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

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) Lesson 2 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 kg 1 meter 100 centimeters 1,000 grams 1 kilogram

Fluency practice continued Lesson 2 2,000 g = ____ kg 2 3,000 g = ____ kg 3 7,000 g = ____ kg 1,000 grams 1 kilogram 7 5,000 g = ___ kg 5

Number Bonds 2kg 1 kg __ g 1000 1 kg + 1, 000 g = 1 kg + 1kg = 2 kg Fluency Lesson 2 Number Bonds 2kg 1 kg __ g 1000 1 kg + 1, 000 g = 1 kg + 1kg = 2 kg

Number Bonds 3kg 2 kg __ g 1000 2 kg + 1,000 g = 2 kg + 1kg = 3 kg Fluency Lesson 2 Number Bonds 3kg 2 kg __ g 1000 2 kg + 1,000 g = 2 kg + 1kg = 3 kg

Number Bonds 5 kg 4 kg __ g 1,000 4 kg + 1,000 g = 4 kg + 1kg = 5 kg Fluency Lesson 2 Number Bonds 5 kg 4 kg __ g 1,000 4 kg + 1,000 g = 4 kg + 1kg = 5 kg

Unit counting (4 minutes) Fluency Lesson 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!

Unit counting (4 minutes) Fluency Lesson 2 Unit counting (4 minutes) Count by 50 cm in the following sequence and change directions when you see the arrow. 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!

Unit counting (4 minutes) Fluency Lesson 2 Unit counting (4 minutes) Count by 50 cm in the following sequence and change directions when you see the arrow. You did it! 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

Add and subtract meters and centimeters (4 minutes) Fluency Lesson 2 Add and subtract meters and centimeters (4 minutes) 540 cm + 320 cm = _______ Materials: Personal white boards Say 540 cm in meters and centimeters. Say 320 cm in meters and centimeters. 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. 5 meters 40 cm 3 meters 20 cm

Add and subtract meters and centimeters (4 minutes) Fluency Lesson 2 Add and subtract meters and centimeters (4 minutes) 420 cm + 350 cm = _______ Materials: Personal white boards Say 420 cm in meters and centimeters. Say 350 cm in meters and centimeters. 4 m 20 cm + 3 m 50 cm = _______ Add the meters: 4 m + 3 m = 7 meters Add the cm: 20 cm + 50 cm = 70 cm The sum is 7 m 70 cm. 4 meters 20 cm 3 meters 50 cm

Add and subtract meters and centimeters (4 minutes) Fluency Lesson 2 Add and subtract meters and centimeters (4 minutes) 650 cm - 140 cm = _______ Materials: Personal white boards Say 650 cm in meters and centimeters. Say 140 cm in meters and centimeters. 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. 6 meters 50 cm 1 meter 40 cm

Add and subtract meters and centimeters (4 minutes) 780 cm - 210 cm = _______ Materials: Personal white boards Say 780 cm in meters and centimeters. Say 210 cm in meters and centimeters. 7 m 80 cm - 2 m 10 cm = _______ Subtract the meters: 7 m - 2 m = 5 meters Subtract the cm: 80 cm - 10 cm = 70 cm The difference is 5 m 70 cm. 7 meters 80 cm 2 meter 10 cm

Application problem ( 8 minutes) Lesson 2 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

Algorithm solution 3,469 m + 4,301 m 7,770 m Application Problem Lesson 2 Algorithm solution 3,469 m + 4,301 m 7,770 m

Application Problem Lesson 2 Mental math solution 7 km = 7,000 m 7,000 m + 770 m = 7,770 m OR 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) Lesson 2 Problem 1 Concept development (30 minutes) Materials: Teacher: 1- L water bottle, small paper clips, dollar bill, dictionary, balance scale or weights. Student: Personal White Board

Experiments make me thirsty. Please give me a kilogram of H2O please! Concept Development Lesson 2 Problem 1 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!

1 kilogram = 1 gram The dictionary weighs about 1 kilogram. Concept Development Lesson 2 Problem 1 The mass of this small paper clip is about 1 gram. A dollar bill weighs about 1 gram too. 1 kilogram = 1 gram

Concept Development Lesson 2 Problem 1 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. Concept Development Lesson 2 Problem 1 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. or or

Gram How many grams are in 2 kilograms? 2000 g Concept Development Lesson 2 Problem 1 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. Gram

Mass Reference chart Concept Development Lesson 2 Problem 1 kg g 1 1,000 2 2,000 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 Concept Development Lesson 2 Problem 1 Mass: Relationship between kilograms and grams kg g 1 1,000 2 _____ 3 3,000 4 5,000 6,000 7 8 9,000 10

Compare kilograms and grams. Concept Development Lesson 2 Problem 1 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.

Let’s convert 1 kg 500 g to grams. Concept Development Lesson 2 Problem 1 Let’s convert 1 kg 500 g to grams. 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 300 g to grams. Concept Development Lesson 2 Problem 1 Let’s convert 1 kg 300 g to grams. 1 kilogram 300 grams is equal to how many grams? 1,300 grams

Let’s convert 5 kg 30 g to grams. Concept Development Lesson 2 Problem 1 Let’s convert 5 kg 30 g to 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!

2,500 grams is equal to how many kilograms? Concept Development Lesson 2 Problem 1 2,500 grams is equal to how many kilograms? 2 kg 500 g We made two groups of 1,000 grams, so we have 2 kilograms and 500 grams.

5,005 grams is equal to how many kilograms? Concept Development Lesson 2 Problem 1 5,005 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.

Concept Development Lesson 2 Problem 2 Problem 2 Add mixed units using the algorithm or simplifying strategies 8kg + 8,200 g =______ 8,000 g + 8,200 g = 16,200g Talk with your partner about how to solve this problem. 8 kg + 8kg 200 g = 16 kg 200g Or we can rename 8,200 g to 8 kg 200 g We can rename the kilograms to grams before adding. We can’t add different units together. We can rename 8kg to 8,000 g.

Concept Development Lesson 2 Problem 2 Problem 2 Add mixed units using the algorithm or simplifying strategies 8kg + 8,200 g =______ 8,000 g + 8,200 g = 16,200g 8 kg + 8kg 200 g = 16 kg 200g There is no regrouping and we can add the numbers easily mentally. Will we use the algorithm or a simplifying strategy? Why? A simplifying strategy!

Should we use a simplifying strategy or the algorithm? Concept Development Lesson 2 Problem 2 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. There is regrouping and the numbers are not easy to combine. I think the algorithm because the numbers are too big. I think I can use a simplifying strategy.

If you finish before the two minutes, try solving the problem another way. Choose the way you want to tackle the problem and work for the next two minutes on solving it. 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. Concept Development Lesson 2 Problem 2 25 kg 537 g + 5 kg 723 g = ____

Algorithm Solution A Algorithm Solution b Concept Development Lesson 2 Problem 2 25 kg 537 g + 5 kg 723 g = ____ Algorithm Solution A Algorithm Solution b 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 c Concept Development Lesson 2 Problem 2 25 kg 537 g + 5 kg 723 g = ____ Simplifying strategy c Simplifying strategy d 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

A simplifying strategy or the algorithm? Discuss with a partner. Concept Development Lesson 2 Problem 3 Problem 3 Subtract 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. 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. 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.

Algorithm Solution b Algorithm Solution A How did our first simplifying strategy pair solve the problem? They subtracted the 2 kg first. And then? Subtracted the 250 g from 1 kg. Concept Development Lesson 2 Problem 3 10 kg – 2 kg 250 g = Algorithm Solution A Algorithm Solution b What did they do in the second solution? Look at the first example algorithm. How did they prepare the algorithm for subtraction? 9 0 1010 10 kg 1,000 g - 2 kg 250 g 7 kg 750 g 9 0 9 9 10 10,000 g - 2,250 g 7,750 g 7 kg 750 g They renamed 10 kilograms as 9 kilograms and 1,000 g first. Converted kilograms to grams.

Simplifying strategy c 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. Concept Development Lesson 2 Problem 3 10 kg – 2 kg 250 g = Simplifying strategy c Simplifying strategy d 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?

Simplifying strategy c 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. They added up from 2 kilograms 250 grams to 3 kilograms first, and then added 7 more kilograms to get to 10 kilograms. Concept Development Lesson 2 Problem 3 10 kg – 2 kg 250 g = Simplifying strategy c Simplifying strategy d 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 What does the number line show? How did our mental math team solve the problem?

Concept Development Lesson 2 Problem 3 10 kg – 2 kg 250 g = Simplifying strategy + 750 g + 7 kg 2 kg 250 g 3 kg 10 kg 750 g + 7 kg = 7 kg 750 g

Concept Development Lesson 2 Problem 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.

Concept Development Lesson 2 Problem 3 32 kg 205 g – 5 kg 316 g

Tell your partner the known and unknown information. Concept Development Lesson 2 Problem 4 Problem 4 Solve a word problem involving mixed units of mass modeled with a tape diagram. 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? 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. Read with me. Take one minute to draw and label a tape diagram.

Algorithm solution A Algorithm solution b simplifying solution c Concept Development Lesson 2 Problem 4 Will you use an algorithm or a simplifying strategy? Label the missing part on your diagram and make a statement of solution Algorithm solution A Algorithm solution b simplifying solution c

Use the RDW approach for solving word problems. 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. 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 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.

Lesson 2 Problem Set Problems 1 and 2

Lesson 2 Problem Set Problem 3 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?

Lesson 2 Problem Set Problems 4 and 5

Lesson 2 Problem Set Problems 6 and 7 Explain to your partner how you solved Problem 7. Was there more than one way to solve it? In Problem 6, did it make sense to answer in the smaller unit or mixed unit?

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 2 Homework

Module 2 Lesson 2 Homework

Module 2 Lesson 2

Module 2 Lesson 2