This Number Talk encourages students to use what they know about multiples of 100, the relationship between hundreds and thousands, and properties of operations to mentally solve problems. The reasoning students do here will be helpful later in the lesson when students explore the relationship between kilometers and meters, and convert measurements from the former to the latter.
Launch
Display one expression.
“Give me a signal when you have an answer and can explain how you got it.”
“How does knowing help you find ?” (1,000 is 10 times 100, so if we know , we can multiply that by 10 to find .)
Activity 1
Standards Alignment
Building On
Addressing
4.MD.A.1
Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs , , , …
The purpose of this activity is to build students’ intuition for 1 kilometer. Previously, students used centimeter grid paper and counted 100 units to build a length of 1 meter. Since building a kilometer is impractical, here students relate 1 kilometer to the length of other objects that may be more familiar. For instance, if an Olympic-size pool is 50 meters long, the length of 2 pools is 100 meters and the length of 20 pools is 1,000 meters or 1 kilometer.
The blackline master shows copies of a few objects: a soccer field, the Statue of Liberty, an Olympic-size pool, or a basketball court. Students work with their group to cut out these images and use the copies of each object to reason about the length of 1 kilometer.
Launch
Groups of 4
“How long do you think 10 meters is?”
Consider asking students to use the meter strips to illustrate 10 meters.
“How long is 100 meters? How many meter-long strips do we need to make 100 meters?” (100 of the meter-long strips, or 10 of the 10-meter-long strips)
Activity
“Now we will work with kilometers. Read the first problem and solve it on your own.”
2 minutes: independent work time
Invite students to share their responses and their reasoning.
Highlight that if we take 10 of the 100-meter sections of the track and lay them end to end in a straight line, the total length would represent 1,000 meters or 1 kilometer.
Give each group a pair of scissors and a copy of the blackline master.
“You will now use the length or the height of some other objects to represent 1 kilometer: a soccer field, the Statue of Liberty, an Olympic-size pool, and a basketball court.”
“Work with your group to complete the rest of the activity.”
“Each group member should choose a different object and think about how many of them are needed to represent exactly or approximately 1 kilometer.”
“Think about how many more of your chosen object you’ll need to reach 1 kilometer.”
10–12 minutes: group work time
There are 1,000 meters in 1 kilometer.
The shaded section of the track is the length of a 100-meter race. How many 100-meter races does it take to travel 1 kilometer?
Your teacher will give you images of something with a length or a height measured in meters.
About how many of the items in the handout are needed to make 1 kilometer? Explain or show how you know.
Work with your group to write a number in the blank so that each statement is true. Decide if your length is “about” or “exactly” 1 kilometer, and circle the correct word.
One kilometer is the length of (about, exactly) __________ soccer fields.
One kilometer is the length of (about, exactly) __________ Statues of Liberty.
One kilometer is the length of (about, exactly) __________ Olympic-size swimming pools.
One kilometer is the length of (about, exactly) __________ basketball courts.
Estimate where you might end up if you travel 1 kilometer from your school’s front door.
Activity Synthesis
Select students to share their work on how the four objects compare to 1 kilometer.
For each response, ask: “How did you know how many of that object it would take to make a length of 1 kilometer?” (For the soccer field:
I added 110 repeatedly until it reached 1,000.
I know that 5 soccer fields make 550, and I thought about how many of that length would make 1,000.
I tried multiplying 110 feet by different numbers to reach 1,000.
I thought about how many 110s would go into 1,000.)
Invite students to share their responses to the last problem.
Consider giving or displaying for students a map showing one or more points that are 100 meters from school, and asking them to identify a place that is 1 kilometer away from the school.
Emphasize that 1 kilometer is 1,000 times as long as 1 meter. If we use 1 meter as a unit of measurement, we’ll need 1,000 of it to make 1 kilometer. Explain that kilo means “thousand.”
Activity 2
Standards Alignment
Building On
Addressing
4.MD.A.1
Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs , , , …
The purpose of this activity is for students to convert measurements from kilometers into meters and to reason the other way around. When the given measurement is a whole number of kilometers, students likely will multiply the whole number by 1,000 to find its equivalent in meters. For kilometer, they likely will reason that half of 1,000 is 500, or that 1,000 divided by 2 is 500. Students are not expected to reason multiplicatively or to know that is 500. The Lesson Synthesis focuses on discussing Andre's reasoning from the task.
MLR7 Compare and Connect. Synthesis: After all strategies have been presented, lead a discussion comparing, contrasting, and connecting the different approaches. Ask students: “What did the strategies have in common?” “How were they different?” and “Why did the different approaches lead to the same outcome?” Advances: Representing, Conversing
Action and Expression: Internalize Executive Functions. Invite students to choose a starting place that feels most comfortable to them, and to verbalize their strategy before they begin. Students can speak quietly to themselves, or share with you or a partner. Supports accessibility for: Conceptual Processing, Language, Organization
Launch
Groups of 2
Display the table for all to see.
“What do you notice? What do you wonder?”
30 seconds: quiet think time
30 seconds: partner discussion
Students may have noticed and wondered about the “km” and the “m” in the table. Clarify that these are abbreviations for kilometers and meters, respectively.
Activity
6–7 minutes: independent work time
2–3 minutes: partner discussion
Monitor for the different ways students reason about 27 kilometers. For instance, they may:
Count by 1,000 twenty-seven times.
Reason that 10 groups of 1,000 make 10,000, that 20 groups make 20,000, and that 7 more groups make 7,000.
Use the previous values in the table, reasoning that and adding the corresponding values in meters ().
Multiply 27 by 1,000.
Activity Synthesis
Display the table.
Invite selected students to share their reasoning on how they converted each whole-number measurement. Start with students who reasoned by counting and end with those who reasoned multiplicatively.
Discuss how students found the number of meters in kilometer and kilometers. Record their reasoning.
Lesson Synthesis
“Today we learned about the relationship between meters and kilometers.”
“Did you agree with Andre that 100 meters is longer than 10 kilometers? How did you know whether what he said was true?” (No, because a kilometer is 1,000 meters, which is already longer than 100 meters.)
“Why might Andre have believed this was true?” (He compared the numbers 100 and 10 and saw that 100 was larger.)
Highlight explanations that made it clear that we cannot simply compare the number measurements, without considering the units in which they were measured.
Standards Alignment
Building On
Addressing
Building Toward
4.NBT.B.5
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Complete the table with the unknown lengths in meters or in kilometers.
kilometers (km)
meters (m)
1
1,000
5
6,000
10
12,000
27
Andre says 100 meters is longer than 10 kilometers. Do you agree or disagree? Explain or show your reasoning.
Which is greater?
2,000 meters or 3 kilometers
500 meters or 1 kilometer
14 kilometers or 14,000 meters
8 kilometers or 80,000 meters
Student Response
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Advancing Student Thinking
Building Toward
4.MD.A.2
Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.