Common Core Mathematical Practices (MP) Domains • Number and Operations in Base Ten (NBT) • Number and Operations–Fractions (NF) • Measurement and Data (MD) INVESTIGATION 1 Geometric Solids Skip this Investigation. Day Session Common Core Adaptation Common Core Standards 1.1 What’s the Shape? 1.2 Silhouettes of Geometric Solids 1.3 City Landscapes 1.4 Assessment: Match the Silhouettes INVESTIGATION 2 Making and Visualizing Cube Buildings Skip this Investigation. Day Session Common Core Adaptation Common Core Standards 2.1 Building with Cubes 2.2 Drawing Silhouettes of Cube Buildings 2.3 Drawing Before Building 2.4 Integrating Views to Make a Cube Building 2.5 Assessment: Drawing Silhouettes Moving Between Solids and Silhouettes Unit 7 Instructional Plan CC71
Transcript
Common CoreMathematical Practices (MP)
Domains• Number and Operations in Base Ten (NBT)• Number and Operations–Fractions (NF)• Measurement and Data (MD)
I N V E S T I G AT I O N 1
Geometric Solids Skip this Investigation.
Day Session Common Core Adaptation Common Core Standards
1.1 What’s the Shape?
1.2 Silhouettes of Geometric Solids
1.3 City Landscapes
1.4 Assessment: Match the Silhouettes
I N V E S T I G AT I O N 2
Making and Visualizing Cube Buildings Skip this Investigation.
Day Session Common Core Adaptation Common Core Standards
2.1 Building with Cubes
2.2 Drawing Silhouettes of Cube Buildings
2.3 Drawing Before Building
2.4 Integrating Views to Make a Cube Building
2.5 Assessment: Drawing Silhouettes
Moving Between Solids and Silhouettes
Unit 7
Instructional Plan CC71
INV12_TE04_U07.indd 71 6/3/11 3:39 PM
I N V E S T I G AT I O N 3
Understanding Volume
Day Session Common Core Adaptation Common Core Standards
1 3.1 How Many Cubes? MP1, MP4, MP8 4.NF.7SESSION FOLLOW-UP
Daily Practice and Homework
Family Letter: Make copies of C47-C48, Family Letter, as a replacement for M7-M10, Family Letter.
2 3.2 Patterns from the Bottom Up
MP1, MP4, MP8 4.NF.7
3 3.3 Volume of Boxes MP1, MP4, MP8
4 3.4 Volume of Boxes, continued
MP1, MP4, MP8
5 3.5A Measurement Equivalents See p. CC73. MP8 4.NBT.2, 4.MD.1
Daily Practice: In addition to Student Activity Book page 52, students complete Student Activity Book page 52H or C56 (Solving Measurement Problems) for reinforcement of the content of this unit.
CC72 UNIT 7 Moving Between Solids and Silhouettes
INV12_TE04_U07.indd 72 6/6/11 11:56 AM
s e s s i o n 3 . 5 A
Vocabularyweightmasscapacity
Today’s Plan MaterialsAcTiViTy
Converting Weights and Masses 30 Min clAss PAirs
•Student Activity Book,p.52Aorc49, converting Weights and MassesMakecopies.(as needed)
•Student Activity Book,p.52Borc50, More conversions Makecopies.(as needed)
•MeasurementEquivalentschart
session FolloW-UP
Daily Practice •Student Activity Book,p.52Corc51, converting Measurements Makecopies.(asneeded)
Measurement EquivalentsMath Focus Points
Converting measurements in larger units to smaller units
Making tables of equivalent measurements
Ten-Minute MathPracticing Place Value: Comparing Numbers Using Digit Cards, make two 3-digit numbers. Ask students to write down the numbers and compare them using the <, >, or = signs. Have one or two students give the answer and explain how they compared numbers. Repeat the activity using 4-digit, then 5-digit numbers.
Remind the class of the work they did with linear measurements earlier in the year. Tell students that today they will learn how to convert measurements of weight, mass, capacity, and time.
Let’s say we want to know how heavy something is. We could weigh it on a scale. What units are used to measure weight?
Collect a few answers. Then focus on pounds and ounces.
A loaf of bread weighs about 1 pound, and a slice of bread weighs about 1 ounce.
Direct the class’ attention to the chart of measurement equivalents you prepared. (Keep the chart posted for this session and the next two sessions.)
These measurement equivalents tell you how different units are related. The first equation in the chart tells you that there are 16 ounces in a pound. That means a pound is 16 times as heavy as an ounce.
You can use these equivalents to help you convert from one unit to another. For example, suppose a sack of sugar weighs 4 pounds. How many ounces is that? Work with your partner to figure this out. Then explain your thinking.
Students might say:“Since there are 16 ounces in 1 pound, I multiplied 4 times 16 to figure out how many ounces are in 4 pounds. 4 × 16 = 64, so 4 pounds is 64 ounces.”
Ask students how they would convert 3 pounds 10 ounces to ounces.
Students might say:
“First, multiply 3 times 16 to change 3 pounds to ounces. That’s 48. Then add on the extra 10 ounces. You get 58 ounces.”
Kilograms and grams can be used to measure mass or weight. 1
A cantaloupe has a mass of about 1 kilogram, and a grape has a mass of about 1 gram.
Ask students to convert 6 kilograms to grams using the information in the chart and explain how they found the answer. 2
Students might say:
“It’s 6,000 grams. I multiplied 6 by 1,000 and got 6,000. That’s easy!”
Have students convert 15 kilograms to grams. Then have them complete Student Activity Book page 52A or C49. Be sure students understand that when they convert from larger units to smaller, they start by multiplying. There should always be a greater number of smaller units because it takes more of them to represent the same amount.
OngOing ASSeSSment: Obser ving Student s at Work
• Do students use the correct equivalent?
• Do students multiply by the correct conversion factor?
▲ Student Activity Book, Unit 7, p. 52A; Resource masters, C49
math note 1 Weight vs. Mass Students are not
expected to know the difference between weight and mass. The difference between these two terms is cognitively difficult. For these sessions a distinction will not be made between weight and mass. If students want to know the difference between weight and mass, the weight of an object depends on the pull of gravity on that object. The weight, say, of a 200-pound man on Earth is only 33 pounds on the Moon. The mass of an object is the amount of matter the object contains. It is not affected by gravity. The mass of a 90-kilogram man on Earth is still 90 kilograms on the Moon.
teaching note2 Multiplying by 10, 100, and 1,000 As
students convert within the metric system of measurement, it is a good time to discuss patterns for multiplying by 10, 100, and 1,000. Use examples such as the following: 8 × 10 = 80 8 × 100 = 800 8 × 1,000 = 8,000
diFFerentiAtion: Suppor ting the range of Lear ner s
For students who struggle with the computations, provide problems with smaller numbers. Some students will benefit from making and using a multiple tower for 16 to help in their work with pounds and ounces.
Students who easily make these conversions can be challenged to try some that involve fractions of a unit. For example, ask students to complete the following conversions:
41 _ 2 pounds = ___ ounces
2.5 kilograms = ___ grams
A c t i v i t y
Converting CapacitiescLASS15 Min
When you measure how much liquid a container holds, you are finding its capacity. Some of the U.S. standard units for measuring capacity are cups, pints, quarts, and gallons. In the metric system, liters and milliliters are often used to measure capacity.
Focus on the time equivalents given in the chart. Ask students to make the following conversions:
• Convert 8 hours to minutes.
• Convert 5 minutes to seconds.
• Convert 2 hours 10 minutes to minutes.
Have students complete the capacity and time conversions on Student Activity Book page 52B or C50. Remind them to refer to the equivalents on the chart as they solve the problems.
S e S S i o n F o l l o w - U p
Daily Practice DailyPractice: For reinforcement of this unit’s content,
have students complete Student Activity Book page 52C or C51.
•Student Activity Book,p.52Eorc53, Time Problems Makecopies.(asneeded)
•MeasurementEquivalentschart
session Follow-uP
Daily Practice •Student Activity Book,p.52Fand52Gorc54, More Measurement Problems and c55, More Measurement conversions Makecopies.(asneeded)
Problem Solving Involving MeasurementsMath Focus Points
Using the four operations to solve word problems involving measurements
Ten-Minute MathPracticing Place Value: Comparing Numbers Using Digit Cards, make two 3-digit numbers. Ask students to write down the numbers and compare them using the <, >, or = signs. Have one or two students give the answer and explain how they compared numbers. Repeat the activity using 4-digit, then 5-digit numbers.
Draw students’ attention to the Measurement Equivalents chart.
You have been using these equivalents to convert measurements. Sometimes you need to convert measurements to solve word problems. Talk to your partner and solve this problem:
A chef made 20 quarts of soup. How many 1-gallon storage containers can the chef fill with the soup?
Students might say:“We knew we had to divide. We looked at the chart and saw that a gallon is the same as 4 quarts. So we divided 20 by 4 and got 5. 5 containers would be filled.”
“We drew 20 dots for the quarts. Then we circled groups of 4 to divide them into gallons. We got 5 groups, so that’s 5 gallons.”
Have students work in pairs to complete Student Activity Book page 52D or C52. Tell them to be prepared to share their solutions to Problem 4.
• Dostudentsselectthecorrectoperationtosolvetheproblem?Do they use diagrams to help picture the situation?
DIFFerenTIATIOn: Suppor ting the range of lear ner s
Students who are having difficulty may be uncertain whether they need to make conversions and, if so, which ones to make. Explain that if there are two different units in the problem, they should convert the measurement given in larger units to the smaller units of measurement.
▲ Student Activity Book, Unit 7, p. 52D; resource Masters, C52
Session 3.5B problem Solving Involving Measurements CC79
Time ProblemsSolve each problem and show your work.
1. Ramona went on a long hike. She started her hike at 8:00 a.m. and hiked for 2 hours 45 minutes. When did Ramona finish her hike?
2. A television station ran a 2-minute commercial about pet food. It was followed by a 90-second commercial about an airline. Which commercial was longer? How much longer was it?
3. A party started at 7:30 p.m. and ended at 9:45 p.m. How long did the party last?
4. Mr. Chin wants to get 8 hours of sleep. If he needs to get up at 6:15 a.m., when should he go to sleep?
5. Ms. Curtis is driving 5 hours to visit her aunt. She drove for 2 _ 5 of the time and then stopped for lunch. For how many hours has she already driven?
Math Focus Points for Discussion Usingthefouroperationstosolvewordproblemsinvolving
measurements
Use Problem 4 from Student Activity Book page 52D or C52 as the focus for this discussion. Read the problem and ask students to share their solutions.
There are 21_2 pints of apple juice and 11_2 pints of grape juice in the refrigerator. How much juice is there in all?
Students might say:“We didn’t think we had to change anything since it’s all in pints. We drew it on a number line so we could add. We got 4 pints. I guess we could change this to quarts, but the problem didn’t say so.”
2 12_ 1 1
2_
0 1 2 3 4 5
“We drew squares and shaded them, so we could see we had 4 pints in all.”
“We just added the numbers. 1 _ 2 of a pint and 1 _ 2 of a pint makes 1 pint. Then we added the whole numbers. 1 + 2 = 3. And we put it all together and got 4 pints.”
▲ Student Activity Book, Unit 7, p. 52E; Resource Masters, c53
cc80 invEStigAtion 3 Understanding volume
INV12_TE04_U07_S3.5B.indd 80 6/3/11 4:18 PM
DateNameMoving Between Solids and Silhouettes Daily Practice
More Measurement Problems Solve each problem and show your work.
1. Marisol used 2 3 _ 4 gallons of paint to paint the walls of her bedroom and 3 _ 4 of a gallon to paint the ceiling. How much paint did she use in all?
2. Jill went shopping from 3:45 p.m. to 5:00 p.m. How long did she shop?
3. The mass of a melon is 2 kilograms. The mass of a plum is 75 grams. How much greater is the mass of the melon? (1 kilogram = 1,000 grams)
4. Bill went to the museum at 11:30 a.m. He stayed for 3 1 _ 2 hours. When did he leave?
5. Terrell made 4 pints of soup. How many 2-cup servings of soup would this be? (1 pint = 2 cups)
note Students use the four operations to solve problems involving measurements.
“We knew 1 _ 2 of a pint is a cup. So we changed everything to cups and then added 5 cups and 3 cups. We got 8 cups. Then we changed that back to 4 pints for our answer.”
Discuss these and other strategies for solving the problem. Ask students to consider whether some strategies seem easier or more efficient.
A C t i v i t y
Time ProblemsClASS20 Min
Explain that times from midnight to noon are called a.m. times and that times from noon to midnight are called p.m. times.
Suppose you get to school at 8:30 a.m. and stay there for 6 hours and 45 minutes. What time is it when you leave school? Explain how you figured it out.
Students might say:“3:15 p.m. I counted 4 hours to 12:30. Then I counted 2 more hours to 2:30, and 45 minutes more. I ended up at 3:15. It’s past noon, so it’s p.m.”
“It is 3:15 p.m. We drew a clock to help keep track of everything.”
Now, suppose you saw a movie that started at 7:15 p.m. and ended at 9:00 p.m. How long did the movie last?
After students solve this problem and share their answers, have them complete Student Activity Book page 52E or C53.
S e S S i o n F o l l o w - U p
Daily Practice DailyPractice: For reinforcement of this unit’s content,
have students complete Student Activity Book pages 52F and 52G or C54 and C55.
Session 3.5B problem Solving involving Measurements CC81
Time ProblemsSolve each problem and show your work.
1. Ramona went on a long hike. She started her hike at 8:00 a.m. and hiked for 2 hours 45 minutes. When did Ramona finish her hike?
2. A television station ran a 2-minute commercial about pet food. It was followed by a 90-second commercial about an airline. Which commercial was longer? How much longer was it?
3. A party started at 7:30 p.m. and ended at 9:45 p.m. How long did the party last?
4. Mr. Chin wants to get 8 hours of sleep. If he needs to get up at 6:15 a.m., when should he go to sleep?
5. Ms. Curtis is driving 5 hours to visit her aunt. She drove for 2 _ 5 of the time and then stopped for lunch. For how many hours has she already driven?
More Measurement Problems Solve each problem and show your work.
1. Marisol used 2 3 _ 4 gallons of paint to paint the walls of her bedroom and 3 _ 4 of a gallon to paint the ceiling. How much paint did she use in all?
2. Jill went shopping from 3:45 p.m. to 5:00 p.m. How long did she shop?
3. The mass of a melon is 2 kilograms. The mass of a plum is 75 grams. How much greater is the mass of the melon? (1 kilogram = 1,000 grams)
4. Bill went to the museum at 11:30 a.m. He stayed for 3 1 _ 2 hours. When did he leave?
5. Terrell made 4 pints of soup. How many 2-cup servings of soup would this be? (1 pint = 2 cups)
Unit 7 Session 3.5B
Moving Between Solids and Silhouettes
note Students use the four operations to solve problems involving measurements.
note Students use the four operations to solve problems involving measurements.
Daily Practice
Solving Measurement ProblemsSolve each problem and show your work.
1. A large canned ham has a mass of 3 kilograms. A small canned ham has a mass of 1.5 kilograms. What is the total mass of the two canned hams?
2. Mrs. Corelli worked in her garden from 1:30 p.m. to 3:15 p.m. How long did she work in her garden?
3. How many 5-minute cartoons can be shown in one hour? (The cartoons are shown one at a time.)
4. Enrique used 3 1 _ 2 gallons of apple juice and 2 1 _ 2 gallons of orange juice to make some fruit punch for a school picnic. How many quarts of juice are in the punch?
5. One fish bowl holds 10 liters of water and another holds 7,500 milliliters of water. Which fish bowl holds more water? How much more? (1 liter = 1,000 milliliters)
FechaNombreDe sólidos a siluetas Carta a la familia
Sobre las Matemáticas de esta unidad
Estimada familia:
Nuestra clase está empezando una nueva unidad de Matemáticas sobre geometría y
medición que se llama De sólidos a siluetas. En esta unidad los estudiantes trabajarán con
cubos y cajas de papel para desarrollar su comprensión de cómo medir el volumen de los
prismas rectangulares.
A lo largo de esta unidad, los estudiantes trabajarán para lograr este objetivo:
PUNTOS DE REFERENCIA/OBJETIVOS
EJEMPLOS
Hallar el volumen de edificios construidos con cubos y de prismas rectangulares.
¿Cuál es el volumen de este edificio construido con cubos?
La capa de abajo es de 4 unidades por 5 unidades, así que 20 cubos van a caber en la primera capa. El edificio tiene 3 capas de alto, por tanto el volumen es 3 × 20, o sea, 60 cubos.
En nuestra clase de Matemáticas, los estudiantes comentan problemas a fondo
y se les pide que comenten sus razonamientos y soluciones. Es importante que los
estudiantes resuelvan problemas de matemáticas de maneras que tengan sentido
para ellos. En el hogar, anime a su hijo/a a que le explique su razonamiento
Problemas de mediciónResuelve cada problema y muestra tu trabajo.
1. Lucy compró 3 cuartos de leche con chocolate y 2 galones de leche. ¿Cuántos cuartos de leche compró Lucy en total?
2. La masa de un conejo es 4 kilogramos. La masa de un ratón es 45 gramos. ¿Cuánto más grande es la masa del conejo?
3. Noemí vertió 1.2 litros de agua en una olla de 3 litros. ¿Cuánta más agua debe añadir para llenar completamente la olla?
4. Hay 2 1 _ 2 pintas de jugo de manzana y 1 1 _ 2 pintas de jugo de uva en el refrigerador. ¿Cuánto jugo hay en total?
5. El Sr. Dakarian compró 3 cuartos de jugo de naranja. Si su familia bebe 3 tazas de jugo de naranja cada día, ¿cuántos días durará el jugo de naranja?
Problemas de tiempoResuelve cada problema y muestra tu trabajo.
1. Ramona tomó una larga caminata. Comenzó su caminata a las 8:00 a.m. y caminó durante 2 horas 45 minutos. ¿Cuándo terminó su caminata Ramona?
2. Una estación de televisión transmitió un anuncio publicitario de 2 minutos sobre comida para mascotas. Fue seguido por un anuncio publicitario de 90 segundos sobre una línea aérea. ¿Qué anuncio publicitario duró más? ¿Cuánto más duró?
3. Una fiesta empezó a las 7:30 p.m. y terminó a las 9:45 p.m. ¿Cuánto duró la fiesta?
4. El Sr. Lin quiere dormir durante 8 horas. Si se tiene que levantar a las 6:15 a.m., ¿a qué hora debe ir a dormir?
5. La Srta. Curtis maneja 5 horas para visitar a su tía. Manejó 2 _ 5 del tiempo y luego se detuvo para almorzar. ¿Cuántas horas ya ha manejado?
Más problemas de mediciónResuelve cada problema y muestra tu trabajo.
1. Marisol usó 2 3 _ 4 galones de pintura para pintar las paredes de su dormitorio y 3 _ 4 de galón para pintar el techo. ¿Cuánta pintura usó en total?
2. Jill fue de compras de las 3:45 p.m. a las 5:00 p.m. ¿Cuánto tiempo estuvo de compras?
3. La masa de un melón es 2 kilogramos. La masa de una ciruela es 75 gramos. ¿Cuánto más grande es la masa del melón? (1 kilogramo = 1,000 gramos)
4. Bill fue al museo a las 11:30 A.M. Se quedó allí durante 3 1 _ 2 horas. ¿A qué hora se fue?
5. Terrell preparó 4 pintas de sopa. ¿Cuántas porciones de 2 tazas de sopa sería esto? (1 pinta = 2 tazas)
Unidad 7 Sesión 3.5B
notA Los estudiantes usan las cuatro operaciones para resolver problemas que incluyen mediciones.
Resolver problemas de mediciónResuelve cada problema y muestra tu trabajo.
1. Un jamón enlatado grande tiene una masa de 3 kilogramos. Un jamón enlatado pequeño tiene una masa de 1.5 kilogramos. ¿Cuál es la masa total de los dos jamones enlatados?
2. La Sra. Corelli trabajó en su jardín de la 1:30 p.m. a las 3:15 p.m. ¿Cuánto tiempo trabajó en su jardín?
3. ¿Cuántas caricaturas de 5 minutos se pueden mostrar en una hora? (Las caricaturas se muestran de una en una).
4. Enrique usó 3 1 _ 2 galones de jugo de manzana y 2 1 _ 2 galones de jugo de naranja para hacer refresco de frutas para un picnic escolar. ¿Cuántos cuartos de jugo hay en el refresco?
5. Una pecera contiene 10 litros de agua y otra contiene 7,500 mililitros de agua. ¿Qué pecera contiene más agua? ¿Cuánta más agua contiene? (1 litro = 1,000 mililitros)
Unidad 7 Sesión 3.5
notA Los estudiantes usan las cuatro operaciones para resolver problemas que incluyen mediciones.
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