open ended problem solving grade 5

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CHALLENGE ZONE 5th Grade Math Problems

Welcome to our 5th Grade Math Problems. Here you will find our range of challenging math problem worksheets which are designed to give children the opportunity to apply their skills and knowledge to solve a range of longer problems.

These problems are also a great way of developing perseverance and getting children to try different approaches in their math.

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5th Grade Math Problems

Here you will find a range of problem solving worksheets.

The 5th grade math problems on the sheets are longer math problems designed to encourage children to use a range of math skills to solve them.

The skills the problems will help to develop include:

• systematic working
• logical thinking
• number fact knowledge
• fraction problems
• trial and improvement strategies
• working backwards
• working systematically
• searching for all possible answers.

At fifth grade, the problems are more advanced with children needing to become more systematic in their approach and experimenting using trial and improvement strategies.

Many of the problems have addition 'What if ...' questions with them to extend learning and get children looking for alternative solutions.

These sheets are great for extending learning for more able mathematicians, or using in a whole class problem solving lesson.

• 5th Grade Math Word Problems
• Bertie's Big Win

Bertie's Big Win is a problem involving both money and fractions which can be worked backwards. The aim of the problem is to work out how much money Bertie started with from the clue that are given.

• PDF version
• Fox vs Rabbit #2

Fox vs Rabbit is an activity involving mathematical modelling of a fox chasing a rabbit. The rabbit has a head-start, but the fox is faster. The aim is to find out when the fox will catch the rabbit, and whether or not the rabbit has time to reach his burrow.

• 1..2..3..4.. Challenge

The 1..2..3..4.. Challengs is a number problem involving using the numbers 1, 2, 3 and 4 along with arithmetic operators to make the numbers from 1 to 20. It is great for practicing PEMDAS and getting children to persevere and develop their mental arithmetic skills.

There are 2 versions of the problem sheet, one with a pre-prepared template for filling in, and a second blank version for children to show their own recording system.

• Blank version
• Frazer's Wall #2

Frazer's Wall #2 is a fraction problem solving activity which involves trying to work out the number of bricks that were laid in each day to find out how long it would take to make a wall. This problem is best solved by using a table or working it out one day at a time.

• Millenary Math

Millenary Math is a time problem involving what the time will be in a thousand years/weeks/hours/minutes, etc. It is a good activity for converting units of time and knowing facts like how many days are in each month. There is no answer sheet, as the activity involves using the current time.

• Sally's Fruit Punch #3

Sally's Fruit Punch is a money and scaling activity. The aim is to use the information to work out how much ingredients are needed. The ingredients then need to be priced to work out a total cost.

• Sally's Fruit Punch #3 UK Version
• Share the Treasure #5

Share the Treasure is a fraction sharing activity where the aim is to work backwards to find out how many bars of treasure the pirates had before they shared them all out. It is a good activity for developing fraction problem solving and working backwards.

• Something Fishy #2

Something Fishy is a money problem which involves working out exactly how many of each fish were bought in order to have spent a fixed amount of money on the fish. It is a good activity for using lists and tables to find all possibilities. It is also great for perseverance!

• Something Fishy #2 UK Version
• The Five Primes

The Five Primes is a number activity involving finding five primes with different totals. It is a good activity for learning prime numbers up to 30, and also for working systematically.

• The Rock Race #3

The Rock Race is a 5th grade math problem which needs some perseverance to complete. The aim of the activity is to try different routes around the 6 rocks to determine which route is the shortest.

• Who Chose Which?

Who Chose Which is a logical number activity where you need to use the clues to work out which numbers each of the salamanders chose.

• Birthday Bonanza

Birthday Bonanza is a logic problem which requires logical thinking to work out who got which present and how old each of them was.

• Number Totals Investigation

Number Totals Investigation is a PEMDAS number task which involves using 3 digits and operations to make the largest or smallest possible total.

Looking for some easier math problems?

We have a range of easier word problems on our 4th grade math problems page.

The problems on this page are at a simpler level than those here.

Many of the problems, e.g. Share the Treasure, The Rock Race, Something Fishy have easier versions on this page.

• 4th Grade Math Problems

Looking for some more fifth grade math word problems?

Here you will find our selection of free 5th grade math word problems.

Each sheet is availabel in both standard and metric units (where applicable).

Each sheet comes complete with a separate answer sheet.

All the problems are based around 'real life' such as the planets, heights of mountains, or length of rivers.

Using these sheet will help your child to:

• apply their addition, subtraction, multiplication and division skills;
• apply their knowledge of rounding and place value;
• solve a range of problems including "real life" problems and ratio problems.

All the worksheets help to support Elementary math benchmarks.

• 5th Grade Math Puzzles

Here you will find a range of printable 5th grade math puzzles for your child to enjoy.

The puzzles will help your child practice and apply their addition, subtraction, multiplication and division facts as well as developing their thinking and reasoning skills in a fun and engaging way.

Using these puzzles will help your child to:

• learn and practice their addition facts, including decimals;
• practice their subtraction facts, including decimals;
• practice and apply multiplication and division facts;
• develop problem solving skills and reasoning.

All the puzzles support elementary math benchmarks for 5th grade.

Fifth Grade Math Games

Here you will find a range of free printable 5th Grade Math games.

All children like to play Math games, and you will find a good range of Grade 5 Math Games here for your child to play and enjoy.

The following games involve different 5th Grade Math activities which you and your child can enjoy together.

All the free 5th Grade Math Worksheets in this section follow the Elementary Math Benchmarks for Grade 5.

• Math Games 5th Grade

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Open-Ended Maths Problems Task Cards

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Are you looking to extend your students’ mathematical thinking? Are you seeking ways to apply maths concepts you have taught engagingly and authentically? Are you after easy yet effective ways to differentiate and assess mathematical understandings? If so, these open-ended maths task cards are the perfect resource for your class.  

With 24 open-ended problems across a range of mathematics content areas, this set of cards challenges students to flexibly combine and apply a range of mathematical skills, with the opportunity to demonstrate multiple answers.

These task cards can be used for independent or guided practice. Selected cards can be used as formative assessment tools within focused units, or the set can be used throughout the year to continue to consolidate prior learning, regardless of your classroom’s current topic.

Designed with four problems per page and with the option of colour or black and white cards, simply print, cut and distribute to students. (They can also be laminated to be used again and again with different students).

Ensure your students get the most out of these challenges and know how to show their best thinking with our Solving Open-Ended Problems PowerPoint. Or you can have all the open-ended challenges in one place in our Open-Ended Maths Problems Booklet.

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Open-Ended Tasks and Questions in Mathematics

by CristinaM. | Sep 13, 2014 | inquiry , math , thinking | 5 comments

One way to differentiate in math class is creating open-ended tasks and questions (I talked about several differentiation strategies I use here – Mathematically Speaking ).

I think it is useful to clarify the scheme of mathematical problems – below I used Foong Pui’s research paper:

“Problems in this classification scheme have their different roles in mathematics instruction as in teaching for problem solving, teaching about problem solving, or teaching via problem solving.”

1.   CLOSED problems   are well-structured problems in terms of clearly formulated tasks where the one correct answer can always be determined in some fixed ways from the necessary data given in the problem situation.

 A. Routine closed problems – are usually multi-step challenging problems that require the use of a specific procedure to arrive to the correct, unique, answer.

B. Non-routine closed problems – imply the use of heuristics strategies * in order to determine, again, a single correct answer.

*Problem-solving heuristics: work systematically, tabulate the data, try simpler examples, look for a pattern, generalize a rule etc.

Routine problem : Minah had a bag of rice. Her family ate an equal amount of rice each day. After 3 days, she had 1/3 of the rice left. After another 7 days, she had 24 kg of rice left. How much rice was in the bag at first?

Non-routine problem : How many squares are there in a chess board?

2. OPEN –ENDED problems – are often named “ill-structured” problems as they involve a higher degree of ambiguity and may allow for several correct solutions. Real-life mathematical problems or mathematical investigations are of this type – e.g. “How much water can our school save on a period of four months?” or “Design a better gym room considering the amount of money we can spend.”

FEATURES of open-ended problems :

• There is no fixed answer (many possible answers)
• Solved in different ways and on different levels (accessible to mixed abilities)
• Empower students to make their own mathematical decisions and make room for own mathematical thinking
• Develop reasoning and communication skills

HOW do you create open-ended tasks?

Usually, in order to create open-ended questions or problems, the teacher has to work backwards :

• Indentify a mathematical topic or concept.
• Think of a closed question and write down the answer.
• Make up a new question that includes (or addresses) the answer.

STRATEGIES to convert closed problems/questions

• Turning around a question

CLOSED: What is half of 20?

OPEN: 10 is the fraction of a number. What could the fraction and the number be? Explain.

CLOSED:  Find the difference between 23 and 7.

OPEN: The difference between two numbers is 16. What might the numbers be? Explain your thinking.

CLOSED: Round this decimal to the decimal place 5.7347

OPEN: A number has been rounded to 5.8. What might the number be?

CLOSED: There are 12 apples on the table and some in a basket. In all there are 50 apples. How many apples are in the basket?

OPEN: There are some apples on the table and some in a basket. In all there are 50 apples. How many apples might be on the table? Explain your thinking.

• Asking for similarities and differences.

Choose two numbers, shapes, graphs, probabilities, measurements etc. and ask students how they are alike and how they are different.

Example: How are 95 and 100 alike? How are they different?

Possible answers:

They are alike because you can skip count by 5s, both are less than 200, both are greater than 90 etc.

They are different because one is a three-digit number, only one ends in 5, only one is greater than 99 etc.

Example: How are the numbers 6.001 and 1.006 alike? How are they different?

• Asking for explanations.

Example: Compare two fractions with different denominators. Tell how you compare them.

Example: 4 is a factor for two different numbers. What else might be true about both numbers?

• Creating a sentence

Students are asked to create a mathematical sentence that includes certain numbers and words.

Example: Create a sentence that includes numbers 3 and 4 along with the words “more” and “and”.

• 3 and 4 are more than 2
• 3 and 4 together are more than 6
• 34 and 26 are more than 34 and 20 etc.

Example: Create a question involving multiplication or division of decimals where the digits 4, 9, and 2 appear somewhere.

Example: Create a sentence involving ½  and 64 and the words “less” and “twice as much”.

• Using “soft” words.

Using the word “close” (or other equivalents) allows for a richer, more interesting mathematical discussion.

Example: You multiply two numbers and the product is almost 600. What could the numbers have been? Explain.

Example: Add two numbers whose sum is close to 750. What can the numbers be? Explain.

Example: Create two triangles with different but close areas. (*instead of, “Create a triangle with an area of 20 square inches.”)

……………………………………………………………………………………………………………………………………………………………………………………………………

A few important considerations are to be made when creating open-ended problems or questions.

• Know your mathematical focus .
• Develop questions with the right degree of ambiguity (vague enough to be interesting and to allow for different responses, but not too vague so as students get frustrated).
• Plan for two types of prompts :
• enabling prompts (for students who seem unable to start working)
• extension prompts (for students who finish quickly)

High quality responses from students have the following features:

• Are systematic (e.g. may record responses in a table or pattern).
• If the solutions are finite, all solutions are found.
• If patterns can be found, then they are evident in the response.
• Where a student has challenged themselves and shown complex examples which satisfy the constraints.
• Make connections to other content areas.

……………………………………………………………………………………………………………………………………………………………………………………………………………….

References:

Designing Quality Open-Ended Tasks in Mathematics , Louise Hodgson, 2012

Using Short Open-ended Mathematics Questions to Promote Thinking and Understanding , Foong Pui Yee, National Institute of Education, Singapore

Good Questions – Great Ways to Differentiate Mathematics Instruction , Marian Small, 2012

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Thank you for posting this. I appreciate how there is a comparison between the two (closed and open ended) types of questions and the considerations that go along with each. Thanks!

You are welcome!

Wow, well-written, thank you. I’m excited that my teaching is getting great, clear, and organized at the level that I’m at. But this article reminds me there are many higher levels I can get to, including this area of more open-endedness. Thank you!

I am happy to have helped even in a small way!

Thank you so much

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Think Math!

Children love to find order and regularity, to solve puzzles, and to make sense of the world. The Think Math! curriculum for grades K–5 takes advantage of (and fosters) this natural curiosity, building skills by embedding useful practice in puzzles, investigations, and games. Think Math! also helps children develop strong mathematical habits of mind—the mathematical practices—by providing opportunities for surprise, pattern finding, and mathematical thinking even in “routine” exercise.

All EDC curriculum development is based on the practical knowledge of teachers, grounded in the classroom, and supported by research. The principles behind Think Math! were particularly influenced by research in developmental psycholinguistics and child language, cognitive science, child development, and, of course, research on teaching and learning mathematics. Think Math! was rigorously field-tested in classrooms across the country.

The development of Think Math! was supported by the National Science Foundation, under grant number ESI-0099093. Schools may download and print PDFs from this website for classroom use as needed, following the requirements of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Kindergarten

What ‘s included in Think Math! ?

• Student materials for grades K–5 include daily student pages, additional practice pages, extension work pages, and games.
• Headline Stories are a daily mathematical classroom routine that provides very brief open-ended problems that promote creative problem-solving and deductive thinking.
• Mental Math activities provide daily, fast-paced, highly focused activities that build mastery and skill fluency in the critical arithmetic foundations.
• Developing Mathematical Language provides suggestions for introducing, developing, and understanding mathematical language, notation, and vocabulary.
• Differentiated Instruction offers suggestions both for easy entry and for extra depth or challenge, allowing all students to participate with reflective thinking and discussion.
• Teacher guides for grades K–5 describe the components of each lesson and offers suggestions for enhancing students’ skills and understanding. Standards, objectives, and materials are organized and listed at the beginning of each lesson. About the Lesson conveys the lesson’s purpose and mathematical focus. About the Mathematics extends and deepens, for the teacher, important ideas in the lesson.

Think Math! Student and Teacher Materials include:

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Open-Ended Maths Problem Solving Cards - Upper Primary

Updated:  12 Jul 2024

Boost your students’ problem-solving skills with rigorous open-ended maths problems for Year 5 and 6 students.

Editable:  Google Slides

Non-Editable:  PDF

Pages:  11 Pages

• Curriculum Curriculum:  AUS V9

Years:  5 - 6

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Solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient calculation strategies and using digital tools where appropriate; check the reasonableness of answers

Boost Math Skills With Open-Ended Maths Problems!

Are you looking for a fresh, engaging way to enhance your students’ maths skills? Open-ended maths problems might be the solution you’ve been searching for! Unlike traditional problems with a single correct answer, open-ended problems encourage creative thinking, multiple solution paths, and deeper understanding.

24 Open-Ended Maths Word Problems for Years 5 & 6

This printable resource includes a set of 24 rigorous, cross-discipline, open-ended maths word problems for Year 5 and 6 students. These cards include a variety of maths skills and encourage students to collaborate to find different solutions to the scenarios presented. Some skills included in these open-ended problems include:

• Multi-digit addition, subtraction, multiplication, and division
• Adding and subtracting fractions
• Determining area and perimeter
• Place value to the ten-thousands place

Your download includes printable task cards (in colour and black/white), a recording sheet, and an answer key with possible solutions.

Download and Print!

This resource is available as an easy-to-use Google Slides or Printable PDF Resource file. To get your copy, click the dropdown arrow on the download button to select your preferred file format. 

This resource was created by Kaylyn Chupp, a teacher and Teach Starter Collaborator.

Even More Upper-Level Problem Solving Printables

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Check Out These 50 Fifth Grade Math Word Problems of the Day

Three trains pulled into the station at 3 p.m.

Opening your daily math lesson with a Fifth Grade Math Word Problem of the Day is an excellent way to set the stage for learning! Incorporate them at the start of your math block to build confidence, critical thinking skills, and a learning community. Students will get used to reading for meaning while also identifying key information. Encourage students to write out equations and draw pictures to explain their thinking, since this helps them see the light when they are stuck!

Topics in these fifth grade math word problems cover patterns and place value, addition and subtraction, multiplication, division, fractions, decimals, measurement, and comparisons.

Want this entire set of word problems in one easy document? Get your free Google Sheet bundle by submitting your email here . All you need to do is post one of the problems on your whiteboard or projector screen. Then let kids take it from there.

50 Fifth Grade Math Word Problems

1. three trains pulled into the station at 3 p.m. the menton train had 2,589 passengers. the reston train had 671 passengers. the pearson city train had 1,024 passengers. how many passengers were there all together.

2. Grow Up Farmer’s Market had 4 crates of lemons delivered. One crate had 2,100 lemons. Two other crates had 2,010 lemons. The last crate had 1,999 lemons. How many lemons were delivered in all?

3. Ruffle Truffle Candy Company got an order for 850 chocolate truffles from the candy shop. They also got an order for 7,309 truffles from a food store. Then one more order came in for 3,125 truffles from a restaurant. How many truffles does the factory have to make to fill these orders?

4. The Tri-City Peninsula has 3 cities. 405,245 people live in Sunset City. 695,212 people live in Sunrise City. 415,937 people live in Sunup City. How many people live on Tri-City Peninsula all together?

5. Smiley’s Greeting Card Store ordered 25,294 birthday cards and 15,280 Mother’s Day cards to sell last year. They sold 11,065 Mother’s Day cards and 24,229 birthday cards. How many birthday cards did they have left?

6. Flyaway Airlines has 3 flights to New Park City every day from San Sandoz. Each plane seats 400 passengers. On Monday, the first flight had 325 passengers. The second flight had 387 passengers. The third flight had 221 passengers. How many empty seats were there all together?

7. In 1999 a million people lived in Western Deskateria. 350,268 are native to that country. The rest have moved there from another country. How many people have moved there from somewhere else?

8. Birthday candles from The Happy Hippy Candle Company are sold in packs of 8. They manufactured 6,000 boxes this past week and sold 8,000 candles. How many boxes of candles did they sell this past week?

9. Some of the new books in the South City Library were non-fiction. There were 25,025 new hardback books and 7,333 new paperbacks. 15,000 hardbacks were fiction. How many hardback books were non-fiction?

10. Giganto Mall has 6 levels. The top 5 levels each have 2,950 workers. There are 15,000 workers at the mall. How many workers work on the bottom level?

11. There are 96 frozen turkeys and 65 hams in the meat freezer at Frosty Food Mart. Each turkey weighs 19 pounds. Each ham weighs 10 pounds. How much do the turkeys weigh all together?

12. Each new dictionary purchased for the school has 355 pages. There are 35 dictionaries ready for each classroom. They weigh almost 300 pounds. How many pages is that in total?

13. Each Penguin Fruit Tree has 10,251 leaves. There were 96 fruit trees in Uncle Arch’s Orchard. Half of them were Penguin Fruit Trees. How many leaves were there on those Penguin Fruit Trees all together?

14. Benny’s Bait Shop sells worms in 12 packs. There are twelve packs in a gross. They sold 12 gross of worms this week. How many worms did they sell this week?

15. The Kwik Kar Rental Company has 27 locations in 12 states. They have 1,350 cars to rent out. If they distribute all the cars evenly among their locations, how many cars will each location get?

16. It was a sellout crowd at the football game. There were 42,500 fans in attendance. Every seat was filled. There are 85 rows of seats that wrap around the stadium. There is the same number of seats in every row. How many fans were seated in each row?

17. Mr. Sketch had 180 colored pencils in his classroom art bin. He bought new boxes of colored pencils that had 10 in a box. Now he has 400 colored pencils. How many new boxes did he buy?

18. 4,500 people arrived at the stadium for the rock concert on buses. another 4,500 came by train. the rest came in cars. each bus could hold 225 people and every bus was filled. how many buses were there.

19. Super Duper Corporation pays rent on their big headquarters building every month. Last year they paid $60,756 in rent and about the same amount on heat. They pay the same amount every month for the rent. How much is the rent per month?

20. Straight Arrow Dress Shirts sold a lot of dress shirts last month. Each shirt has 7 buttons down the front and 1 button on each sleeve. They used 72,000 buttons on the shirts sold last month. How many shirts did they sell?

21. Lake Louie has boats that take tourists on cruises around the lake. On Saturday, 8,112 tourists wanted to cruise around the lake. 3 boats cruise at a time in a shift. Each boat holds 500 people. A cruise lasts 30 minutes. How many shifts did they need to run so every tourist could cruise?

22. Superstar Sam is a professional baseball player and practices pitching every day. He spent 12,000 minutes practicing his pitching in July. He practices batting for 1 hour each week. How many hours did he practice his pitching in July?

23. The new sidewalk leading up to the front door of Elemental Elementary School was 55 feet long and 36 inches wide. 25 feet of it were painted gold and the rest was silver. How many inches long was the silver section?

24. The Dig-It Mining Company dug up 12,000 pounds of a rare mineral, Bobodium, every day for a week. They sell it in 8-ounce boxes. How many boxes will they need to pack up that week’s Bobodium?

25. Rita Writealot, the famous author, is visiting Collegial College and giving everyone who attends one of her two lectures 2 of her books. 600 people came to her first lecture. The second lecture had a good turnout also. She gave out 2,468 books all together. How many people came to her second lecture?

26. Mr. Amazing is preparing his magic act. There are 12,366 gold coins that he uses in one of his acts. He uses some in each scheduled appearance. He put aside 229 gold coins for each appearance. How many appearances is he planning on?

27. Rick has 4/5 of a Choco-bar. Sid has 6/7 of a Choco-bar. Nick has 6/8 of a Choco-bar. Who has the biggest piece of a Choco-bar?

28. ginny has 6/4 of some watermelons. william has 3/9 of another watermelon. steve has ½ of a different watermelon. who has the smallest amount of watermelon.

29. Luz is going to make a cheese dip. She bought ½ pound of American cheese. She also bought ¾ pound of Swiss cheese and ¼ pound of cheddar cheese. How much cheese did she buy?

30. Mercy had to select how much of a pepperoni pizza she wanted. She could have 7/8, 8/16, or 8/10. If she wants the most pizza, which amount should she choose?

31. Explorer Elmo Adventure found an ancient site with gold bars. He found three. The first was 5/12 of a pound. The second bar was 7/12 of a pound, and the third was 3/6 of a pound. How much did the bars weigh all together?

32. Sandy had 3/4 of a loaf of fresh-baked bread her mom made. She gave half of it to her cousin Stella. How much of the loaf did Sandy have left?

33. The fifth grade teacher, Ms. Marvelous, had 9/10 of an apple pie. She gave 3/10 to her principal, Mr. Pal, and 3/10 to her co-teacher, Mrs. Merry. How much pie did Ms. Marvelous have left?

34. Grace was laying pieces of ribbon she had end-to-end. The blue piece was 3/12 of a foot. The red piece was ½ of a foot and the white piece was 8/12 of a foot long. How long was the total?

35. Rob was reading a book that had 400 pages. He read 1/3 of it on Monday and another ¼ of it on Tuesday. What fraction of the book does he have left to read?

36. Ty had ½ of his whole birthday cake left. He gave his sister, Janelle, ¼ of that. How much of the whole cake did Janelle get?

37. The high school football team was meeting for the first time for practice. There were 64 players. ¾ of them were seniors. The rest were underclassmen. How many players were underclassmen?

38. The treasure hunters dug up a shoebox with $1,500 in it. There were five people on the treasure hunter team, so each got to keep 1/5 of the money. How much money did each person get to keep?

39. Tristan only has 1/8 of his deck left to paint. The whole deck has a total area of 100 square feet. He figured he could get ½ of what’s left done on Friday and the rest on Saturday. What fraction of the total deck does he plan to paint on Saturday?

40. three friends were keeping track of their running. these are the results from their runs on saturday. paige ran 0.75 miles. tanner ran 0.09 miles. liza ran 0.706 miles. who ran the farthest.

41. Gary’s professional kickball cards are divided among 3 teams. ¼ of his cards are San Fransisco Seals players. 0.25 are New York Yaks players. The rest play for the Nova Scotia Salmon. What decimal would best describe how much of his collection is Salmon players?

42. Molly the miner was weighing small amounts of gold dust. She had 3 packets of gold dust. They weighed 0.29 ounces, 1.07 ounces, and 0.92 ounces. She has to get 3 ounces of gold dust before she sells it. How much more gold dust does she need to make the sale?

43. Heather has 4 bank accounts. The first has $25.09 in it. The second has $106.75 in it and the third and fourth each have $108.08 in them. What is the total amount of money Heather has in these accounts?

44. each member of kirk’s family got a payment of $1,070.09 from their family business. there are 12 people in kirk’s family, including him. they range in age from 12 to 99. how much did the family get paid in total.

45. The number of t-shirts Ollie sells at the flea market runs in a predictable pattern. He sold 120 shirts in January, 60 shirts in February, 240 shirts in March, 120 shirts in April, 480 shirts in May, and 240 shirts in June. If the pattern of sales continues, how many shirts will he sell in August?

46. A number code is used to unlock the special vault. Three numbers must be entered in the correct order on a keypad numbered 0-100. The first is an odd number less than 20 that has 2 digits, both the same. The second number is even and is ½ of the number that is ¼ of 16. The third number is the product of the first two numbers and then doubled. What is the code?

47. Kim noticed this pattern on an old piece of parchment. 2, 5, 11, 23, 47, 95. Kim figured out the next two numbers. What are they?

48. Al is 5 years older than Ted. Ted is 2 years older than Alice. Alice is a year younger than Fran. Fran is 8 years old. How old is Al?

49. Liam finally got to the ferry dock at 4 p.m. He had taken the train to the ferry from Chairtown station. That train took half an hour to get to the ferry. To get to the station, he had driven for 4 and a half hours from Deskville Airport. He flew to Deskville from Tabletown Airport that morning. The flight was 2 and a half hours. What time did he fly out of Tabletown Airport?

50. Chris worked three jobs on Saturday. She mowed a lawn and finished it at 6 p.m. She washed windows for 3 hours. Also, she washed, waxed, and vacuumed 3 cars. Each car took an hour and a half to do. Chris started her day working at 9 a.m. How many minutes did it take her to mow the lawn?

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Parallel and Open Task Problem-Solving Math Bank

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Subjects: mathematics, levels/grades: grade 1, grade 2, grade 3, grade 4, grade 5, junior, kindergarten, primary, focus: critical thinking, differentiated instruction & learning.

Practical-Ready To Use differentiated math word problems inspired by the teachings of Dr. Marion Small, a long-time Canadian professor of education. Covering all five math strands, EACH word problem will engage ALL students at levels 1,2,3,4 from Kindergarten to Grade 5. Included are a generic math rubric for problem solving and a daily tracking sheet for a problem based classroom.

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Investigate Math: Grade 5: Open-Ended Math Problems to Develop Flexible Thinking Skills

• ISBN-10 1338751727
• ISBN-13 978-1338751727
• Publisher Scholastic Teaching Resources
• Publication date February 1, 2022
• Language English
• Dimensions 10.8 x 8.4 x 0.2 inches
• Print length 64 pages
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• Publisher ‏ : ‎ Scholastic Teaching Resources (February 1, 2022)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 64 pages
• ISBN-10 ‏ : ‎ 1338751727
• ISBN-13 ‏ : ‎ 978-1338751727
• Reading age ‏ : ‎ 10 - 11 years
• Grade level ‏ : ‎ 5 and up
• Item Weight ‏ : ‎ 5.6 ounces
• Dimensions ‏ : ‎ 10.8 x 8.4 x 0.2 inches
• #861 in Elementary Education
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Opening Minds with Open-Ended Math Problems in the Primary Classroom

by Model Teaching | December 21, 2018.

Wait, so, what is the RIGHT answer?” “Sarah got a different answer than I did…how can we BOTH be right?” You will most likely hear all kinds of responses like this when you start to incorporate open-ended math activities into your classroom. At first, they’ll probably make your students look at you as if you have two heads. But, these kinds of reactions will begin to subside once your students have been exposed to the idea that there are many ways to solve problems, even math problems! Encouraging this kind of “endless possibility” thinking is an effective way to teach your students to challenge themselves and think outside of the “normal” problem solving thinking.

What are open-ended math problems?

Open-ended math problems are problems that have more than one possible answer. These problems might present an end result and then ask students to work backward to figure out how that end result might have been achieved or they might ask students to compare two concepts that can be compared in a variety of different ways. But whatever way they are presented, the purpose of open-ended math problems is always to encourage students to use higher order thinking skills to solve problems and understand that some problems can be solved in many ways, with many outcomes.

Examples of Open-ended Math Problems

If you teach pre-k or kindergarten, an open-ended math problem might be: “You have 2 shapes that have a different amount of sides. What 2 shapes could you have? Show and name the shapes.” You would provide them with crayons, paper, pattern blocks, or whatever other manipulative they might be used to using when discussing shapes and students would use these manipulatives to come up with as many answers as they can. Your little ones may answer with a variety of answers based on their current skill level. You may get answers like “triangle and square”, “hexagon and parallelogram”, or “a circle is a shape” depending on what each student knows about shapes. This is a great way to reinforce what students already know and to quickly assess where they are in their knowledge.

If you teach first grade, an open-ended math problem might be: “I’m thinking of the number 8. What two numbers work could work together to make the number 8?” Again, you would provide them with manipulatives they normally use for composing and decomposing numbers, like counters, small erasers, counting bears, unifix cubes, or even playdoh balls. The extra bonus about this kind of problem is that it’s extremely easy for students to show their math skills. Some might use addition, others will use subtraction, and you may even run into a kiddo or two who can use multiplication to find the number. However students choose to explore all the possibilities for answers, be sure to give them a few options for how to show their thinking. This might include simply writing equations, drawing pictures with the equations, or even building the number with a manipulative and then taking a picture of it with an iPad.

As students get older and move onto more abstract thinking in second and third grade, you might incorporate more word problems like: “The difference between the temperature on Monday and Tuesday was 13 degrees. What could the temperature have been on each day? Find and explain at least 5 different answers.” Or “Penelope sees 37 children playing in a corn maze. If those children split into four groups, how many children could be in each group? Find and explain at least 5 different answers.” As always, be sure to provide students with manipulatives, paper and pencils, dry erase markers and whiteboards, or whatever you normally use to help them solve problems and then let them go to work! By presenting these kinds of word problems, you’ll expose students to a variety of math concepts (such as division in this example) just by allowing them to think about how to solve the problem on their own. Then, when these concepts are formally introduced, they will hopefully feel more familiar to some students.

Why should I use open-ended math problems with my students?

There are many benefits to incorporating these kinds of problems into your students’ daily routine, but here are a few of the most obvious and effective ones:

• Open-ended problems encourage higher order thinking skills. Students will not only be “recognizing”, “identifying”, or “describing” their thinking; they’ll be “justifying”, “defending”, and “evaluating” their problem solving skills and how they arrived at their answers.
• Open-ended problems build confidence in your students. Once students recognize that there are many possibilities for correct answers and thinking, they begin to participate more readily because they can bring to the table. Students who normally struggle with math might solve the problem on a very basic level, using a basic strategy, but they’ll be correct! And your advanced students can solve it on their advanced level and be just as correct as the student who struggles. Simply knowing that the way that they specifically thought and solved the problem was considered correct builds confidence for students.
• Open-ended problems are engaging! Students are immediately engaged in these kinds of problems because they recognize that there are so many different ways to solve it. Whether students are working in small groups or independently, there is possibility for so many different ideas and answers to be correct that everyone wants in on it. This engagement, in turn, encourages collaboration among students and soon, they’re sharing their thinking and learning from each other to solve problems.
• Open-ended problems encourage creativity. Students are capable of using so many strategies that they’ve learned over the years to solve problems and, given the space and time, they can even come up with some of their own strategies for solving problems. Open-ended problems give students permission to be creative in their thinking and problem solving.
• Open-ended problems make it easy for teachers to see what levels students are working at. Simply by walking around the room while students are working to solve an open-ended math problem, you’ll be able to informally assess what kind of level they are independently working on. This can be extremely beneficial as you are collecting data, forming groups, or simply getting a feel for what kind of skills each student is working with.

For more information about the benefits of using open-ended math problems, read:

https://nzmaths.co.nz/benefits-problem-solving

How do I incorporate open-ended math problems into my math instructional time?

Some of the simplest ways to incorporate open-ended math problems into your math instructional time is to include them in math stations, use them in small groups, and use them as a warm up.

• Math Stations:  You can implement open-ended problems into your math stations a number of ways, including thinking mats, task cards, or interactive math journals. The simplest way to implement them into your math stations is by using task cards. Task cards are pre-made cards that you can create or purchase to cut and laminate for students to use repeatedly. Task cards usually include words, pictures, diagrams, or a combination of all to present a problem to students. To use task cards in a math station, simply create or purchase the cards you want with open-ended word problems or picture problems. Then, simply print them out and cut/laminate them to make them durable and easily reused. (TEACHER TIP: Most dry erase markers wipe off of lamination pretty easily if it’s wiped off within a reasonable amount of time. Your students may want to mark the important parts of the problem on the actual task card with dry erase marker if you want them to. Just wipe if off after use!) I would suggest storing cards in a labeled plastic container or ziplock bag to keep them organized. It is suggested that you always allow students to use manipulatives as needed, as this can help students feel allowed to express their creative problem-solving thoughts. So, be sure your task card station provides anything students might use to solve problems in their own way: whiteboards, markers, papers, crayons, counters, manipulatives, thinking mats, laminated task cards, etc. For example, if you give students a task card with this problem on it: “Marcy finds 47 apples on the ground. What 3 addends could create this sum? Find and explain at least 5 answers.”, I would provide them with small apple erasers or counters, a whiteboard and dry erase marker, and an iPad to take picture evidence of their five (or more!) answers when they’re finished.  Please refer to pages 10-16 in the resource provided to you below this article for some sample open-ended word problem task cards that you can use with your students immediately!
• Small Groups: To implement open-ended problems in your small groups, using thinking mats, manipulatives, and prepared open-ended problems is a great way to ease students into working on open-ended problems independently. This is a great way to model your own thinking and problem-solving to allow students to see how they can begin their own ways of solving the problems. Take a moment to download and look at the thinking mat activity in the downloadable resource below. You can incorporate these mats into your small group activity by providing each student with a laminated copy of the mat you want to use and manipulatives for them to work with to follow the mat’s directions. For example, the thinking mat that says “Make patterns out of these shapes and name them.” would be an excellent open-ended activity for a group of kindergartners who are working on shapes OR patterns. Give each student a few of each of the pattern blocks shown on the mat and a dry erase marker. Explain and model how YOU would complete the activity by creating a pattern with the pattern blocks, tracing the blocks or drawing your pattern, and then naming it with letters (ie.: rhombus, rhombus, circle would be named an AAB pattern). This will give your students an idea of what’s expected and their little brains can get started coming up with their own patterns!
• Warm Up: Using your warm-up time to practice with open-ended problems is a great way to model your own thinking to the whole. Modeling how to solve these problems step-by-step along with the whole class can help give reluctant participants the courage and understanding to participate and ready participants the reassurance that they’re on the right track. As an example, look at “Activity 3: Creating and Solving Problems” in the downloadable resource. You will notice a few thinking mats included, along with cards that correspond to the mats. For a warm-up activity before you begin your lesson for the day, you could give each student a laminated thinking mat and a corresponding manipulative (like, pass out the table and basket cards and give every student some small apple erasers). Then, project a corresponding task card so that everyone can see it. Read the card together, model one way you could solve the problem using your own thinking mat and manipulatives, and then allow students to solve it their own way to find one or two other answers. I would ask students to record their thinking and answers in a math journal or something similar so I could look back on their skills from early in the year and compare them to the end of the year. This is a quick, great way to collect data on student’s skills without a lot of involvement from you!

These are just a few ways to incorporate open-ended problems into your math time. I encourage you to try one way for a week or two and then experiment with another way once your students are showing they feel confident in the first implementation.

How do I make sure to provide students with open ended math problems during math each day?

In order to provide your students with activities and resources that encourage deep thinking and allow every student to participate, detailed planning is required. Deciding what standards and concept you want to focus on and choosing the best way to practice skills related to that concept before having students complete an activity is crucial to creating an effective learning time. If you peek at page 37 of the resource below, you’ll see a planning page that you can use to plan out the open-ended activities you want to use in your classroom. By editing this page with your own information, you can plan for a week of open-ended activities quickly and efficiently. This is also a great way to hold yourself accountable for how often you’re giving your students the opportunity to work on open-ended activities.

Any way you choose to implement open-ended problems in your classroom, your students are sure to grow in their problem-solving abilities and confidence. Creating a space that is safe for your students to take chances and risks with their learning is one of the greatest gifts you can give them. By incorporating ways for your students to express their individual ways of thinking, like open-ended math problems, you’ll foster a love of creative thinking and confidence in problem-solving skills.

Notes About the Included Resources:

The resources included in this blog post are for you to use in your classroom with your students. More detailed explanations for how to incorporate the activities are included in the resources themselves. There are also a few blank templates within the resource so that you can create your own task cards, thinking mats, and activity plans.

Related Professional Development Courses:

Math Stations for PreK-2nd Grade

Efficient Classroom Processes

Inquiry-Based Learning: Using Inquiry as a Teaching Strategy

(10 PD Hours) Explore the strategies involved in planning and executing inquiry-based lesson plans. The components of an inquiry-led lesson will be outlined and discussed, and participants will learn to develop and plan an inquiry-led lesson.

Project Based Learning

(22 PD Hours) This course gives participants a thorough understanding of Project-Based Learning, including the critical components, as well as common misconceptions. Throughout the course, participants will design their own cycle of PBL they can immediately implement in their own classroom.

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DOWNLOADS & RESOURCES

Open Ended Math Activities for the Primary Classroom

Use these templates and graphic organizers for students who may need additional support. Feel free to download and modify the editable version, including the Frayer model template and word bank template.

IMPLEMENTATION GOAL

Choose or create an open-ended math activity to incorporate into your math instructional time. Plan to introduce the activity to your students at the beginning of the week, model and practice how to complete the activity together, and then allow them to work on the activity for 10-15 minutes per day throughout the rest of the week. Take anecdotal notes about growth you notice and how your students react to these kinds of problems. Do they enjoy them? Dread them? Are you seeing improvement in their thinking and willingness to participate? Take note of these kinds of things as the week goes on. Then, decide what open-ended problems you’ll implement the following week.

• What is Open-Ended Problem Solving? – https://mste.illinois.edu/users/aki/open_ended/WhatIsOpen-ended.html
• The Effect of Open-ended Tasks- http://journals.yu.edu.jo/jjes/Issues/2013/Vol9No3/8.pdf
• Clip art generated by Creative Clips Clipart by Krista Walden, http://www.teacherspayteachers/store/krista-walden

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