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Illustrative Math
Grade 6
Let’s contrast double number lines and tables.
Illustrative Math Unit 6.2, Lesson 13 (printable worksheets)
The following diagram shows how to use a table or a double number line to represent a situation.
Find the product mentally.
150 ÷ 2
150 ÷ 4
150 ÷ 8
Locate and label the quotients on the number line.
The other day, we saw that Han can run 100 meters in 20 seconds.
Han wonders how long it would take him to run 3,000 meters at this rate. He made a table of equivalent ratios.
20 | 10 |
10 | 50 |
1 | 5 |
3,000 |
The International Space Station orbits around the Earth at a constant speed. Your teacher will give you either a double number line or a table that represents this situation. Your partner will get the other representation.
The 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 the Earth?
The speed of the International Space Station is approximately 8 km/s.
The distance of the orbit is approximately 40,000 km.
The time taken for one orbit is 40,000 ÷ 8 = 5000 seconds.
5000 seconds = 5000/60 minutes which is approximately 84 minutes (rounded up since the orbit is bigger than the circumference of the earth)
Make a table that represents the same situation.
olive oil (tablespoons) | crushed garlic (cloves) |
3 | 2 |
1 | 1 |
2 | 11 |
5 | 11 |
10 | 11 |
At this rate, how far does she travel in each of these intervals of time? Explain or show your reasoning. If you get stuck, consider using a table.
a. 1 hour
b. 3 hours
c. 6.5 hours
4. Lin and Diego travel in cars on the highway at constant speeds. In each case, decide who was traveling faster and explain how you know.
a. During the first half hour, Lin travels 23 miles while Diego travels 25 miles.
b. After stopping for lunch, they travel at different speeds. To travel the next 60 miles, it takes Lin 65 minutes and it takes Diego 70 minutes.
5. A sports drink recipe calls for 5/3 tablespoons of powdered drink mix for every 12 ounces of water. How many batches can you make with 5 tablespoons of drink mix and 36 ounces of water? Explain your reasoning.
6. In this cube, each small square has side length 1 unit.
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
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