PROBLEMSOLVING

Set B

Compiled by members of the TEAM project"Teaching Excellence and Mathematics"

Department of Public Instruction301 N. Wilmington StreetRaleigh, NC 27601-2825

Michael E. Ward, Superintendent

There are many commercial resourcesavailable to challenge students tobecome better problem solvers. This isa collection of some of our favoriteproblems.

You might consider allowing studentsto work with partners. Many of theseproblems are best solved withcalculators. All of these problems lendthemselves to students telling and writ-ing about their thinking.

Consider expanding this problemsolving deck by adding your ownproblems on the backs of the cards orphotocopying the blank master wehave included for you.

We hope you will share your greatproblems with us. Send them to :

Mathematics SectionDepartment of Public Instruction

301 N. Wilmington St.Raleigh, NC 27601-2825Original funding through D. D. Eisenhower

Mathematics and Science Education Program

ProblemSolving Strategies

1. Act out the problem 2. Use models and

manipulatives 3. Make a picture or a

diagram 4. Make a table or chart 5. Make an organized list 6. Work backwards 7. Use logical reasoning;

deduction 8. Guess and check 9. Use or look for a

pattern10. Solve a simpler

problem11. Write an equation12. Brainstorm ideas

There are many commercialresources available to challengestudents to become betterproblem solvers. This is acollection of some of our favoriteproblems.

You might consider allowing stu-dents to work with partners. Manyof these problems are best solvedwith calculators. All of theseproblems lend themselves to stu-dents telling and writing abouttheir thinking.

Consider expanding this problemsolving deck by adding your ownproblems on the backs of the cardsor photocopying the blank masterswe have included for you. Wehope you will share your greatproblems with us. Send them toMath Staff at the address on theback of this card.

Set B Set B

If McDonald’s sells Big Macs for$1.59 each, how many could youbuy with a $10.00 bill? Write aletter to a friend to tell how youfigured this out.

A school cafeteria sells popsiclesfor 25¢, nutty buddies for 40¢, andice cream sandwiches for 30¢. Ifa student spent $6.00 in the monthof October for ice cream, whatcould the student have bought?List as many combinations as youcan find.

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Set B Set B

Sarah owes a friend $2.38. Shehas $5.25. Will she have enoughmoney for a $2.25 movie aftershe pays her friend? Exactlyhow much money does she haveleft?

How can you make each stackhave the same number of penniesand use all the pennies?

Explain how you figured this out.

25¢ 20¢ 3

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Set B Set B

If you must use 15 or fewercoins, how many differentcombinations of coins can beused to make $1.00?

Every bike slot in a bicycle rackwas filled. Donna’s bike was inthe middle. There were six bikesto the right of Donna’s. Howmany bicycles were in the bicyclerack?

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Set B Set B

At a school store the followingitems are for sale:

Erasers 5¢Pencils 10¢Paper 15¢Markers 20¢

Ronald has 50¢. Whatcombination of supplies can hebuy?

What different single digits canyou put in the circles so that thesum of 3 numbers in a line willequal 17?

Extension: How many differentcombinations could you have?

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Set B Set B

Write the last 4 digits of atelephone number. List all the 4-digit numbers you can make usingthose four numbers.

• What is the highest number youcan make?• What is the lowest number youcan make?• Find the difference in the highestand lowest number.

Joey got a new puppy. The puppyweighed four pounds. This washalf the weight of his bowlingball. How much does his bowlingball weigh?

What would five puppies of thesame size weigh?

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Set B Set B

How many different ways canAlex make change for a 50¢ piecewithout using pennies?

Make a chart to show all of thepossible ways.

If John usually walks four milesper hour, about how long wouldit take him to walk two miles?Explain how you got youranswer.

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Set B Set B

Your calculator is showing ananswer of 242. What problemscould have been put into thecalculator to get this answer?

In Friday night's football game,North High School lost to SouthHigh School 20-12. What are thedifferent ways North High couldhave scored 12 points?

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Set B Set B

Daniel has a bad cold and has totake 1 teaspoon of cough syrupevery 45 minutes. He took his firstdose at 2:20 p.m. He is supposedto take 6 doses before he goes tobed at 8:00. Can he do this?Explain.

11112222

9999

6666

3333

David was playing darts andscored exactly 21 with 3 darts.Show where his darts might havelanded.

If he got all three darts on theboard, what other scores could hehave made?

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Set B Set B

The key for number 5 does notwork on Hector’s calculator.

How can he use his brokencalculator to figure out 235 - 198?

Explain what Hector will push onhis calculator.

You have $2.00 with which tobuy marbles. Aggies cost 14¢each and migs cost 18¢ each.How many of each kind ofmarbles can you buy for $2.00?

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Set B Set B

Using digits 1 to 9, arrange thenumbers in three groups so thatthe sum is the same in each group.Is there more than one way to dothis? Explain.

Write math problems that thischart would help you to solve:

MENU

Turkey sandwich $0.75Ham and cheese sandwich $1.60Potato salad $0.80Lemonade $0.90Milk $0.85

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Set B Set B

Eugene had 33¢ in his pocket.He had 9 coins. He did not havea quarter. What were the coinshe had in his pocket?

In Booth’s Bicycle Shop, Henrycounted some bicycles andtricycles. He counted 19. Whenhe counted the wheels, he got atotal of 45. How many bicyclesand tricycles were there?

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Set B Set B

A basketball player can score3-point baskets and 2-pointbaskets. If the player scored 37points, what combinations ofbaskets could he have made?

Arlene wants to participate in tworunning events in the track meet.She can select from the 50 mdash, the 75 m dash, 100 m dash,and the 400 m relay. How manydifferent choices does Arlenehave?

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Set B Set B

A Nintendo game costs $53.25,including tax. John got $10.00for his birthday and he can save$4.00 each week to go towardsthe game. How many weeksuntil John can afford the game?Explain how you know.

For breakfast in the morning, youmay choose among three differentcereals; corn flakes, oatmeal, orwheat chunks. You might alsochoose a juice, either apple juiceor orange juice. What are all thedifferent breakfast combinationsthat you could have if you haveone cereal and one juice?

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Set B Set B

At the Burnsville School library,34 students can sit at seven tableswith no empty seats. There aresmall tables for four studentsand large tables for six students.How many small tables are inthe library? How many largetables are in the library? Explainhow you found your answer.

If all of the tables were small,how many students could sit inthe library?

If all of the tables were large,how many students could sit inthe library?

A group of students is sitting in acircle. Every student facessomeone across the circle. Thestudents count off in order,starting with number one. Studenttwo sits directly across fromstudent seven. How manystudents are in the circle? Explain.

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Set B Set B

?

Jo gave a number problem toNelda. She told her to pick anumber, add 10 to it, double thatsum, and then subtract 5. Nelda’sanswer was 39. What numberdid Jo pick?

Write a number in each emptyshape to complete the chain.

–––– 9999

–––– 7777

–––– 4444

++++ 8888

++++ 3333

18

17

EEEENNNNDDDD

SSSSTTTTAAAARRRRTTTT

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Set B Set B

I am a 2-digit number over 50.When you put me in groups of 7,two are left over. The sum of mydigits is 11. What number am I?

Write another number puzzle fora friend to solve. Make yourpuzzle have three or four clues.

Complete the pattern, then write asentence that tells how to writemore numbers in the pattern:

50, 44, 38, 32, ___, ___, ___.

What comes next in this pattern?

1, 4, 2, 5, 3, 6, 4, ___, ___.

Explain how you know.

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Set B Set B

What seven coins together areworth 50¢?

If you have seven coins, but nopennies or fifty-cent pieces, whatis the most money you couldhave?

Sandra is more than 20 years oldand less than 60 years old. Youcan count by 7’s to reach Sandra’sage. Next year you will be ableto count by 5’s to reach Sandra’sage. How old is Sandra? Explainhow you figured this out.

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Set B Set B

In the product: 1 x 2 x 3 x 4 x 5 x 6, which one of the six numbersshould be increased by 1 tocause the greatest increase inthe product? Predict and thencheck your prediction on acalculator. Check otherpossibilities until you are certainyou know the correct answer.

Using a total of 15 straws of twodifferent lengths and clay or pipecleaners as connectors, make astructure which illustrates asmany different geometricvocabulary words as possible.

Note: If you have tinker toys,use 15 rods and no more than 8wheels.

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Set B Set B

Given this table, what comesnext in the pattern?

BAGS CANDIES

2 48 3 72 4 __ 5 __ 6 __ 7 __

A cook is making a cakerequiring four cups of flour.She only has two measures,which hold 7 cups and 10 cups.How can she use her measuresto measure exactly 4 cups?

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Set B Set B

How many triangles are here? The answer is 8. What couldthe question be? Write threedifferent possible questions.Try to make the questions verydifferent from each other.

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Set B Set B

How many different ways canyou show one-half on ageoboard?

Using digits 0 - 9, only onceeach, choose three digits to makean addend and three other digitsto make a second addend. Usingthe two addends, make thelargest possible sum.

Using the same 0 - 9 digits onetime each, find the smallestpossible sum when you add three2-digit numbers.

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Set B Set B

The Nine-Patch Quilt

Laura is making a nine-patchquilt for her doll. She is using redand blue patches. How manysymmetrical designs can shecreate with the two colors ofpatches? What could she makewith three colors of patches?Show the possibilities and drawthe line or lines of symmetry oneach.

Amy painted three pictures inart class. She wants to hangthem in a triangle-shapedarrangement, like the oneshown. How many differentways can Amy hang her threepictures in this triangle-shapedarrangement?

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Set B Set B

January 1 is on a Tuesday.Su-Lin’s birthday is in January.

1. It is not on a weekend.2. The date has two digits.3. You say the date when

you count by twos.4. The sum of the two digits

is 7.

What is the date of herbirthday?

The people of Domino City usedominoes to show their housenumbers. Each domino has twosets of dots on it. Different sets ofdots are used on each street. Thepeople who live on Peach Streetuse just these sets to make theirhouse numbers:

What are all the different housenumbers that people on PeachStreet can make?

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• • •• •

• •• •• •

• •• •• •

Set B Set B

If a person starts with 9 andrepeatedly adds 4 on a calculator,what would the number showingin the display be after sixadditions?

To get the greatest product, whereshould a student place thenumbers 2, 3, 4, 5, and 6 in theboxes below?

X

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One of the letters in the boxdoes not belong.

S C D U O

Which letter does not belong?Explain why.

Can you classify these letters inanother way so that one letterdoes not belong?

Set B Set B

The answer is 3. Write threedifferent math questions.

How many triangles and howmany rectangles are in thisfigure?

Cindy rides her bike to hergrandmother’s house onSaturdays. Her grandmotherlives 12 blocks away.

Last Saturday, Cindy rode 6blocks, then realized that a bookhad fallen out of her basket. Sherode back and found her book.Then she rode 8 blocks andarrived at her grandmother’shouse. At which block did shedrop her book? How do youknow?

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Set B Set B

If each car will hold one driverand five students, how many carswill be needed to take Mrs.Wilson’s 28 students on their fieldtrip?

How many total people (studentsand drivers) will there be?

If there were three students absent,how would the answers to thesequestions change?

Trace these figures and cutalong the dotted lines. Howmany different polygons canyou create using 2, 3, or 4pieces?

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Set B Set B

Holly checked a book out of thelibrary and read this notice aboutfines:

If Holly’s book is 7 days overdue,what is the fine? Make a table toshow how much the fine will be.

If a book is:

Days Amount of Overdue Fine

1 1¢ 2 2¢ 3 4¢ 4 8¢

Tilly gets 40¢ for an allowanceevery week. Her mother likes togive her different coins eachweek, but she never uses pennies.

What are the ways Tilly couldhave gotten her allowance duringthe last four weeks?

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Set B Set B

Kim has three coins worth atotal of less than a dollar. If shewere to lose one of her coins,she would have exactly half asmuch money as she has now.What coins does Kim have?Explain.

How many pennies laid in arow would there be in a mile?

What do you have to know tofigure out this problem? Writethe steps in a plan to figure thisout.

How many pennies would ittake?

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Set B Set B

At the grocery store, eggs cost49¢ for a half-dozen. A dozeneggs cost 91¢. Which is a betterbuy? Explain your answer.

Toni has a piggy bank filled withnickels, dimes and quarters. Shehas a total of $3.00. If she hasfewer than 12 coins, Whatcombination of coins could shehave in her bank? How manypossibilities can you discover?

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Set B Set B

How Many Tiles Do I Have?

Clues:

A. If I have this manysquare tiles, I can arrangethem into a square and havethree left over.

B. With these tiles, I canform a rectangle whose oneside is 10 more than the otherside.

C. I have less than 60.

How many tiles do Ihave?

There are 10 pages in Anthony’sbaseball card album. Each sideof the page has 12 pockets forcards. When his book is halffull, how many cards willAnthony have collected?

Write a letter to your friendtelling how you figured this out.

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Set B Set B

Suppose that red counters cost18¢ and yellow counters cost14¢. You bought 12 countersand paid exactly $2.00. Howmany of each color did youbuy?

Which is worth more: 30 cmof quarters placed side by sideor 60 cm of dimes placed sideby side?

Write the steps you use insolving this problem.

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Set B Set B

There are four boys in the Grantfamily. Alex is older than Jerryand younger than Stuart. Rossis not the oldest or the youngest.Alex does not have two olderbrothers. Write the names ofthe boys from oldest toyoungest.

Pizzas come two ways at thePizza Delite. You can buy awhole pizza cut into six slices ora half pizza cut into three slices.How many pizzas should be or-dered for this table if the stu-dents want this many slices?

Timeka 4Jose' 5Benny 3Laura 2Alba 6

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