Comprehension
QuickStart
Introduction
“Somehow I had to get my students to apply their reading strategies to the mathematical problem-solving
process . . . I could tell that my students were not interacting with the text . . . To comprehend text, good
readers engage in mental processes before, during, and after they read. My students were zooming through
their mathematics work in search of a grade, not necessarily understanding. It was time for us to get
involved with our text, even if it was just a mathematics problem. I had to show the students how to read
the mathematics problem with the purpose of gaining full understanding of the situation.”1
How can teachers help students combine the power of strategic reading and the power of strategic
thinking to unlock the problem-solving process?
The Paths to Problem Solving Comprehension QuickStart activities integrate good reading
practices into the problem-solving process for every problem-solving activity. Through the engaging and
motivating QuickStart activities, teachers help students to build background knowledge, activate prior
knowledge, make connections, and acquire new vocabulary. These prereading comprehension activities
spark the creative and critical thinking necessary to understand what the mathematical problems are asking,
and to explore and apply options for successful solutions.
Comprehension QuickStart Objectives
The purpose of combining reading comprehension activities with the corresponding math problem-solving
activities is to ensure that students are primed to understand the problem and are ready to work a solution
without stumbling on the words or concepts.
Activate prior knowledge (What do you know already?)
Build background knowledge (What do you need to know?)
Preview the problem title (What do you predict will happen in this problem?)
Work with special text features (graphs, lists, technical illustrations)
Preview vocabulary (math or other special words needed to present the problem)
1
Teaching Children Mathematics, “The Day Math and Reading Got Hitched.” Reston, VA: National Council of Teachers of
Mathematics, 14:4 (November 2007): 196–197.
2
Miriam P. Trehearne, Comprehensive Literacy Resource for Grades 3–6 Teachers. Vernon Hills, IL: ETA hand2mind™, 2005.
© ETA hand2mind™
What Is a Comprehension QuickStart Activity?
It is a 5-minute warm-up activity that gets students ready to tackle the problem presented in the
corresponding math activity. Comprehension of the problem is essential to the ability to solve it. The
teacher models and actively engages students in the prereading strategies that reading research indicates are
key to reading comprehension.2
The five prereading comprehension strategies used in the activities are—
Teachers are given question prompts for each strategy that is appropriate for the particular problem.
Because not all problems include special text features or vocabulary that is new to students, these two
strategies will not be a part of every activity. However, teachers should activate prior knowledge for all
problems and ask students to predict what is happening in the problem based on its title.
© ETA hand2mind™
Making the Most of Comprehension QuickStart Activities
Teacher-student interaction is critical. Students will look forward to their problem-solving activities
when they are engaged in thoughtful, imaginative, and fun discussions during the QuickStart activities.
By having a good time working with ideas and words, students will become involved with the events in
a problem-solving activity and might even imagine themselves in the situation and wanting to find a
solution. At the very least, students will find the math activity to be more approachable when it’s time to
solve it, because they are prepared to read and comprehend the question.
Comprehension QuickStart Introduction
Comprehension QuickStart Activity 1
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Tile Designs
Marta was arranging color tiles. She made some patterns as she laid out the tiles.
Design 1
1
Design 2
1+3
Design 3
1+3+5
How many tiles would be in each of Designs 4, 5, 6, and 7? How many tiles would
be in the Design 20?
Activate Prior Knowledge
Stand up if you are wearing an article of clothing with a pattern on it.
Describe the pattern you are wearing.
Now, who can tell us what a pattern is?
Build Background Knowledge
Many things in our homes and schoolroom have patterns. Many of us have seen tiles on the floor,
and the tiles are laid in a pattern.
If I asked you to make a pattern with tiles on the floor, how would you get started??
Preview the Problem Title
Open your Student Journal to Activity 1 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
None
Comprehension QuickStart Activity 1
Comprehension QuickStart Activity 2
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Class Picnic
36 students are going to the class picnic. Hamburgers will be one of the foods served at the picnic.
Mr. Jordan will buy the hamburgers and buns. He can buy hamburgers in bags of 8. He can buy
buns in bags of 12. He wants to buy enough so that every student can have the same amount. But
he does not want to have any extra hamburgers or any extra buns. How many bags of hamburgers
should Mr. Jordan buy? How many bags of buns? How many hamburgers can each student have?
Activate Prior Knowledge
Raise your hand if you’ve gone to a picnic with lots of food? What kinds of food were served?
Who was in charge of bringing the food for the picnic? If you helped prepare some of the food, what did you make?
Talk with your neighbor. What sorts of things do you have to think about when planning to feed a lot of people?
Build Background Knowledge
Hot dog buns usually come in bags of eight, but hot dogs usually come in bags of twelve.
Talk with your neighbor. Why would bakers make eight buns, and why would hot dog makers
put twelve hot dogs in a package?
Preview the Problem Title
Open your Student Journal to Activity 2 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
None
Comprehension QuickStart Activity 2
Comprehension QuickStart Activity 3
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Washing Windows
Mr. Tanabe stood on the middle rung of his ladder to wash windows of an office building. He
stepped up 3 rungs to reach more of the windows. Then he saw a spot he had missed on one of
the windows below, so he climbed down 5 rungs. After he cleaned that spot, he climbed up 7
rungs and washed the rest of the windows. After he finished, he climbed the remaining 6 rungs
to the top of the building to pick up all his equipment. How many rungs did the ladder have?
Activate Prior Knowledge
Have you ever climbed a ladder? Why were you using the ladder? How high did the ladder go?
How high did you go?
Who can tell us some things to do to keep safe when we are on a ladder?
Build Background Knowledge
Many people work at jobs where they use ladders. Talk with your neighbor. How many
jobs can you think of that involve the use of ladders?
Preview the Problem Title
Open your Student Journal to Activity 3 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word rung on the board. Point to the word and read it aloud.
There are ten rungs on my ladder. I can climb safely to the eighth rung.
If I climb to the last rung of a ladder, the ladder is in danger of tipping over.
Who can tell us what rung means?
Comprehension QuickStart Activity 3
Comprehension QuickStart Activity 4
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Party Tables
The sixth graders are planning a party to celebrate the end of the school year. They have 36 square card tables. Each
card table seats 4 people. How can the 36 card tables be joined together in a rectangle to seat the greatest number
of people possible?
Activate Prior Knowledge
Stand up if you have a round dining table at home.
Stand up if you have a square or rectangular dining table at home.
Talk with your neighbor. Which do you like better: round tables or square tables? Why?
Build Background Knowledge
At some formal parties like weddings, the hosts make a seating chart showing how tables
will be set up and where people will sit.
Talk with your neighbor. Why do you think party hosts make seating charts?
Preview the Problem Title
Open your Student Journal to Activity 4 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the words greatest number on the board. Point to the words and read them aloud.
One hundred fifty is the greatest number of people that can be seated at the restaurant.
The greatest number of dogs we’ve ever had in the Downtown Dogs Parades was thirty-four.
What does the phrase greatest number mean?
Can you think of another word or words that mean the same as the phrase greatest number?
[most, biggest number, largest number, maximum]
Comprehension QuickStart Activity 4
Comprehension QuickStart Activity 5
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
A Garden Puzzle
My neighbor planted her garden with 5 tomato plants, 5 pepper plants, 5 eggplant plants, 5 lettuce
plants, and 5 zucchini plants. Her garden is a square of 5 rows of 5 plants each. Each row and each
column has exactly 1 plant of each variety and so do the center diagonals. How might the plants
be arranged?
Activate Prior Knowledge
Stand up if you have ever grown anything in a garden.
Talk with a neighbor who has grown something in a garden. What did he or she grow and why?
Talk with a neighbor who has NOT grown something in a garden. What would he or she LIKE to grow and why?
Build Background Knowledge
Gardeners usually arrange garden plants in rows. This ensures that each plant has plenty of room to grow.
Talk with a neighbor. What other sorts of things do we arrange in rows?
Preview the Problem Title
Open your Student Journal to Activity 5 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
Write the words row and column on the board. Point to the words and read them aloud.
Ten students lined up into two rows. Five students stood in each row.
I stacked my chips into two columns. I put ten chips in each column.
The chart had three rows and two columns.
Who can tell us the difference between a row and a column?
© ETA hand2mind™
Write the words center diagonal on the board. Point to the words and read them aloud.
A center diagonal is a straight line that runs through the center of a square or rectangle
and joins opposite corners.
I’ll draw a square on the board. Who wants to draw one of its center diagonals?
Comprehension QuickStart Activity 5
Comprehension QuickStart Activity 6
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Guitars Galore
Johnny Integer saved $100 to buy a guitar. Then he bought one for $80. Johnny lost patience
learning to play it and decided to sell it to his friend Michael. Michael had also saved $100. Michael
really wanted the guitar, so he paid Johnny $90 for it. After Johnny saw his favorite guitar player
in a concert, he wanted to buy back the guitar. He bought it back from Michael for $95. Now
Michael has offered Johnny $85 for the guitar. Johnny is deciding whether he will accept the offer.
If he does, will he have lost any money on the guitar? If so, how much?
Activate Prior Knowledge
Stand up if you have ever given something away or sold something and then
later wished you hadn’t. Tell us what the item was.
What can we do with things we no longer want or need?
Build Background Knowledge
What are some ways people can sell things they no longer want?
[garage sales, second-hand stores, Internet stores]
Preview the Problem Title
Open your Student Journal to Activity 6 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
Write the words lost money on the board.
I lost money when I sold my cupcakes for less than I paid for the ingredients.
I will lose money if I give you five dollars and you give me three.
What does it mean to lose money?
Comprehension QuickStart Activity 6
© ETA hand2mind™
Write the words galore and patience on the board. Point to the words and read them aloud.
Sally had a lot of roses in her garden. When my grandmother saw Sally’s garden, she said,
“Sally has roses galore in her garden!”
There were bargains galore at the garage sale! I hardly knew which bargain to look at first!
Who can define the word galore?
Thank you for your patience. I’m sorry you had to wait so long.
I lost my patience when I had to stand in line for one hour. I decided to go back tomorrow.
What do you think patience means?
Comprehension QuickStart Activity 7
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Basketball Players
A basketball team has 14 players in 3 positions: forward, center, and guard. When the manager counts
the centers and guards, she counts 8 players. When she counts the forwards and the centers, she counts 9
players. How many forwards, how many centers, and how many guards are on the team?
Activate Prior Knowledge
Stand up if you have ever played a team sport. What sport did you play?
What do you like about the sport?
Talk to your neighbor. See how many team sports you can name in a minute.
Build Background Knowledge
Raise your hand if you know how to play basketball.
How many players from one team are on the court at one time? [5]
Who can tell us the positions on a basketball team? [forward, center, guard]
Who would like to tell us how to play the game of basketball?
Preview the Problem Title
Open your Student Journal to Activity 7 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the words forward, center, and guard on the board.
These are the names of positions on a basketball team.
Who wants to point to a position, read the word, and tell us what the person
who plays that position is supposed to do?
Comprehension QuickStart Activity 7
Comprehension QuickStart Activity 8
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
The County Fair
At the county fair, Amy played a game to win a big stuffed bear. The game she played used
4 cubes in a box: 1 red cube, 1 blue cube, 1 yellow cube, and 1 green cube. Without peeking,
Amy reached into the box and drew 1 cube. She put the cube back and drew again. If
the cubes on both draws were the same color, Amy won a bear! How many different
combinations could Amy draw? How many of these would be winning combinations?
Activate Prior Knowledge
Raise your hand if you have ever been to a fair or carnival. Did you play any of the games?
What were they? Did you win anything?
Talk with your neighbor about what you like about going to a fair or a carnival.
The rides? The food? The games? The animal exhibits?
Build Background Knowledge
At fairs and carnivals, there are usually games set up for people to win prizes like stuffed animals.
These games might involve throwing a ball, tossing a coin, or doing some sort of puzzle.
Talk with your neighbor about what kind of game you would want to play? Which one do you think
would be easiest to win? Why?
Preview the Problem Title
Open your Student Journal to Activity 8 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the words different combinations and winning combinations on the board.
Point to the words and read them aloud.
A combination is a mixture of things that make up something. For example,
a cake is made from a combination of ingredients.
Two different cakes have two different combinations of ingredients.
In a cake contest, the winning cake has the winning combination of ingredients.
Who can make up a sentence with the words different combination in it?
Who can make up a sentence with the words winning combination in it?
Comprehension QuickStart Activity 8
Comprehension QuickStart Activity 9
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Alex’s Allowance Plan
Alex always has a scheme for everything. He has just asked his parents for a new deal on his
allowance. Instead of getting a weekly allowance, he wants to be paid for his daily chores in the
following way. He wants to get paid 1 cent on the first day, 2 cents on the second day, 4 cents on
the third day, and so on. In this way, each day’s pay will be double the amount of the previous day.
If Alex’s parents agree to this plan, how much will Alex get paid on the 14th day?
Activate Prior Knowledge
Raise your hand if you get an allowance or know somebody who does.
Talk with your neighbor. What should be a fair allowance for sixth graders? Why?
Build Background Knowledge
Do you think you should have to do chores in order to get an allowance? Why or why not?
What kind of chores do you think someone your age should be able to do?
Preview the Problem Title
Open your Student Journal to Activity 9 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word scheme on the board. Point to the word and read it aloud.
My sister worked up a scheme to get out of doing the dishes. My mom figured it
out so now my sister has to do dishes for a week!
Our class has been scheming for weeks to throw a surprise party for our teacher.
What do you think a scheme is?
Comprehension QuickStart Activity 9
Comprehension QuickStart Activity 10
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Tiles in the Bag
Mrs. Fairweather has placed 10 tiles in a bag. Some are red, some are blue, and some are
yellow. How many different combinations of the colors are possible?
Activate Prior Knowledge
Raise your hand if you’ve ever picked a name or number out of a container. Why were you
picking a name or number? Were you happy or disappointed by your choice? Why?
If I said you could pick two names instead of just one, do you think your name would have
a better chance of being picked? Why or why not?
Build Background Knowledge
None
Preview the Problem Title
Open your Student Journal to Activity 10 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the words different combinations on the board. Point to the words and read them aloud.
I’ll give you a combination of colored pens: I’ll give you red ones and green ones and blue ones.
Who can think of a different combination of colors?
Comprehension QuickStart Activity 10
Comprehension QuickStart Activity 11
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Gobs of Grapes
Mom just got home from the store with a big bunch of fresh juicy grapes. My brother came home from
football practice and took _12 the grapes. My sister came home from her piano lesson and took _12 of what
was left. When my dad got home from work, he took _12 of the remaining grapes. By the time I finished
my homework, there were only 6 grapes left. How many grapes were in the bunch that Mom bought?
Activate Prior Knowledge
Raise your hand if you have a brother or a sister at home.
What kinds of things do you share with your brother or sister?
How do you decide how to share so each of you gets a fair amount?
Build Background Knowledge
Talk with your neighbor. What is one-half of one-half? What is one-half of one-fourth?
Preview the Problem Title
Open your Student Journal to Activity 11 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word gobs on the board. Point to the word and read it aloud.
I had gobs of stickers! I had so many I gave some away.
There were gobs of people at the show and I thought I wouldn’t be able to find a seat.
Who knows what gobs means?
Comprehension QuickStart Activity 11
Comprehension QuickStart Activity 12
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Circles on the Square
Look at the 3 x 3, 4 x 4, and 5 x 5 square patterns shown here. See how many circles are in each pattern.
How many circles would be in a 75 x 75 pattern?
Activate Prior Knowledge
Look around your classroom. How are the desks arranged? In rows? In a circle?
How many desks are in each grouping? How many groups are in the classroom?
Talk with your neighbor on the left. How would the groups change if ten more students
joined the class? If ten students left the classroom?
Build Background Knowledge
None
Preview the Problem Title
Open your Student Journal to Activity 12 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word square on the board.
Who can tell us what a square is?
Comprehension QuickStart Activity 12
Comprehension QuickStart Activity 13
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Dividing the Square
The City of Pleasantville is celebrating its 75th anniversary. The sixth grade
helped decorate the city square. Students were divided into 7 groups,
A through G. Each group helped decorate a section of the square as shown
in the drawing. Estimate the fraction of the square that each group helped
decorate. Assume that the drawing is scaled correctly.
Activate Prior Knowledge
Who can explain what an anniversary is?
Is your birthday a kind of anniversary? What kind of anniversary celebrations can you think of?
How do people celebrate anniversaries?
Build Background Knowledge
Some towns have a main square in the center of town that might contain
a park or historical buildings.
Talk with your neighbor. Does your town have a main square or a place
that is of historical importance to the town?
Preview the Problem Title
Open your Student Journal to Activity 13 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word scale on the board. Point to the word and read it aloud.
We drew the map of our room and furniture to scale so that we could see how each
piece would fit in the room.
The six-inch doll was a perfect scale replica of the original person, who was five feet tall.
What does the term scale mean?
What other things might be drawn or built to scale.
Comprehension QuickStart Activity 13
Comprehension QuickStart Activity 14
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Decimal Divide
That last math quiz was really tricky! Alice, Julio, and Lida were discussing their answers after the quiz. The quiz
had only one problem on it, and the 3 students got different answers. Alice said the answer is 0.18. Julio said the
answer is 1.8. Lida said the answer is 18. One of the students is correct. Which one is it? Explain your reasoning.
Activate Prior Knowledge
What subject do you think you’re the best in? Why do you like it?
Talk with your neighbor. Did you ever take a test in your best subject and were disappointed
in your score? How could you have gotten a better score?
Build Background Knowledge
Write the number 125 on the board.
I’d like a volunteer to put a decimal point in this number so that it expresses the fraction 12 _12 .
Who can move the decimal point so 12 _12 becomes the whole number 125?
Who can move the decimal point again and make 125 so that it expresses the fraction 1 _14 ?
Preview the Problem Title
Open your Student Journal to Activity 14 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word reasoning and tricky on the board. Point to the words and read them aloud.
We used our reasoning skills to come up with the answer to the puzzle.
The detective reasoned that the crime had most likely taken place between midnight and five in the morning.
What do you think reasoning means?
That problem was very tricky. I wasn’t sure I got the right answer.
Following that map was tricky. It had so many paths, I lost track of where to turn.
What do you think tricky means?
Comprehension QuickStart Activity 14
Comprehension QuickStart Activity 15
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Lilies on the Pond
One day there was a water lily on a pond. The next day there were 2 water lilies on the pond.
The next day there were 4. The number of water lilies continued to double every day. On the
30th day, the pond had become completely covered with lilies. On which day was the pond
half covered?
Activate Prior Knowledge
Picture a pond in your mind. Talk to your neighbor and describe the pond that you see.
How big is it? What is in the pond?
Build Background Knowledge
Water lilies are a type of plant that grows in ponds. The flowers of the water lily
float on the surface of the water.
Who has seen a water lily? Where did you see it?
What other kinds of plants grow in water?
[seaweed, cattails, hyacinths, duckweed, horsetails, algae]
Preview the Problem Title
Open your Student Journal to Activity 15 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word double on the board. Point to the word and read it aloud.
My age is double my brother’s age. I’m twelve and he is six.
I doubled my baseball card collection from fifty cards to one hundred.
What does it mean to double something?
Comprehension QuickStart Activity 15
Comprehension QuickStart Activity 16
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
What Comes Next?
Look at each of these figures. If the pattern continues, how many tiles will it take to
build Figure 15? Describe any patterns you find.
Activate Prior Knowledge
Stand up if you are wearing clothing with a type of pattern on it. Describe the pattern.
Talk with a neighbor. Find a pattern somewhere in the room. What are the rules of this pattern?
Build Background Knowledge
A pattern is a predictable sequence, such as counting by twos. When we count by twos,
we follow a pattern of adding two to the previous number.
Pick a number from one to nine. Tell your neighbor. Ask your neighbor to count by two and
tell you the next two numbers in the pattern. Do you agree?
Preview the Problem Title
Open your Student Journal to Activity 16 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
None
Comprehension QuickStart Activity 16
Comprehension QuickStart Activity 17
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Strawberry Picking
Each spring, Paul and his family go to Grandpa’s farm to pick strawberries. Paul eats 2 strawberries for
every 15 strawberries he puts in his basket. If Paul ate 18 strawberries, how many strawberries did he
put in his basket?
Activate Prior Knowledge
What is your favorite fruit? How does it grow? On a tree? On a vine? On a bush?
Who knows how strawberries grow?
Who has picked strawberries? Where did you go to pick them? Who many did you pick?
Is it easy to pick strawberries or is it hard work?
Build Background Knowledge
Some farmers allow customers to pick fruit themselves and pay for what they pick.
Talk to your neighbor. If you were a farmer, what rules would you make for picking fruit at your farm?
Should customers be allowed to eat the fruit before they pay for it? Should customers bring their
own containers? Would customers pay by the pound? Pay per piece of fruit?
Preview the Problem Title
Open your Student Journal to Activity 17 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
None
Comprehension QuickStart Activity 17
Comprehension QuickStart Activity 18
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Baking Brownies
James wants to make 2 pans of brownies. Each brownie will be 2 inches by 2 inches square. James has 1 pan
that is 8 inches by 12 inches. He looks around for another pan and finds one that is twice as long and twice as
wide. How many brownies will James get from each pan?
Activate Prior Knowledge
Stand up if you have ever baked anything like cookies or a cake. What did you bake?
Who helped you? How did you know what kind of pan to use?
Talk with your neighbor. What is your favorite kind of baked treat?
Build Background Knowledge
None
Preview the Problem Title
Open your Student Journal to Activity 18 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the phrase twice as on the board. Point to the words and read them aloud.
My aunt will be twice as old as I am when she is thirty and I am fifteen.
I should eat twice as many servings of vegetables per day as I do now.
What does the phrase twice as mean?
What are other words that mean the same as twice as. [double, two times]
Comprehension QuickStart Activity 18
Comprehension QuickStart Activity 19
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Painted Cube
Marsha constructed a large cube by gluing together smaller cubes. The large cube is made up of 64 of the
smaller cubes. Marsha painted the outside of the large cube red. Later, when she took apart the large cube,
Marsha noticed that some of the cubes had paint on 3 faces, some had paint on 2 faces, some had paint
on 1 face, and some had no paint on them at all. Find out how many cubes of each kind she had.
Activate Prior Knowledge
Who likes to build things? What have you built? Did you paint it? What colors did you use?
Raise your hand if you’ve ever used blocks to build something? What did you build?
How big was it? How many blocks did you use?
Build Background Knowledge
Talk with your neighbor. What sorts of objects could be modeled out of square blocks?
Preview the Problem Title
Open your Student Journal to Activity 19 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word face on the board. Hold up a cube, such as a centimeter cube.
What is this shape called?
I need a volunteer to show us which part of this shape is a face.
What are some other words for face when we talk about the face of the cube?
[surface, side, outside]
Comprehension QuickStart Activity 19
Comprehension QuickStart Activity 20
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Riddles Everywhere
Riddle 1
What number am I?
I am a multiple of 2 and 7.
I am less than 100 and greater than 50.
I am the product of 3 prime numbers
that are all different.
Riddle 2
What number am I?
I am a perfect square.
The only number in my prime
factorization is 2.
I am a factor of 32.
The sum of my digits is odd.
Activate Prior Knowledge
I have a riddle for you! Why do birds fly south? [It’s too far to walk.]
Who has a riddle you can ask the class?
Who can explain to us what a riddle is?
Build Background Knowledge
None
Preview the Problem Title
Open your Student Journal to Activity 20 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Write the words multiple, prime number, perfect square, factor, and prime factorization on the board.
Point to the words and read them aloud.
Let’s review some math vocabulary.
A multiple of a number is the product of the number and another number. For example, thirty-five is
a multiple of five. Five times seven is thirty-five. Who can give us a multiple of two?
Who can define prime number? A prime number is a whole number greater than one that has exactly
two factors, one and itself. The first five prime numbers are two, three, five, seven, and eleven.
Who knows what a perfect square is? A perfect square is a whole number that is the square of another
whole number. For example, four is the perfect square of two, and nine is the perfect square of three.
Who can tell us what a factor is? A factor is a whole number that divides exactly (leaves no remainder)
into another whole number. So, one, two, four, and eight are factors of eight.
Now we can define prime factorization. Who wants to give us a definition? A prime factorization
is the expression of a number as a product of prime factors; for example, twelve equals two times
two times three.
Comprehension QuickStart Activity 20
© ETA hand2mind™
Preview Vocabulary
Comprehension QuickStart Activity 21
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
A Cup of Pennies
Emma’s grandmother gave her a plastic cup containing 40 shiny 1976 pennies. The cup and all 40 pennies
weighed 135 grams. Emma took half of the pennies out of the cup. Then she weighed the cup and the
remaining pennies. The cup and 20 pennies weighed 75 grams. How much did the cup weigh?
Activate Prior Knowledge
What do you do with your loose coins? Put them in a bank? In a box?
Raise your hand if you collect coins or know someone who does.
What kinds of coins do you or the person you know collect?
Do you or the person you know display the coins in a special way?
Do you know what the collection is worth?
Build Background Knowledge
Many people collect coins. Coins from certain years are worth more than others,
and so are coins with certain mistakes on them, such as a misprinted date.
Talk with your neighbor. Have you ever found a coin that you thought was unusual or special?
What did you find out about it?
Preview the Problem Title
Open your Student Journal to Activity 21 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
None
Comprehension QuickStart Activity 21
Comprehension QuickStart Activity 22
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Welcome to Flatville
The houses in Flatville are built from squares and equilateral triangles. Each street has
1 more house than the previous street. On each street, the houses are built side to side
as shown in the figure. The figure also shows the perimeters of the houses on the first
3 streets. What is the perimeter of the houses on Street 10? Find a pattern to help you
determine the perimeter of the houses on any street in Flatville.
Activate Prior Knowledge
Raise your hand if you live in a house. Raise your hand if you live in an apartment.
Have you ever looked at the roof of your house or apartment building? What do you think it’s made of?
What is the purpose of a roof? What are some reasons a roof might be in the shape of a triangle?
Build Background Knowledge
In some cities, identical houses are built side by side in a group and are connected by a
common side wall. They are called row houses or townhouses.
Does anyone live in a row house or townhouse, or know someone who does? How many
houses do you think make up the group?
Preview the Problem Title
Open your Student Journal to Activity 22 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the words equilateral triangle and perimeter on the board. Point to the words and read them aloud.
Who can remind us what an equilateral triangle is? An equilateral triangle is a triangle with all
three sides having the same length.
Who can remind us what the perimeter of a figure is? The perimeter of a figure is the distance around it.
Comprehension QuickStart Activity 22
Comprehension QuickStart Activity 23
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Triangle Toothpicks
Tracy can make an equilateral triangle with 3 toothpicks. She can make 2 triangles with
5 toothpicks. She can make 3 triangles with 7 toothpicks. She says she can make 4 triangles
with 6 toothpicks. Show how this is possible.
Activate Prior Knowledge
Who likes to solve puzzles? What kind of puzzle do you like to solve? Word puzzles?
Picture puzzles? Number puzzles? Jigsaw puzzles?
Talk to your neighbor about your favorite kind of puzzle. What do you like about it?
Build Background Knowledge
Sometimes we run out of ideas when we are trying to figure something out.
Talk to your neighbor. What are some ways to come up with new ideas?
Who could you go to for help? Where could you find more information?
Preview the Problem Title
Open your Student Journal to Activity 23 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the words equilateral triangle on the board. Point to the words and read them aloud.
Who can remind us what an equilateral triangle is? An equilateral triangle is a triangle with
all three sides having the same length.
Comprehension QuickStart Activity 23
Comprehension QuickStart Activity 24
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Computer Room
The computer room in Albert’s house is in the attic and is shaped like the trapezoid shown
here. Albert wants to determine the area of the room so he can buy carpet for the floor.
What is the area of the trapezoid? Explain a method for finding the area of the trapezoid.
Activate Prior Knowledge
When you think of a living room, what shape is it? What about a bedroom?
Have you ever seen a room with round walls? What was the room used for?
Have you ever seen a room with a slanted ceiling? What was the room used for?
Talk with your neighbor. What shape would you choose for your own bedroom? A circle? A triangle?
A square? A combination of shapes? Do you think it could really be built that way?
Build Background Knowledge
Some houses have attics, which are spaces just under the roof. Some attics are big enough for a room,
but many attic rooms have unusual shapes.
Talk with your neighbor. Why do you think an attic room might not have a rectangular shape?
Preview the Problem Title
Open your Student Journal to Activity 24 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word trapezoid on the board. Point to the word and read it aloud.
Let’s review some math vocabulary. A trapezoid is a four-sided shape with exactly
two parallel sides.
I’d like a volunteer to draw a trapezoid on the board.
Look around the room. Can you find something in the shape of a trapezoid?
Comprehension QuickStart Activity 24
Comprehension QuickStart Activity 25
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Moose’s Play Area
Tommy and Tessa want to fence in a play area for their dog, Moose. Moose is a big
dog, and they want to give him as much room as they can. They have 64 feet of fence.
They can use up to 36 feet of the side of their barn as one side of the play area. The
area must be rectangular, and each side must be a whole number of feet. Determine
the best size for Moose’s play area.
Activate Prior Knowledge
Stand up if you have a pet at home. What kind of pet do you have? What is your pet’s name?
Talk with a neighbor. What are some reasons for keeping a pet in a safe area instead of allowing the
pet to run free? What kind of space could you make for your pet? Would you build a fence? A cage? Would
you keep your pet indoors with you?
Build Background Knowledge
None
Preview the Problem Title
Open your Student Journal to Activity 25 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the words whole number on the board. Point to the words and read them aloud.
The numbers two, four, fifteen, and twenty-seven are whole numbers.
One-half and one-fourth are not whole numbers.
Who can tell us what a whole number is?
Comprehension QuickStart Activity 25
Comprehension QuickStart Activity 26
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Follow the Yellow Brick Road
Dorothy and Toto started down the yellow brick road with a full basket of apples. When Dorothy
met the Scarecrow, she gave him half her apples, plus 2 more. Then Dorothy met the Tin Man.
She gave him half her remaining apples, plus 2 more. Later, Dorothy met the Cowardly Lion and gave
him half her remaining apples, plus 2 more. After that, Dorothy had 2 apples left in her basket. How
many apples did Dorothy have in the basket before she gave any away?
Activate Prior Knowledge
Who can tell us what a scarecrow is? Have you ever seen a real one?
Why do you think it’s called a scarecrow?
Build Background Knowledge
Who knows the story of the Wizard of Oz? What do you know about the story?
Did you read the story? Did you ever see the movie?
It is a famous story about a girl who is transported to an enchanted land and meets
friends who try to help her get back home. She travels down a yellow brick road to
meet a wizard whom she hopes will help her.
Preview the Problem Title
Open your Student Journal to Activity 26 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
Write the names Dorothy, Toto, Scarecrow, Tin Man, and Cowardly Lion on the board.
These are the names of some characters in the story of the Wizard of Oz.
Who can pick a character and read the name? Can you tell us something about that character?
Comprehension QuickStart Activity 26
© ETA hand2mind™
Write the word plus on the board. Point to the word and read it aloud.
Mom gave me a sandwich for lunch, plus two pieces of fruit, so I had three things to eat.
Sandy gave me a quarter, plus four nickels, which made forty-five cents.
What other words could we use instead of plus? [and, and also, along with, as well as]
Comprehension QuickStart Activity 27
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Flip that Chip
You have 2 chips. 1 chip has a green circle on both sides. The other chip has a green circle on 1 side and a
red circle on the other side. You will place the chips in a container and shake the container. You will pour
out the chips. If the 2 chips match, you will get a point. If the 2 chips do not match, your friend will get a
point. Is this a fair game? Explain your thinking.
Activate Prior Knowledge
Have you and a friend ever each tossed a coin to see what came up? Heads or tails?
What were you doing? Playing a game? Trying to make a decision?
Build Background Knowledge
Let’s try it now and see if two people come up with the same or different side of a coin.
Who wants to make the first toss? I need two volunteers.
Let’s keep going until everyone has a chance to toss the coins. Tell us what you get each time.
Think about the tosses. What happened more often? The tosses matched or the tosses did not match?
Preview the Problem Title
Open your Student Journal to Activity 27 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
None
Comprehension QuickStart Activity 27
Comprehension QuickStart Activity 28
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Baking Cookies
Martin and Maria are planning to bake oatmeal cookies for the bake sale. The recipe
they found makes 48 cookies using the following ingredients:
3
_
3 cups rolled oats (not instant)
4 pound (3 sticks) unsalted butter
1 cup light brown sugar
1_12 cups all-purpose flour
3
_
1_14 cups granulated sugar
4 teaspoon kosher salt
1 large egg
2_12 teaspoons baking soda
2 teaspoons vanilla extract
1_34 cups raisins
If Martin and Maria want to bake 6 dozen cookies, how much of each ingredient will they need?
Activate Prior Knowledge
Stand up if you have ever baked or helped someone bake cookies. What kind of cookies did you bake?
Talk with a neighbor. What do you think goes into your favorite kind of cookie? Where would
you shop for what you need?
Build Background Knowledge
Cookies are usually counted in dozens, or twelves. This is a very old method of counting baked goods.
There is even a term known as a “baker’s dozen,” which is twelve plus one extra! We don’t really know
where that term came from, but one story is that centuries ago, a baker would be punished if he or she didn’t
deliver exactly twelve items. So bakers put an extra item in the batch just to be sure there were enough.
Talk with a neighbor. How many dozen cookies would you need to bring to class if you wanted
to share them with your classmates?
Preview the Problem Title
Open your Student Journal to Activity 28 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
This problem includes a recipe. Raise your hand if you have ever read or followed a recipe.
What was the recipe for? Were there many steps?
What kinds of things are included in a recipe besides ingredients? [steps for mixing ingredients;
temperature to cook at; time to cook; serving suggestions]
Write the words recipe and ingredients on the board. Point to the words and read them aloud.
We’ve been talking about recipes. Who can give us a definition of recipe?
A recipe can have many ingredients, such as raisins, salt, sugar, and eggs.
I needed so many ingredients to make the cake, I had to go grocery shopping first.
What does the word ingredients mean?
Comprehension QuickStart Activity 28
© ETA hand2mind™
Preview Vocabulary
Comprehension QuickStart Activity 29
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Palindromes
A palindrome is a word or a number that reads the same forwards and backwards.
Here are 3 word palindromes and 3 numeric palindromes. How many numeric
palindromes can you find between 100 and 1,000?
Activate Prior Knowledge
Who knows how to spell the word “radar”? I’ll write it on the board. What is the word “radar”
spelled backwards?
Who can spell the word “noon”? What is the word “noon” spelled backwards?
Talk to your neighbor. Try to think up two more words that say the same thing spelled
backwards or forwards.
Build Background Knowledge
Words that are spelled the same backwards and forwards are called “palindromes.”
Preview the Problem Title
Open your Student Journal to Activity 29 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the words numeric palindromes on the board. Point to the words and read them aloud.
Palindromes are words that are spelled the same backwards and forwards.
What do you think numeric palindromes are?
Comprehension QuickStart Activity 29
Comprehension QuickStart Activity 30
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Steps to the Average
The sixth graders counted how many steps it takes them to walk from their
classroom to the playground. They put their results in the line plot shown here.
Find the mean, median, and mode of their data.
Activate Prior Knowledge
How do you keep track of things you want to remember?
Have you ever made a to-do list? How did you organize your list?
Build Background Knowledge
Scientists need to keep track of information they learn. Pretend you are a scientist and you want to
know how many times the puppies in a litter of four bark.
Talk to your neighbor. What are some ways you can keep track of how many times the puppies bark?
How could you record the information?
Preview the Problem Title
Open your Student Journal to Activity 30 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
This problem includes a line plot. A line plot is a graph that uses Xs (or other symbols) above
numbers on a number line to show how often something happens.
Which information do you think could be recorded on a line plot? The heights of your
classmates or the items on your to-do list?
Preview Vocabulary
© ETA hand2mind™
Write the words mode, median, and mean and the numbers 1, 1, 1, 2, 5 on the board. Point to the words and read them aloud.
The mode is the number that appears the most times in a set of data.
Who can tell us the mode for the list of numbers here?
The median is the number that appears in the middle of a list of numbers in numeric order.
Who can tell us the median in the list of numbers here?
The mean is the average of a set of numbers.
Who can figure out the mean for this list of numbers here?
Comprehension QuickStart Activity 30
Comprehension QuickStart Activity 31
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Counting on Carl
Carl loves to count. He counts everything. He counts every way! Yesterday I
overheard him counting, and this is the way he began: 1, 4, 7, 10. He kept going and
going. Last I heard, Carl was still counting before he fell asleep. What was the 100th
number Carl counted?
Activate Prior Knowledge
Have you ever heard of counting sheep to fall asleep? Do you know what that means? It is a mental
exercise to put you to sleep. You think of an endless number of sheep jumping over a fence
and count each one. You get bored and fall asleep. Do you think that would work? Why or why not?
What is the highest number you have ever counted? What were you counting?
Build Background Knowledge
There is more than one way to count. We can count by twos, threes, and so on.
What kinds of things do we usually count by twos? [shoes, gloves, socks]
Talk with your neighbor. How would you count piles of quarters if you wanted to know
how many dollars you have?
Preview the Problem Title
Open your Student Journal to Activity 31 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word overheard on the board. Point to the word and read it aloud.
I overheard my mom say she was planning a surprise party, but she didn’t know I
was playing in the next room.
It was wrong to repeat the rumor I overheard in the cafeteria.
What does overheard mean?
Comprehension QuickStart Activity 31
Comprehension QuickStart Activity 32
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
The Frozen Yogurt Bandit
Yolanda loves yogurt. Her favorite flavor is Frozen Fruit Melody. Her younger brother, Frank, also loves
frozen yogurt. He’s not fussy about the flavor! One day, Yolanda put a gallon of yogurt in the freezer. That
night, Frank opened the freezer and ate _12 of Yolanda’s yogurt. The next night, he ate _12 of what was left.
He continued this for 5 nights. On the sixth day, Yolanda decided to have some of her yogurt. Boy was she
surprised when she opened the container! How much yogurt did Yolanda find?
Activate Prior Knowledge
What does it mean to “raid the refrigerator”? It means going to the refrigerator between meals and
finding something to eat. Do you ever raid the refrigerator? What do you hope to find?
What kinds of healthy snacks might be in the refrigerator?
What is your favorite snack you find in the refrigerator?
Build Background Knowledge
Let’s review liquid measures. Who can tell us how many cups are in a pint? How many pints are in a quart?
How many quarts are in a gallon?
Dairy products such as milk, sour cream, and yogurt usually come in containers measuring one cup, one pint,
one quart, one-half gallon, and one gallon.
Talk with your neighbor. If a recipe called for three cups of sour cream, what size container would you
buy to have the least amount of sour cream left over?
Preview the Problem Title
Open your Student Journal to Activity 32 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word bandit on the board. Point to the word and read it aloud.
The bandit stole the jewelry while Susan was out of the house.
The bandit made his living by robbing from the citizens of the town.
What are some other words for bandit? [thief, robber, outlaw, crook, gangster]
Comprehension QuickStart Activity 32
Comprehension QuickStart Activity 33
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Pasta for All
The Jeffersons went to their favorite Italian restaurant for dinner. They ordered
2 plates of lasagna. Fred served himself _23 of the lasagna from one plate, but he could
eat only _12 of what he took. Patty served herself _12 of the lasagna from the other plate,
but she ate only _23 of what she took. Who ate more lasagna, Fred or Patty?
Activate Prior Knowledge
Who likes Italian food? What is your favorite kind of Italian food?
Who can name some Italian dishes?
Who has eaten lasagna? Can you tell us what lasagna is? What does it look like?
Build Background Knowledge
Some restaurants serve food “family style.” What do you think “family style” means?
Talk with a neighbor. What would be the best way to share a bowl of pasta and sauce
evenly among a family of four?
Preview the Problem Title
Open your Student Journal to Activity 33 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
Write the word lasagna on the board. Point to the word and read it aloud.
The spelling of the word lasagna might surprise you, because of how we pronounce the word.
How many thought there was a Z in the word? Who thought there was a Y in the word?
Lasagna is a word from the Italian language. The letters la are pronounced /l /. The letters sa
are pronounced /zän/. The letters gna are pronounced /y /.
e
© ETA hand2mind™
e
Comprehension QuickStart Activity 33
Comprehension QuickStart Activity 34
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Hexominoes
A hexomino is a figure made up of 6 squares placed side to side. Each square shares at least 1 of its sides. A
side can be shared between 2 squares only. 2 examples are shown here. There are 35 different hexominoes. A
hexomino is not different from another if turning or flipping the first one makes it look like the second one. Try
to find all 35 hexominoes.
Activate Prior Knowledge
Who likes to play matching games? Have you seen matching games where you try to find the same shape in a group
of similar shapes? What kinds of changes does the artist make to trick you into thinking it’s the same shape?
Talk with a neighbor. What are some ways you can change an equilateral triangle but still
keep it an equilateral triangle? [color, orientation, size]
Build Background Knowledge
Many number terms come to English from Greek. For example, the word “decathlon,” which is a type of
Olympic sport involving ten separate events, has as its root the Greek word “deca” which means “ten.”
The Greek root “tri” means “three”? Name a shape that begins with “tri.” How many sides does a triangle have?
The Greek root “hex” means six. Who can name a shape that begins with “hex”? How many sides does a hexagon have?
What do you think a hexomino is? It is a figure made out of six squares placed side to side.
Preview the Problem Title
Open your Student Journal to Activity 34 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
Write the words turn and flip on the board. Draw three arrows and labels as shown.
Point to the words and read them aloud.
A
B
Can you turn Figure A to make Figure B? To make Figure C?
Can you flip Figure A to make Figure B? To make Figure C?
Write the word hexomino on the board. Point to the word and read it aloud.
Who remembers the Greek root for this word? What does the root mean?
Comprehension QuickStart Activity 34
© ETA hand2mind™
C
Comprehension QuickStart Activity 35
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Bull’s-Eye!
Barney and Frieda are at the archery range. Frieda scored 12.2 points. Find 3 ways Frieda could have
scored this amount.
Activate Prior Knowledge
Raise your hand if you have ever played a game of darts or watched someone else play the game.
Who can tell us how darts is played?
How does a player win points?
Build Background Knowledge
The center of a round target is called the “bull’s-eye.” Hitting the bull’s-eye is considered the greatest skill.
We use the term “hitting a bull’s-eye” in English to mean “being successful” or “being exactly right.”
Can you think of any other ways we talk about hitting the bull’s-eye?
[hitting the nail on the head, hitting the mark, being on target]
Preview the Problem Title
Open your Student Journal to Activity 35 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the words archery and range on the board.
At the driving range, my dad can practice hitting golf balls without having to play an entire game of golf.
According to legend, William Tell was an excellent archer who shot an apple off his son’s head with an arrow!
Based on these sentences, what do you think an archery range is?
Comprehension QuickStart Activity 35
Comprehension QuickStart Activity 36
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Fractured Fractions
Jack and Jill are playing a game with the spinner shown here. They spin twice and add the fractions. If the
sum is greater than _12 , Jack gets a point. If the sum is less than _12 , Jill gets a point. Is the game fair? Explain
your reasoning.
Activate Prior Knowledge
Raise your hand if you have played a game that uses a spinner. What is the game? Describe the spinner.
What is on it? Pictures? Numbers? Colors?
Talk with your neighbor about games you have played that use a spinner.
What is the importance of the spinner to playing the game? What does it tell you?
Build Background Knowledge
Let’s pretend you want to design a game for two people. You want to be sure the game is fair.
But your friend doesn’t think the game needs to be fair.
Talk to you neighbor about what it means to be fair. Is being fair important? Why or why not?
Preview the Problem Title
Open your Student Journal to Activity 36 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the words fractured and fractions on the board. Point to the words and read them aloud.
She fractured her leg and had to wear a cast for many weeks.
The clay pot was fractured and now it leaks.
What is another word for fractured? [broke, broken, cracked, split]
What does the Latin root “fract” most likely mean? What is a word in math that uses this Latin root?
Comprehension QuickStart Activity 36
Comprehension QuickStart Activity 37
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Patio Perimeter
The patio in the middle of my backyard is a rectangle that measures 4.5 meters by 7.5 meters.
I would like to put a border of bricks around the outside edge of the patio. The bricks are 0.3 meter
long. I don’t need to fill in the corners, because Mom wants to plant a lilac bush in each corner.
How many bricks do I need to complete the border?
Activate Prior Knowledge
Who knows what a patio is? Who has a patio at home or knows someone who does? What is the
patio made out of? Stone? Brick? Concrete? Something else?
Talk to a neighbor. If you had a patio, how would you use it? What furniture would you put on it?
Would you want to eat outside and have a grill for making hamburgers?
Build Background Knowledge
People call outdoor sitting areas different things in different parts of the country. What do we call an
outdoor sitting area? Do you know any other names for it? [porch, veranda, lanai, stoop, deck]
Preview the Problem Title
Open your Student Journal to Activity 37 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word border on the board. Point to the word and read it aloud.
Our yard is bordered on all sides by a high fence to keep our dog inside.
The card had a border of little blue flowers all around the edge.
The border of our state is formed by the Mississippi River.
Based on these sentences, what is a border?
Comprehension QuickStart Activity 37
Comprehension QuickStart Activity 38
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Password Problems
My brother forgot his computer password again! He remembers that it is 3 digits. He knows that
digits might be repeated. The product of the digits is 24. What could his password be?
Activate Prior Knowledge
Stand up if you use a password for anything. Can you tell us why the password is needed?
What can you do if you forget a password?
Talk with your neighbor. What are some activities that require passwords?
Build Background Knowledge
Today, many people use passwords for computers. Before computers, however, passwords were used even
during ancient times among Roman soldiers.
Talk with your neighbor. What are some good methods for remembering passwords?
Preview the Problem Title
Open your Student Journal to Activity 38 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word digit on the board.
Who can tell us what a digit is?
Comprehension QuickStart Activity 38
Comprehension QuickStart Activity 39
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
How Many Trains?
I have a bag of red and blue connecting cubes. I want to build a “train” of cubes that is 10 cubes long.
How many different ways can I arrange the colors to make my train? The order of the colors makes a
difference. Red, red, blue is different from red, blue, red.
Activate Prior Knowledge
Stand up if you have ever ridden on a train. How often do you ride the train?
Where are you going when you ride the train?
Talk with your neighbor. Describe what a train looks like? How many cars does it have?
What do the cars carry? How many engines pull the train?
Build Background Knowledge
There are passenger trains and freight trains. Passenger trains carry people; freight trains may carry
livestock, crates, chemicals, vehicles, or even truck trailers.
Talk with a neighbor. Why do you suppose most trains today are either passenger or freight trains and not both?
Preview the Problem Title
Open your Student Journal to Activity 39 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word order on the board.
I arranged the names in my address list in alphabetical order by the last names.
The scores were listed in order from largest to smallest.
What does the word order mean?
Discuss some other types of information that go in a specific order.
Comprehension QuickStart Activity 39
Comprehension QuickStart Activity 40
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Funny Faces
Have you seen the new computer program that lets you create faces to attach to your
e-mails? There are 4 different kinds of eyes, 2 different noses, 3 different mouths, and 4
different kinds of hair. How many different faces are possible?
Activate Prior Knowledge
Raise your hand if you ever tried to draw a picture of yourself? What did you draw? Just your face?
Your whole body? Do you think it looked like you?
Talk with a neighbor. If you drew a picture of your face, what parts would you be sure to include?
Build Background Knowledge
Some computer programs let users create cartoon-like images of themselves they can use while
chatting online or playing computer games.
Has anyone ever created a computer-generated image of yourself? How did you do it?
Preview the Problem Title
Open your Student Journal to Activity 40 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
None
Comprehension QuickStart Activity 40
Comprehension QuickStart Activity 41
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Peter, Paul, and Patrick
Peter gave Paul and Patrick as much money as each already had. Then Paul gave Peter and Patrick as much as
each then had. Then Patrick gave Peter and Paul as much money as each then had. Now they each have $24.
How much money did each person have to start with?
Activate Prior Knowledge
Raise your hand if you have ever borrowed money from a friend or relative.
Raise your hand if you have ever lent money to a friend or relative.
Who can give us some advice about borrowing or lending money?
Build Background Knowledge
None
Preview the Problem Title
Open your Student Journal to Activity 41 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
None
Comprehension QuickStart Activity 41
Comprehension QuickStart Activity 42
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Sweater Sale
Bull’s Eye Department Store is having a big sale this week. All items in the store are marked
down 50%. And on Friday, all items will be marked down an additional 50%. Marcy is excited.
She says the $80 sweater that she wants will be free on Friday! Is Marcy correct? What will the
sale price of the sweater be on Friday?
Activate Prior Knowledge
Who likes to go shopping? What do you like to shop for?
Do you ever buy something on sale? What does “on sale” mean?
Talk with your neighbor. If a $50 toy is on sale for 50% off, how much will it cost?
Build Background Knowledge
Advertisers try to make sales sound better by playing with numbers. Careful shoppers know
when they’re being fooled!
Talk with your neighbor. Which is the better deal, a thirty-dollar shirt on sale for twenty percent
off, or a forty-eight-dollar shirt on sale for fifty percent off?
Preview the Problem Title
Open your Student Journal to Activity 42 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the words marked down and sale price on the board. Point to the words and read them aloud.
Because the couch was slightly damaged, its price was marked down from three hundred dollars
to one hundred twenty dollars.
I marked down the price because the sweater didn’t sell at the higher price.
The store is offering a twenty percent discount on all purchases, so the sale price of that twenty-dollar
vase will be sixteen dollars.
The sale price of the candlestick is fifty percent of its original price.
Based on these sentences, what do the terms marked down and sale price mean?
Discuss what the opposites of these terms would be. [marked up, full price, regular price]
Comprehension QuickStart Activity 42
Comprehension QuickStart Activity 43
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Palace Perimeter
It happened again! The handsome prince turned into a slimy frog. However, there is a
twist to this tale. Instead of kissing a lovely princess so he can return to his royal self, the frog
must hop around the palace and count his hops. Each frog hop is exactly 1 foot in length.
How many hops will the frog prince hop? In the figure, the marked lengths are in feet.
Activate Prior Knowledge
Who knows the story about the frog that became a prince? How did the frog get to be a prince?
Talk with a neighbor. If you were a frog, what would you want to change into? Why?
Build Background Knowledge
Royal families often live in palaces, which can be very big. For example, Buckingham Palace, where the
Queen of England lives, has more than 600 rooms! The Imperial Palace in Tokyo, Japan, is laid out
on more than one square mile!
Talk with a neighbor. What do you think it would be like to grow up in a palace?
Preview the Problem Title
Open your Student Journal to Activity 43 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
What do you call the drawings that builders make to show all the measurements
of a building? [blueprint, plot, diagram, layout, sketch]
Who has ever made a drawing of something and put its measurements on the drawing?
What were you trying to show?
This problem includes a drawing showing the floor plan of the prince’s palace.
It shows the lengths along the sides of the building.
Preview Vocabulary
© ETA hand2mind™
Write the word perimeter on the board. Point to the word and read it aloud.
Who can remind us what the perimeter of a figure is? The perimeter of a figure is the distance around the figure.
Comprehension QuickStart Activity 43
Comprehension QuickStart Activity 44
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Pattern Block Patterns
We are designing geometric patterns in art class. My first 3 designs are shown here. I used 4
pieces for Design 1 and more for Designs 2 and 3. How many pieces will I need for Design 20 if I
continue the pattern? How many pieces will I need for Design 50? How can I find the number of
pieces that I would need for any design, Design n?
Activate Prior Knowledge
Raise your hand if you enjoy drawing or making any other kind of art.
Tell us what kinds of things you enjoy doing.
Have you ever been to an art museum? What did you see there that you liked?
Build Background Knowledge
None
Preview the Problem Title
Open your Student Journal to Activity 44 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the words design and geometric pattern on the board. Point to the words and read them aloud.
I designed a pretty sweater, and I asked my mother if she could make it for me.
The kitchen design included a special place for me to feed the cat.
What do you think design means?
The circles and triangles were placed in such a way to make an interesting geometric pattern.
The letters A, B, A, B make an alphabetical pattern. The figures red square, blue square, red square,
blue square make a geometric pattern.
Look around the room and try to find an example of a geometric pattern.
Comprehension QuickStart Activity 44
Comprehension QuickStart Activity 45
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Something Fishy
Jay sells tropical fish. You should see the huge fish tank in his store! He has 2 pieces of
hose that he uses to fill the tank with water. If he uses the first hose, it takes him 3 hours
to fill the tank. If he uses the second hose, it takes him 6 hours to fill the tank. How long
will it take Jay to fill the tank if he uses both hoses at the same time?
Activate Prior Knowledge
Raise your hand if you have, or ever had, a pet fish. What kind of fish? How many?
What kind of container do you keep your fish in?
Fish need a clean and healthy environment to live. Who has some ideas about how to keep a fish tank
in good condition for the fish? What kind of equipment would you need?
Build Background Knowledge
An aquarium is a tank filled with water for keeping live fish. Some cities have huge aquariums that
can even keep certain kinds of whales! One aquarium in Chicago, Illinois, holds beluga whales, dolphins,
and other marine animals and contains three million gallons of salt water!
Has anyone been to a large aquarium? What did you see?
Preview the Problem Title
Open your Student Journal to Activity 45 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word tropical on the board. Point to the word and read it aloud.
A tropical climate is warm and humid.
Our family won a vacation to a tropical island so we all had to go out and get swimsuits, sunscreen, and sunglasses.
Based on these sentences, what do you think a tropical fish is?
Comprehension QuickStart Activity 45
Comprehension QuickStart Activity 46
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
The Treasure of Bubba Baba
Have you heard the tale of Ali Baba and the 40 thieves? I’ll bet you never heard the
story about Ali Baba’s brother Bubba Baba. One night Bubba Baba watched Ali Baba
enter the cave where the stolen fortune was hidden. Later that night, Bubba Baba
returned to the cave and spoke the magic words, “Open sesame.” The cave door
opened and Bubba Baba went inside. He was amazed to find 2,290 pounds of rubies
and emeralds! There were 4 times as many 1-pound rubies as 3-pound rubies. There
were 3 times as many 3-pound emeralds as 6-pound emeralds. Bubba was most
amazed by the fifty 6-pound emeralds. How many rubies and how many emeralds of
each size did Bubba Baba find in the cave?
Activate Prior Knowledge
Raise your hand if you have ever heard the phrase “open sesame.” Who can tell us what it means?
Have you ever heard the story where that phrase came from? It’s a story about Ali Baba.
Can someone tell us what the story is about? [Ali Baba is the hero of an Arabian folktale. He accidentally
overhears the magic words “open sesame,” which open a cave holding stolen treasures.]
Build Background Knowledge
Everyone’s birthday month has a gemstone called a “birthstone.” Do you know your birthstone? What is it?
Preview the Problem Title
Open your Student Journal to Activity 46 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word fortune on the board. Point to the word and read it aloud.
It would cost a small fortune to buy a baseball team.
While digging in our backyard, we found a fortune in old coins.
Based on these sentences, what is a fortune?
Comprehension QuickStart Activity 46
Comprehension QuickStart Activity 47
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Oven Gone Mad
Kate’s father is a baker at the Morning Muffin Bakery. This morning, the oven wasn’t working
correctly, and 2 dozen muffins burned. Kate’s father gave _14 of what was left to Kate to take
to school. He wrapped up _12 of the remaining muffins and sold them to the coffee shop next
door. He wrapped up _13 of the remaining muffins and sold them to the grocery store down
the street. That left Kate’s father with a dozen muffins to sell at the bakery. How many
muffins did Kate’s father bake?
Activate Prior Knowledge
Raise your hand if you have ever been to a bakery. What kinds of baked goods did you see there?
How did the bakery smell? Did you buy anything? What was it?
Where else can you buy baked goods besides from a bakery?
What do you think bakeries should do with the baked goods they can’t sell?
Build Background Knowledge
What is the most common amount in which baked goods are sold?
How many muffins are in a dozen? How many in a half dozen? How many in two dozen?
Preview the Problem Title
Open your Student Journal to Activity 47 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word remain on the board. Point to the word and read it aloud.
After all the other actors left the stage, only I remained to do my solo.
When I divide ten by three, I get a remainder of one.
I had five dollars and spent three dollars on lunch. Now I have two dollars remaining in my wallet.
Based on these sentences, what does remain mean?
Comprehension QuickStart Activity 47
Comprehension QuickStart Activity 48
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Peanut Problems
At CD Heaven, you can win a free CD if you can solve the peanut puzzle. Next to the
entrance is a sign with this information:
There are 950 peanuts in a jar.
There are 320 more shelled peanuts than unshelled peanuts.
How many shelled peanuts and how many unshelled peanuts are in the jar?
If you are correct, you could win a CD.
How many of each kind of peanut are in the jar?
Activate Prior Knowledge
Raise your hand if you like to eat peanuts. What is your favorite peanut treat?
Who can tell us the difference between shelled and unshelled peanuts?
How many shells does a peanut have? [a hard outer shell called a “pod,” and a brown, paperlike inner
shell around each peanut] When you take the hard outer shell off, you can eat the brown shell or
you can take it off too.
Did you know that peanuts are not really nuts? Who knows what they are? [legumes, like beans and peas]
Build Background Knowledge
Some stores hold contests to attract customers. The winner of the store contest might
get a shopping spree or free merchandise.
Has anyone ever won a contest? What kind of contest was it? How did you win?
Preview the Problem Title
Open your Student Journal to Activity 48 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word solve on the board.
The detective followed the clues to solve the crime.
After doing a little arithmetic, I solved the teacher’s problem of the day.
Based on these sentences, what does it mean to solve a puzzle?
Comprehension QuickStart Activity 48
Comprehension QuickStart Activity 49
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
The Smith Families
10 children at Maple Middle School have the last name Smith. The children belong to
3 different families. They gave their mathematics teacher this riddle to solve.
“All the children in our families go to this school,” said Suzie Smith.
“No two families have the same number of children,” added Sammy Smith.
“My family has the greatest number of children,” said Sarah Smith. “How many children
are in my family?”
“Hmmm,” said the very smart teacher. “I need a little more information. Are any of you an only child?” With this information
the teacher told Sarah how many children are in her family. How many children are in Sarah Smith’s family?
Activate Prior Knowledge
Raise your hand if you have a brother or sister.
Stand up if you have more than one brother or sister.
Stand up if you have more than two brothers or sisters. [Continue until the student with the most siblings is identified.]
Who has the most brothers and sisters? How many do you have?
Talk to your neighbor. What are the good things about having a large number of brothers and sisters?
What are the good things about having no brothers or sisters?
Build Background Knowledge
In the United States, the most common last name is “Smith.” A smith is someone who works with metals.
Who can think of a word that has “smith” in it. [blacksmith, metalsmith, goldsmith]
What are some other common names that you have heard?
Preview the Problem Title
Open your Student Journal to Activity 49 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Write the words greatest number and only child on the board. Point to the words and read them aloud.
I have found that eight is the greatest number of oranges needed to make a pitcher of orange juice.
The greatest number of players allowed on the basketball court for each team is five.
Based on these sentences, what does the term greatest number mean?
What is another word or term that means the same thing? [most, maximum, highest number, limit]
My mom was an only child so I don’t have any aunts or uncles on that side of my family.
I was an only child until my little brother came along.
Based on these sentences, what does the term only child mean?
Comprehension QuickStart Activity 49
© ETA hand2mind™
Preview Vocabulary
Comprehension QuickStart Activity 50
Increase students’ reading comprehension with this 5-minute Comprehension
QuickStart Activity.
Problem
Crazy Quilts
My grandma is teaching me to quilt. I have made each of the quilts
shown here. Grandma says it’s time for me to make a full-size quilt. That
would be Quilt 10. How many white squares and how many dark squares
of fabric do I need for Quilt 10?
Activate Prior Knowledge
Raise your hand if you know what a quilt is. Describe a quilt you saw. Tell us the colors and
what kind of pattern was on it.
Do any of you have a quilt on your bed? What does it look like?
Build Background Knowledge
When pieces of fabric are patched together to make a quilt, we have what’s called a patchwork quilt.
Some people uses patches of fabric from old clothing to make their quilts.
If we made a class quilt, what patch of fabric would you bring for us to add to the quilt pattern? Why?
Preview the Problem Title
Open your Student Journal to Activity 50 and read the title of the problem.
What do you predict this problem is about? Why?
Work with Special Text Features
None
Preview Vocabulary
© ETA hand2mind™
Write the word full-size on the board. Point to the word and read it aloud.
A single bed sleeps one person. A full-size bed is big enough for two.
My sister has a half-size violin. My brother has a full-size one.
Based on these sentences, what does the term full-size mean?
Comprehension QuickStart Activity 50