In the previous lesson, students used the context of shopping to explore how equivalent ratios and ratios involving one can be used to find unknown amounts. In this lesson, they revisit these ideas in a new context—constant speed—and through concrete experiences. Students measure the time it takes them to travel a predetermined distance—first by moving slowly, then quickly—and use it to calculate and compare the speed they traveled in meters per second.
Here, double number lines are used to represent the association between distance and time, and to convey the idea of constant speed as a set of equivalent ratios (e.g., 10 meters traveled in 20 seconds at a constant speed means that 0.5 meters is traveled in 1 second, and 5 meters is traveled in 10 seconds). Students come to understand that, like price, speed can be described using the terms per and at this rate.
The idea of a constant speed relating the quantities of distance and time is foundational for the later, more abstract idea of a constant rate, and is important in the development of students’ ability to reason abstractly about quantities (MP2).
Lesson overview
 9.1 Warmup: Number Talk: Dividing by Powers of 10 (10 minutes)
 9.2 Activity: Moving 10 Meters (25 minutes)

9.3 Activity: Moving for 10 Seconds (10 minutes)
 Includes "Are you Ready for More?" extension problem
 There is a digital applet in this activity.
 Lesson Synthesis
 9.4 Cooldown: Train Speeds (5 minutes)
Learning goals:
 Calculate the distance an object travels in 1 unit of time and express it using a phrase like “meters per second” (orally and in writing).
 For an object moving at a constant speed, use a double number line diagram to represent equivalent ratios between the distance traveled and elapsed time.
 Justify (orally and in writing) which of two objects is moving faster, by identifying that it travels more distance in the same amount of time or that it travels the same distance in less time.
Learning goals (student facing):
 Let’s use ratios to work with how fast things move.
Learning targets (student facing):
 If I know an object is moving at a constant speed, and I know two of these things: the distance it travels, the amount of time it takes, and its speed, I can find the other thing.
 I can choose and create diagrams to help me reason about constant speed.
Required materials:
 stopwatches
 string
 meter sticks
 masking tape
Required preparation:

Before class, set up 4 paths with a 1meter warmup zone and a 10meter measuring zone.
Glossary:
 meters per second  Meters per second is a unit for measuring speed. It tells how many meters an object goes in one second. For example, a person walking 3 meters per second is going faster than another person walking 2 meters per second.
 Access the complete Grade 6 glossary.
Standards
 This lesson builds on the standard:CCSS.5.NBT.A.1MS.5.NBT.1
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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