Module 2 Topic A Lesson 1 Metric Unit Conversions

transcript

MODULE 2 TOPIC A LESSON 1METRIC UNIT CONVERSIONS4.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

• 100 cm = _______ m

200 cm = ________m

• 300 cm = ________m

• 800 cm = ________m

• 1 m = _______ cm

• 2 m = ________cm

• 3 m = ________cm

• 7 m = ________cm

METER AND CENTIMETER BONDS 8 MINUTES

Materials: Personal white boards

FluencyLesson 1 Convert Units 2 min.

How many centimeters are in a meter?

100 cm

1 m 50cm

1 m ?20 cm

105 cm

1 m ?5 cm

FluencyLesson 1 Convert Units

1 m ? cm100 cm

Write the whole as an addition sentence with mixed units.

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

2 m ? cm100 cm

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

5 m ? cm100 cm

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

2 m 100 cm

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

100 cm 5 m

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

Application Problem8 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

1 1,0002 _____________________

3 _____________________

7 ______________________

70 _______________________

Distance

2,0003,0007,00070,00

Problem 1

How many meters are in 2 km?2000 m

7,000 m

HOW MANY METERS ARE IN….

20,000 m

70,000 m

PROBLEM 1 CONTINUEDWrite 2,000 m = ____ km on your board.

If 1,000 m = 1 km, 2,000 m = how many kilometers?

1 1,000? 8,000

? 9,000

? 10,000

Distance

HOW MANY KILOMETERS ARE IN….

8,000 meters

10,000 meters

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

Concept DevelopmentLesson 1Problem 1PROBLEM 1

1,300 m

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

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

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 m

700 34 300 96

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

1 km 734 m + 4 km 396 m

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 =

SUBTRACT MIXER UNIT OF LENGTH USING THE ALGORITHM OR MIXED UNITS OF LENGTH.

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.

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

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.

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

LESSON 2 OBJECTIVE

Express metric mass measurements in terms of smaller units.

Model and solve addition and subtraction word problems involving metric mass.

FLUENCY PRACTICE (12 MINUTES)

Materials: Personal White Boards

1 m = ___ cm

1 meter is how many centimeters?

100 centimeters

1,000 g = ___ kg

1,000 g is the same as how many kilograms?

1 meter

100 centimeters

1,000 grams 1 kilogram

FluencyLesson 2

FLUENCY PRACTICE CONTINUED

1,000 grams 1 kilogram

FluencyLesson 2

2,000 g = ____ kg

3,000 g = ____ kg

7,000 g = ____ kg

5,000 g = ___ kg

1 kg __ g

Number Bonds

1 KG + 1, 000 G = 1 KG + 1KG = 2 KG

FluencyLesson 2

2 kg __ g

Number Bonds

2 KG + 1,000 G = 2 KG + 1KG = 3 KG

FluencyLesson 2

4 kg __ g

Number Bonds

4 KG + 1,000 G = 4 KG + 1KG = 5 KG

FluencyLesson 2

UNIT COUNTING (4 MINUTES)

Count by 50 cm in the following sequence and change directions when you see the arrow.

• 50 cm• 100 cm• 150 cm• 200 cm• 250 cm• 300 cm

• 250 cm• 200 cm• 150 cm• 100 cm• 50 cm• 0 cm

You did it!

FluencyLesson 2

• 50 cm• 1 m• 150 cm• 2 m• 250 cm• 3 m

• 250 cm• 2 m• 150 cm• 1 m• 50 cm• 0 m

You did it!

FluencyLesson 2

• 50 cm• 1 m• 1 m 50

cm• 2 m• 2 m 50

cm• 3 m

• 2 m 50 cm• 2 m• 1 m 50 cm• 1 m• 50 cm• 0 m

You did it!

FluencyLesson 2

ADD AND SUBTRACT METERS AND CENTIMETERS (4 MINUTES)

540 cm + 320 cm = _______

Say 540 cm in meters and centimeters.

5 meters

3 meters

FluencyLesson 2

5 m 40 cm + 3 m 20 cm = _______ Add the meters: 5 m + 3 m = 8 meters

Add the cm: 40 cm + 20 cm = 60 cm The sum is 8 m 60 cm.

420 cm + 350 cm = _______

4 meters

3 meters

FluencyLesson 2

650 cm - 140 cm = _______

6 meters

1 meter

FluencyLesson 2

6 m 50 cm - 1 m 40 cm = _______ Subtract the meters: 6 m - 1 m = 5

meters

Subtract the cm: 50 cm - 40 cm = 10 cm The difference is 5 m 10 cm.

780 cm - 210 cm = _______

7 meters

2 meter

meters

APPLICATION PROBLEM ( 8 MINUTES)

The distance from school to Zoie’s house is 3 kilometers 469m. Camie’s house is 4 kilometers 301 meters farther away. How far is it from Camie’s house to school? Solve using simplifying strategies or an algorithm.

School Zoie’s house

Camie’s house

ApplicationLesson 2

ALGORITHM SOLUTION

3,469 m + 4,301 m

7,770 m

MENTAL MATH SOLUTION

7 km = 7,000 m 7,000 m + 770 m = 7,770 m

469 + 301 = 470 + 300 = 770 m

300 1 3 km + 4 km = 7 km 7km 770 m Camie’s house is 7 km 770 m from school.

CONCEPT DEVELOPMENT (30 MINUTES)Materials:

Teacher: 1- L water bottle, small paper clips, dollar bill, dictionary, balance scale or weights.

Student: Personal White Board

This bottle of water weighs 1 kilogram. We can also say that it has a mass of 1 kilogram. This is what a scientist would say.

Experiments make me thirsty. Please give me a kilogram of

H2O please!

The dictionary weighs about 1 kilogram.

The mass of this small paper clip is about 1 gram.A dollar bill weighs about 1 gram too.

1 kilogram = 1 gram

If the mass of this dictionary is about 1 kilogram, about how many small paperclips will be just as heavy as this dictionary?

1,000!

Let’s investigate using our balance scale.

Take a minute to balance one dictionary and 1,000 small paperclips on a scale.

OR use a 1 kg weight. Also balance 1 small paperclip with a 1 gram weight.

How many grams are in 2 kilograms?

2000 g

How many kilograms is 3,000 g? 3 kg

Let’s fill in the chart all the way up to 10kg.

MASS REFERENCE CHART

1 1,000

3 3,000

4 4,000

5 5,000

6 6,000

7 7,000

8 8,000

9 9,000

10 10,000

MASS: RELATIONSHIP BETWEEN KILOGRAMS AND GRAMS

1 1,000

2 _____

3 3,000

4 _____

_____ 5,000

_____ 6,000

7 _____

8 _____

_____ 9,000

10 _____

COMPARE KILOGRAMS AND GRAMS. 1 kilogram is 1,000 times as much as 1 gram.

= 1,000 x A kilogram is heavier because we need 1,000g to equal 1

kilogram.

1 kilogram is equal to how many grams?

1,000 grams

1,000 grams plus 500 grams is equal to how many grams?

1,500 grams.

Let’s convert 1 kg 500 g to grams.

1 kilogram 300 grams is equal to how many grams?

1,300 grams

Did I hear someone say 530 grams? Let’s clarify that.

5 kilogram is equal to how many grams?

5,000 grams

5,000 grams plus 30 grams is equal to how many grams?

5,030 grams.

Wrong answer!

2 kg 500 g

We made two groups of 1,000 grams, so we have 2 kilograms and 500 grams.

2,500 grams is equal to how many kilograms?

5 kg 5 g

We made five groups of 1,000 grams, so we have 5 kilograms and 5 grams.

5,005 grams is equal to how many kilograms?

8kg + 8,200 g =______

Problem 2Add mixed units using the algorithm or simplifying strategies

Talk with your partner about how to solve this problem.

We can’t add different

units together.

We can rename the kilograms to grams before

adding.We can

rename 8kg to 8,000 g.

8,000 g + 8,200 g = 16,200g

Or we can rename

8,200 g to 8 kg 200

8 kg + 8kg 200 g = 16 kg 200g

8kg + 8,200 g =______

Problem 2Add mixed units using the algorithm or simplifying strategies

Will we use the algorithm or a simplifying strategy?

A simplifying strategy!

8,000 g + 8,200 g = 16,200g

There is no regrouping and we can add the numbers easily

mentally.

8 kg + 8kg 200 g = 16 kg 200g

Now try:

25 kg 537 g + 5 kg 723 g = ____

Should we use a simplifying strategy or the algorithm?

Discuss your strategy with a partner. I think the algorithm because the

numbers are too big.

There is regrouping and the numbers are not easy to

combine.

I think I can use a simplifying strategy.

Choose the way you want to tackle the problem and work for the next two

minutes on solving it.

If you finish before the two minutes, try solving the problem another way.

Let’s have two pairs of students

work on the board. One pair will solve

using the algorithm and the other pair will try

and use a simplifying strategy.

25 kg 537 g + 5 kg 723 g = ____

25 kg 537 g + 5 kg

723 g 30 kg 1,260 g

30 kg + 1 kg 260 g =

31 kg 260 g

25,537 g + 5,723 g

31,260 g

31 kg 260 g

ALGORITHM SOLUTION B

25 kg 537 g + 5 kg 723 g = ____Concept DevelopmentLesson 2Problem 2

SIMPLIFYING STRATEGY C

25 kg 537 g + 5 kg

723 g 30 kg 1,260 g

30 kg + 1 kg 260 g =

31 kg 260 g

25,537 g + 5,723 g

31,260 g

31 kg 260 g

SIMPLIFYING STRATEGY D

25 kg 537 g + 5 kg 723 g = ____

PROBLEM 3SUBTRACT MIXED UNITS OF MASSING USING THE ALGORITHM OR A SIMPLIFYING STRATEGY.

10 kg – 2 kg 250 g =

There are no grams in the number, so it is best to use the algorithm because there is a lot of regrouping involved.

A simplifying strategy can be used as well.

A simplifying strategy or the algorithm? Discuss with a partner.

Choose the way you want to solve the problem.If you finish before the two minutes are up, try solving the

problem a different way.

Let’s have two pairs of students work on the board. One pair will solve using the algorithm and the other pair will try and

use a simplifying strategy.

10 kg – 2 kg 250 g =Concept DevelopmentLesson 2Problem 3

ALGORITHM SOLUTION A ALGORITHM SOLUTION B

9 0 1010

10 kg 1,000 g - 2 kg 250 g 7 kg 750 g

0 9 9 10

10,000 g

- 2,250 g

7,750 g

7 kg 750 g

Look at the first example

algorithm. How did they prepare the algorithm for

subtraction?They renamed 10

kilograms as 9 kilograms and 1,000

g first.

Converted kilograms to

grams.

• How did our first simplifying strategy pair solve the problem?

• They subtracted the 2 kg first.• And then?• Subtracted the 250 g from 1

What did they do in the second

solution?

SIMPLIFYING STRATEGY C SIMPLIFYING STRATEGY D

10 kg – 2 kg 250 g =

10 kg – 2 kg 250 g =10 kg – 2 kg = 8 kg 8 kg – 250 g = 7 kg 750 g

7 kg 1000 g 750 g

Does anyone have a

question for the mental math team?

How did you know 1 thousand minus

250 was 750?

We just subtracted 2

hundred from 1 thousand and

then thought of 50 less than 800. Subtracting 50

from a unit in the hundreds is easy.

SIMPLIFYING STRATEGY C SIMPLIFYING STRATEGY D

10 kg – 2 kg 250 g =

10 kg – 2 kg 250 g =10 kg – 2 kg = 8 kg 8 kg – 250 g = 7 kg 750 g

7 kg 1000 g 750 g

How did our mental math

team solve the problem?

They added up from 2 kilograms 250 grams to 3 kilograms first, and then added 7

more kilograms to get to 10 kilograms.

What does the number line show?

It shows how we can count up from 2

kilograms 250 grams to 10 kilograms to find

our answer. It also shows that 7

kilograms 750 grams is equivalent to 7,750

grams.

+ 750 g + 7 kg 2 kg 250 g 3 kg 10 kg

750 g + 7 kg = 7 kg 750 g

10 kg – 2 kg 250 g =Concept DevelopmentLesson 2Problem 3

32 kg 205 g – 5 kg 316 g

Which strategy would you use? Discuss it with a partner.

Those numbers are not easy to subtract, so I would probably use an algorithm. There are not enough grams in the first number, so I know we will have to regroup.

Choose the way you want to solve.

32 kg 205 g – 5 kg 316 g

A suitcase cannot exceed 23 kilograms for a flight. Robby packed his suit case for his flight, and it weighs 18 kilograms 705 g. How many more grams can be held in his suit case without going over the weight limit of 23 kg?

SOLVE A WORD PROBLEM INVOLVING MIXED UNITS OF MASS MODELED WITH A TAPE DIAGRAM.

Read with me. Take one minute to draw and label a tape diagram.

We know how much Robert's suitcase is allowed to hold and how much it is holding. We don’t know how many more grams it can hold to reach the maximum allowed weight of 23 kilograms.

Tell your partner the known and unknown

information.

Will you use an algorithm or a simplifying strategy? Label the missing part on your diagram and make a statement of solution

ALGORITHM SOLUTION BSIMPLIFYING SOLUTION C

Lesson Objective: Express metric mass measurements in terms of a smaller unit, model and solve addition and subtraction word problems involving metric mass.

PROBLEM SET (10 MINUTES)

You should do your personal

best to complete the Problem Set

within 10 minutes.

Use the RDW

approach for solving word problems.

PROBLEM SET REVIEW AND STUDENT DEBRIEF

Review your Problem Set with a partner and compare work and answers.

In our lesson, we solved addition and subtraction problems in two different ways but got equivalent answers. Is one answer “better” than the other? Why or why not.

What did you do differently in Problem 3 when it asked you to express the answer in the smaller unit rather than the mixed unit?

In Problem 6, did it make sense to answer in the smaller unit or mixed unit?

Explain to your partner how you solved Problem 7. Was there more than one way to solve it?

PROBLEM SET STUDENT DEBRIEF CONTINUED

How did the Application Problem connect to today’s lesson?

How did today’s lesson of weight conversions build on yesterday's lesson of length conversions?

What is mass?When might we use grams rather than

kilograms?

Homework

Module 2 Lesson 2

Module 2 Lesson 2Homework

Module 2 Lesson 2

LESSON 3 OBJECTIVE

Express metric capacity measurements in terms of a smaller unit

Model and solve addition and subtraction word problems involving metric capacity

• 1 m = _______ cm

• 2 m = ________cm

• 4 m = ________cm

• 4 m 50 cm = ________cm

• 8 m 50 cm = _______ cm

• 8 m 5 cm = ________cm

• 6 m 35 cm = ________cm

• 4 m 7 cm = ________cm

• 1,000 m = _______ km

• 2,000 m = ________km

• 7,000 m = ________km

• 9,000 m = ________km

1 km ? m1,000

1 km + 1,000 m = 1 km + 1 km = 2 km

2 km ? m1,000

2 km + 1,000 m = 2 km + 1 km = 3 km

1,000 m ? km7 km

1,000 m + 7 km = 1 km + 7 km = 8 km

Count by grams in the following sequence and change directions when you see the arrow.

• 500 g• 1,000 g• 1,500 g• 2,000 g• 2,500 g• 3,000 g

• 2,500 g

• 2,000 g

• 1,500 g

• 1,000 g

• 500 g• 0 g

You did it!

FluencyLesson 3

• 500 g• 1 kg• 1,500 g• 2 kg• 2,500 g• 3 kg

• 2,500 g

• 2 kg• 1,500

g• 1 kg• 500 g

You did it!

FluencyLesson 3

• 500 g• 1 kg• 1 kg 500 g• 2 kg• 2 kg 500 g• 3 kg

• 2 kg 500 g

• 2 kg• 1 kg 500

g• 1 kg• 500 g

You did it!

FluencyLesson 3

Count by grams in the following sequence. You will not change directions.

• 200 g• 400 g• 600 g• 800 g• 1 kg• 1 kg 200

g• 1 kg 400

g• 1 kg 600

g• 1 kg 800

g• 2 kg

You did it!

FluencyLesson 3

• 600 g• 1,200 g• 1,800 g• 2,400 g• 3 kg

• 2,400 g• 1,800 g• 1,200 g• 600 g You

did it!

FluencyLesson 3

• 600 g• 1 kg 200 g• 1 kg 800 g• 2 kg 400 g• 3 kg

• 2 kg 400 g

• 1 kg 800 g

• 1 kg 200 g

• 600 g

You did it!

FluencyLesson 3

560 cm + 230 cm = _______

5 meters

2 meters

FluencyLesson 3

meters

650 cm - 230 cm = _______

6 meters

2 meter

FluencyLesson 3

Add the cm: 70 cm + 20 cm = 50 cm The difference is 9 m 50 cm.

470 cm + 520 cm = _______

4 meters

5 meter

FluencyLesson 3

Application Problem 8 minutes

The Lee family had 3 liters of water. Each liter of water weighs 1 kilogram. At the end of the day, they have 290 grams of water left. How much water did they drink? Draw a tape model and solve using mental math or an algorithm.

CONCEPT DEVELOPMENT 30 MINUTES

Materials: Several 3-liter beakers

with measurements of liters and milliliters

Water Personal white boards

Concept Development Lesson 3 Problem 1

Directions: Compare the sizes and note the relationship between 1 liter and 1 milliliters.

Look at the mark on your beaker that says 1 liter. Pour water into your beaker until you reach that

amount. How many milliliters are in your beaker? 1,000 mL How do you know? 1 liter is the same as 1,000 milliliters. The beaker

shows that the measurements are the same.

1 L = 1,000 ML CONCEPT DEVELOPMENT LESSON 3 PROBLEM 1

With your partner, locate 1,500 milliliters and pour in more water to measure 1,500mL.

How many liters do you have?

Less than 2 L but more than 1L. 1 liter 500 milliliters.

Yes, we just named mixed unit of grams and kilograms in our previous lesson. Now we will can use mixed units of liters and milliliters by using both sides of the scale of the beaker.

CONCEPT DEVELOPMENTLESSON 3 PROBLEM 1

1 L 500 ML = 1,500 ML

• Pour water to measure liters. How many milliliters equals 2 liters?

• 2,000 mL

• Pour more water to measure 2,200 mL of water. How many liters equals 2,200 mL?

• 2 L 200 mL

LESSON 3 PROBLEM 1

Activity

I have several beakers of different amounts of water prepared. You will circulate to each beaker, recording the amount of water as mixed units of liters and milliliters and milliliters.

We will now compare answers as a class and record finding on the board to show equivalency between units of liters and milliliters and milliliters.

32 L 420 mL + 13 L 858 mL= ______

Problem 2Add mixed units of capacity using the algorithm or a simplifying strategy.

What strategy would you

A simplifying strategy because 420 mL

decomposed to 15 ml and 5 mL and 400 mL plus 585

makes 600 mL. 600 mL + 400mL is 1 L with 5 mL left over. 46 liters 5 milliliters.

There are some renamings so an algorithm could

work too.

I can solve it mentally and

then check my work with an

algorithm.

Choose the way you want to do it. If you finish before two

minutes is up, try solving a different way. Let’s have two pairs of students work at the

board, one pair using the algorithm, one pair recording a

simplifying strategy.

32 L 420 mL + 13 L 858 mL= ______

Algorithm A:

32 L 420 mL + 13 L 858 mL= ______

Algorithm B:

32 L 420 mL + 13 L 858 mL= ______

Simplifying Solution C:

Problem 3Subtract mixed units of capacity using the algorithm or a simplifying strategy

12 L 215 mL - 8 L 600 mL= ______ A simplifying

strategy or the algorithm?

Oh for sure I’m using the

algorithm. We have to rename

a liter.

A simplifying strategy. I can count on from 8

liters 600 milliliters.

I can do mental math. I’ll show you

when we solve.

Choose the way you want to do it. If you finish before two minutes is up, try solving

a different way. Let’s have two pairs of students work at the board, one pair using

the algorithm, one pair recording a simplifying strategy.

Problem 3Subtract mixed units of capacity using the algorithm or a simplifying strategy

12 L 215 mL - 8 L 600 mL= ______Algorithm A:Algorithm B:Algorithm C:

Algorithm D:Algorithm E:

Jennifer was making 2,170 milliliters of her favorite drink that combines iced tea and lemonade. If she put in 1 liter 300 milliliters of iced tea, how much lemonade does she need?

Problem 4Solve a word problem involving mixed units

of capacity.

Problem Set(10 Minutes)

Problem Set Lesson 3 Problems 1 and 2

Concept DevelopmentLesson 3 Problem SetProblem 3

Lesson 3Problem SetProblems 4 and 5

• In Problem 4(a), what was your strategy for ordering the drinks?

• Discuss why you chose to solve Problem 5 using mixed units or converting all units to milliliters.

• Which strategy do you prefer for adding and subtracting mixed units?

• Why is one way preferable to the other for you? • What new terms to describe capacity did you learn today? • What patterns have you noticed about the vocabulary used to

measure distance, mass, and capacity? • How did the Application Problem connect to today’s lesson? • Describe the relationship between liters and milliliters. • How did today’s lesson relate to the lessons on weight and

length?

DebriefLesson Objective: Express metric capacity measurements in terms of a smaller unit;Model and solve addition and subtraction word problems involving metric capacity

Problem SetDebriefLesson 3

Homework

MODULE 2 TOPIC B LESSON 4METRIC UNIT CONVERSIONS4.MD.1 and 4.MD.2

LESSON 4 OBJECTIVE

Know and relate metric units to place value units in order to express measurements in different units

3 units

PERIMETER AND AREA (4 MINUTES)FluencyLesson 4

5 units

What’s the length of the longest side?What’s the length of the opposite side?

5 units 10 Units

What is the sum of the rectangle’s two

longest lengths?

What’s the length of the shortest side?

What’s the length of the missing side?

6 UnitsWhat is the sum of the rectangle’s two shortest lengths?

3 square units

Let’s see how many square

units there are in the rectangle,

counting by threes.

5 square units

How many square units are in one

How many rows of 3 square units are

there?

3 units

4 units

What’s the length of the longest side?What’s the length of the opposite side?

4 units 8 Units

What is the sum of the rectangle’s two shortest lengths?

3 square units

counting by threes.

4 square units

there?

6 UnitsWhat is the sum of the rectangle’s two

longest lengths?

6 units

4 units

What’s the length of the opposite side?

4 units

8 Units

What’s the length of the longest side?

What is the sum of the rectangle’s two longest lengths?

6 square units

counting by sixes.

4 square units

there?

12 UnitsWhat is the sum of the rectangle’s two shortest lengths?

FLUENCY PRACTICE – SPRINT A

Think!

Take your

Get set!

FLUENCY PRACTICE – SPRINT B

There is a mistake in the module - they have no sprint B. Perhaps they will correct this error in

later versions of the module.

Think!

Take your

Get set!

• 1 m 20 cm = _______ cm

• 1 m 80 cm = ________cm

• 1 m 8 cm = ________cm

• 2 m 4 cm = ________cm

• 1,500 g = ____kg ___g

• 1,300 g = ____kg ____g

• 1,030 g = ____kg ____g

• 1,005 g = ____kg ____g

• 1 liter 700 mL = _______ mL

• 1 liter 70 mL = ________mL

• 1 liter 7 mL = ________mL

• 1 liter 80 mL = ________mL

Count by 500 mL in the following sequence and change directions when you see the arrow.

• 500 mL• 1,000 mL• 1,500 mL• 2,000 mL• 2,500 mL• 3,000 mL

• 2,500 mL• 2,000 mL• 1,500 mL• 1,000 mL• 500 mL• 0 mL

You did it!

FluencyLesson 4

• 500 mL• 1 liter• 1,500 mL• 2 liters• 2,500 mL• 3 liters

• 2,500 mL• 2 liters• 1,500 mL• 1 liter• 500 mL• 0 liters

You did it!

FluencyLesson 4

Count by 200 mL in the following sequence. You will not change directions this time.

• 200 mL• 400 mL• 600 mL• 800 mL• 1 liter• 1 liter 200

mL• 1 liter 400

• 1 liter 600 mL• 1 liter 800 mL• 2 liters• 2 liters 200

mL• 2 liters 400

mL• 2 liters 600

mL• 2 liters 800

mL• 3 liters

You did it!

FluencyLesson 4

• 400 mL• 800 mL• 1,200 mL• 1,600 mL• 2,000 mL• 2,400 mL

• 2,000 mL• 1,600 mL• 1,200 mL• 800 mL• 400 mL• 0 mL

You did it!

FluencyLesson 4

• 400 mL• 800 mL• 1 liter 200 mL• 1,600 mL• 2 liters• 2 liters 400

• 2 liters• 1,600 mL• 1 liter 200 mL• 800 mL• 400 mL• 0 mL

You did it!

FluencyLesson 4

Application ProblemApplication ProblemLesson 4

Adam poured 1 liter 460 milliliters of water into a beaker. Over three days, some of the water evaporated. On day four, 979 milliliters of water remained in the beaker. How much water evaporated?

Concept DevelopmentNote patterns of times as much among units of length, mass, capacity, and place

value.

Concept DevelopmentProblem 1Lesson 4

Turn and tell your neighbor the units for mass, length,

and capacity that we have learned so far.

Gram, kilogram, centimeter, meter, kilometer, milliliter,

liter.

What relationship have you discovered between milliliters

and liters?1 liter is 1,000

milliliters. 1 liter is 1,000 times

as much as 1 milliliter.

1 L = 1,000 x 1 mL

value.

What do you notice about the

relationship between grams and kilograms?

Meters and kilometers? Write your answer as an

equation.

1 L = 1,000 x 1 mL

1 kg = 1,000 x 1 g

1 km = 1,000 x 1 m

1 kilogram is 1,000 times as much as 1 gram.

1 kilometer is 1,000 times as much as 1 meter.

value.

I wonder if other units have similar relationships. What other units have we discussed in fourth grade so far?

OnesTens

HundredsThousands

Ten thousands

Hundred thousands

value.

What do you notice about the units of place value? Are the relationships similar to those of metric units?

value.

What unit is 100 times as much as 1 centimeter?Write your answer as an equation.

Can you think of a place value unit relation that is similar?

1 meter = 100 x 1 centimeter

1 hundred is 100 times as much as 1 one.

1 hundred thousandis 100 times

as much as 1 thousand.

Concept DevelopmentRelate units of length, mass, and capacity to units of place value

• 1 m = 100 cm• One meter is 100 centimeters. What unit is 100 ones?• 1 hundred = 100 ones• 1 thousand = 1,000 ones• 1,200 mL = 1 liter 200 mL• 1,200 = 1 thousand 200 ones• 15,450 mL = 15 liters 450 mL• 15,450 ones = 15 thousand 450 ones• 15,450 kilograms = 15 kilograms 450 grams• 895 cm = 8 meters 95 cm• 895 ones = 8 hundreds 95 ones

Concept DevelopmentRelate units of length, mass, and capacity to units of place value

1 L 100 mL 10 mL 1 mL

1 ,2 0 0

1,000100100

Thousands Hundreds Tens Ones

1 ,2 0 0

1,000 100100

1,200 mL = 1 liter 200 mL

1,200 = 1 thousand 200 ones

How are the two charts similar?

15,450 mL = 15 liter 450 mL

15,450 = 15 thousands. 450 ones

10 L 1 L 100 mL 10 mL 1mL

l lllll llll lllll

10 thousands

1 Thousands

100s 10s 1s

l lllll llll lllll

15,450 g = 15 kg 450 g

15,450 = 15 thousands 450 ones

10 kg 1 kg 100 g 10 g 1g

l lllll llll lllll

10 thousands

1 Thousands

100s 10s 1s

l lllll llll lllll

724,706 mL____ 72 L 760 mLWhich is more? Tell your partner how you can use place value

knowledge to compare.

100 L 10 L 1 L 100 mL

10 mL 1 mL

7 2, 7 6 0

7 2 4, 7 0 6

Problem 3Compare metric units using place value

knowledge and a number line.

I see that 724,706

milliliters is 724 liters and 724 is greater

than 72.

Draw a number line from 0 km to 2 km. One kilometer is how many meters?

1,000 meters

2 kilometers is equal to how many meters?

2,000 meters

Discuss with your partner how many centimeters are equal to 1 kilometer.

1 meter is 100 centimeters. 1 kilometer is 1 thousand meters. So, 1 thousand times 1 hundred is easy, it is 100 thousand. 2 meters is 200 centimeters so 10 meters is 1,000

centimeters. Ten of those is 100,000 centimeters.

Work with your partner to place these values on the number line.

7,256 m, 7 km 246 m and 725,900 cm

I know that 100 cm equals 1 meter. In the number 725,900 there are 7,259 hundreds. That means that 725,900 cm = 7,259 m. Now I am able to place 725,900 cm on the number line.

725,900

7,256 m is between 7,250 m and 7,260 m. It is less that 7,259 m. 7 km 246 m is between 7 km 240 m (7,240 m) and 7 km 250 m (7,250 m ).

7,256 m

Since all the measures have 7 kilometers, I can compare meters. 256 is more than 246. 259 is more than 256.

7 km 246

Lesson 4 Problem Set Problems 2 - 4

What patterns did you notice as

you solved Problem 2?

• Explain to your partner how to find the number of centimeters in 1 kilometer. Did you relate each unit to meters? Place value?

• Do you find the number line helpful when comparing measures? Why or why not?

• How are metric units and place value units similar? Different? Do money units relate to place value units similarly? Time units?

• How did finding the amount of water that evaporated from Adam’s beaker (in the Application Problem) connect to place value?

• How did the previous lessons on conversions prepare you for today’s lesson?

DebriefLesson Objective: Know and relate metric units to place value units in order express

measurements in different units.

Problem SetDebriefLesson 4

Homework

MODULE 2 TOPIC B LESSON 5METRIC UNIT CONVERSIONS4.MD.1 and 4.MD.2

LESSON 5 OBJECTIVE

Use addition and subtraction to solve multi-step word problems involving length, mass, and capacity

FLUENCY PRACTICE – SPRINT A

Think!

Take your

Get set!

FLUENCY PRACTICE – SPRINT B

Think!

Take your

Get set!

• 1 L 400 mL = ________mL

• 1 L 40 mL = ________mL

• 1 L 4 mL = ________mL

• 1 L 90 mL = ________mL

• 800 cm• 1,600 cm• 2,400 cm• 3,200 cm• 4,000cm

• 3,200 cm• 2,400 cm• 1,600 cm• 800 cm You

did it!

FluencyLesson 5

• 800 cm• 1,600 cm• 2,400 cm• 3,200 cm• 40 m

• 3,200 cm• 2,400 cm• 1,600 cm• 800 cm You

did it!

FluencyLesson 5

• 80 cm• 1 m 60 cm• 2 m 40 cm• 3 m 20 cm• 4 m

• 3 m 20 cm• 2 m 40 cm• 1 m 60 cm• 80 cm You

did it!

FluencyLesson 5

Problem SetLesson 5 42 min.Concept

Development

R DDraw

WWrite

Can you

draw some

-thing

What can you

What conclusions

can you make from

your drawing?

Problem 1 Problem SetLesson 5 42 min.

The first four problems of today’s Problem Set are the Concept

Development portion of the lesson.You will complete the final two

problems independently.

Your turn! Try the

next two by

yourself!

Debrief question:How was the work completed to solve

Problem 5 different than the other problems?

Problem 6

Debrief question:How was drawing a model helpful in

organizing your thoughts to solve Problem 6?

Problem SetLesson 5 42 min.

• Did you find yourself using similar strategies to add and to subtract the mixed unit problems?

• How can drawing different models to represent a problem lead you to a correct answer?

• Describe a mixed unit. What other mixed units can you name?

• How can converting to a smaller unit be useful when solving problems? When is it not useful?

• How is regrouping a mixed unit of measurement similar to regrouping a whole number when adding or subtracting?

• In what ways is converting mixed units of measurement useful in everyday situations?

Student Debrief

Problem SetLesson 5 42 min.

Exit TicketLesson 5 .

Homework

Module 2 Topic A Lesson 1 Metric Unit Conversions

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