IM 6.2.13 Lesson: Tables and Double Number Line Diagrams

Find the following quotients mentally.
[math]150\div2[/math]
[math]150\div4[/math]
[math]150\div8[/math]
Locate and label the quotients on the number line.
The other day, we saw that Han can run 100 meters in 20 seconds. [br][br]Han wonders how long it would take him to run 3,000 meters at this rate. He made a table of equivalent ratios.[br][br]Do you agree that this table represents the situation? Explain your reasoning.[br][img]data:image/png;base64,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[/img]
Complete the last row with the missing number.
What question about the situation does this number answer?[br]
What could Han do to improve his table?
Priya can bike 150 meters in 20 seconds.
At this rate, how long would it take her to bike 3,000 meters?[br]
Priya’s neighbor has a dirt bike that can go 360 meters in 15 seconds. At this rate, how long would it take them to ride 3,000 meters?[br]
The International Space Station orbits around the Earth at a constant speed. Your teacher will assign you either the double number line or the table that represents this situation. Complete the parts of your representation that you can figure out for sure
Share information with your partner, and use the information that your partner shares to complete your representation.[br][br]What is the speed of the International Space Station?
Look at the two completed representations side by side. Discuss with your partner some ways in which they are the same and some ways in which they are different.[br][br]Record at least one way that they are the same and one way they are different.
Earth’s circumference is about 40,000 kilometers and the orbit of the International Space Station is just a bit more than this. About how long does it take for the International Space Station to orbit Earth?
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Information: IM 6.2.13 Lesson: Tables and Double Number Line Diagrams