Mathematical Thinking at Grade 5 Homework Packet · Mathematical Thinking at Grade 5 Homework...

Mathematical Thinking at Grade 5

Homework Packet

Also includes homework for the

following Ten-Minute Math Activities:

Exploring Data

Quick Images

What is Likely?

Today’s Number

Grade 5 Mathematical Thinking at Grade 5

Name______________________ Date__________________

Investigation 1 Session 1 Dear Parents/Guardians: The mathematical focus for this question is representing factor pairs as dimensions of a rectangular array. Khalik sells eggs. Typically, eggs are sold by the dozen (1 dozen = 12) in cartons containing 2 rows of 6 eggs.

2 6

Khalik wants to sell his eggs by the dozen using a different kind of carton.

a. Draw all the possible cartons Khalik could use. Each carton must contain an equal amount of eggs in each row.

b. Label the dimensions of each carton.

c. Khalik considers selling his eggs in cartons of 13. His wife, Chavonne, says this is not a practical idea. Explain her thinking.

2


Name______________________ Date__________________

Investigation 1 Session 2

Dear Parents/Guardians: The mathematical focus for this question is representing factor pairs as dimensions of a rectangular array.

The Boxwood Elementary School is preparing for their annual talent show. Mr. Diaz, the gym teacher, sets up the auditorium with 4 rows of chairs. Each row has 8 chairs in it.

4

8 a. The principal comes into the auditorium and tells Mr. Diaz

to make sure there are at least 30 chairs set-up. Are there enough chairs set-up already? Explain how you got your answer.

b. Ten minutes before the show begins, the principal runs into the auditorium and tells Mr. Diaz to set-up 16 more chairs. How could Mr. Diaz add these chairs to the existing rows so that they remain even? Draw a picture, label the dimensions, and give the total number of chairs in the resulting set-up. Explain how you got your answers.

c. Are there any other possibilities? If so, what are they?

3


Name______________________ Date__________________


Dear Parents/Guardians: The mathematical focus for this question is describing numbers and number relationships with mathematical terms such as factor, multiple, prime, and square.

Use the Hundred Chart below to answer the following questions.

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

a. Shade in all the multiples of 8 on the Hundred Chart.

b. Which shaded number is a square number? Explain how you got your answer.

c. List all the factors of this square number. Are any prime? If so, which one(s)? Explain how you got your answers.

4


Name______________________ Date__________________


Dear Parents/Guardians: The mathematical focus for this question is reasoning about number characteristics such as factor, multiple, prime, and square.

Guess My Number • my number is a factor of 24.

• my number is a factor of 36.

• my number is NOT prime or square.

What is my number?

List all the possibilities. Explain how you got your answer(s).

5


Name______________________ Date__________________ Ten-Minute Math: Exploring Data Dear Parents/Guardians: The mathematical focus for this question is describing important features of data.

The 5th Graders at Hope Valley Elementary School took a survey that asked, “How many pets do you have?”

The resulting data is displayed in the line plot below.

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

0 1 2 3 4 5

Number of Pets

a. What is the MOST number of pets a 5th grader from Hope Elementary School owns? Explain how you got your answer.

b. What is the typical number of pets a 5th grader from Hope Elementary School owns? Explain how you got your answer.

c. If this survey was given to the same students one year later, do you think the resulting data would be similar to the present data? Explain your answer.

d. If this survey were done in your class, do you think you would collect similar data? Explain why or why not.

6


Name______________________ Date__________________ Investigation 1 Session 5 Dear Parents/Guardians: The mathematical focus for this question is reasoning about number characteristics such as factor, multiple, prime, and square.

Guess My Number • my number is a multiple of 8.

• my number is a factor of 100.

What is my number?

List all the possibilities. Explain how you got your answer(s).

7


Name______________________ Date__________________

Investigation 1 Session 6 Dear Parents/Guardians: The mathematical focus for this question is reasoning about number characteristics such as factor, multiple, prime, and square.

Chan is skip counting by 15 up to 300.

Malique is skip counting by 20 up to 300.

a. Which numbers do Chan and Malique both say?

b. All these numbers are multiples of what number(s)?

8


Name______________________ Date__________________ Investigation 2 Session 1 Dear Parents/Guardians: The mathematical focus for this question is skip counting by factors of 100 and their multiples.

Use the chart below to answer the following questions.

Hilarious Henrietta’s Clothing Factory Inventory Product Monday Tuesday Wednesday Thursday Friday Saturday

Jeans 50 100 150

T-Shirts 200 400 800

Shoes 150 300 450

Hilarious Henrietta’s clothing factory makes the same number of jeans, t-shirts, and shoes every day.

a. Complete the inventory chart to show how many jeans, t-shirts, and shoes the factory has by the end of Thursday, Friday, and Saturday. Explain how you got your answers.

b. How many shoes does the factory make each day? Explain how you got your answer.

c. If the factory continued making t-shirts for six more days, how many t-shirts would they have? Assume no t-shirts are sold during this time. Explain how you got your answer.

9


Name______________________ Date__________________ Investigation 2 Session 2 Dear Parents/Guardians: The mathematical focus for this question is becoming familiar with factor pairs of 100.

One day, all the animals of the Hidden Forest gather together for a jumping race. The finish line is 100 feet away – but only those animals that land exactly on the finish line can win.

The chart below shows how long each animal can jump.

Animal Length of Jump

Turtle 1 foot

Badger 2 feet

Sparrow 3 feet

Skunk 4 feet

Owl 5 feet

Rabbit 6 feet

Fox 7 feet

Squirrel 8 feet

Chipmunk 9 feet

Coyote 10 feet

a. Which animals will land exactly on the finish line? Explain how you got your answers.

b. How many jumps will it take each of those animals to finish the race? Explain how you got your answers.

10


Name______________________ Date__________________ Ten-Minute Math: Exploring Data Dear Parents/Guardians: The mathematical focus for this question is graphing and interpreting data.

A group of first graders from Boston were asked the following question: “What is your favorite month?” The data from the survey is in the table below.

Month Number of Students

January lll

February llll

March llll llll

April llll llll llll ll

May llll llll llll llll

June llll llll llll llll llll l

July llll llll llll llll llll llll

August llll llll llll llll llll ll

September llll llll lll

October llll l

November llll ll

December llll llll llll llll llll

a. Which months were the most popular among the first graders? Why

do you think these months were so popular?

b. Which months were the least popular among the first graders? Why do you think these months were not very popular?

c. Group the data by season (winter, spring, summer, fall). Draw a line plot or a bar graph of this data using these new categories.

d. What fraction of first graders like summer the most? What familiar fraction is this close to? Explain how you got your answers.

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Name______________________ Date__________________ Investigation 2 Session 3 Dear Parents/Guardians: The mathematical focus for this question is finding relationships among factor pairs of different multiples of 100.

a. Name the factors that 100 and 200 share in common. Explain how you got your answer.

b. Write the factor pairs of 100 and 200 that include these common factors. Explain how you got your answers.

c. What relationships do you notice between these factor pairs of 100 and 200?

d. Using what you know from part c., name at least 4 factor pairs of 400. Show how you got your answers.

12


Name______________________ Date__________________ Investigation 2 Session 4 Dear Parents/Guardians: The mathematical focus for this question is becoming familiar with factor pairs of 1000.

Navel and Houston are building rectangles with 1000 squares.

They have an unlimited number of rectangles with the following dimensions:

25 x 10

20 x 25

40 x 5

a. How many different ways could Navel and Houston put these rectangles together to make rectangles with 1000 squares? Give the dimensions of each rectangle they can make. Explain how you solved this problem.

b. Did you find all the possibilities? Explain how you know.

13


Name______________________ Date__________________ Ten-Minute Math: Quick Images Dear Parents/Guardians: The mathematical focus for this question is using geometric vocabulary to describe shapes and patterns.

Use the figure below to answer the following question.

a. How many rectangles do you see in the figure above?

b. How many trapezoids do you see in the figure above?

c. How many octagons do you see in the figure above?

d. Do you see any other shapes in the figure above? How would you describe these shapes?

e. How would you describe the difference between a rectangle and a trapezoid? What do a rectangle and a trapezoid have in common?

14


Name______________________ Date__________________ Investigation 2 Session 5 Dear Parents/Guardians: The mathematical focus for this question is becoming familiar with skip-counting patterns leading to 1000.

Use the incomplete Thousand Chart below to answer the following questions. 1 2 3 4 5 20 140 300 500 720 1000

a. Fill in the following numbers in the Thousand Chart: 100,

280, 462, 820, 975. Explain how you found the right position for each number.

b. How far away is 820 from 280? Explain how you got your answer.

15


Name______________________ Date__________________ Investigation 3 Session 1 Dear Parents/Guardians: The mathematical focus for this question is using knowledge of landmarks up to 1000 to explore landmarks up to 10,000. Rasheem owns a candy bar factory. His factory makes the candy bars and then sends them to stores. One day, he receives an order for 1,000 candy bars from a large supermarket. a. Rasheem always tries to package the bars in the least possible

number of boxes. He has boxes that can hold bars in multiples of 50, up to 250. To make sure the bars do not break during shipment, each box must be completely filled with candy bars. What size box should Rasheem choose?

b. How many of those boxes will Rasheem need?

c. The candy bars were so popular that the following week the supermarket ordered 10,000 candy bars. What size boxes should Rasheem send this shipment in? How many will he need

Explain how you got your answers using numbers, pictures, or words.

16


Name______________________ Date__________________ Investigation 3 Session 2 Dear Parents/Guardians: The mathematical focus for this question is developing mental multiplication and division strategies that rely on landmarks up to 10,000.

Marta’s 5th grade class has 25 students in it. Each student received 7 pencils from their teacher at the beginning of the year.

a. How many pencils did their teacher buy for his students? Explain how you got your answer using pictures, numbers, or words. Do not use a calculator or a standard algorithm.

b. Marta’s principal wants to buy 14 pencils for all of the students in the school next month. There are 250 students in the school. How many pencils does he need to buy? Explain how you got your answer using pictures, numbers, or words. Do not use a calculator or a standard algorithm.

17


Name______________________ Date__________________ Ten-Minute Math: Quick Images Dear Parents/Guardians: The mathematical focus for this question is using geometric vocabulary to describe shapes and patterns.

Use the figure below to answer the following questions.

a. Describe this figure in your own words.

b. What smaller shapes do you see in the figure? How many of each shape are there?

c. How are the two types of triangles different from each other?

18



Paris collects stamps. Every month she gets 20 new stamps.

a. How many stamps will she have at the end of four years? Explain how you got your answer using pictures, numbers, or words. Do not use a calculator or a standard algorithm.

b. Paris thinks she will collect stamps forever! How many stamps will she have at the end of twenty years? Explain how you got your answer using pictures, numbers, or words. Do not use a calculator or a standard algorithm.

19


Name______________________ Date__________________ Ten-Minute Math: What is Likely? Dear Parents/Guardians: The mathematical focus for this question is exploring the relationship between a sample and the group of objects from which it comes.

Mrs. Fong has a jar filled with bean bags. Some bean bags are striped and some bean bags are spotted.

Mrs. Fong’s Jar

a) Mrs. Fong reaches into the jar and pulls out a bean bag without looking. Which kind of bean bag is she likely to pull out?

b) Which kind of bean bag is she unlikely to pull out?

c) Mrs. Fong pulls a bean bag from her jar 10 times, each time recording the bag she pulled and then replacing it in the jar. She ends up pulling out 5 striped bean bags and 5 spotted bean bags. Is this what you would expect to happen? Why or why not?

d) Mrs. Fong pulls out a bean bag from her jar 10 more times, as before. How many times do you expect her to pull out a spotted bean bag? Explain your answer.

20



The chart below shows the office supply inventory of the Boxwood elementary school:

Item Quantity

Boxes of Paper Clips 300

Reams of Paper 250

Bottles of Glue 1,000

Pencils 3,500

There are 25 teachers at the Boxwood elementary school, and all these supplies need to be passed out in equal numbers to each teacher.

a. How many boxes of paper clips will each teacher get?

b. How many reams of paper will each teacher get?

c. How many bottles of glue will each teacher get?

d. How many pencils will each teacher get?

Explain how you got your answers using pictures, numbers, or words. Do not use a calculator or a standard algorithm.

21


Name______________________ Date__________________ Investigation 3 Session 5 Dear Parents/Guardians: The mathematical focus for this question is finding factor pairs of one number by using knowledge of related factor pairs and number relationships. Radio station WXYZ, AM1150, is giving away $1,150. The first five people to call in will share the money evenly.

a. How much money will each caller win?

b. After the give-away, many listeners complain they did not win. The owners of the station decide to give away $1,150 again, but this time to have more winners. How many winners should they have? Give three possibilities, including how much money each of the winners will receive. The money must still be shared equally among all the winners, and the prize money must be paid in whole-dollar amounts.

Explain how you got your answers using pictures, numbers, or words.

22


Name______________________ Date__________________ Investigation 4 Session 1 Dear Parents/Guardians: The mathematical focus for this question is finding pairs of three-digit numbers that sum to 1000.

Melinda is driving from Boston to Chicago. The trip is 1,000 miles long.

a. She stops in Albany, New York on the way after driving 154 miles. How many more miles does she have to go?

b. When she reaches Cleveland, Ohio, she sees a sign that says Chicago is 382 miles away. How many miles has she traveled so far?

Explain how you got your answers using pictures, numbers, or words.

23


Name______________________ Date__________________ Investigation 4 Session 2

Dear Parents/Guardians: The mathematical focus for this question is ordering numbers to 10,000; using knowledge of landmarks up to 10,000 to solve a variety of problems.

The chart below shows the annual harvest from Asaph’s Apple Farm.

Year Bushels of Apples

1998 4,767

1999 4,675

2000 4,667

2001 4,757

a. Which year produced the least amount of apples? Explain your answer.

b. Which year produced the most amount of apples? Explain your answer.

c. If the 2002 harvest yields 150 more bushels of apples than the 1999 harvest, how many bushels will it yield? Explain how you got your answer using numbers, pictures, or words.

24


Name______________________ Date__________________ Ten-Minute Math: What is Likely? Dear Parents/Guardians: The mathematical focus for this question is exploring the relationship between a sample and the group of objects from which it comes.

Willette has a box of 100 popsicles. There are:

• 25 grape popsicles

• 50 cherry popsicles

• 25 orange popsicles

Willette has 10 friends who each pick one popsicle out of the box without looking.

a) How many do you think will pick cherry?

b) How many do you think will pick grape?

c) How many do you think will pick orange?

d) Suppose Willette takes all the cherry popsicles out of the box before her friends pick. How will this affect the flavors the friends pick? Is it more likely to pick an orange or a grape popsicle now?

Explain how you got your answers.

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Name______________________ Date__________________


Dear Parents/Guardians: The mathematical focus for this question is using knowledge of landmarks up to 10,000 to solve a variety of problems.

Juliana earns $400 every week working as a cashier at the supermarket.

Ramon earns $250 every week working an attendant at the laundromat.

They each want to buy a new car that costs $10,000.

a. How long will it take Juliana to earn $10,000?

b. How long will it take Ramon to earn $10,000?

c. If Juliana and Ramon put all their money together, how long will it take them to have $10,000?

Show how you got your answers using numbers, pictures, or words.

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Name______________________ Date__________________ Investigation 4 Session 4

Dear Parents/Guardians: The mathematical focus for this question is using knowledge of landmarks up to 10,000 to solve a variety of problems.

Oliver’s Game Shop sells video games for $75. He always keeps track of how many games he sells. One day, he loses his record of the day’s sales. He knows he sold between $9,000 and $10,000 worth of games. All of his customers that day paid with $100 bills, and received no change back.

a. How many video games did Oliver sell? Explain how you got your answer using numbers, pictures, or words.

b. Are there any other possible answers? Why or why not?

27


Name______________________ Date__________________ Investigation 4 Session 5 Dear Parents/Guardians: The mathematical focus for this question is reasoning about factors of 1,000 and 10,000 and their multiples.

Francine has between 200 and 300 chickens. Each chicken lays one egg each day. Each day, Francine collects the eggs and places them in egg cartons. Each egg carton can hold a dozen eggs (1 dozen = 12). At the end of 5 days, all the eggs she has collected fill more than 100 cartons, with no cartons partially-filled.

a. How many chickens could Francine have? Find all possible answers. Explain how you got your answers using numbers, pictures, or words.

b. Write another clue that gives this puzzle just one answer. Do not give a clue that tells a number less than or greater than the answer. What is the answer? Explain how you came up with your clue and how you found the answer.

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Name______________________ Date__________________ Ten-Minute Math: Today’s Number

Dear Parents/Guardians: The mathematical focus for this question is using knowledge of landmarks up to 1000 to explore landmarks up to 10,000. Write 5 number sentences that equal 1,500.

• Use only factors and multiples of 100.

• Do NOT use the digits 1 or 2

• Use each operation (addition, subtraction, multiplication, and division) at least once.

29


Name______________________ Date__________________

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Investigation 4 Session 6 Dear Parents/Guardians: The mathematical focus for this question is reasoning about factors of 1,000 and 10,000 and their multiples.

Kendra is training for the 10,000 meter track and field race in the 2008 Summer Olympics. A standard track is 400 meters around. Kendra runs 25 times (laps) around it during her race.

400 meter track

Kendra has found other tracks of different lengths she would like to run on. The lengths are listed in the chart below.

Track Length (meters) Laps Required for 10,000m race

400 25

200

250

500

1000

How many times will she have to run around each track to complete her 10,000 meter race? Write your answers in the chart. Explain how you got your answers using numbers, pictures, or words.

Name That Portion

Grade 5 Homework Packet



Exploring Data

Guess My Number

Seeing Numbers

Graph Stories

Also includes homework to review:


Picturing Polygons

Copyright © 2003 Boston Public Schools

Grade 5 Name that Portion Name _________________________ Date ________________________

Investigation 1, Session 1 Dear Parents/Guardians: The mathematical focus for this question is expressing the same quantity as a fraction, decimal, and percent. 1. Khayla is running in a 5-mile race. She has 2.5 miles left to go. a. How much has Khayla run so far? b. What fraction of the race has Khayla finished so far? c. What percentage of the race has Khayla finished so far? Show how you got your answers using numbers, pictures, and words. 2. Tonea has 2 sisters and 1 brother. a. What fraction of children in Tonea’s family are girls? b. What percentage of children in Tonea’s family are girls? c. What fraction of children in Tonea’s family are boys? d. What percentage of children in Tonea’s family are boys? Show how you got your answers using numbers, pictures, or words.


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 1, Session 2 Dear Parents/Guardians: The mathematical focus for this question is using fractions to describe how many in a group share a particular characteristic. Mei Mei is cataloging her books: 28 are biographies 13 are novels 34 are histories 9 are reference books a. What fraction of Mei Mei’s books are novels? b. What fraction of Mei Mei’s books are biographies? c. What fraction of Mei Mei’s books ARE NOT reference books? Show how you got your answers using numbers, pictures, or words.


Grade 5 Name that Portion Name _________________________ Date ________________________ Ten-Minute Math: Exploring Data Dear Parents/Guardians: The mathematical focus for this question is graphing and interpreting data.

The 5th graders at Hope Valley Elementary School were asked the question: “How old are you?” The answer of each student is below:

Miguel – 10 Esther – 10 Mackenzie – 11

Flora – 11 Juan – 10 Nia – 11

Peter – 12 Amos – 10 Shineequa – 10

Kayleena – 10 Ana – 10 Kelli – 9

Wei – 11 Moses – 10 Felix – 11

Demetrius – 10 Khalil – 10 Contance – 11

a. Display the data in a line plot.

b. What is the typical age of students in this class? Explain your answer.

c. What fraction of students are older than 10? What familiar fraction is this close to? Explain your answer.

d. If the same group of students took this survey 6 months from now, do you think the results would be the same? Explain your answer.



Investigation 1, Session 3 Dear Parents/Guardians: The mathematical focus for this question is identifying equivalent fractions and percents. Use the following advertisement to answer the following question:

Fabulous Frantzie’s Fall Fashion Sale

Item Fraction Off Percent Off Dresses 25% Skirts 1/3 33 1/3% Jeans 6/8 75% Shirts 3/6

Sweaters 4/8 40%

Fabulous Frantzie’s Fashion Store is having their fall fashion sale. For the convenience of the customers, the discounts on the listed items are listed both as a fraction and a percent. a. What fraction off are dresses? b. What percentage off are shirts? c. Which item is advertised wrong? What is the mistake? Explain how you got your answers using numbers, pictures, or words.


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 1, Session 4 Dear Parents/Guardians: The mathematical focus for this question is identifying equivalent fractions and percents. Cristiane has 100 rabbits. ¼ are white 40% are black the rest are gray a. How many rabbits are white? b. How many rabbits are gray? c. What percentage of rabbits are gray? d. What fraction of rabbits are gray? Explain how you got your answers using numbers, pictures, or words.


Grade 5 Name that Portion Name _________________________ Date ________________________ Review from Mathematical Thinking at Grade 5 Dear Parents/Guardians: The mathematical focus for this question is becoming familiar with skip-counting patterns leading to 10,000.

a. Dottie is skip-counting by 200. What will be the 13th number she says? Explain how you got your answer.

b. Derrick is counting by 50. He starts by saying the number 1,500. What is the 25th number he says? Explain how you got your answer.

c. Danae is skip-counting by 1500. What is the 5th number she says? Explain how you got your answer.

d. Dottie skip-counts by 200 up to 1,000 and Derrick skip-counts by 50 up to 1,000. What numbers will they both say? Explain how you got your answers.


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 1, Session 5 Dear Parents/Guardians: The mathematical focus for this question is ordering fractions and percents. Eddie is planning a Walk-a-Thon along the Little River. He wants to draw a map of the route to give to all the walkers. This is what he has drawn so far: 1 2 mile miles Help Eddie finish his map by drawing in the following landmarks at the correct distances: there is a fire hydrant at 1 ¼ mile there is a bench at 3/5 mile there is a stop sign at 1/3 mile there is a policeman at 1 3/8 mile there is a school at 7/8 mile there is a lemonade stand at 6/8 mile there is firestation at 1 ¾ mile


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 1, Session 6 Dear Parents/Guardians: The mathematical focus for this question is ordering fractions. Migdalia takes a field trip to the zoo with her 5th grade class. Her favorite animals to watch are the gorillas. The following sign is displayed outside their cage:

Can You Identify the Gorillas? Kiley is 3/5 as tall as Jiray Amanda is 5/8 as tall as Homer Jiray is 5/6 as tall as Homer Homer is 2/3 as tall as Yuri a. Write the names of the gorillas in order, from shortest to tallest. b. Suppose the zoo obtained a new gorilla that was ¾ the height of Homer. How many of the zoo’s gorillas would be shorter than the new one? Show how you got your answers using numbers, pictures, and words.


Grade 5 Name that Portion Name _________________________ Date ________________________ Review from Picturing Polygons Dear Parents/Guardians: The mathematical focus for this question is locating points on a coordinate grid; creating and drawing polygons.

-10

-20

-30

-40

-50

-50 -40 -30 -20 -10 0

50

40

30

20 10

Latoya is drawing a right triangle on thmarked one of the vertices.

a. The next vertex she wants to mark draw a line between it and the verte

b. Mark the third vertex and connect triangle. Name the ordered pair of

c. Could the third vertex be at a diffemarked? Explain your answer.

Copyright © 2003 Bos

10 20 30 40 50

e grid above. She has already

is at (20, 10). Mark the vertex and x already marked.

all the vertices to produce a right the third vertex.

rent location than the one you

ton Public Schools

Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 1, Session 7 Dear Parents/Guardians: The mathematical focus for this question is naming portions with fractions and percents. The table below shows the number of fish Heverthon caught one week.

Day Number of Fish Caught Monday 12 Tuesday 6

Wednesday 8 Thursday 16

Friday 6

a. What percentage of his weekly catch did Heverthon get on Monday? b. What percentage of his weekly catch did Heverthon get on Wednesday? c. If Heverthon only went fishing on Monday and Thursday, would he still have achieved 50% of his weekly catch? Explain your answer. Explain how you got your answers using numbers, pictures, and words.


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 2, Session 1 Dear Parents/Guardians: The mathematical focus for this question is representing fractions as rotation around a circle. Gaenslie looks at the clock on his wall. The hour hand is 2/3 around the clock and the minute hand is ¾ around the clock. a. Draw Gaenslie’s clock using the circle below. b. According to Gaenslie’s clock, what time is it? Explain how you got your answers using numbers, pictures, or words.


Grade 5 Name that Portion Name _________________________ Date ________________________ Ten-Minute Math: Exploring Data Dear Parents/Guardians: The mathematical focus for this question is interpreting data.

A group of middle school students visited the zoo. Afterward, their teacher asked them, “What was your favorite animal?” The results from the survey are below.

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

Lions Gorillas Kangaroos Zebras Giraffes Leopard

a. Which animals were the most popular among the middle school students? Explain your answer.

b. What fraction of the students liked leopards the most? What familiar fraction is this close to? Explain your answers.

c. Why do you think some animals were more popular than others? Can you group the data in a different way to support your hypothesis?

d. If a class of 1st graders took this same survey, would you expect the same results? Explain your answer.



Investigation 2, Session 2 Dear Parents/Guardians: The mathematical focus for this question is adding fractions. Davina is sending thank-you cards to all of her friends. Sending a letter that weighs up to 1 ounce requires one first-class stamp. Letters weighing more than one ounce require additional postage. Davina would like to put some of the following in her cards: Item Weight

a thank-you note 5/12 ounce

a bookmark 1/3 ounce

a sticker 1/12 ounce

a photograph 1/4 ounce

a comic-strip 1/6 ounce

The envelope Davina is using weighs 1/6 ounce. a. If Davina includes a thank-you note in her card, what else could she include without going over 1 ounce? List all of Davina’s options. b. Davina decides to send everything on her list to her friends. How much will one card weigh? Explain how you got your answers using numbers, pictures, or words.


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 2, Session 3 Dear Parents/Guardians: The mathematical focus for this question is comparing fractions of different denominators. Julius Bear, Augustus Bear, and Caesar Bear are going for a walk together in the Great Woods.

Caesar Bear’s step is ¾ the size of Julius Bear’s step. • Caesar Bear’s step is 3/5 the size of Augustus Bear’s step.

a. Which Bear takes the biggest step? b. The three bears go for a 1-mile walk to Grandma’s House. Assuming

each bear steps at the same pace, which bear will arrive first? Which bear will arrive second? Which bear will arrive third?

c. It took Julius Bear 200 steps to get to Grandma’s House. How many

steps did it take Caesar Bear? Challenge: How many steps did it take Augustus Bear to get to Grandma’s House? Explain how you got your answers using numbers, pictures, or words.


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 2, Session 4 Dear Parents/Guardians: The mathematical focus for this question is labeling fractions on number lines. Use the number line below to answer the following questions. 1 ½ A B 2 C 2 1/3 D E a. In the spaces provided, write the value of the following points.

A ______

B ______

C ______

D ______

E ______

Explain how you got your answers using numbers, pictures, or words.

b. How far away is point D from point A? Explain how you got your answer.

c. How far away is point C from point E? Explain how you got your answer.


Grade 5 Name that Portion Name _________________________ Date ________________________ Ten-Minute Math: Guess My Number Dear Parents/Guardians: The mathematical focus for this question is learning to use mathematical terms that describe numbers.

Guess My Number • my number is between 1 and 2

• my number is a multiple of ¼

• my number is NOT a multiple of ½

a. What is my number? List all the possibilities. Explain how you got your answer(s).

b. If there is more than one answer, write one more clue that will make the puzzle have only one answer.


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 2, Session 5 Dear Parents/Guardians: The mathematical focus for this question is comparing the relative size of fractions up to 3/2.

Australia's Precipitation

March April May June July Aug. Sept. Oct.

Tota

l Pre

cipi

tatio

n (m

m/d

ay)

Use the graph above to complete the table below. Explain how you got your answers using numbers, pictures, or words.

Total Precipitation (mm/day) Month

¾

1 2/5

5/6

1

9/10

2/3

7/8

4/5


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 2, Session 6 Dear Parents/Guardians: The mathematical focus for this question is adding fractions.

Dardanian is making a fruit salad. He cuts up the following amounts of each fruit:

Apples 3/5 quart

Peaches 2/3 quart

Grapes 5/8 quart

Pears ¼ quart

a. Dardanian wants to combine all this fruit in a 2 quart bowl. Is the bowl big enough? Explain your answer.

b. Dardanian decides he wants 1 whole quart of grapes in his fruit salad. What amount of grapes should he add? Explain how you got your answer.


Grade 5 Name that Portion Name _________________________ Date ________________________ Review from Picturing Polygons Dear Parents/Guardians: The mathematical focus for this question is finding an unknown angle in a triangle or quadrilateral.

For each polygon below, give the measure(s) of the unmarked angle(s). Explain your answers.

27°

45°

right triangle right triangle

Challenge:

63°

equilateral triangle isosceles trapezoid



Investigation 2, Session 7 Dear Parents/Guardians: The mathematical focus for this question is comparing fractions and finding equivalent fractions.

Mrs. Joseph is throwing a pizza party for her fifth-grade class. She orders 5 extra-large pepperoni pizzas.

Pizza #1 is cut into 6 equal slices





a. A slice from which pizza is the biggest?

b. Marjoun takes 2 slices from Pizza #4. Sheila takes 3 slices from Pizza #3. Who got more pizza?

c. Mar-jo takes 4 slices from Pizza #5. Michael wants to take the same amount of pizza from Pizza #1. How many slices should he take? How many slices of Pizza #3 would equal the same amount?

Explain all your answers using numbers, pictures, and words.



Ten-Minute Math: Guess My Number Dear Parents/Guardians: The mathematical focus for this question is learning to use mathematical terms that describe numbers.

Guess My Number • my number is a multiple of 500

• my number is a factor of 6000

• my number is more than 2000

a. What is my number? List all the possibilities. Explain how you got your answer(s).

b. Prove that there are no other possible answers.


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 2, Session 8 Dear Parents/Guardians: The mathematical focus for this question is adding fractions.

Wilbert the Worm has fallen into a hole that is 2 feet deep.

Wilbert climbs 1/3 of a foot on Mondays, Wednesdays, and Fridays

Wilbert climbs 1/6 of a foot on Tuesdays and Thursdays

Wilbert climbs 1/4 of a foot on Saturdays

On Sundays, Wilbert slips down 1/6 foot

Wilbert starts his climb on Tuesday, December 10.

a. When will Wilbert get out of the hole?

b. What is the TOTAL distance Wilbert climbed in these days?

Explain how you got your answers using numbers, pictures, and words.


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 2, Session 9 Dear Parents/Guardians: The mathematical focus for this question is finding percents and fractional parts of whole numbers.

Boxwood Elementary School Enrollment

Students 300

Teachers 20

The day before School Vacation, 25% of students at the Boxwood Elementary School were absent. 10% of teachers were absent.

a. What percent of teachers were present? How many teachers were present?

b. What percent of students were present? How many students were present?

Challenge: The fifth-grade class had 80% of its students present. 5 students were absent. How many students were present?

Show how you got your answers using numbers, pictures, and words.



Investigation 3, Session 1 Dear Parents/Guardians: The mathematical focus for this question is interpreting common uses of decimals.

Ayda’s Tropical Foods sells bananas for $0.35/pound.

Lavaughn buys 4 bananas that weigh 2.13 pounds altogether.

Kerly buys 7 bananas that weigh 3.27 pounds altogether.

Marcos buys 4 bananas that weigh 2.84 pounds altogether.

Chandra buys 7 bananas that weigh 3.46 pounds altogether.

a. Who paid the least for their bananas? Explain how you got your answer using pictures, numbers, or words.

b. Who paid the most for their bananas? Explain how you got your answer using pictures, numbers, or words.

c. Who paid closest to $1.00 for their bananas? Explain how you got your answer using pictures, numbers, or words.


Grade 5 Name that Portion Name _________________________ Date ________________________ Ten-Minute Math: Seeing Numbers Dear Parents/Guardians: The mathematical focus for this question is exploring number relationships such as factors and fractions of a whole.

Write at least 5 number sentences describing the arrangement of shapes below. (Do not use the example as one of your five.)

Example: 6 x (3+2) = 30


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 3, Session 2 Dear Parents/Guardians: The mathematical focus for this question is ordering decimals.

Hieu records the amount of gasoline he purchases every time he fills-up his car’s gas tank. Here is his record from the month of December:

Date Gasoline (Gallons)

December 2 14.496

December 7 14.5

December 14 14.490

December 19 14.399

December 21 14.4

December 27 14.455

a. On which date did Hieu buy the most gasoline? Explain how you got your answer using pictures, numbers, or words.

b. On which date did Hieu buy the least gasoline? Explain how you got your answer using pictures, numbers, or words.

c. What was Hieu’s median (middle) amount of gasoline purchased in December? Explain how you got your answer using pictures, numbers, or words.


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 3, Session 3 Dear Parents/Guardians: The mathematical focus for this question is ordering decimals.

Marquisha is writing a paper about the history of Ethiopia. She took 5 books out of the library with the following Dewey Decimal Numbers:

963.24 963.48 963.352 963.2 963.41

When Marquisha returns the books to the library, the librarian asks Marquisha to reshelve them. The shelf has the following books on it:

963.198 963.3 963.35 963.8 963.397 963.52 964.08

Marquisha reshelves her books in their correct order. Below is a picture of the shelf with all the books on it. Label each book with its proper Dewey Decimal number.

Explain how you got your answer.


Grade 5 Name that Portion Name _________________________ Date ________________________ Review from Picturing Polygons The mathematical focus for this question is predicting the lengths and angles of similar shapes. Figures A and B are similar right triangles.

Figure A Figure B 8

60°

18

4

2

a. What is the measure of Triangle B’s unmarked acute angle? b. What is the measure of Triangle B’s unmarked side? c. What are the measures of Triangle A’s three angles? Mark them on the triangle. d. What is the measure of Triangle A’s unmarked side? Explain how you got your answers using numbers, pictures, or words.


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 3, Session 4 Dear Parents/Guardians: The mathematical focus for this question is adding decimals and ordering decimals.

Tamara’s car

10 feet

Enrique’s car

Tamara and Enrique both made electric cars for their Science Fair projects. The cars race against each other three times on a 10 foot track. The results of the races are in the table below:

Race 1 Race 2 Race 3 Total

Tamara’s car 0.7 sec 0.75 sec 0.6 sec

Enrique’s car 0.75 sec 0.5 sec 0.7 sec

a. In which race did Tamara’s car go the fastest? Explain how you got your answer using pictures, numbers, or words.

b. Which car won more races? Explain how you got your answer using pictures, numbers, or words.

c. Calculate the total amount of time it took for each car to finish all three races. Which car finished in the least amount of time? Explain how you got your answer using pictures, numbers, or words.


Grade 5 Name that Portion Name _________________________ Date ________________________ Ten-Minute Math: Seeing Numbers Dear Parents/Guardians: The mathematical focus for this question is exploring number relationships such as factors and fractions of a whole.

Write at least 3 number sentences describing the arrangement of numbers below. (Do not include the example as one of your three.)

100x5 100x5 100x5 100x5 100x5

100x5 100x5 100x5 100x5 100x5

100x5 100x5 100x5 100x5 100x5

100x5 100x5 100x5 100x5 100x5

Example: 20 x 500 = 10,000


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 3, Session 5 Dear Parents/Guardians: The mathematical focus for this question is finding decimals in between the value of other decimals.

Use the graph below to answer the following questions.

Inches of Rain

Mon. Tues. Wed. Thurs. Fri.

It rained 1.418 inches on Monday and 1.436 inches on Wednesday.

a. Estimate how many inches it rained on Tuesday. Explain how you got your answer using pictures, numbers, or words.

b. Estimate how many inches it rained on Thursday. Explain how you got your answer using pictures, numbers, or words.

c. Estimate how much more it rained on Tuesday than on Thursday. Explain how you got your answer using numbers, pictures, or words.


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 3, Session 6 Dear Parents/Guardians: The mathematical focus for this question is finding decimal equivalents for common fractions, including fractions greater than 1.

1. Naomi has ten dollars. She decides to share it equally with her three sisters. How much money does each sister receive? Explain how you got your answer using numbers, pictures, or words.

2. Hiram has a 5-inch piece of wood. He wants to cut it into 4 pieces of equal length. How many inches long will each piece be? Explain how you got your answer using numbers, pictures, or words.

3. The Boxwood Beavers Football team has won 5 games and lost 4. What is their winning percentage? Explain how you got your answer using number, pictures, or words.


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 3, Session 7 Dear Parents/Guardians: The mathematical focus for this question is computing with fractions, decimals, and percents.

Carlos is running a 5 kilometer road race. He is 50% through the race.

a. How many kilometers has Carlos run so far? Explain how you got your answer.

b. Carlos’ friend, Mike, is 0.25 kilometers in back of him. How many kilometers does Mike have to run until he crosses the finish line? Explain how you got your answer.

c. Sergei is currently in the lead. He is 3/10 of a kilometer ahead of Carlos. How much further does he have to run to reach the finish line? Explain how you got your answer.

d. How far ahead of Mike is Sergei? Explain how you got your answer.


Grade 5 Name that Portion Name _________________________ Date ________________________ Ten-Minute Math: Graph Stories Dear Parents/Guardians: The mathematical focus for this question is understanding graphs representing change over time.

Wydell and Winona are having their house built. The graph below shows the progress the construction company has made so far.

Time

% of house built

Tell a story about how the construction of the house has gone so far using the data from the graph. Include details about why the speed of the construction changed so many times.



Investigation 3, Session 8 Dear Parents/Guardians: The mathematical focus for this question is comparing common fractions.

Vitaly’s chess club has 6 members. After winning a tournament, they order two large pizzas to celebrate.

• Vitaly suggests cutting each pizza into 8 slices and giving each member an equal share until all the pizza is gone.

• Alexandra suggests cutting each pizza into 10 slices and giving each member an equal share until all the pizza is gone.

a. If the chess club follows Vitaly’s suggestion, how big will each slice be? Explain how you got your answer.

b. If the chess club follows Alexandra’s suggestion, how big will each slice be? Explain how you got your answer.

c. Whose suggestion will produce bigger slices? Explain how you got your answer.

d. Whose suggestion will result in each member getting more slices? Explain how you got your answer.

e. Whose suggestion will result in each member getting more pizza? Explain how you got your answer.


Grade 5 Name that Portion Name _________________________ Date ________________________ Review from Mathematical Thinking at Grade 5 Dear Parents/Guardians: The mathematical focus for this question is developing mental multiplication and division strategies that rely on landmarks up to 10,000.

Hector is taking an exam. He is asked to solve the following math problem:

72 x 58

He begins to solve the problem by writing the following number sentences on his answer sheet:

7 x 5 = 35

70 x 5 = 350

70 x 8 = 560

Finish solving the math problem using the number sentences that Hector already wrote down. Show all your work clearly.


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 4, Session 1 Dear Parents/Guardians: The mathematical focus for this question is representing a population as fractions and percents.

Far-Out Toothpaste is planning an advertising campaign to try and increase their sales. The results of a recent marketing survey are below.

Population Use Far-Out Toothpaste

Use another kind of toothpaste

Men (age >17) 78 422

Women (age >17) 43 457

Boys (age <17) 176 324

Girls (age <17) 107 393

a. About what fraction of boys (age <17) use Far-Out Toothpaste? Explain how you got your answer.

b. About what fraction of girls (age <17) use Far-Out Toothpaste? Explain how you got your answer.

c. Is Far-Out Toothpaste being used more by children or adults? Give some reasons why this may be.


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 4, Session 2 Dear Parents/Guardians: The mathematical focus for this question is interpreting circle graphs.

Victor’s Victory Garden has grown 5000 pieces of fruit. The relative amounts of each fruit are represented in the circle graph below.

Pears

Oranges Apples

Complete the table below to show how many pieces of each kind of fruit the Victory Garden grew. Explain how you got your answers.

Fruit Number of Pieces

Apples

Oranges

Pears


Grade 5 Name that Portion Name _________________________ Date ________________________ Ten-Minute Math: Graph Stories Dear Parents/Guardians: The mathematical focus for this question is understanding graphs representing change over time.

One cold February morning, it begins to snow. For the first couple hours of the day there is only flurries. Then, it begins to snow rapidly. There are blizzard conditions for about 6 hours. As the blizzard winds down, there are flurries again for another hour. It stops snowing for 3 hours and then snows moderately for one more hour before stopping altogether.

Draw a line graph showing how the amount of snow on the ground changes over time on the day described above.

Inches of

Snow on the Ground

Time

Explain how the details of your graph relate to the story.


Grade 5 Name that Portion Name _________________________ Date ________________________ Investigation 4, Session 3 Dear Parents/Guardians: The mathematical focus for this question is constructing circle graphs.

Represent each set of data below on a circle graph. Make sure you label each graph, as well.

a. There are 24 children in Ms. Scott’s 5th grade class. 6 are boys and 18 are girls.

b. 80% of students at the Boxwood Elementary School like pizza.

c. 1/5 of students like mathematics the most. 3/10 prefer reading. One-half say their favorite subject is science.


Grade 5 Name that Portion Name _________________________ Date ________________________ Review from Picturing Polygons Dear Parents/Guardians: The mathematical focus for this question is developing an understanding of parallel lines.

a. Which of the following letters contain a set of parallel lines? Mark the parallel lines.

A E F H K

L M N R T

V W X Y Z

b. How can you tell whether two lines are parallel?




Investigation 4, Session 4 Dear Parents/Guardians: The mathematical focus for this question is interpreting everyday situations that involve percents.

Use the data from the table below to answer the following questions.

Room 210 Attendance for the Week of December 10

Day Percent of Students Present

Monday 95%

Tuesday 80%

Wednesday 90%

Thursday 90%

Friday 60%

a. Room 210 has 20 students in it. How many students were absent on Wednesday? Explain how you got your answer.

b. How many students were absent on Friday? Explain how you got your answer.

c. Make a circle graph showing the attendance data from Monday.

Picturing Polygons

Grade 5 Homework Packet



Today’s Number

Estimation and Number Sense

Creating a Likelihood Line and Using Spinners

Also includes homework to review:



Grade 5 Picturing Polygons Name______________________ Date__________________

Investigation 1 Session 1 Dear Parents/Guardians: The mathematical focus for this question is distinguishing between polygons and shapes that are not polygons; drawing polygons.

Arianne is looking at the picture below and wants to identify all the polygons.

a. Draw all the polygons you see in the picture (including polygons embedded in other shapes).

Example:

b. Draw all the shapes in the picture that are not polygons. Explain why these shapes are not polygons.


Grade 5 Picturing Polygons Name______________________ Date__________________ Investigation 1 Session 2 Dear Parents/Guardians: The mathematical focus for this question is recognizing polygons by numbers of sides.

Arianne continues looking at the picture on the previous page.

a. How many of the polygons in the picture have 3-sides? Draw them below.

b. How many of the polygons in the picture have 4-sides? Draw them below.

c. Draw the remainder of the polygons below and label each one according to the number of sides it has.


Grade 5 Picturing Polygons Name______________________ Date__________________ Investigation 1 SessioDear Parents/Guardiancoordinate grid; creati

-50 -40

Eric is drawing amarked two of th

a. The next vertvertex and dralready marke

b. Mark one morpolygon. Wha

c. Finish drawingmany sides do

n 3
s: The mathematical focus for this question is locating points on a
ng and drawing polygons.

10 20 30 40 50

50

40

30

20 10

-10

-20

-30

-40

-50

-30 -20 -10 0

polygon on the grid above. He has already e vertices.

ex he wants to mark is at (30, -30). Mark the aw a line between it and one of the vertices d.

e vertex on the grid that will complete the t is the ordered pair for this vertex?

the polygon using the vertices on the grid. How es the polygon have?


Grade 5 Picturing Polygons Name______________________ Date__________________ Ten-Minute Math: Today’s Number

Dear Parents/Guardians: The mathematical focus for this question is using knowledge of landmarks up to 1000 to explore landmarks up to 10,000.

Write 5 number sentences that equal 7,500.

• Use only factors and multiples of 500.

• Use each operation (addition, subtraction, multiplication, and division) at least once.

• Include AT LEAST two different operations in each number sentence.



Investigation 1 Session 4 Dear Parents/Guardians: The mathematical focus for this question is locating points on a coordinate grid; creating and drawing polygons.

-50 -40 -30 -20 -10 0

-10

-20

-30

-40

-50

50

40

30

20

10

a. Draw a 16-gon on the grid above.

b. List the ordered pairs for all the vedrew.

Copyright © 2003 Boston Pu

10 20 30 40 50

rtices of the polygon you

blic Schools

Grade 5 Picturing Polygons Name______________________ Date__________________ Investigation 2 Session 1 Dear Parents/Guardians: The mathematical focus for this question is sorting and classifying triangles.

Chaquin is trying to sort the triangles below according to their properties.

a. Sort the triangles into between 3 and 5 groups. Label each triangle with its group number.

b. Explain how you sorted the triangles. Give each group a name.


Grade 5 Picturing Polygons Name______________________ Date__________________ Review from Mathematical Thinking at Grade 5 Dear Parents/Guardians: The mathematical focus for this question is reasoning about number characteristics such as factor, multiple, prime, and square.

Guess My Number • my number is a multiple of 25.

• my number is a factor of 10,000.

• my number is a square number.

What is my number?

a. List all the possibilities. Explain how you got your answer(s).

b. Explain how you know you have found all the possibilities.


Grade 5 Picturing Polygons Name______________________ Date__________________ Investigation 2 Session 2 Dear Parents/Guardians: The mathematical focus for this question is exploring attributes of quadrilaterals.

a. Draw a quadrilateral with only one pair of parallel lines and one right angle. Name this shape.

b. Draw a quadrilateral with two pairs of parallel lines and at least one right angle. Name this shape.

c. Draw a quadrilateral with all sides of equal length but no right angles. Name this shape.


Grade 5 Picturing Polygons Name______________________ Date__________________ Investigation 2 Session 3 Dear Parents/Guardians: The mathematical focus for this question is developing an understanding of parallel lines.

L

I

H G

F

E

D

A

C

B

Which line segments appear

List all sets of parallel lines.

Copyright ©

J

K

to be parallel?

2003 Boston Public Schools

Grade 5 Picturing Polygons Name______________________ Date__________________ Ten-Minute Math: Estimation and Number Sense

Dear Parents/Guardians: The mathematical focus for this question is looking at a problem as a whole.

62 + 74 + 98 + 26

a. Take about 30 seconds to mentally estimate an answer to the addition problem above. Do not use pencil and paper or a calculator. Write your estimate below. Explain how you got your estimate.

b. Now, find the exact answer to the problem. Do not use a calculator or a standard algorithm. Show your strategy below.

c. Was your estimate from part a. reasonable? If not, explain your error(s) in estimating.


Grade 5 Picturing Polygons Name______________________ Date__________________ Investigation 2 Session 4 Dear Parents/Guardians: The mathematical focus for this question is generating geometric figures from descriptions of their properties.

-50 -40 -30 -20 -10 0

-10

-20

-30

-40 -50

50

40

30

20 10

Draw a polygon with the following propmarking all vertices clearly:

• the polygon has 8 sides

• the polygon has only one pair of p

• the polygon has only one pair of e

List all the vertices of the polygon belit?


10 20 30 40 50

erties on the grid above,

arallel sides

quidistant sides

ow. What is the name of

blic Schools

Grade 5 Picturing Polygons Name______________________ Date__________________ Investigation 2 Session 5 Dear Parents/Guardians: The mathematical focus for this question is generating geometric figures from descriptions of their properties.

Ayisha is drawing a polygon on the gridmarked three of the vertices.

-50 -40 -30 -20 -10 0

-10

-20

-30

-40 -50

50

40

30

20

10

a. If Ayisha wanted to draw a right trone right angle), what would the ordbe?

b. If Ayisha wanted to draw a rhombuvertex be?

c. Is it possible for Ayisha to draw a rthree vertices already marked? Ex


10 20 30 40 50

above. She has already

apezoid (a trapezoid with ered pair of the 4th vertex

s, where would the 4th

ectangle that includes the plain why or why not.

blic Schools

Grade 5 Picturing Polygons Name______________________ Date__________________ Investigation 2, Session 6 Dear Parents/Guardians: The mathematical focus for this question is seeing relationships between turns and angles. Liu is hiking in the Blue Hills. He starts at the Trailside Museum and walks 1 mile in a straight line. Then, using his compass, he turns right 120° and walks another mile in a straight line. Now, Liu wants to return to the Trailside Museum using the shortest route possible. a. What direction should Liu turn? (Include the number of

degrees of his turn.) b. How far is it to the Trailside Museum? Explain your answers using numbers, pictures, or words.


Grade 5 Picturing Polygons Name______________________ Date__________________ Ten-Minute Math: Estimation and Number Sense

Dear Parents/Guardians: The mathematical focus for this question is looking at a problem as a whole.

502 + 305 – 198 + 293

a. Take about 30 seconds to mentally estimate an answer to the addition problem above. Is the answer more than or less than 1,000? Do not use pencil and paper or a calculator. Write your answer below. Explain how you got your estimate.

b. Now, find the exact answer to the problem. Do not use a calculator or a standard algorithm. Show your strategy below.

c. Was your estimate from part a. reasonable? If not, explain your error(s) in estimating.


Grade 5 Picturing Polygons Name______________________ Date__________________ Investigation 2, Session 7 Dear Parents/Guardians: The mathematical focus for this question is defining categories of triangles and quadrilaterals more precisely. a. Is it possible to draw an obtuse right triangle? Explain why or

why not. b. What quadrilateral is formed when two congruent isosceles

right triangles are put together? Why is this always the case? c. Is it possible to draw a scalene right triangle? Explain why or

why not. d. What kind of triangle is formed when a rhombus is cut in half by drawing a line connecting two of its opposite vertices? Why is this always the case?


Grade 5 Picturing Polygons Name______________________ Date__________________ Investigation 2, Session 8 Dear Parents/Guardians: The mathematical focus for this question is using known angles to find measures of other angles. Regular Pentagon Nonregular Pentagon The angles of a triangle measure 180 degrees altogether. The angles of a quadrilateral measure 360 degrees altogether. a. What is the measure of all the angles in a pentagon? b. What is the measure of each angle in a regular pentagon? (A

regular pentagon’s sides and angles all have the same measure.) c. Estimate the measure of each angle in the nonregular pentagon

shown above. State whether each angle is acute, obtuse, or a right angle.

Explain your answers using numbers, pictures, or words.


Grade 5 Picturing Polygons Name______________________ Date__________________ Investigation 2, Session 9

Dear Parents/Guardians: The mathematical focus for this question is seeing relationships between turns and angles. Karina is sailing in the Boston Harbor in her new boat. She starts off sailing in a straight line from the dock. Then, she turns right 150 degrees. a. What angle does Karina make (measured from her original

path)? Explain your answers using numbers, pictures, or words. b. Karina continues straight on her new course for several

minutes. Now, she wants to turn again, this time making a 75 degree angle. What size turn does Karina need to make? Explain your answers using numbers, pictures, or words.

c. Karina sails straight ahead for a few more minutes. Draw a

picture of what Karina’s sailing course might look like so far. Be sure to mark all the angles and turns.


Grade 5 Picturing Polygons Name______________________ Date__________________ Investigation 3, Session 1

Dear Parents/Guardians: The mathematical focus for this question is distinguishing regular polygons from nonregular polygons. Which of the figures below are regular polygons? For each figure, explain why it is or is not a regular polygon. 1. 2. 3. 4. 5.


Grade 5 Picturing Polygons Name______________________ Date__________________ Review from Mathematical Thinking at Grade 5 Dear Parents/Guardians: The mathematical focus for this question is becoming familiar with factor pairs of 1000.

The chart below shows the hourly wage for a variety of professions.

Profession Wage

Waiter at a Restaurant $5/hour

Telephone operator $10/hour

Policeman $20/hour

Lawyer $40/hour

College Professor $50/hour

Doctor $100/hour

How many hours is it necessary to work to earn $1000 in each profession? Explain how you got your answer.


Grade 5 Picturing Polygons Name______________________ Date__________________ Investigation 3, Session 2 The mathematical focus for this question is using the size of angles for regular polygons to solve problems. The Springfield Soldiers football team just built a new stadium. It is in the shape of a regular hexagon. The playing field is in the shape of a rectangle, and the stadium seats form two triangles on either side of the field. Below is a diagram of the new stadium. Springfield Soldiers Stadium What is the measure of each angle found in the new stadium shown above? Label each angle on the diagram above. Explain how you got your answers using numbers, pictures, or words.


Grade 5 Picturing Polygons Name______________________ Date__________________ Ten-Minute Math: Creating a Likelihood Line

Dear Parents/Guardians: The mathematical focus for this question is distinguishing among events with different probabilities.

impossible unlikely maybe likely certain

a. Place the following events in their correct place on the likelihood line. Explain how you made your decision for each event.

I will go to school tomorrow.

Next year I will graduate from high school.

We will get homework tomorrow.

A kangaroo will escape from the zoo.

I will get my driver’s license when I am sixteen.

It will be a sunny day tomorrow.

I will eat pizza sometime this month.

b. Write down two different events: one likely and one unlikely. Explain how you chose these events.


Grade 5 Picturing Polygons Name______________________ Date__________________ Investigation 3, Session 3 The mathematical focus for this question is using knowledge of the sums of turns and angles for regular polygons to solve problems. a. Which regular polygon has angles measuring 120 degrees? b. Which regular polygon has angles measuring 135 degrees? c. How many sides does a regular polygon with angles measuring

162 degrees have? d. How many sides does a regular polygon formed by making turns

of 15 degrees have? Explain how you got your answers using numbers, pictures, and words.


Grade 5 Picturing Polygons Name______________________ Date__________________ Investigation 3, Session 4 The mathematical focus for this question is recognizing and drawing similar shapes. a. Are these two rectangles similar? Explain why or why not. b. Are these two rectangles similar? Explain why or why not. c. Draw a rectangle similar to the one below. Tell how you know it

is similar.


Grade 5 Picturing Polygons Name______________________ Date__________________ Investigation 3, Session 5 The mathematical focus for this question is predicting the lengths and angles of similar shapes. Figures A and B are similar right triangles.

10

4 Triangle a. What is the m b. What is the m c. What are the d. What is the m Explain how you gwords.

53°

3

8

A Triangle B

easure of Triangle A’s unmarked acute angle?

easure of Triangle A’s unmarked side?

measures of Triangle B’s three angles?

easure of Triangle B’s unmarked side?

ot your answers using numbers, pictures, and


Grade 5 Picturing Polygons Name______________________ Date__________________ Ten-Minute Math: Using Spinners

Dear Parents/Guardians: The mathematical focus for this question is interpreting a probability as a measure or quantity. Onochi spins the spinner below 100 times.

11

14

a. How many times do yonumber? Explain how

b. How many times do yoExplain how you got y

c. How many times do yonumber? Explain how

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oston Public Schools



Investigation 3, Session 6 The mathematical focus for this question is using the relationship between the side lengths and the areas of similar shapes to solve problems. Farmer Brown’s pasture is enclosed by a rectangular fence like the one below: 50 meters

25 meters

Pasture Area = 1250 square meters Recently, Farmer Brown bought 100 new cows. He needs a new pasture to feed all these cows. He figures out that his new pasture needs nine times the space of his old one. He wants to build a fence around the new pasture that is geometrically similar to his old one. How many meters of fence does Farmer Brown need to buy to enclose his new pasture?

Mathematical Thinking at Grade 5 Homework Packet · Mathematical Thinking at Grade 5 Homework...

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