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

Module 2 Topic A Lesson 1Metric 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

FluencyLesson 1 Convert Units 2 min.Convert

Units

• 100 cm = _______ m

200 cm = ________m

• 300 cm = ________m

• 800 cm = ________m

1

2

3

8

FluencyLesson 1 Convert Units 2 min.Convert

Units

• 1 m = _______ cm

• 2 m = ________cm

• 3 m = ________cm

• 7 m = ________cm

100

200

300

700

Meter and Centimeter Bonds 8 minutes Materials: Personal white boards

150cm

1 m ?

FluencyLesson 1 Convert Units 2 min.

How many centimeters are in a meter?

100 cm


150cm

1 m 50cm


120cm

1 m ?20 cm


105 cm

1 m ?5 cm


FluencyLesson 1 Convert Units

2 m

1 m ? cm100 cm

Write the whole as an addition sentence with mixed units.

1 m + 100 cm = 1 m + 1 m = 2 m

3 m

2 m ? cm100 cm


2 m + 100 cm = 2 m + 1 m = 3 m


6 m

5 m ? cm100 cm


5 m + 100 cm = 5 m + 1 m = 6 m


? m

2 m 100 cm

3 m


2 m + 100 cm = 2 m + 1 m = 3 m


? m

100 cm 5 m

6 m


100 cm + 5 m = 1 m + 5 m = 6 m


Application Problem

8 minutes

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 ProblemLesson 1

Concept Development 32 minutes

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 DevelopmentLesson 1Problem 1

Centimeter cm

Width of a staple

Width of a paper clipWidth of a pencil


Meter mHeight of a countertop

Width of your arms stretched wide

Width of a door


Kilometer Km

Distance of several laps around a track

Distance of your home to the nearest town


Make a chart documenting what types of objects are measured in centimeters, meters, and kilometers.

Centimeter Meter Kilometer

• 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


• Compare the sizes and note the relationships between meters and kilometers as conversion equivalencies.

Concept DevelopmentLesson 1Problem 1Problem 1

1 km = 1,000 m

km m

1 1,0002 _____________________

3 _____________________

7 ______________________

70 _______________________

Distance

2,0003,0007,000

70,000


Problem 1

How many meters are in 2 km?2000 m




7,000 m

How many meters are in….


7 km

20,000 m



20 km

70,000 m



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


km m

1 1,000? 8,000

? 9,000

? 10,000

Distance


8

10

9

8 m

How many kilometers are in….


8,000 meters

10 km



10,000 meters

9 km



9,000 meters

PROBLEM 1 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.**


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 + 500 meters is equal to ____ meters.1, 500 meters


PROBLEM 1

1,300 m

How many meters are in…. Concept DevelopmentLesson 1Problem 1

1 km 300 m

5,030 m


5 km 30 m

2 km 500 m



2,500 m

We made 2 groups of 1,000 meters, so we have 2 kilometers and 500

meters.

5 km 5m



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


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. • 96+34 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!


• 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!


Algorithm

Simplifying Strategy

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


Algorithm Examples

1 km 734 m + 4 km 396 m

Algorithm Example


1 km 734 m + 4 km 396 m

Simplifying strategy

1 km + 4 km = 5 km734 m + 396 m = 1130 m

730 4 = 1130 m

1 km + 4 km = 5 km1130 m = 1 km 130 m

5 km + 1 km 130 m = 6km 130 m


1 km 734 m + 4 km 396 m

734 + 396 m = 1130 m700

34 300 96

5km + 1 km 130 m = 6km 130 m

1 km 734 m + 4 km 396 m

Simplifying strategy


10 km – 3 km 140 m =


Problem 3Subtract 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 =



ALGORITHM STRATEGY: SOLUTION A

Look at solution A. How did they set up for the

algorithm?

10 km – 3 km 140 m =



ALGORITHM STRATEGY: SOLUTION B

What did they do for solution B?

10 km – 3 km 140 m =



ALGORITHM STRATEGY: SOLUTION C

What happened in C?

10 km – 3 km 140 m =



MENTAL MATH STRATEGY: SOLUTION D

They used a number line to show a counting up

strategy.

10 km – 3 km 140 m =



MENTAL MATH STRATEGY: SOLUTION 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.


Problem 4Solve 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?


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.


1st

2nd

1 m = 100 cm 1 m 47 cm= 147 cm

147 cm - 98 cm 49 cm

1 m 47 cm

98 cm x


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


147 cm – 98 cm = 49 cm

100 47 2

47 cm + 2 cm = 49 cm

Mental math strategy c


+ 2 + 47 98 cm 1 m 1 m 47 cm

Sam jumped 49 cm further on his first attempt than his second attempt.


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

Module 2 Lesson 1

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

Documents

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