Grade 2 Linear Measurement-­‐ Conceptual Lessons Type of Knowledge & SBAC Claim RK-­‐ 2, 3, 4 Lesson Title and Objective/Description Hook Lesson: Designing a Shoe Cover In this hook lesson, students will come to understand that one foot is a standard measure and not the same as the size of their foot by designing a shoe cover, trying on and analyzing different classmate’s covers. C, RK-­‐ 1, 2, 3, Measurement Olympics 4 Students will compete in games that all involve linear measurement in the measurement Olympics. Each team will be given a different measurement tool and final results will compare the numbers only (not taking units into account). By comparing results, students will understand the necessity to use a common measurement tool to be able to compare results. C, P-­‐ 1, 2, 3 Building a Foot Students will estimate the length of objects using a unit of 1 (1 inch), and then attempt to measure by iterating the one unit. Students will then tape 12 units together and label each whole unit length as 1 inch to understand how to use a ruler as well as the relationship between inches and feet. C, P-­‐ 1, 2, 3 Building a Meter Students will estimate the length of objects using a unit of 1 (1 cm), and then exchange 10 ones for a ten rod, and line up 10 of these, labeling each whole unit length as 1 cm to understand how to build and use a meter stick as well as the relationship between centimeters and meters. P-­‐1 Practice Measuring in cm, inches, meters or feet C, RK-­‐ 1, 2, 3 Measurement Graphing Challenge CM vs In Students will estimate the height of objects in inches, then measure, and then predict the height in centimeters, and then measure. Students will graph the data and use what they notice to determine the approximate Suggested Time Frame Math Practice embedded 1 class period 3, 4, 5, 6 1-­‐2 class periods 1, 2, 3, 6, 7 1-­‐2 class periods 5, 6, 7, 8 1-­‐2 class periods 5, 6, 7, 8 1-­‐2 class periods 1 class period 1, 2, 3, 7 1 LM_T1
height of an object for which a) they know its measure in one unit but not the other or b) for which they do not know anything about its measure, but for which they can compare it to objects they have measured. C-­‐ 1 Who is the Farthest Students will move a given number of steps on number lines marked in different units to compare how long each unit is and how the size of the unit relates to the distance measured. C, RK-­‐ 1, 2, 3 Estimate, Throw, Compare Challenge Students will choose a unit and estimate how far they can throw something. They will throw and measure the estimated distance and actual distance and represent the difference with a number sentence and on a number line. Practice/Problem Solving-­‐ Inverse relationship between size and number of units C, RK-­‐ 1, 2, 3 How Much was Cut? Students will measure a length of string, cut some from it, measure what remains and then estimate and measure to determine how much was cut. Students will represent the scenario with a bar model and an addition or subtraction equation. Students will use this experience to solve problems involving missing side lengths or sums of measurement lengths. Problem Solving-­‐ Liner Measurement RK-­‐ 2, 3 Shark Bait Students will play a game in which they try to get to the other side, a distance of 10 meters, by asking to take a certain number of steps in certain units and then moving that distance until either crossing or having the Shark turn and tag them. Students will practice measuring in cm, inches, feet, and meters as well as get a better sense for how far each of the units of measure will move them All Summative Assessment NOTES: 3 Week Unit Addresses Standards: MD 1, 2, 3 & 6 Types of Knowledge: Facts (F) Procedures (P) Concepts (C ) Relational Knowledge (RK) 1 class period 1, 2, 3, 7, 8 1 class period 1, 2, 3, 5 1 class period 2 class periods 1, 2, 3, 5, 7, 8 1 class period 1 class period 1, 6 1 class period SBAC Claims: 1) Concepts & Procedures 2) Problem Solving 3) Communicating & Reasoning 4) Modeling & Data Analysis 2 LM_T2
Teacher Directions
Materials:
◊ Colored paper, Tissue Paper (easiest to work with) or construction paper (a few
sheets per student)
◊ Colored Pencils
◊ Scissors
◊ Tape
◊ Book, “How Big is a Foot” by Rolf Myller
Objective:
In this hook lesson, students will come to understand that one foot is a standard measure
and not the same as the size of their foot by designing a shoe cover, trying on and
analyzing different classmate’s covers.
Directions
Pass out the activity sheet and have a student read the background. If needed, show a few
pictures of shoe covers and ask if anyone has ever seen these used (they are typical in a
hospital surgery room or if visiting a new house, etc.) Ask another student to read the
task. Help the class understand that their cover must cover the bottom of their shoe. It is
fine if they cannot make it fold well to cover the top part of the shoe; they can just fold up
the end of the paper by their heel and toes and alongside the width (so they can make an
open box). Set the time for 15 minutes for the shoe design.
Once 15 minutes have passed, explain that students will now critique each other’s shoe
cover designs. Go over the table provided to rate the covers and complete a sample.
Choose one student’s design and hold it up under your shoe. Ask the class what they
would choose to represent the fit: too big, too small or just right. Circle this and then ask
for a few comments, such as “this would not work as it is way too short”. Now decide
what rating you would give design and give a comment. Once the class understands,
have them number off into 1’s and 2’s. Have the 1’s bring their shoe cover and paper and
stand around the perimeter of the room (facing the center). Have all the number 2’s take
their shoe cover and paper and stand facing a #1. When they begin with their partner,
they have 30 seconds to explain their shoe cover design and then they must trade shoe
covers, try them out and complete the rating. Allow 5 total minutes for this. At the end
of 5 minutes, ask the # 2’s to rotate 1 person to their right. Repeat the process (another 5
minutes) and then have the # 2’s move one last time (so everyone has had 3 partners).
Ask the class to return to their seats. Use think-pair-share to have students answer the
analysis questions (#’s 1-4). Below are the big ideas:
1) Likely not, as the teachers foot is longer than yours.
2) 1 foot (1 of their “feet”)
3) Most students have a different length foot.
4) Explain how long a foot is with a standard unit or have them measure by iterating
(repeating) one unit (such as a unifix cube)
Read the class the story, “How Big is a Foot?”. Close out the lesson by having students
record their ideas to question #5.
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Materials: See page 4 for Set-Up
Teacher Directions
Objective: Students will compete in games that all involve linear measurement in the measurement
Olympics. Each team will be given a different measurement tool and final results will compare the numbers
only (not taking units into account). By comparing results, students will understand the necessity to use a
common measurement tool to be able to compare results.
Running the Olympics
Begin by putting the students into groups of about four and give them 2 minutes to come up with a team
name (it does not have to be a country).
Depending upon the help you have, you can have everyone complete the same event at the same time (in
multiple stations) or you can have groups rotate to stations where adults are overseeing each one. Either
way, you need all the groups to complete in all four events. You only need the measure of the best single
trial from each team for each event!
Before doing any event, model what to do and the rules for the event, stressing the fact that each person gets
three trials and they only measure the best trial.
Give each team their measuring tool, being discreet. Have each group try to keep their tool as a secret. After
a team has completed an event, have them record the BEST score from their group on the class chart (see
below for what to project or create on the board). They should record ONLY the numbers, not the tool/unit.
Note: Participants should have some complaints (i.e. they figured out that they all have different measuring
tools); let them know that they will be able to voice their complaints later to the Olympic committee (you).
If not, ask prompting questions, such as, “was this country really that much better than everyone else?”
Once all the final results are up, circle which group wins each event. Give each group 3-5 minutes to discuss
if the results were fair or if they have any complaints to bring to the committee. Each group can record their
appeal on the bottom of their activity sheet and have a representative present an argument to you as to why
the results are not fair or accurate (have each group share aloud with the class listening). Lead the discussion
to have students conclude that it is not fair to compare the results if everyone used a different tool to
measure. Ask what they could do to decide who really won. Ask questions to guide the class to agree they
could all use the same tool, in particular, unit cubes (or rulers) would work well.
Explain that it would take a while for each group to measure everything again, but you can use what they
told you to write each result in terms of unit cubes. Tell them you will do this later today or before
tomorrow so they can know who did win.
Tell the class you are going to play a detective game and show them the measurement tools for each group
(but don’t say which group had which tool). Give the groups 5 minutes to try to figure out which group used
each tool based upon the results on the board. Call on each group to share one prediction they are confident
with and ask them to explain why they chose this.
Ask the class how this activity relates to the book, “How Big is a Foot?” that you read during the previous
lesson.
Later in the day or before the next day, convert each measuring tool to unit cubes or cm and write up the
final results so you can announce the winners.
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Event Descriptions- to be copied onto cardstock and made as table tents by each event.
Q-Tip Throw
From behind the starting mark, throw a Q-tip as far as you can. Using your unit of measure,
determine how far your Q-tip went (measure from the tape to the furthest end of the Q-Tip).
Everyone on the team gets three tries; measure the result that went the furthest and
record the result on your sheet.
Cotton Ball Blow
Place your cotton ball on the starting mark. Sit or stand behind the table and use your straw
to blow the cotton ball as far as you can with one breath. Everyone on the team gets three
tries; measure the result that went the furthest and record the result on your sheet.
Please throw out your straw when done.
Styro-peanut Serve
From behind the starting mark, serve (throw and then hit over hand or underhand) the peanut
as far as you can. Everyone on the team gets three tries; measure the result that went the
furthest and record the result on your sheet.
Dice High Jump
Begin this competition seated on the floor. Using a die, your goal is to underhand hit the die
as high up as possible so that it goes over the rope. Begin with your partners holding the
rope at whatever height you want to try. If you succeed at a height, have your partners raise
the rope. You are finished when you miss three times. The next person starts from the
height that the last person was able to make it over. Measure the result from the last
height (this should be the highest) and record the result on your sheet.
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Teacher Directions- Set-up
Measuring Tools
◊
Each team should have a different measuring tool (hands, feet, popsicle
sticks, pieces of paper, a string, post-it notes, etc)
Q-Tip Throw Station
◊
Put down a piece of masking tape to mark the starting point.
◊
Box of Q-tips
Cotton Ball Blow
◊
Clear a long table with a piece of masking tape to mark the starting point.
◊
Post-it notes (so that people can mark how far the cotton ball goes)
◊
Cotton Ball
◊
Straws (1 per student)
◊
Trash Can for disposal of straws
Styro-peanut Serve
◊
Put down a piece of masking tape to mark the starting point.
◊
Styro-peanuts
Dice High Jump
◊
Rope- about 5-10 feet in length
◊
Foam Dice (nice to have a few)
◊
Chairs or somewhere safe on which two people can stand to hold rope.
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Teacher Directions
Materials:
◊ Copies of unit of “1” for each student (12 squares each) OR 1inch square tiles or cubes
◊ Ruler- 1 per student
◊ 4 objects the class can measure, one of each of the following lengths: 5 inches, 8 inches,
12 inches and 36 inches. (Ideally, you will have more than one of each object; e.g., 2 pencils
each measuring 5 inches, etc).
◊ Tape for each student (or glue and a 1 foot piece of paper on which to glue the 1 inch
squares)
Objective
Students will estimate the length of objects using a unit of 1 (1 inch), and then attempt to
measure by iterating the one unit. Students will then tape 12 units together and label each whole
unit length as 1 inch to understand how to use a ruler as well as the relationship between inches
and feet.
Directions: Part 1
Pass out 1 unit squares (or a 1-inch tile or cube) to each student and explain that each square has
a length of 1. Show the class 4 objects you have chosen for them to estimate the length of (one
being 5in, 8 in, 12 in and 36 in) and pass out the activity sheet. Have a student read problem 1
aloud and make sure students understand to estimate, given what 1 is. Take a few estimates and
then move onto problem 2. For this task, have each group send two representatives to measure
each object, using only their 1 unit. If you have multiple copies of each object, allow each group
to have one and rotate them around. Pay attention to what groups do to measure; e.g., combine
their units to be longer or mark off each unit as they go.
Bring the class back together and gather the class data. Use purposeful selection to have groups
answer problem 3, beginning with groups who use simpler methods. Use think-pair-share to
have students answer problem 4, with the goal being to see that if they had a lot of units together
or a strip marked in units, it would be faster than just having 1 unit.
Part 2
Pass out 12 one-inch squares to each student as well as tape (or glue sticks and a 1 foot strip of
paper). Model how to glue or tape the 12 unit squares so that they begin at the left end and are
touching, but not overlapping. Have early finishers answer question 1, “What do you think a
ruler is used for?” Once each student has their ruler, make sure they know it is called a ruler and
then model how to label the left edge with a 0. Model how to lay down 1 square (or tile or cube)
and draw a vertical line at the end of this length on the ruler, labeling it with a 1. Have students
repeat this for a length of 2 units, 3 units, up until 12. When done with question 5, they should
have a 12-inch ruler built and labeled in whole units. Have students confirm with a partner how
many 1 units fit in the ruler (should be 12!).
Note: A major struggle in using a ruler is understanding that it is the length from 0 to 1 that
represents 1 unit, so it is important the students connect the length of the blocks to the number
read on the ruler in this next section.
Part 3
Walk the class through the example, showing how to measure with squares/tiles/cubes and then
laying the ruler underneath to connect the numbers on the ruler to the total number of blocks
measuring the length. Have the class now measure the original 4 objects using their tiles or
IMP Activity: Building a Foot
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cubes AND their ruler. Have them record the results in the table, noting they should be the same
as before.
Pass out a real ruler to each student and have them line it up with their paper ruler to find where
the 0-12 line up. If a student asks about the other marks, feel free to ask the class why they think
there are more marks and help them know they will learn to use these to measure more precisely
when objects are between unit lengths.
For question 3, you can either select 4 objects or let each pair choose 4 objects to measure. Have
one student use their paper ruler while the other uses the real ruler. Have them compare results
and trade tools for the next object. Have each pair record their objects and measurement in the
table. Select a few pairs to share how they measured using the ruler.
Part 4
Close out the lesson using think-pair-share to have students answer the questions. Below are
some big ideas to highlight in the discussion.
1) It’s easier than repeating a single unit!
2) 12 inches in 1 foot
3) 24; could be 12 + 12 or they can count 2 rulers, etc.
4-7) Answers will vary.
Units of “1” for Students to use (Each Student needs 12 cut out)
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Teacher Directions
Materials:
◊ Ten “10-rods”, base 10 blocks- 10 per student OR Copies of strip of “10” for each
student (10 strips each)
◊ 10 cm cubes per students (the “ones” of base 10 blocks)
◊ Meter Stick- 1 per pair or group
◊ 4 objects the class can measure, one of each of the following lengths: 10 cm, 50 cm, 80
cm, 100 cm (1 meter). (Ideally, you will have more than one of each object; e.g., 2 erasers
each measuring 10 cm, etc).
◊ a 1-meter piece of paper (suggest width of about 3-4 inches)- 1 per student
Objective
Students will estimate the length of objects using a unit of 1 (1 cm), and then exchange 10 ones
for a ten rod, and line up 10 of these, labeling each whole unit length as 1 cm to understand how
to build and use a meter stick as well as the relationship between centimeters and meters.
Directions:
Note: This lesson should run very similarly to “Building a Foot”.
Pass out 10 cm cubes to each student and explain that the side of each cube has a length of 1.
Show the class 4 objects you have chosen for them to estimate the length of and pass out the
activity sheet. Have a student read problem 1 aloud and make sure students understand to
estimate, given what 1 is. Take a few estimates and then use think-pair-share to have the class
answer problem #2. They should see that it would be very hard to lay that many small units
down to measure. Use think-pair-share to have students answer the first part of problem 3.
Students should recall that 10 ones can be traded for a 10-rod. Give each student 10 of the tenrods and have a group representative use these rods to measure each of the 4 objects and record
their data in the table.
Part 2
Pass out a 1-meter strip of paper to each student. Model how to lay down a 10-rod at the left end
of the strip and then model how to label the left edge with a 0. Model how make a short vertical
line at the end of each 1 cm, and label these lines 1-10, with the 10 getting a longer line. Have
students repeat this for a length of 2 rods, and then continue counting on to label. When done
with question 5, they should have a meter stick built, labeled as 100 centimeters. Have students
confirm with a partner how many 10’s fit in a meter (should be 10) and how many 1 units fit in
the ruler (should be 100). Have students present how they determined this; i.e., 10 added 10
times, counting one-by-one, etc.
Part 3
Have each pair use their paper meter stick to measure the 4 objects for which they estimated
length. Make sure they use cubes/rods, lying end-to-end, for the shortest one to make the
connection between the number of cubes used and the number representing this length on the
meter stick. Select a pair to show how they measured each of the 4 objects and ensure consistent
measurements (give or take a few cm).
Pass out a real meter stick to each pair or group and have them line it up with their paper meter
stick to find where the 0-100 line up. If a student asks about the other marks, feel free to ask the
class why they think there are more marks and help them know they will learn to use these to
measure more precisely when objects are between unit lengths.
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For question 3, you can either select 4 objects or let each pair choose 4 objects to measure. Have
one student use their paper meter stick while the other uses the real meter stick. Have them
compare results and trade tools for the next object. Have each pair record their objects and
measurement in the table. Select a few pairs to share how they measured using the meter stick.
Part 4
Close out the lesson using think-pair-share to have students answer the questions. Below are
some big ideas to highlight in the discussion.
1) It’s easier than repeating a single unit! Most countries use meters.
2) 100 cm in 1 meter
3) 20; could be 100 + 100 or 20 tens or any other way they see to count.
4-5) Answers will vary.
6) Inch- they should recall the length of the 1-inch square as opposed to today’s cm cube.
7-10) Have the class use their paper or real meter stick to get comfortable with using it more
as a number line by joining you in counting aloud as directed. Make sure students touch each
number as they count. This is the foundation of addition and subtraction on the number line
students will begin in future units.
Strips of 10 for Students to use IF you don’t have 10-rods (Each Student needs 10 cut out)
0
1
2
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Teacher Directions
Materials:
• Rulers with inches and centimeters OR student’s paper rulers/meter sticks built in past
lessons (or meter sticks can be used for centimeters as well) • Objects students can measure Objective: Students will estimate the height of objects in inches, then measure, and then predict
the height in centimeters, and then measure. Students will graph the data and use what they
notice to determine the approximate height of an object for which a) they know its measure in
one unit but not the other or b) for which they do not know anything about its measure, but for
which they can compare it to objects they have measured.
Directions:
Choose an object that is longer than your hand, but shorter than your height. Pass out rulers and
have students show each other where they can find the inches. Ask the class to estimate how
many inches long this object is. Pass out the activity sheet and have students record their
estimates on the top in addition to the name or a picture of the object you are using. Have a
student come measure the actual length in inches and have students record this. Next have
students find centimeters on their ruler and show each other where these are. Ask the students to
predict how many centimeters long the same object is. Have the students record their estimates
and then have a few students share. Have a student come measure the object in centimeters and
have the students record the actual measurement.
Put the students in groups of four, and explain that they will repeat the same steps for any 4
objects they choose in the room (including tall things like a door). For each object, they will
record its name (or a picture), estimate the height in inches, measure in inches, estimate height in
centimeters and measure in centimeters.
Once the class understands, set the timer for 20-25 minutes for groups to collect data.
Once data has been collected, model how to graph the data from the 5 objects (the one you did as
a class and the four they picked). Write the names of the 5 objects along the x-axis (horizontal),
skipping a line in between. Have the students do the same for their 5 objects. Next, show how
to draw the bar to go up to the height matching the actual measurement in centimeters. Have
students complete this for the other 4 objects they measured in centimeters. Have the groups
create the graph for inches using the same process.
Bring the class back together for the challenges (described below).
Challenge 1
Pick an object and hold it for the class to see. Measure it using centimeters. Ask each team to
give its best estimate for the length in inches. Record the estimates and ask some teams to
explain how they arrived at their estimate. Measure and see who was closest.
Challenge 2
Pick an object and hold it for the class to see. Measure it using inches. Ask each team to give its
best estimate for the length in centimeters. Record the estimates and ask some teams to explain
how they arrived at their estimate. Measure and see who was closest.
Challenge 3
Pick an object and hold it for the class to see. Do not measure it. Ask each team to give its best
estimate for the length in inches and in centimeters. Record the estimates and ask some teams to
explain how they arrived at their estimate. Measure and see who was closest.
Note: The goal of this lesson is NOT to convert between units! It is to practice measurement and
get a sense of how long objects are in terms of inches and centimeters.
IMP Activity: Measurement Graphing Estimation Challenge CM vs In
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Teacher Directions
Materials:
◊ Number lines drawn in chalk and labeled as follows: 5 marked from 0 to 10 in
centimeters; 5 marked from 0 to 10 in inches; and 5 marked from 0 to 10 in feet
Objective:
Students will move a given number of steps on number lines marked in different units to
compare how long each unit is and how the size of the unit relates to the distance
measured.
Directions
Explain to the class you will be playing Simon Says today and ensure all students
understand the rules of the game. Put the class into teams of two. Have one student
begin on the number line with the other partner waiting at the end of the number line. As
soon as the partner on the number line makes a mistake or gets “out”, partners will trade
roles. Take the class outside and assigns groups of two to each number line.
Simon Says Outside
Begin Simon Says using the statements below.
1) Walk two units forward.
2) Simon says, “Walk two units forward.”
3) How many units are you from 0?
4) Simon says, “Tell me how many units you are from 0?’
5) Who is the farthest from 0?
6) Simon says, “Tell me who is the farthest from 0?”
7) Walk three more units forward.
8) Simon says, “Walk three more units forward.”
9) What number on you standing on now?
10) Simon says, “Tell me what number you are standing on now.”
11) Who is the farthest from 0?
12) Simon says, “Tell me who is the farthest from 0?”
13) Go back to 0.
14) Simon says, “Go back to 0.”
15) Walk 3 units forward and then 4 more units forward.
16) Simon says, “Walk 3 units forward and then 4 more units forward.”
17) What number are you standing on now?
18) Simon says, “Tell me what number you are standing on.”
19) Who is the farthest from 0?
20) Simon says, “Tell me who is the farthest from 0?”
21) Go back to 0.
22) Simon says, “Go back to 0.”
23) Simon says, “Walk forward 8 units and then walk back 6 units.”
24) What number are you standing on now?
25) Simon says, “Tell me what number you are standing on now.”
26) Who is the farthest from 0?
27) Simon says, “Tell me who is the farthest from 0.”
28) Who is the closest to 0?
29) Simon says, “Tell me who is the closest to 0.”
Bring the class back together to sit on the ground. Use think-pair-share to have
students discuss: “Why is it that if everyone was standing on the same number, not
everyone was the same distance from 0.” Lead a discussion to help students
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understand how different units refer to different distances and you need more of a
smaller unit to measure the same distance with fewer of a larger unit.
Part 2 Outside
Select 4 students to compete while the rest of the students sit along the base of the
number lines. Explain that you will make a statement and the four students will race
to the number line of their choice to show their answer. Select a new group of 4
students for each statement below.
Choose your Number Line
1)
2)
3)
4)
5)
6)
7)
8)
9)
Goal: be the farthest from 0 after walking a distance of 2 units.
Goal: be the closest to 0 after walking a distance of 2 units.
Goal: be the farthest from 0 after walking a distance of 6 units.
Goal: be the closest to 0 after walking a distance of 6 units.
Goal: From any given point, walk the least distance when going back 4 units.
Goal: From any given point, walk the greatest distance when going back 4 units.
Goal: Walk the greatest number of steps to get to 10.
Goal: Walk to 10 and take short steps.
Goal: be the farthest from 0 after walking a distance of 3 units, but the “feet”
number line is not available.
Answers :
1) feet
2) centimeters
3) feet
4) centimeters
5) centimeters
6) feet
7) Same (all 10 steps, unless a student argues they had to take steps in between)
8) centimeters
9) inches
Bring the class back inside. Pass out the activity sheet. The students will now do a
similar activity to Simon Says, but using cm and inches. Have students work on problem
sets 1-4. Bring the class together and have students present their answers to these. Use
questions 5-8 as formative assessment. You can use think-pair-share for a few and then
collect the others as a ticket out the door or use other methods to assess if students
understood and can apply the big idea: the smaller the unit, the shorter the distance and
the larger the distance, the farther the distance.
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Teacher Directions
Materials:
◊ Chalk- 1 piece per group
◊ Measuring Tools for each group- rulers, meter sticks, tape measures, yardsticks
(have a number of each and allow groups to choose)
◊ Cotton Balls- 1 per student
◊ Ball to throw (any type)- 1 per group
Objective:
Students will choose a unit and estimate how far they can throw something. They will
throw and measure the estimated distance and actual distance and represent the difference
with a number sentence and on a number line.
Directions
Model the steps students will take in this activity. Explain that you will be throwing a
cotton ball as far as you can. Use think-pair-share to have students decide which unit
would be best to use to measure in and how many of this unit they think you can throw.
(They should realize that meters are too large, but perhaps cm are too small). Use tape to
mark a starting point (explain they will use chalk outside) and then have a student choose
a measuring tool and measure out the class prediction. Place a piece of tape where the
estimate is. Throw the cotton ball. Have a student measure the distance you threw.
Record the estimated distance and the actual distance on the table. Now have a student
measure the distance between the actual and estimated distances (it will work best if you
have a continuous measuring tool lying out from the starting point to the farthest distance
(like a measuring tape) so they can measure from one point to the other.) As a student
counts the number of units, model this in the picture section of the table (see example).
Ask the students to come up with a math sentence to represent the difference (it can be
addition or subtraction). Record this on the table.
Make sure the class understands that they will all predict, all mark their estimate, all
throw, all measure, and all record everyone’s data. Once the class understands, put them
into groups of 4 and give each group 4 cotton balls, 4 activity sheets, 1 piece of chalk and
have them select their measurement tool.
Allow about 10-15 minutes for challenge #1. Note: if the class struggles following
directions, can you do challenge 1 as a whole class, with one group participating and
others sitting, observing and recording. You can also consider using only 2 of the 3
challenges.
Challenge #2 Bring the class together (outside) and have them trade their cotton ball for
an actual ball (you can have different ones for each group). You also need your
measuring tools outside and should allow groups to trade their tool once they decide
which unit they will measure in for challenge #2. Give groups about 10-15 minutes to
complete challenge #2.
Challenge #3 Bring the class back together, collect the balls and explain the final
challenge. Model how to do a 2-footed hop and then allow groups to discuss which unit
they will measure in and which tool they would like. Give groups 10-15 minutes to
collect data for challenge #3.
Bring the class back inside and close out the lesson with the two practice questions. Call
on students to present their solutions and methods, making sure to look for students who
used different methods to calculate.
IMP Activity: Estimate, Throw, Compare Challenge
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Teacher Directions
Materials:
◊ String- about 15-20 pieces per pair, each about 1 foot in length
◊ Scissors- 1 per pair
◊ Rules or Meter Sticks- 1 per pair
Objective:
Students will measure a length of string, cut some from it, measure what remains and
then estimate and measure to determine how much was cut. Students will represent the
scenario with a bar model and an addition or subtraction equation. Students will use this
experience to solve problems involving missing side lengths or sums of measurement
lengths.
Directions
Model game 1 with the class. To do this, take a piece of string and cut some off and
measure what is left. Agree as a class what unit you will use to measure in and always
measure to the nearest whole unit. Record this measurement in the table as “Original
Length of String”. Now choose a student to come up front, turn his/her back to the class
and cut off a piece of this string and hide it. Take what is left and show the class. Ask the
class to estimate how much the student cut off and record this on the table next to the
“estimate”. Now have a volunteer come measure the piece you have and record this in
the table. Have students think silently about how long the hidden piece is. Have students
tell their neighbor how long they think it is and then have your first volunteer who is
hiding the piece show the class and measure it. Record this in the table as “How much is
left”. Finally, show how to use a bar model to represent the scenario and ask the class
what math sentence they would write (try to get as many options as possible- there should
be two addition and two subtraction sentences that can be written).
Once the class understands, pass out the activity sheet, about 15 pieces of string, scissors
and a measurement tool to each pair. Have them decide who partner A and B will be and
make sure they trade roles after each round.
Set the timer for 15 minutes and bring the class back together. Select a few pairs to share
and explain a row from their table.
Game #2
Model how to play game #2. Agree upon which unit you will use to measure. Cut any
length string you want, measure it, but don’t tell the class the length. Have a student
come up and do the same from a new piece of string. Show the class the two pieces of
string lying end-to-end and have them estimate the total length. Write the length of your
piece in the table and then have your volunteer do the same for their piece. Have students
think silently about how long they think the total length will be and then have them tell a
partner. Have another student come measure the total ad record this in the table. Model
how to represent this with a bar model and equation. Once the class understands, give
them 15 minutes to play this game.
Bring the class back together. Select a few pairs to share and explain a row from their
table.
Problem Solving
This section is challenging! Encourage the use of string to model each scenario and
require a picture (bar model or more elaborate one) as well as an equation. Give students
about 10-15 minutes to work alone on each problem (after making sure students
IMP Activity: How Much Was Cut?
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understand the language of each problem). Then allow students to continue working
alone or work in pairs for the next 10-15 minutes. Circulate to ask guiding questions, but
allow students to struggle with the math. Provide string to anyone who is not
understanding and have them model and cut to represent the numbers in each problem.
Bring the class back together and have pairs or individuals present solutions to each
problem. Look for different approaches to solve and have students critique the reasoning
of their peers and work on justifying their explanations.
Answers:
1)
2)
3)
4)
5)
6)
7)
14 feet
24 feet
17 inches
5 feet
Any two addends of 28; e.g., 20 and 8, 14 and 14
18 cm
28 inches
IMP Activity: How Much Was Cut?
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Teacher Directions
Materials:
 Rulers and meter sticks (1 per group of 6)
 10 meter Open Space for each group of 6 to play game (need about 2 meters in width)
 String or chalk to mark beginning and edges edges of the river
 Measurement unit cards- 4 sets per group (see end of lesson for template)
Objective:
Students will play a game in which they try to get to the other side, a distance of 10 meters, by
asking to take a certain number of steps in certain units and then moving that distance until either
crossing or having the Shark turn and tag them. Students will practice measuring in cm, inches,
feet, and meters as well as get a better sense for how far each of the units of measure will move
them.
Directions
Model game 1 with the class. To do this, select a student to be the shark and have him/her stand at
one end of the class with his/her back facing the class. Select another student to be the measurer
and then 4 students to be fish. Have the fish stand at the opposite side of the room from the shark.
Give each fish the 4 “unit” cards and write the following sentence frame on the board: “Mr. Shark,
Mr. Shark, may I take ______ (number) ________ (unit) steps forward?”
Have fish #1 use the frame to ask the shark for permission to move, holding up the card
representing the units they have requested. Write the three options for the shark’s response on the
board as well: “yes”, “yes, but in ______ units” (meaning if the fish asked for meters, they can say
“yes, but in cm”) or “no”. Set a limit on the number of “no” responses that can be give, such as 1
per fish or 4 per game. Have the shark decide which reply to give and then have the measurer
come in front of the fish and measure out the distance. Have the fish move this distance. Repeat
the same process for each of the other three fish. Then have fish #1 go a second time. Explain that
the goal is for the fish to cross to the other side without being tagged. Explain that at ANY point,
the shark can turn around and try to tag the fish. When the shark turns, the fish can run to either
side of the “river” for safety. After fish #1 has had a second turn, ask the shark to turn and chase
(using inside walking to model!). Explain how points are now awarded: 5 to the shark for each
fish the shark touches; 1 to each safe fish and 2 to any fish who made it across before the shark
attacked (this will rarely happen as most “sharks” are not that patient!) Explain that once the fish
are all safe or the shark has attacked, the team will trade roles and play again, until everyone has
had a chance to be shark and measurer (or until time is up).
Once the class understands, put them in groups of 6 and assign the first shark and measurer for
each group. Have the measurer come get the ruler and meter stick. Have the shark come get 4 unit
cards for each fish. Take the class outside to where you have marked two lines 10 meters apart for
each group and let them play.
Once back inside, ask a few students to explain their strategy to win as fish and to win as shark.
Suggestion: Play this game often during PE time!
IMP Activity: Shark Bait
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Unit Cards for each fish
cm
meters
cm
meters
cm
meters
cm
meters
IMP Activity: Shark Bait
inches
feet
inches
feet
inches
feet
inches
feet
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