1. Multi-Step Unit Conversion Word Problems
21st Century Lessons
Multi-Step Unit Conversion Word Problems
Primary Lesson Designer:
Lisa Schad

2. This project is funded by the American Federation of Teachers.

3. Click for how to solve Warm-Up #1
OBJECTIVE: SWBAT solve multi-step unit conversion word problems using a calculator. They will also make conjectures and seek to understand the approaches of others.
Use your knowledge of how to convert units and your calculator to make these conversions. Round answers to the nearest tenth.
Note: 1.6 km ≈ 1 mi
and 1 gallon ≈ 3.8 Liters
2.4
1.) 1.5 miles = ____ kilometers
Hint for how to solve #1
x 1.5
228.1
2.) 365 kilometers = _______ miles =
(Time on this slide – 5 min) Time passed 5 min
In-Class Notes
Make sure students have calculators.
Calculator icon will hyperlink to Google Calculator online.
Help students to understand how to round to the nearest tenth. Click red box to show more details for how to solve these warm-up problems.
Problem 1 is exactly Problem 2 is requiring no rounding up just cut off the decimal.
Problem 3 is requiring the 1 to round to Problem 4 is … requiring dropping the other numbers but not rounding up.
You can also talk about why to divide or multiply without using the equivalent ratios but most students will not be ready for this yet.
Preparation Notes
This lesson presumes an ability to convert units. If students have trouble with the warm-up maybe they haven’t had Lesson 13 Unit Conversions yet. Please see this lesson for detailed instruction and guided practice for using equivalent ratios to convert units.
16.2
3.) gallon = _____ liters
9.2
4.) 35 liters = ____ gallons
click
Click for how to solve Warm-Up #1
Agenda

4. Launch The Griffin Family is taking a road trip across the country.
On Day 2 of their trip they are going to travel from Buffalo, New York to Detroit, Michigan.
(Time on this slide – ½ min) Time passed 6.5 min
In-Class Notes
Don’t spend too much time here. These slides are meant to build background and interest in the problem.
Agenda

5. Launch
On Day 2 of their trip they are going to travel from Buffalo, New York to Detroit, Michigan.
CANADA
(Time on this slide – ½ min) Time passed 7 min
In-Class Notes
Students may know that the Griffins are from Quahog, Rhode Island. You can point out Providence, RI as near their starting point. Buffalo and Detroit are circled on the map. Point out that the yellow region is Canada – a different country.
Don’t spend too much time here.
Agenda

6. Launch
The Northern Route takes them through Canada. The Southern Route stays in the U.S.
They have two possible routes to go from Buffalo to Detroit.
CANADA
The Northern Route
(Time on this slide – ½ min) Time passed 7.5 min
In-Class Notes
Make sure students can see the two routes and that they understand the meaning of “route”.
The Southern Route
Agenda

7. Launch
Canada has a different currency, the Canadian dollar, and uses the metric system for measurements.
The Northern Route
412 kilometers (km)
Speed limit is 100 kilometers per hour
The Northern Route
The Southern Route
CANADA
The Southern Route
362 miles (mi)
Speed limit is 55 miles per hour
(Time on this slide – ½ min) Time passed 8 min
In-Class Notes
This information is provided on the Class Worksheet (and the modified Class worksheet for students who need more structure for solving the problems).
Make sure students have the Classwork Worksheet or Classwork modified
Preparation Notes
The modified version provides more scaffolding for students.
Agenda

8. Explore
Task 1) Find which route is longer by comparing both distances using the same unit of measure.
Task 2) Find out how much time it will take to travel each route if the Griffins drive the speed limit the entire length.
The Northern Route
412 kilometers (km)
Speed limit is 100 kilometers per hour
1 mile = 1.6 kilometers
The Northern Route
The Southern Route
CANADA
The Southern Route
362 miles (mi)
Speed limit is 55 miles per hour
(Time on this slide – 1 min) Time passed 9 min
In-Class Notes
The first two tasks are introduced on this slide. Both are also on the worksheet. Encourage students to look on the worksheet as you read them on the slide.
Agenda

9. Explore
Task 3) Find out how much it will cost to fill a 15 gallon tank once for each route.
Task 4) Answer: Which route would you recommend that the Griffins take? Provide evidence for your opinion.
The Northern Route
Average price of gas in the area is $1.26 Canadian dollars per liter.
$1 US ≈ $1.25 Canadian
The Northern Route
The Southern Route
CANADA
1 gallon = 3.8 Liters
The Southern Route
Average price of gas in the area is $3.48 per gallon
(Time on this slide – 1 min) Time passed 10 min
In-Class Notes
The last two tasks are introduced on this slide. Both are also on the worksheet. Encourage students to look on the worksheet as you read them on the slide.
Agenda

10. Explore Task 1) Find which route is longer by comparing
You will have 20 minutes to work on these tasks with your group. Be prepared to present your answers.
Task 1) Find which route is longer by comparing
both distances using the same unit of measure.
Task 2) Find out how much time it will take to travel each route if the Griffins drive the speed limit the entire length.
Task 3) Find out how much it will cost to fill a 15 gallon tank once for each route.
(Time on this slide – 22 min) Time passed 32 min
In-Class Notes
Make sure students understand that they will be working on these tasks in their groups.
Preparation Notes
Set up some system so students know not to ask the teacher to help them with the tasks. For example, “Ask 3 and then me” requires students to ask three people before they can ask the teacher a question.
The goal is to struggle and persevere in solving these problems. If that is an unfamiliar goal then students will become easily frustrated and managing students’ emotions may be a necessary role for the teacher. The more that students are asked to struggle and persevere the less resistance they will have to the request.
Task 4) Answer: Which route would you recommend that the Griffins take? Provide evidence for your opinion.
Agenda

11. Summary The Northern Route 412 kilometers (km) The Southern Route
Task 1) Find which route is the longer by comparing
both distances using the same unit of measure.
The Northern Route
412 kilometers (km)
The Southern Route
362 miles (mi)
Let’s change the kilometers to miles.
1 mi = 1.6 km
257.5
Answer: The Southern Route is longer.
(Time on this slide – 5 min) Time passed 37 min
In-Class Notes
Have student groups share their answers to each task by assigning a presenter from the group.
Ask the student presenter to show his/her work and explain what decisions the group made. Make sure the question is answered.
All unit conversions will be shown using the equivalent ratios method taught in the previous lesson.
Preparation Notes
Answer shown is to convert the kilometers (Northern Route) to miles. They might also have chosen to convert miles to kilometers:
------x
1 mile = miles 1.6 x 362 = km for the Southern Route
1.6 km ? Km
------x compared to 412 km for the Northern Route
The Southern Route is longer. x
257.5
Agenda

12. Summary The Northern Route 412 kilometers (km)
Task 2) Find out how much time it will take to travel each route if the Griffins drive the speed limit the entire length.
The Northern Route
412 kilometers (km)
Speed limit is 100 kilometers per hour
The Southern Route
362 miles (mi)
Speed limit is 55 miles per hour
412 km ÷ 100 = 4.12 hrs
362 mi ÷ 55 = 6.6 hrs
(Time on this slide – 3 min) Time passed 40 min
In-Class Notes
Have student groups share their answers to each task by assigning a presenter from the group.
Ask the student presenter to show his/her work and explain what decisions the group made. Make sure the question is answered.
All unit conversions will be shown using the equivalent ratios method taught in the previous lesson.
Agenda

13. Summary
Task 3) Find out how much it will cost to fill a 15 gallon tank once for each route.
Let’s calculate the cost for the Southern Route first.
The Southern Route: The price of gas in the area is $3.48 per gallon.
15 gallons x $3.48 per gallon =
$52.20
Gas Tank
$3.48
$3.48
$3.48
$3.48
$3.48
$3.48
$3.48
$3.48
$3.48
$3.48
The tank of the car holds 15 gallons of gas.
(Time on this slide – 2 min) Time passed 42 min
In-Class Notes
The work to solve Task 3 is covered in 6 slides. This is the most complex task for this problem.
Have student groups share their answers to each task by assigning a presenter from the group.
Ask the student presenter to show his/her work and explain what decisions the group made. Make sure the question is answered.
All unit conversions will be shown using the equivalent ratios method taught in the previous lesson.
$3.48
$3.48
$3.48
$3.48
$3.48
Agenda

14. Summary
Task 3) Find out how much it will cost to fill a 15 gallon tank once for each route.
The problem here is that we have the same 15 gallon tank in the same car but gas isn’t sold in gallons, it’s sold in liters.
The Northern Route The price of gas in the area is $1.26 Canadian dollars per liter.
Now, let’s calculate the cost for the Northern Route.
How many liters is 15 gallons?
Gas Tank ?
The tank of the car holds 15 gallons of gas.
(Time on this slide – 2 min) Time passed 44 min
In-Class Notes
The 2nd of 6 slides solving Task 3. This detailed explanation can be used after student presenter makes their presentation on Task 3.
Agenda

15. Now how much does 57 Liters cost in Canadian dollars?
Summary
Task 3) Find out how much it will cost to fill a 15 gallon tank once for each route.
The Northern Route The price of gas in the area is $1.26 Canadian dollars per liter.
Let’s convert 15 gallons into liters.
1 gallon ≈ 3.8 liters x 15
Now how much does 57 Liters cost in Canadian dollars?
(Time on this slide – 2 min) Time passed 46 min
In-Class Notes
The 3rd of 6 slides solving Task 3. This detailed explanation can be used after student presenter makes their presentation on Task 3. 57
x 15
Agenda

16. Summary
Task 3) Find out how much it will cost to fill a 15 gallon tank once for each route.
Now that we know the amount of gas in liters we can figure out the cost.
The Northern Route The price of gas in the area is $1.26 Canadian dollars per liter.
Now there’s a new problem. Do you know what it is?
57 liters x $1.26 CAN per liter =
$71.82 CAD
The cost is in Canadian dollars. We need to convert it to American dollars.
Gas Tank
57 liters of gas
(Time on this slide – 2 min) Time passed 48 min
In-Class Notes
The 4th of 6 slides solving Task 3. This detailed explanation can be used after student presenter makes their presentation on Task 3.
Agenda

17. Summary $1 US ≈ $1.25 Canadian x 57.46 $57.46 x 57.46
Task 3) Find out how much it will cost to fill a 15 gallon tank once for each route.
The Northern Route The price of gas in the area is $1.26 Canadian dollars per liter.
Let’s calculate how much $71.82 Canadian is in US dollars.
$1 US ≈ $1.25 Canadian x
57.46
$57.46
Filling 15 gallons (or 57 Liters) in Canada will cost $57.46.
(Time on this slide – 2 min) Time passed 50 min
In-Class Notes
The 5th of 6 slides solving Task 3. This detailed explanation can be used after student presenter makes their presentation on Task 3.
x 57.46
Agenda

18. Summary
Task 3) Find out how much it will cost to fill a 15 gallon tank once for each route.
Let’s review our calculations.
The Southern Route
The Northern Route
Average price of gas in the area is $3.48 per gallon.
Average price of gas in the area is $1.26 Canadian dollars per liter.
1. We multiplied 15 gallons x $3.48 and got a cost of $52.20.
1. We converted 15 gallons into liters and found that the tank holds 57 liters.
2. We multiplied 57 liters x $1.26 CAD and got a cost of $71.82 CAD
(Time on this slide – 2 min) Time passed 52 min
In-Class Notes
The last of 6 slides solving Task 3. This detailed explanation can be used after student presenter makes their presentation on Task 3.
So now we can clearly see that the Northern route will cost more in gas.
3. We converted $71.82 CAD into American dollars and got $57.46 USD.
Agenda

19. Summary
Task 4) Answer: Which route would you recommend that the Griffins take? Provide evidence for your opinion.
How did you answer this question and why?
The Southern Route is a longer distance.
The Southern Route takes longer to drive.
But the gas is cheaper on the Southern Route.
Which route would you recommend?
(Time on this slide – 6 min) Time passed 58 min
In-Class Notes
Answers to this may vary. Most people would say that the savings in time traveled outweigh the minimal difference in gas prices, making the Northern Route preferred.
This slide presents a great opportunity to exercise the CCSS Math Practice #1. Encourage students to share their ideas and use your role as facilitator to help students understand each others’ ideas. See Math Practice #1 standard highlights below.
Measuring with Smoots problem can be used the same day for advanced students or an advanced class or on another day as an additional lesson.
Preparation Notes
Math Practice #1 standard highlights:
Make sense of problems and persevere in solving them
Analyze givens, constraints, relationships, and goals
Make conjectures
Understand the approaches of others
Go to Exit Ticket problem.
Go to additional problem: Measuring with Smoots
Agenda

20. Assessment – Exit Ticket
Mrs. S is pregnant with twins. At the latest appointment the doctor estimated that Baby A weighs 35 ounces and Baby B weighs 37 ounces. How many total pounds of baby weight is Mrs. S carrying?
16 oz = 1 pound
Multiply 35 oz by 16, then multiply 37 oz by 16, then add the answers together.
Add 35 oz and 37 oz, then multiply the answer by 16
Divide 35 oz by 16, then divide 37 oz by 16 then add the answers together.
Add 35 oz and 37 oz, then divide the answer by 16.
(Time on this slide – 2 min) Time passed 60 min
In-Class Notes
Have students raise their hands to indicate which letter gives the procedure or procedures that will give you the answer to the problem. Students do not need to actually solve the problem – only identify the procedure.
Which of the above procedures will give you the answer:
a) Only b) Only 2 c) Only 3
d) Only 4 e) 1 and 2 f) 3 and 4
Agenda