Module 2 Topic A Lesson 1 Metric Unit Conversions 4.MD.1 and 4.MD.2

Lesson 1 Objective Express metric length measurements in terms of a smaller unit Model and solve addition and subtraction word problems involving metric length

Fluency Lesson 1 Convert Units 2 min. Convert Units 100 cm = _______ m 200 cm = ________m 300 cm = ________m 800 cm = ________m

Fluency Lesson 1 Convert Units 2 min. Convert Units 1 m = _______ cm 2 m = ________cm 3 m = ________cm 7 m = ________cm

Meter and Centimeter Bonds 8 minutes Materials: Personal white boards

150 cm 1 m? Fluency Lesson 1 Convert Units 2 min.

How many centimeters are in a meter? 100 cm Fluency Lesson 1 Convert Units 2 min.

150 cm 1 m50cm Fluency Lesson 1 Convert Units 2 min.

120 cm 1 m ? 20 cm Fluency Lesson 1 Convert Units 2 min.

105 cm 1 m ? 5 cm Fluency Lesson 1 Convert Units 2 min.

Fluency Lesson 1 Convert Units 2 m 1 m ? cm 100 cm Write the whole as an addition sentence with mixed units. 1 m cm = 1 m + 1 m = 2 m

3 m 2 m ? cm 100 cm Write the whole as an addition sentence with mixed units. 2 m cm = 2 m + 1 m = 3 m Fluency Lesson 1 Convert Units

6 m 5 m ? cm 100 cm Write the whole as an addition sentence with mixed units. 5 m cm = 5 m + 1 m = 6 m Fluency Lesson 1 Convert Units

? m 2 m 100 cm 3 m Write the whole as an addition sentence with mixed units. 2 m cm = 2 m + 1 m = 3 m Fluency Lesson 1 Convert Units

? m 100 cm 5 m 6 m Write the whole as an addition sentence with mixed units. 100 cm + 5 m = 1 m + 5 m = 6 m Fluency Lesson 1 Convert Units

Martha, George, and Elizabeth sprinted a combined distance of 10,000 m. Martha sprinted 3,206 m. George sprinted 2,094 m. How far did Elizabeth sprint? Solve using a simplifying strategy or algorithm. Application Problem Lesson 1

Objective: You will understand the lengths of 1 centimeter, 1 meter, and 1 kilometer in terms of concrete objects and objects you know. We’ve got this! Concept Development Lesson 1 Problem 1

Centimeter cm Width of a staple Width of a paper clip Width of a pencil Concept Development Lesson 1 Problem 1

Meter m Height of a countertop Width of your arms stretched wide Width of a door Concept Development Lesson 1 Problem 1

Kilometer Km Distance of several laps around a track Distance of your home to the nearest town Concept Development Lesson 1 Problem 1

Make a chart documenting what types of objects are measured in centimeters, meters, and kilometers. CentimeterMeterKilometer Length of a staple Fingernail Length of a base ten block Length of a countertop The outstretched arms of a child Distance from the school to the train station Four times around the soccer field Concept Development Lesson 1 Problem 1

Compare the sizes and note the relationships between meters and kilometers as conversion equivalencies. Concept Development Lesson 1 Problem 1

km m 1 1,000 2 _____________________ 3 7 ______________________ 70 _______________________ Distance 2,000 3,000 7,000 70,000 Concept Development Lesson 1 Problem 1

How many meters are in 2 km? 2000 m How many meters are in 3 km? 3000 m How many meters are in 4 km? 4000 m Concept Development Lesson 1 Problem 1

7,000 m How many meters are in…. Concept Development Lesson 1 Problem 1 7 km

20,000 m How many meters are in…. Concept Development Lesson 1 Problem 1 20 km

70,000 m How many meters are in…. Concept Development Lesson 1 Problem 1 70 km

Problem 1 Continued Write 2,000 m = ____ km on your board. If 1,000 m = 1 km, 2,000 m = how many kilometers? 2 km Concept Development Lesson 1 Problem 1

km m 1 1,000 ? 8,000 ? 9,000 ? 10,000 Distance Concept Development Lesson 1 Problem

8 m How many kilometers are in…. Concept Development Lesson 1 Problem 1 8,000 meters

10 km How many kilometers are in…. Concept Development Lesson 1 Problem 1 10,000 meters

9 km How many kilometers are in…. Concept Development Lesson 1 Problem 1 9,000 meters

Compare kilometers and meters. 1 ____ is 1,000 times as much as 1 ______. 1 km is 1,000 times as much as 1 meter. **A kilometer is a longer distance because we need 1,000 meters to equal 1 kilometer.** Concept Development Lesson 1 Problem 1

1 km 500 m = _____ m Let’s convert the kilometers to meters. 1 km is worth how many meters? 1,000 meters 1,000 meters meters is equal to ____ meters. 1, 500 meters Concept Development Lesson 1 Problem 1

1,300 m How many meters are in…. Concept Development Lesson 1 Problem 1 1 km 300 m

5,030 m How many meters are in…. Concept Development Lesson 1 Problem 1 5 km 30 m

2 km 500 m How many kilometers are in…. Concept Development Lesson 1 Problem 1 2,500 m We made 2 groups of 1,000 meters, so we have 2 kilometers and 500 meters.

5 km 5m How many kilometers are in…. Concept Development Lesson 1 Problem 1 5,005 We made 5 groups of 1,000 meters, so we have 5 kilometers and 5 meters.

Talk with your partner about how to solve this problem. 2 km 500 m How many meters are in…. Concept Development Lesson 1 Problem 2 5 km + 2,500 m We can’t add different units together. We can rename the kilometers to meters before adding. Simplify or use the algorithm? Simplify 5 kilometers equals 5,000 meters, so 5,000 m + 2,500 m = 7,500 m

Problem 2 continued 1 km 734 m + 4 km 396 m = Simplify Strategy or Algorithm? Simplify strategy because 7 hundred and 3 hundred meters are a kilometer is easy since the 4 will get the 96 to 100 meters. Then I have 6km 130 m. But, there are three renamings and the sum of the meters is more than a thousand. Is your head spinning? Mine is! Concept Development Lesson 1 Problem 2

We are going to try it mentally then check it with the algorithm, just to make sure. Choose the way that you want to set up the algorithm. If you finish before the two minute work time is up, try solving it a different way. We will also have two pairs of students solve the problem on the board. One pair will solve it using the simplying strategy. The other pair will solve it using the algorithm. Let's get to work! Concept Development Lesson 1 Problem 2 1 km 734 m + 4 km 396 m

1 km 734 m +4 km 896 m 5km 1130 m + 1 km 130 m 6 km 130 m Concept Development Lesson 1 Problem 2 Algorithm Examples 1 km 734 m + 4 km 396 m

Algorithm Example Concept Development Lesson 1 Problem 2 1 km 734 m + 4 km 396 m

Simplifying strategy 1 km + 4 km = 5 km 734 m m = 1130 m = 1130 m 1 km + 4 km = 5 km 1130 m = 1 km 130 m 5 km + 1 km 130 m = 6km 130 m Concept Development Lesson 1 Problem 2 1 km 734 m + 4 km 396 m

m = 1130 m km + 1 km 130 m = 6km 130 m 1 km 734 m + 4 km 396 m Simplifying strategy Concept Development Lesson 1 Problem 2

10 km – 3 km 140 m = Concept Development Lesson 1 Problem 3 Problem 3 Subtract mixer unit of length using the algorithm or mixed units of length. Simplifying Strategy or Algorithm? Definitely using the algorithm. There are no meters in the number so you would have to subtract. It really is like 10 thousand minus 3 thousand 140. Choose the way you want to set up the algorithm. If you finish before the two minutes is up, try solving the problem a different way. Let’s have two pairs of students work on the board. One pair using the algorithm and one pair recording a mental math strategy.

10 km – 3 km 140 m = Concept Development Lesson 1 Problem 3 Problem 3 Subtract mixer unit of length using the algorithm or mixed units of length. A LGORITHM S TRATEGY : S OLUTION A Look at solution A. How did they set up for the algorithm?

10 km – 3 km 140 m = Concept Development Lesson 1 Problem 3 Problem 3 Subtract mixer unit of length using the algorithm or mixed units of length. A LGORITHM S TRATEGY : S OLUTION B What did they do for solution B?

10 km – 3 km 140 m = Concept Development Lesson 1 Problem 3 Problem 3 Subtract mixer unit of length using the algorithm or mixed units of length. A LGORITHM S TRATEGY : S OLUTION C What happened in C?

10 km – 3 km 140 m = Concept Development Lesson 1 Problem 3 Problem 3 Subtract mixer unit of length using the algorithm or mixed units of length. M ENTAL M ATH S TRATEGY : S OLUTION D They used a number line to show a counting up strategy.

10 km – 3 km 140 m = Concept Development Lesson 1 Problem 3 Problem 3 Subtract mixer unit of length using the algorithm or mixed units of length. M ENTAL M ATH S TRATEGY : S OLUTION E They counted up from 3 km 140 m to 4 km first and then added 6 more km to get to 10 km.

Partner Debrief With your partner, take a moment to review the solution strategies on the board. Talk to your partner why 6 km 840 m is equal to 6,840m. Did you say that… The number line team showed it because they matched kilometers to meters. You can regroup 6 kilometers as 6,000 meters. You can regroup 6,000 meters to 6 kilometers. Both are the same amounts, but represented using different units, either mixed units or a single unit. Concept Development Lesson 1 Problem 3

Problem 4 Solve an application problem using mixed units of length using the algorithm or simplifying strategies. Sam practiced his long jump in P.E. On his first attempt, he jumped 1 meter 47 centimeters. On his second jump, he jumped 98 centimeters. How much further did Sam jump on his first attempt than his second? Concept Development Lesson 1 Problem 4 Take 2 minutes with your partner to draw a tape model to model this problem.

Problem 4 Your diagram should show a comparison between two values. How can you solve for the unknown? Subtract 98 cm from 1 m 47cm Will you use the algorithm or a simplifying strategy? Like before, there will be two pairs of students that show their work on the board as you work at your desks. Concept Development Lesson 1 Problem 4

1 st 2 nd 1 m = 100 cm 1 m 47 cm= 147 cm 147 cm - 98 cm 49 cm 1 m 47 cm 98 cm x Concept Development Lesson 1 Problem 4 Algorithm Solution A

1 m 47 cm – 98 cm = 1m = 100 cm 100 cm – 98 cm = 2 cm 47cm + 2 cm = 49 cm Mental Math Solution B Concept Development Lesson 1 Problem 4

147 cm – 98 cm = 49 cm cm + 2 cm = 49 cm Mental math strategy c Concept Development Lesson 1 Problem 4

cm 1 m 1 m 47 cm Sam jumped 49 cm further on his first attempt than his second attempt. Concept Development Lesson 1 Problem 4 Mental math solution d

Problem set (10 minutes) Do your personal best To complete the problem set in 10 minutes

Lesson 1 Problem Set Problems 1 and 2 What pattern did you notice for the equivalencies in Problems 1 and 2 of the Problem Set? How did converting 1 kilometer to 1,000 meters in Problem 1a help you solve Problem 1b?

Lesson 1 Problem Set Problem 3 How did solving Problem 2 prepare you to solve Problem 3? For Problem 3, Parts c and d, explain how you found your answer in terms of the smaller of the two units. What challenges did you face? When adding and subtracting mixed units of length, what are two ways that you can solve the problem? Explain your answer to your partner.

Lesson 1 Problem Set Problems 4 and 5 Look at Problem 4 in Concept Development. How did you draw your tape diagram? Explain this to your partner.

Lesson 1 Problem Set Problem 6 and 7 How did the Application Problem connect to today’s lesson? How did solving Problems 1,2, and 3 help you to solve the rest of the Problem Set? What new math vocabulary did we use today to communicate precisely?

Complete the Exit Ticket.

Homework Module 2 Lesson 1