Michael Biking Questions (pp. 1 of 2)
Michael Biking Questions (pp. 1 of 2)
Michael Biking Questions (pp. 1 of 2)
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<strong>Michael</strong> <strong>Biking</strong> <strong>Questions</strong> (<strong>pp</strong>. 1 <strong>of</strong> 2)<br />
8th Grade<br />
Mathematics<br />
Unit: 04 Lesson: 01<br />
<strong>Michael</strong> rides his bike at a constant rate for 2 hours and travels 10 miles.<br />
0 miles<br />
10 miles<br />
Distance<br />
Time<br />
0 hours<br />
2 hours<br />
Answer the questions below. Label all the numbers. Justify your response.<br />
1. In <strong>Michael</strong> <strong>Biking</strong>, what are the two quantities being compared?<br />
2. How far can <strong>Michael</strong> ride in one hour? Two hours? Four hours?<br />
3. How long will it take <strong>Michael</strong> to ride 15 miles? 25 miles?<br />
4. What are the two rates to represent the diagram?<br />
5. What are the two unit rates?<br />
6. Where are the two unit rates located on the diagram?<br />
7. How long will it take <strong>Michael</strong> to ride 3.5 miles? 7.5 miles?<br />
8. How long it will take <strong>Michael</strong> to ride 12 miles (providing his speed is constant)?<br />
9. How far <strong>Michael</strong> can ride in 6 hours (providing his speed is constant)?<br />
©2010, TESCCC 08/01/10
<strong>Michael</strong> <strong>Biking</strong> <strong>Questions</strong> (<strong>pp</strong>. 2 <strong>of</strong> 2)<br />
8th Grade<br />
Mathematics<br />
Unit: 04 Lesson: 01<br />
10. If <strong>Michael</strong> rides his bike 3.5 miles, how many yards did he ride his bike?<br />
11. If <strong>Michael</strong> rides his bike 8.25 miles, how many yards did he ride his bike?<br />
<strong>Michael</strong> wants to convert the miles he rides his bike to kilometers. He knows there are<br />
a<strong>pp</strong>roximately 1.61 kilometers in 1 mile.<br />
12. If <strong>Michael</strong> rides his bike 5 miles, a<strong>pp</strong>roximately how many kilometers did he ride his bike?<br />
13. If <strong>Michael</strong> rides his bike 8 miles, a<strong>pp</strong>roximately how many meters did he ride his bike?<br />
©2010, TESCCC 08/01/10
<strong>Michael</strong> <strong>Biking</strong> <strong>Questions</strong> (<strong>pp</strong>. 1 <strong>of</strong> 2) KEY<br />
8th Grade<br />
Mathematics<br />
Unit: 04 Lesson: 01<br />
<strong>Michael</strong> rides his bike at a constant rate for 2 hours and travels 10 miles.<br />
0 miles<br />
1 mile<br />
5 miles<br />
10 miles<br />
Distance<br />
Time<br />
0.2 hour 1 hour<br />
0 hours<br />
2 hours<br />
Answer the questions below. Label all the numbers. Justify your response.<br />
1. In <strong>Michael</strong> <strong>Biking</strong>, what are the two quantities being compared?<br />
Distance in miles and time in hours<br />
2. How far can <strong>Michael</strong> ride in one hour? Two hours? Four hours?<br />
Half <strong>of</strong> 2 hours is 1 hour: half <strong>of</strong> 10 miles is 5 miles<br />
The diagram shows 2 hours aligns with 10 miles<br />
Two times 2 hours is 4 hours: 2 times 10 miles is 20 miles<br />
3. How long will it take <strong>Michael</strong> to ride 15 miles? 25 miles?<br />
1<br />
1<br />
1 <strong>of</strong> ten miles is 15 miles: 1 <strong>of</strong> 2 hours is 3 hours<br />
2 2<br />
1<br />
2 2<br />
<strong>of</strong> ten miles is 25 miles:<br />
1<br />
2 2<br />
<strong>of</strong> 2 hours is 5 hours<br />
4. What are the two rates to represent the diagram?<br />
10 miles 2 hours<br />
and<br />
2 hours 10 miles<br />
5. What are the two unit rates?<br />
1<br />
1<br />
<br />
<br />
10 miles 2 5 miles 2 hours 10 0.2 hour<br />
= and =<br />
2 hours 1 1 hour 10 miles 1<br />
<br />
<br />
1 mile<br />
2 10<br />
6. Where are the two unit rates located on the diagram?<br />
Refer to diagram above.<br />
7. How long will it take <strong>Michael</strong> to ride 3.5 miles? 7.5 miles?<br />
0.2 hours 3.5 0.7 hour 0.2 hours 7.5 1.5 hours<br />
=<br />
and =<br />
1 mile 3.5 3.5 miles 1 mile 7.5 7.5 miles<br />
8. How long it will take <strong>Michael</strong> to ride 12 miles (providing his speed is constant)?<br />
0.2 hour per mile x 12 miles = 2.4 hours<br />
9. How far <strong>Michael</strong> can ride in 6 hours (providing his speed is constant)?<br />
5 miles per hour x 6 hours = 30 miles<br />
©2010, TESCCC 08/01/10
<strong>Michael</strong> <strong>Biking</strong> <strong>Questions</strong> (<strong>pp</strong>. 2 <strong>of</strong> 2) KEY<br />
8th Grade<br />
Mathematics<br />
Unit: 04 Lesson: 01<br />
10. If <strong>Michael</strong> rides his bike 3.5 miles, how many yards did he ride his bike?<br />
1,760 yards<br />
Unit rate:<br />
1 mile<br />
Proportion:<br />
1,760 yards<br />
=<br />
? yards 1,760 yards 3.5 ? yards<br />
; = ; ? = 6,160 yards<br />
1 mile 3.5 miles 1 mile 3.5 3.5 miles<br />
Equation: y = 1,760x, where y represents the number <strong>of</strong> yards and x represents the number <strong>of</strong><br />
miles; y = 1,760(3.5); y = 6,160 yards<br />
11. If <strong>Michael</strong> rides his bike 8.25 miles, how many yards did he ride his bike?<br />
1,760 yards<br />
Unit rate:<br />
1 mile<br />
Proportion:<br />
1,760 yards<br />
=<br />
? yards 1,760 yards 8.25 ? yards<br />
; =<br />
; ? = 14,520 yards<br />
1 mile 8.25 miles 1 mile 8.25 8.25 miles<br />
Equation: y = 1,760x, where y represents the number <strong>of</strong> yards and x represents the number <strong>of</strong><br />
miles; y = 1,760(8.25); y = 14,250 yards<br />
<strong>Michael</strong> wants to convert the miles he rides his bike to kilometers. He knows there are<br />
a<strong>pp</strong>roximately 1.61 kilometers in 1 mile.<br />
12. If <strong>Michael</strong> rides his bike 5 miles, a<strong>pp</strong>roximately how many kilometers did he ride his bike?<br />
1.61 kilometers<br />
Unit rate:<br />
1 mile<br />
Proportion:<br />
1.61 kilometers<br />
=<br />
? kilometers ;<br />
1 mile 5 miles<br />
1.61 kilometers 5 ? kilometers<br />
=<br />
; ? = 8.05 km<br />
1 mile 5 5 miles<br />
Equation: y = 1.61 x, where y represents the number <strong>of</strong> kilometers and x represents the<br />
number <strong>of</strong> miles; y = 1.61(5); y = 8.05 km<br />
13. If <strong>Michael</strong> rides his bike 8 miles, a<strong>pp</strong>roximately how many meters did he ride his bike?<br />
1.61 kilometers<br />
Unit Rate:<br />
1 mile<br />
Proportion:<br />
1.61 kilometers<br />
=<br />
? kilometers ;<br />
1 mile 8 miles<br />
1.61 kilometers 8 ? kilometers<br />
=<br />
; ?=12.88 km<br />
1 mile 8 5 miles<br />
Unit rate:<br />
1,000 meters<br />
1 kilometer<br />
;<br />
1,000 meters 12.88 12,880 meters<br />
=<br />
; 12,880 meters 8 miles<br />
1 kilometer 12.88 12.88 kilometers<br />
©2010, TESCCC 08/01/10
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