MATH PACKET

for

Students Entering the Fifth Grade

(fourth grade review)

Students Name: _____________________________________________________________________ First and Last Student’s Fifth Grade Teacher: ____________________________________________________ Parent’s Signature: _________________________________________________________________

Welcome to the summer math packet for students entering Fifth Grade, curriculum 2.0. The

design of the activities is meant to support instruction in the new curriculum in both its content

and presentation. Therefore the activities are not to be done as independent problems, but to

be worked on with a parent, guardian or older brother or sister. Talking about the problem is an

important part of completing each activity.

In the new curriculum, students explored math concepts based on five standards. The fifteen

activities in this summer math packet reflect the content of those five standards.

To receive credit for this packet, students must complete at least 10 of the activities with at least

one being from each of the 5 standards.

Standard 1: Operations and Algebraic Thinking

Activity A: Micah’s Magic Circles

Activity B: Cities in Montgomery County

Activity C: Stamp Collectors

Standard 2: Number and Operations in Base Ten

Activity A: Mental Math Challenge

Activity B: Mrs. Otis’ Challenge Problems

Activity C: Wanda’s Family Room Project

Standard 3: Number and Operations—Fractions

Activity A: Pattern Blocks Fraction Sentences

Activity B: Tatiana’s Pie Graphs

Activity C: Darwish’s Card Fractions

Standard 3: Measurement and Data

Activity A: Mr. Marcus’ Plant Experiments

Activity B: Diane’s Dad’s Missing Data

Activity C: Andy Flies Over India

Standard 4: Geometry

Activity A: Alphabet Attributes

Activity B: The Brick Wall Accident

Activity C: Quintan and Isadora’s Quilt Squares

Before returning this packet in the fall, please make sure that the front of the packet is complete

and signed. We must have the student’s first and LAST name to ensure that credit will be given

to the right child. Thank you!

Entering Grade 5: Operations and Algebraic Thinking, Activity A

Directions: Read through the following problem and answer the questions. You

may work with a parent, older brother or sister, or friend, but you must show all of

your ideas in words, pictures or symbols to completely answer the questions.

Ever since Kindergarten, Micah has loved discovering patterns and making designs. He

is calling his latest project “Micah’s Magic Circles,” and he needs your help to finish it.

On the back of this page is Micah’s drawing of circles. They are divided into smaller

and smaller portions as they get larger. Micah wanted to number the spaces starting in

the center with the number 1, and going from the middle to the outside in a clockwise

direction until he has all of the spaces numbered. He knows there are 61 spaces all

together. And he’s begun to number the drawing.

A) Begin helping by filling in the missing numbers on the drawing. He was able to

get some of the numbers written down to help you.

B) Next, Micah was

planning on coloring in

the spaces based on

the number of factors

each number has. Use

his key to complete this

part of the project for

him.

C) CHALLENGE: How

many additional spaces

would be created if Micah

added another circle to the outside and continued his pattern of dividing the

circles?

D) Add the next circle, number the spaces, and color it using the key.

Prime Numbers = Yellow

Odd number of factors = Orange

4 to 8 factors = Red

10 or more factors = Purple

Micah Magic Circles

2

3 4

5

1

6

7

14

30

15

35

46

61

E) In the space below, write a description of the final creation using as many

mathematical words as you can.

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Entering Grade 5: Operations and Algebraic Thinking, Activity B

Directions: Read through the following problem and answer the questions. You

may work with a parent, older brother or sister, or friend, but you must show all of

your ideas in words, pictures or symbols to completely answer the questions.

Montgomery County is home to many cities. The 2010 census discovered the

populations of some of these cities. Sixteen of them are listed in the table below.

CITY POPULATION

Aspen Hill 48,759 Bethesda 60,585

Burtonsville 8,323 Chevy Chase 9,545

Clarksburg 13,766

Colesville 14,647 Damascus 15,257

Darnestown 6,802 Gathersburg 59,933

Montgomery Village 32,032 Olney 33,844

Poolesville 4,883

Potomac 44,965 Silver Spring 71,452

Takoma Park 16,715 White Oak 17,403

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

A) What is the difference in the population between the city with the largest

population and the city with the smallest population?

Selected City Populations in

Montgomery County 2010

B) What is the total population of the 5 cities with the lowest populations? Which

other city’s population ranks closest to the total population of the 5 smallest

cities?

C) Use the blank chart below to rearrange the information by population ranked

greatest to least. Place the city with the largest population at the top.

CITY POPULATION

D) CHALLENGE: Compare the information on the chart to determine which two

cities have populations that are different by a factor of 10.

Which two cities populations

are the closest to one

another?

Entering Grade 5: Operations and Algebraic Thinking, Activity C

Directions: Read through the following problem and answer the questions. You

may work with a parent, older brother or sister, or friend, but you must show all of

your ideas in words, pictures or symbols to completely answer the questions.

Three friends all collect postage stamps. Craig, Lorraine, and Theo have a total of 1420

stamps. Craig has twice as many stamps as Lorraine. Lorraine has three times as

many as Theo.

A) How many stamps do each of the friends have?

B) CHALLENGE: Create a Drawing or a Bar Illustration to support your answer.

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Entering Grade 5: Number and Operations in Base Ten, Activity A

Directions: Read through the following problem and answer the questions. You

may work with a parent, older brother or sister, or friend, but you must show all of

your ideas in words, pictures or symbols to completely answer the questions.

Solve the following problems mentally. Write down the answers and then

explain your thinking to a family member or friend. They may check the

box when you’ve successfully explained your strategies. (Then check your

answer using a calculator.)

1) 556 + 67 – 56 = explained

2) 255 + 364 + 145 + 636 = explained

3) 752 + 62 + 38 – 252 = explained

4) 604 + 1796 = explained

5) 60 x 99 = explained

6) 36 x 199 = explained

7) 25 x 16 x 125 = explained

8) 125 x 5 x 32 = explained

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Entering Grade 5: Number and Operations in Base Ten, Activity B

Directions: Read through the following problem and answer the questions. You

may work with a parent, older brother or sister, or friend, but you must show all of

your ideas in words, pictures or symbols to completely answer the questions.

Mrs. Otis is a fourth gade math teacher. She is always creating rigorous

problems to challenge her students. Here are three examples. Start

by finding the answer to each.

A) The product of the ages of two adults is 770. What is the

sum of their ages?

B) At an election for president of the student body, a total

of 240 votes were cast for four candidates. The

winner won over her three opponents with margins of

8, 13, and 15 votes. What was the lowest number of

votes received by a candidate?

C) Two bats and four caps costs $100. Three bats and

seven caps costs $164. How much does one cap

cost?

D) Rank the three problems for Mrs. Otis from 1 to 3. List the most challenging as

#1.

E) Explain why you rated the problem you did as MOST challenging, and explain

the strategy you used to find the answer.

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Entering Grade 5: Number and Operations in Base Ten, Activity C

Directions: Read through the following problem and answer the questions. You

may work with a parent, older brother or sister, or friend, but you must show all of

your ideas in words, pictures or symbols to completely answer the questions.

Wanda is helping her mother retile the floor in their family room.

The room is in their basement and has an unusual shape. Her

mother made this drawing of the shape of the room.

Wanda measured the

perimeter of the room

and found that it

measured 168 ft. In the

drawing the space is

divided into 6 perfect

squares.

A) What is the area of each

square?

B) What is the total area of the family room?

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Entering Grade 5: Number and Operations--Fractions , Activity A

Directions: Read through the following problem and answer the questions. You

may work with a parent, older brother or sister, or friend, but you must show all of

your ideas in words, pictures or symbols to completely answer the questions.

Darnell used the following pattern blocks to make fraction sentences. Here’s one he

made using the 1/2 and the 1/6 blocks.

1/6 + 1/6 + 1/6 = 1/2

A) Using the 4 types of pattern blocks above, how many different fraction sentences

can you make that will equal 1? You can rotate the shapes, and you can mix the

denominators when creating your fraction sentences.

=

1 1/2

1/3

1/6

1/6

Entering Grade 5: Number and Operations--Fractions , Activity B

Directions: Read through the following problem and answer the questions. You

may work with a parent, older brother or sister, or friend, but you must show all of

your ideas in words, pictures or symbols to completely answer the questions.

Tatiana has a problem. She has a set of fractions. Some are written in common

fraction form and some are written in decimal form. She also has a set of circle graphs

and she knows that the fractions match the portions illustrated by the graphs. She

needs to match the fractions with the graphs. Can you help her?

A) Use the fractions on this page to label the portions of the graphs on the following

page. You will have 3 extras that you will not use.

.2 1 10

.65 .50 80 100

.25 .4 6 10

75 100

45 100

35 100

.55 .90 5 10

5 100

B) Look at the three fractions that were extra. Use two of them to create and label a

new pie graph.

C) CHALLENGE: Describe a strategy for checking your work to make sure that your

choices are correct?

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Entering Grade 5: Number and Operations--Fractions , Activity C

Directions: Read through the following problem and answer the questions. You

may work with a parent, older brother or sister, or friend, but you must show all of

your ideas in words, pictures or symbols to completely answer the questions.

Darwish found a stack of cards in an old shoebox in a closet, and his older brother said

they had been his when he was Darwish’s age, but that many of the cards were

missing. He told Darwish that he could have them. When they were spread out, this is

what they looked like. Use them to answer the questions that follow.

4

4

2

2

3

3

1

1

6

6

5

5

7

7

8

8

2

2

3

3

1

1

3

3

4

4

4

4

5

5

4

4

5

5

2

2

8

8

7

7

4

4

7

7

7

7

4

4

A) Match the image on the card with its fractional part of the whole. Draw a line

between the fraction and the word that matches.

B) What is the fractional part that the teddy bear represents written as a base-

fraction? (A Base Fraction is a fraction with 1 in the numerator.)

C) How many different ways can you write a fraction what will represent the portion

of the cards with umbrellas on them?

D) Which number on the cards represents ¼ of the total cards?

E) CHALLENGE: What is the fraction that equals the amount of cards with a

cornucopia on them?

1

2

1

6

1

4

1

3

leaf

snowman

umbrella

umbrella + snowman

F) CHALLENGE: With the following information, can you figure out how many cards

were in the deck of cards when it was new?

The new deck of cards had:

The same number of pictures as the cards in Darwish’s array

Each set of pictures had all the numbers as the cards in Darwish’s array and

no number higher or lower than the ones in the array

The numbers on the cards repeated for each of the pictures by the amount

that is also present in the array

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Entering Grade 5: Measurement and Data, Activity A

Directions: Read through the following problem and answer the questions. You

may work with a parent, older brother or sister, or friend, but you must show all of

your ideas in words, pictures or symbols to completely answer the questions.

Mr. Marcus’ Class is growing flowers for a science experiment. Here are the results of

the heights of the plants so far.

Billy 2 ⁄ ” Kim 2 ” Brenda 2 ⁄ ” Kyle 2 ⁄ ” Carol 1 ⁄ ” Michael 1 ⁄ ” Christopher 2 ⁄ ” Mustafa 3 ⁄ ” Darlene 1 ⁄ ” Nicole 2 ⁄ ” Emmit 2 ⁄ ” Oliver 1 ⁄ ” Fabiana 2 ⁄ ” Phoebe 2 ⁄ ” Franklin 2 ⁄ ” Rachel 3 ⁄ ” Gevorg 1 ⁄ ” Susan 2 ⁄ ” Kelly 2 ⁄ ” Zamir 3 ⁄ ”

A) Use the data in the chart to complete the line plot.

Mr. MARCUS’ Class Plant Growth Chart

1 2 3

B) Use the line plot to determine the difference in height between the following

student’s flowers.

1) Billy and Zamir

2) Darlene and Phoebe

3) Susan and Kyle

4) Franklin and Carol

5) Rachel and Darlene

C) CHALLENGE: Create an original game that you could play using the data on the

chart. Include rules, a description of any components you would need to play it

and how the winner is determined.

Entering Grade 5: Measurement and Data, Activity B

Directions: Read through the following problem and answer the questions. You

may work with a parent, older brother or sister, or friend, but you must show all of

your ideas in words, pictures or symbols to completely answer the questions.

Diane’s dad is an architect. One day she

noticed a drawing of the floor plan of a house.

Each of the rooms was supposed to have the

length, width and area written on the plan, but

some of the information was incomplete. Use

the information that you have on the plan to

complete the missing measurements on the chart

on the next page.

Dining Room

8 ft

Width

Length

80 sq ft

Kitchen Living Room

Wash Rm

6 ft

4 ft

48 sq ft

8 ft

12 ft

208 sq ft

A) Complete the chart using the floor plan from the previous page.

ROOM WIDTH LENGTH AREA

Living Room 12 ft. 208 sq. ft.

Wash Room 6 ft. 4 ft.

Kitchen 8 ft. 48 sq. ft.

Dining Room 8 ft. 80 sq. ft.

B) CHALLENGE: Complete the floor plan of the second floor and make a chart

showing the width, length and area of the rooms. Get at least two bathrooms

and 3 bedrooms into your design.

= 4 sq. ft.

ROOM WIDTH LENGTH AREA

.

Entering Grade 5: Measurement and Data, Activity C

Directions: Read through the following problem and answer the questions. You

may work with a parent, older brother or sister, or friend, but you must show all of

your ideas in words, pictures or symbols to completely answer the questions.

Andy’s grandfather owns a small plane and sometimes Andy gets to go up in the air

with him. Sometimes the pilot uses the 360 degrees on a radial compass to

communicate to the people of the ground the direction they are flying. Here is an

example of a plane flying in the direction of 300 degrees.

Use this radial compass to help you complete the chart on the next page. You will

indicate the compass direction using numbers between cities on the map.

300 degrees

Radial

Use the degree box like you would a word box. All of the degrees you will need are in

the box.

FROM

CITY

TO

CITY DIRECTION IN DEGREES

Amritsar Agra

Mumbai Kandla

Chennai Mumbai

Kolkata Hyderabad

New Delhi Bangalore

Kandla Agra

Kolkata Amritsar

Bangalore Chennai

New Delhi Kolkata

Mumbai Kolkata

Degree Box

150°

309°

114° 330°

312°

245°

087°

240° 077°

001°

Entering Grade 5: Geometry, Activity A

Directions: Read through the following problem and answer the questions. You

may work with a parent, older brother or sister, or friend, but you must show all of

your ideas in words, pictures or symbols to completely answer the questions.

Categorize the letters in the box according to the descriptions on the table below. You

can use letters as many times as the definition of the geometric attribute applies.

A Y

K

H

F

X N

T M E

Parallel Lines

Perpendicular Lines

Intersecting Lines

Acute Angles

Obtuse Angles

Right Angles

A) Which letter/s did you place the most columns?

B) What is another attribute of a geometric shape that you could have included in

the table and how many of the letters would fit that attribute?

C) Design a letter that would fit all of the attributes.

D) CHALLENGE: Now, design substitute letters to spell your first name where each

of the letters is unique and each letter fits all 6 attributes from the table.

Entering Grade 5: Geometry, Activity B

Directions: Read through the following problem and answer the questions. You

may work with a parent, older brother or sister, or friend, but you must show all of

your ideas in words, pictures or symbols to completely answer the questions.

Yua-yan looked out the window when she heard the sound of her neighbor’s truck

backing into the brick wall that surrounds the parking lot of her apartment building.

Fortunately, no one was hurt, but the accident damaged the brick wall.

A) How many bricks were removed from the wall by the truck?

B) Explain the strategy you used to find your answer.

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C) CHALLENGE: How many different mathematical ways can you come up with to

compare the missing bricks to the remaining bricks? One way would be as a

fraction. What are some others?

Entering Grade 5: Geometry, Activity C

Directions: Read through the following problem and answer the questions. You

may work with a parent, older brother or sister, or friend, but you must show all of

your ideas in words, pictures or symbols to completely answer the questions.

Quintan and Isidora are brother and sister. Their aunt taught both of them how to quilt.

Each made a design of their own. They wondered which design contained more right

angles.

A) Predict which design has more right angles. Remember, when a perpendicular is

formed, there are two right angles.

B) Tally the results.

Quintan Isadora

Quintan’s Quilt

Square Design

Isadora’s Quilt

Square Design

C) CHALLENGE: Use the space below to create your own unique quilt square with

24 right angles. Remember to attend to precision by using a ruler or straight

edge to make your design look well crafted.

.