Reading and Writing the Language of Numbers s1

Intermediate Sample Stories For Reading and Writing the Language of Numbers

Debby Head Libby Pollett Kari Vore Jennifer Synold

This is a collection of word problems to accompany your dot charts. They were written by teachers for their students. They are organized by mathematical strand:  Number  Algebra  Measurement  Data Analysis & Graphing  Geometry

Number The Seminoles played in five bowl games in the 1990’s. If they scored in fourteen quarters, did they score in more or less than half of the quarters? (blank grid)

There were ____ cookies left on a plate that once held ____ cookies. If we put __ per container to store the leftovers, how many containers will we need?

You and four friends ride a bus to the park. The fare is $1.25 for each person’s round trip. How much money will be needed for all of you to ride the bus?

You are selling cookies for your scout troop. The fifty boxes you sold were: a dozen boxes of Choco-riffic, twice as many Cocoa-Grams as Choco-rific, 8 Pecan Wonders, and all the rest were Oatmeal Raisin. What fraction (percentage) of the cookies you sold were Oatmeal Raisin?

_____does __push-ups every morning and ____ push-ups before going to bed each night. How many push-ups does he do each week? (blank grid)

Our class needs to collect 360 labels for a free CD player for the classroom. So far we have collected 120. _____ says we have collected 12/36 of the labels needed. ____ says we have collected 1/3. ______says we have collected 3/9. Who, if anyone, is correct? Prove your thinking with the picture! (36 dots or blank 100 grid)

______is reading a book with 402 pages in it. He is finished with about 1/3 of the book. About what page is he on?

______’s aunt and uncle gave him a $20 bill each birthday. He saved each one until he married at age ____. How much money did he have to share with his bride?

There are 14 cars in the parking lot. How many tires would there be? (not counting spares!)

Our class is saving for a soccer goal that costs $300. We have ___% of our money earned. How much more money do we need? (Hint: grid = $300, so each dot/empty = $3)

The soccer stadium holds 10,000 people. Season ticket holders bought ___% of the seats. How many seats are remaining to be sold? (Hint: grid+ 10,000 people, a row/column = 1,000 people, and a dot/empty = 100 people)

© 2010 bby Publications@UWA All rights reserved page 2 Our two classes need $360 for a field trip. Our class has collected half of the total. Our friends have collected one third of the goal. We have two more days to collect. How much more do we need to collect to meet our goal? (36 dots)

______and ______were saving together for a $10 CD. Juan saved 36 dimes in a month. Rachel saved 64 nickels. How much more money do they need to save? (36 dots)

There are 36 people that need to be seated for dinner. We have round tables that seat six people each. We have square tables that seat four people each. Will it take more square tables or round tables to seat everyone? How many more? (36 dots)

I made it to Who Wants to Be a Millionaire! I hoped to win the entire million dollars, but when I left the hotseat, I had only earned ______% of the million. How much did I earn? (the grid = million, row/column is $100,000 and one square = $10,000 so it’s $360,000! Take this opportunity to talk about reasonableness, too. Chances are, on a multiple- choice test the choices will be $360,000; $36,000; and $3,600. No computation is needed if you estimate!)

Six friends found ____ golf balls in a lake and sold them four for a dollar. How much money did they make?

______sells lemonade each day for a week to make money. She makes an average of $9.00 per day. If she wants to buy supplies for $100.00, does she have enough money? (blank 100 grid)

Suppose our class wants to earn $300 for new equipment. If we have earned ___% of our goal, how many more weeks will it take us to reach our goal if we average $65 a week?

Suppose there were 20 people in a class. Divide the class into as many groups as you can with each group having the same # of people. Then, if 8 people were absent from school on Monday, what percentage would be at school that day? If three of the students present at school on Monday were called out of class for tutoring, what percentage of the class would be left in the room? What % of the class was called out? If on Tuesday 4 of the 8 returned, how much did the attendance % increase? (Several days of work on a blank 20 grid)

______has four children. He gave each child 3 packages of markers. Each package has 8 markers. How many markers do his children have?

Of our 50 states, suppose 22 have senators of the same party. What percent of states have senators of the same party? (blank grid or 22 dots)

______has been to a dozen of our fifty states. What percent of our nation has he not visited?

There’s a big sale on shirts! _____ bought eight for $66.14. About how much did he pay for each shirt?

Suppose our high school stadium got new lighting for the track around the football field. If there are fourteen poles and each pole has nine floodlights, how many floodlights are lighting the field?

______wants to buy a computer game that costs $78.00. He/She has a job babysitting the neighbor's 3 children. He/She earns $6.50 per hour. Last week he/she babysat 9 hours. How many hours does he/she need to babysit this week so he/she has enough money for his/her game?

A poll was taken before the 2000 presidential election. 47% of those polled said they were going to vote for George W. Bush. 45% said they supported Al Gore. The others polled were undecided. Of those who were still undecided 75% said they were leaning toward George W. Bush. What percentage of the total number of people polled were undecided but leaning toward voting for George W. Bush?

I went to my cousin's football game. I sat in a section that has 3 bleachers. Each bleacher has 3 rows of seats. Eight people can sit in each row. There are still 32 empty seats. What fraction of the seats are filled?

There are 85 keys on my computer. 37 keys are function or direction keys. 10 are numbers. 11 are symbols. Which number is larger; 1/4 of the total keys or the number of letter keys?

______’s Easter basket had a dollar in it. She got three Easter cards with the same amount of money in each. Her total money received that holiday was $7.00. How much money was in each card? (3n + 1 = 7)

______and ______each need $5 for a necklace. ______needs to save $1 more and ______needs $2 more. How much money do they have so far? [(5-1) + (5-2) = 7]

_____ needs $2.50 for laundry. She found seven quarters so far by looking all around her apartment. How much more money does she need? [$2.50 = 7 (25¢) + n n = 75¢]

Our school needs $10,000 for a new gymnasium. We have earned seven tenths of our goal. How much more money do we need? [.7 ($10,000) + n = $10,000 n = $3,000 so using the ten grid, a square = $1000]

Suppose our high school football team won with a score of 72-28. What are some possible ways the points could have been scored?

______bought a pack of baseball cards for _____. He gave the clerk $1.00. How much change should he receive and what might the coins have been?

Together the children walked 72 laps in the Walkathon. Some of them walked 6 laps and some of them walked 7 laps. How many children walked laps?

______waters the plants in his home. He waters the ivy every third day. He waters the cactus once a week. If he waters them both on the first day of the month, what is the next day he will water them both?

_____ sold 8 more tickets than _____. Together they sold 24 tickets. How many did each sell?

_____ took some money to the store. He spent half of it on a t-shirt. Then he bought a card for $3.00. He had $8.00 left. How much money did he bring to the store?

Suppose you want to jump from a helicopter with a parachute for your next birthday. Nobody believes how much you want to do it, so you decide to save the money yourself. If it costs $200 and you have 30% of your goal saved, how much more money do you need? [$200 + n = $140 n = $160) so a grid = $200 and a square has a value of $2)]

Five classes hope to raise money for a trip to Epcot. Each class must raise 1/5 of the total. Three classes have collected 3/5 of the total. One class collected 1/10. If our class has to raise the remainder, what fraction of the total amount must we collect? [(1/5 + 1/5 + 1/5 + 1/10 + n + 1 n = 3/10 using an empty 10-grid]

© 2010 bby Publications@UWA All rights reserved page 5 Our class needs $500 for an overnight at the museum. We have %70 of the cash needed. How much more money do we need? [$500 = 70% ($500) + 30% ($500) therefore $500 = $350 + $150 using a 100 grid with a value of $500, one dot equals $5]

Betsy and Sally are earning money for a Mother’s Day gift. Betsy has her half. Sally is one dollar short of her half. If they need $8.00 together, how much does Sally have? {n + (n-1) = 7 therefore 4 + (4-1) = 7 Sally owes $3, using 8 dots or a blank 10 frame]

I have ___ M & M’s in my pocket. Some are plain and some are peanut. I have two more plain than peanut M & M’s. How many are plain? (use an even number)

Our class surveyed the fifth-graders to collect data about children's favorite pets. Out of the 100 students in fifth-grade, an equal number of student's favorite pet was either a dog or cat. If the total number of students who did not choose a cat or dog as their favorite pet was 14, then what percentage of students like dogs? What percentage like cats? What percentage liked a different animal? (blank 100 grid)

______had three colors of Juicy Chews in his pocket. Six are purple. Lots are red. There are half as many yellows as reds. There are the same number of purple as yellow. How many are red? (blank 100 grid)

______says she has an even number of coins in her pocket, but the value is odd! Could she be right? If so, show some possible combinations she might have. (blank 100 grid)

Four girl scouts were having a contest, selling cookies. Together they sold ___ boxes. One girl sold sixteen boxes. The other scouts sold exactly the same number of boxes. How many did each of them sell? (even # of dots/empties)

______has $.31 in his pocket. How many different combinations of coins can he possibly have?

You look in the parking lot and see three tricycles parked in the same space between some cars. Altogether you count 33 tires. How many cars are in the parking lot?

______had seven coins in his pocket. They total 48¢. How many possible combinations of coins could he have?

Suppose I have four coins that equal ___¢. What could the coins be?

Thirty-six more than an number is 47. What is the number? (Blank 100 grid)

Together, you and your friend ate _____ cookies. Your friend ate three more cookies than you did. How many did each of you eat? (start with an odd number)

© 2010 bby Publications@UWA All rights reserved page 6 The sum of ______siblings ages is 22. One of the siblings is older than five. The other children are under the age of five. How many brothers and sisters does _____ have?

_____A___, ___B____, and ____C___ earned ten points total. If ___C___ earned twice as much as ___A____, how much did ___B____ earn? What percentage of the points did each person earn? (blank 10 grid)

____’s mother bought 2 dozen eggs. One-half of the eggs were white and one-half of the eggs were brown. One-third of the brown eggs were cracked and one sixth of the white eggs had a black dot on them. About what percentage of the brown eggs were left? About what percentage of the white eggs were without a black dot? About what percentage of the total number of eggs were left when the cracked brown eggs and the white eggs with the black dot were removed from the carton? (24 dots on a 100 grid)

______’s mother gave him ______dollars to spend at the state fair on admission and rides. Admission costs him $4.50. Each ride costs $1.25 and each carnival game is $2.00. How many rides and carnival games could _____ play? (empty 100 grid)

______is very picky about the socks he/she wears. He/She bought a package of socks at Wal-Mart. He/She really liked them so she went back and bought 3 more packages. Now he/she has 20 pairs of those socks. How many socks were in each package?

Measurement

Each dot on the diagram represents twenty years. Approximately, how many decades are represented by the dots?

Watch out! There is a spider crawling near you! It measures 1.7 cm. How many millimeters long is it?

______babysat for 3 children for ____ hours. The children went to bed after _____ hours. How many minutes of peace and quiet will he get?

You are going to the beach in 18 hours. What time will you leave?

______bought a new lease for his dog for $9.50. It is ____yards long. How many feet of leash does he have?

_____ wants to buy some farmland but needs to know the area and perimeter of the farm. If each square on the grid represents 144 square miles, what is the perimeter and area of the plot of land represented by the dots?

______reached for a liter of juice in the refrigerator. It contained 0.78 of a liter. He drank half of it. How much was left? Was it more or less than a quart left?

If each box of crayons weighs 1.5 pounds, how much will a dozen boxes weigh?

© 2010 bby Publications@UWA All rights reserved page 7 ______is making goodies for the school bake sale. In order to make enough goodies, she will need __ quarts of milk. How many gallons must ___ buy?

______has a paper route and delivers 250 papers each day. How many papers will he deliver in a week?

The _____ members of Scout Troop 242 each contributed a cup of juice to the special blend to be served at the cookout. How many quarts of juice will be ready to serve?

Hansel and Gretel were lost in the woods. They dropped a crumb every foot along the path for ____ yards to the cottage, hoping to help their parents find them. How many crumbs did they drop?

______is making pancakes. Each batch needs 1/3 cup of milk. How many batches can be made with a quart of milk? (blank grid of 20 or 100 --12 needed, 4 quarts with 3 thirds each)

______has 3 meters of ribbon. She’s cutting it in lengths of 10 centimeters. How many pieces of ribbon will she have after cutting? (blank 100 grid, perhaps using 30 dots with ten dots=meter)

______drank 3 glasses of water some time during the morning and five more before bedtime. How many glasses of water did he drink in a week? (7 dots or blank grid)

_____ and ____ went on an eight-day cruise with their family. They left at 8 AM on Monday and returned at 8 AM on the following Monday. How many hours were they gone? (blank 10 grid or 8 dots)

The Race for the Cure takes runners on a mile path through the parks. Cones are set up every 500 feet to help runners pace themselves. How many cones are along the path?

In the summer, Sally works at the public swimming pool. One week before opening day, Sally is to fill the pool with water. Each dot on the grid represents 105 gallons of water that has been put into the pool already. How many gallons of water are already in the pool? What percentage of the pool is empty? How many more gallons of water will it take to fill the remainder of the pool? (25 dots or empty 100 grid)

Jane is tiling a room. The room is 16 ft. by 20 ft. Each tile is 2 sq. ft. How many tiles does she need? (blank 100 grid)

Susie sells lemonade each day for a week to make money. She makes an average of $9.00 each day. If she wants to buy supplies for $100.00, does she have enough money? (blank 100 grid)

© 2010 bby Publications@UWA All rights reserved page 8 John wants to plant a garden with tomatoes. He needs at least a one ft. by two ft. area for each tomato plant. If he has an area that is 16 ft. by 20 ft., what is the maximum number that can be planted? (blank 100 grid)

______ran a mile each day for the months of March and April. If his dad gave him $_____ for each mile he ran, how much did he earn?

I have to be at school by 8:00 am. First I need to get dressed which takes me 15 minutes. It takes me 20 minutes to eat my breakfast and then 35 minutes to walk to school. What time do I need to get up?

______is watering the flowerpots around her dad's garden. Each of the 11 flower pots needs 2 cups of water. He/She is using a pitcher which holds 2 quarts of water. How many times does he/she need to fill the pitcher?

I am making snack mix using a recipe that calls for 4.5 pounds of M & M's, 7.33 pounds of nuts, and 3.25 pounds of raisins. This recipe makes a dozen bags of mix. If I have 27 pounds of M & M's, how many bags of snack mix can I make?

Your neighbor is ______years old today at noon. As of noon today, how old will your neighbor be in months (days, hours, minutes, seconds, decades)?

(hundred-grid with one dot or a blank hundred-grid) A colony of bacteria is being grown a laboratory. The lab technicians begin with a single bacterium. Every hour the number of bacteria doubles. How many bacteria will be in the colony in 6 hours?

If each dot represents ____ (1/2, 1/3, ¼ etc) yard, how many _____ (feet, inches) are represented by the dots?

Each dot represents a ton. How many pounds are represented? How many ounces? Create a t-chart to demonstrate the relationships.

(hundred-grid, 4 dots/96 empties or a blank hundred-grid) The height of the national Capitol dome is 96 yards. Describe this same height in feet and again in inches.

Data & Probability

A box contains ____ red, ____black, ____ purple and ____pink marbles. If you pick one out of the bag without looking at it, which color are you most likely to choose?

A number cube has the numbers 1-6 on each face. If you roll the cube 90 times, how many 1’s are you likely to roll? (empty 100 grid)

I have fourteen M & M's in my pocket. 3/7 are red. 1/7 are green. 1/7 are orange. The

When shooting free-throws, your cousin averages 2 of every 7 shots. Today he plans to shoot 100 times and has shot ____(35) times. He has made 4. Is he more likely to make or miss the next shot?

(100 grid with any number of dots)You have rolled a 1-6 number cube 100 times. The dots represent the number of times you rolled an even number. The empty squares represent the number of times you rolled an odd number. Use fractions to describe the results of your experiment.

(48 dots/52 empty squares on a hundred grid) What is the probability that a card chosen from a 52-card deck is one of the 4 jacks?

The game of Scrabble uses 100 letter tiles. There are 42 vowel tiles, of which 12 are the letter E. What is the probability that a tile chosen at random is an E?

The weather channel reports that there is a _____ chance of rain today. What is the probability that it will not rain today?

Geometry

Figure Y has a perimeter of 42 centimeters. Half of that length is shared equally by line segments AE and CD. The remaining 2/5 of the length is shared equally by line segments AB, BC, and DE. How long is line segment BC?

(Draw a figure in one of the quadrants before posing this situation.) Your friend drew this figure on the hundred-grid. Your job is to complete the illustration using the dark, vertical line as a line of symmetry.

(sample)

© 2010 bby Publications@UWA All rights reserved page 10 (Draw a figure in one of the quadrants before posing this situation.) Your friend drew this figure on the hundred-grid. Your job is to complete the illustration using the dark, horizontal line as a line of symmetry.

(sample)

(Draw a portion of a figure in one of the quadrants before posing this situation.) Your friend drew this portion of a figure on the hundred-grid. Your job is to complete the illustration using the dark lines as intersecting lines of symmetry.

(sample)

You drew this design on the hundred-grid. Your friend rotated your design 90 degrees (180, 270 or 360 degrees) and attached the grid to the chart. In what position is the grid attached to the chart?

before rotation after rotation sample

© 2010 bby Publications@UWA All rights reserved page 11 You purchased three 6-packs of sodas. How many sodas did you purchase? Use the grid as a coordinate grid to demonstrate this situation by labeling the axes, plotting the coordinates and writing a related number sentence.

(sample)

The intersecting dark lines are lines of symmetry. Complete the figure. List the coordinates for each vertex.

(sample)