a good idea. Sometimes,
that is all you need.
Large steps are about a meter long. Mark three long lines 1 m apart on the floor. Have
students stand with their heels on one line, facing the second line, and take a step so that their
toes touch the second line. Have students practice taking a step in this way several times. For
multiple steps, show students how to lead off with the same foot each time: take one giant step
(positions 1 and 2 below); bring the back foot forward and place it in front of and to the side of
the first foot, with the heel directly in front of the front toe (position 3); bring the back foot forward
beside the front foot (position 4), then take another giant step (position 5).
2
1
4
5
3
Step 1
Step 2
Have students take 5 steps that they think will be about 1 m each, and have a partner check
using a meter stick. Emphasize that it is much harder to take 5 big steps all in a row than 5
steps walking normally.
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Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
(MP.5) SAY: I want to know about how many meters long the hallway is. Have students take
giant steps along the hallway to help you find out. Remind them to take identical steps and to
lead off with the same foot each time. Then have a volunteer use a meter stick to measure the
length of the hallway. ASK: Did we get the same answer both ways? Were our answers close?
Which way was faster? Explain that when the answer does not have to be exact, we can save
time using giant steps instead of meter sticks. Discuss situations where it is important to know
exact measurements. Examples: competing in a race, ordering glass to fix a broken window,
making a ruler to sell, making paper to put in a book, and making legs for a table.
Estimating distances using a giant step. Have students predict the distance in meters to,
say, the school library. Have them measure the distance in giant steps to check predictions.
Allow students to adjust their prediction after measuring part of the distance.
Repeat with another location at school. Have students think about whether the new location is
farther or closer than the previous one. ASK: Should the estimate be larger or smaller than the
distance just measured? Measure to check the estimates, allowing students to adjust their
estimate after measuring part of the distance.
Extensions
(MP.3) 1. SAY: Let’s estimate how many students with outstretched arms we will need to go all
the way across the room. Will this give an exact measurement of how wide the classroom is?
Why? (no, because the outstretched arms of students are not all the same length even though
they are close) Will we need more or fewer students than meter sticks? What do you predict?
Are outstretched arms longer or shorter than a meter stick? (longer, so we will need fewer
students) Have students use outstretched arms to measure the width of the classroom as
shown. Then have students measure the width using meter sticks and compare the actual width
with their prediction. ASK: Was your prediction correct? Explain.
2. When students are not in the room, draw two lines on the board, both 1 m long, with arrows
at the ends as shown. Ask students to predict which line is longer. (Ignore the arrows.) Then
have a volunteer check by comparing both lines to a self-made meter stick.
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
H-27
MD2-8
Making a Ruler
Pages 190–192
Standards: 2.MD.A.1
Goals:
Students will create their own rulers.
Prior Knowledge Required:
Count numbers to 20 in order
Measure length to the closest centimeter using a ruler
Measure length to the closest unit
Know that length can be measured in different units
Vocabulary: about, centimeter (cm), closer to, estimate, exactly, length, measure, meter (m),
meter stick, ruler, unit of measurement
Materials
objects that can be used as units (e.g., play coins, new erasers, markers, paper clips,
connecting cubes)
strips of paper
masking tape
rulers
modeling clay (see Extension 2)
Review number lines. ASK: How are rulers the same as number lines? (the markings are
equally spaced; the numbers go in order and start at 0; both are tools that do the counting for
you). How are rulers different from number lines? (rulers have units written on them; the space
between the marks is exactly one unit long)
Review using only one copy of a unit to measure. Remind students that when they measure
using fingers, they alternate between their index fingers and place their fingers one beside the
other to make sure there are no spaces or overlaps between units. Remind them to make a
mark where a unit ends, and then align the next unit with the mark.
Making a ruler. Tell students that they will make their own ruler using an object of their choice
as the unit. They will need a pencil and a ruler to make marks and a strip of paper to make their
own ruler. Prepare stations with a variety of objects that can be used as units (for example, play
coins, new erasers, markers, paper clips, cubes), masking tape, and strips of paper. Discuss
problems that might arise with different units—how to align and keep them in place. For
example, for play coins, tell students to place several identical coins in a straight row on a strip
of paper (align the coins with a straight edge, such as a book), and hold them in place using a
long strip of tape across the coins. Have them use a ruler to make the marks. Show how to do
H-28
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
so. For paper clip chains, show students how to place the ruler (used to make the marks) the
same way each time.
Correct: The marks are at the beginning of each paper clip.
Incorrect: The marks are at different ends of the paper clips.
(MP.6) After students have drawn the marks, tell them to remove the objects they used to make
the ruler. Have students complete their own ruler. Remind them to start the number line on the
ruler at zero, and write numbers in order. As you circulate, check that they do not skip numbers.
If there is time, invite students to use a different object to make a ruler. Have students write the
unit they used on each ruler. Invite students to use their rulers to measure lengths of different
classroom objects.
Extensions
1. Have students choose an object and measure it using the rulers produced during the lesson.
If students made only one ruler, have them work in small groups and use each other’s rulers.
How long is the object in terms of each unit of measurement? Have students record the
answers in different units. Example:
Tessa’s lunchbox is about 5 large paper clips long.
Tessa’s lunchbox is about 6 erasers long.
Tessa’s lunchbox is 12 pennies long.
Emphasize that the length of the lunchbox does not change. The different answers result from
using different units. Students might observe that as the unit of measurement gets smaller, the
number of units that fit along the object gets larger, and the number part of the measurement
gets larger.
2. Have students watch the animated film 38 Parrots. Use a version with English subtitles and
read the subtitles to students. The characters discuss how to measure the length of a snake and
measure it in different units: parrots, monkeys, and elephants.
Discuss the units used in the animated film. ASK: Are parrots used to measure length? Explain.
(no, parrot strides) Is a parrot stride a good measurement unit? (yes, good for estimating) What
similar unit do we use to estimate length? (giant steps) Are monkeys used to measure length?
Explain. (no, cartwheels) Is a cartwheel a good measurement unit? Explain. (yes, good for
estimating) Are elephants used to measure length? Explain. (no, wrapping the snake around the
elephant) Is that a good way to measure length? (no) Have students use modeling clay to make
a snake and then try to wrap it around a free-standing object in the same way as shown in the
film. Have students mark the same spot on the snake and then unwrap the clay and measure
Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data
H-29
the distances between the markings. Students should observe that the markings are not the
same distance apart.
Students can measure the clay snakes using the rulers they made during the lesson. Discuss
the conclusion made by the characters in the animation. If a snake measures about 5 paper
clips and about 8 pennies, is it “longer in pennies”? (no) Explain that the snake is the same
length but that using different units results in different numbers. As the unit of measurement
gets smaller, the number of units that fit along the snake gets larger, and the number part of the
measurement gets larger.
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Teacher’s Guide for AP Book 2.1 — Unit 7 Measurement and Data