Math Starters to Ignite Learning

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Problem Solving Activities to Engage your Students

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Creating Rich Math Word Problems

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Problem Solving Techniques: 5 Essentials

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Math Problem Solving: Why I Changed My Format

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10 Problem Solving Resources Your Students will Love!

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Celebrate the Season with Holiday Math Tasks

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Stumped! Critical Thinking Web Games to Challenge Your Students

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Transformation Tuesday: Engaging Critical Thinking Activities- Web Games

Thank you for reading my "Transformation Tuesday" series. Today's post marks the last "Transformation Tuesday" post until September. Until that time, I will be featuring a Summer PD series from June through July. Be sure to check back each week for some new summer learning, in between relaxing at the pool and vacationing of course! :o) 

Today's post features my favorite critical thinking web games. They are sure to keep your students engaged in these last few days. There are two Coolmath.com games that I would like to share with you-- Bridge Crossing and Water Jars. Both games require students to use their strategic thinking skills to successfully complete the activities. They originally appeared in my 2014 "Problem Solving Palooza" series. Check it out here.

The first challenge is one of my favorite web games. It's called "Bridge Crossing." See the screenshot and game details below. 

Grade Level: This website is more suited to the reasoning skills of upper elementary/ middle school students. (See variations below for lower elementary challenges.)

Objective: Help all of the characters cross the bridge.

Task: Only two characters can cross the bridge at the same time. The lantern must be used when the characters cross the bridge. Each character shows how many minutes it takes him/her to cross the bridge. The lantern will lasts for 30 minutes; that's how long the characters have to cross the bridge because they cannot cross the bridge in the dark. 

Note: This is a challenging task, but it is possible. I've had students master this task in the past! 

Ways to Utilize the Activity: This website is a great way to get your student thinking about how to solve problems such as these. Consider displaying the website to the class and review the directions. Then, as a class, discuss ways to approach the task. Ask questions such as: 

• What is the task asking us to do?
• What special conditions do we need to consider?
• Which characters take the shortest time to cross the bridge?
• Which characters take the longest time to cross the bridge?
• How can we pair the characters together so that we use the shortest time possible? 
• Which character can be easily used to travel back and forth across the bridge and hold the lantern?

You may also want to consider allowing students to work in pairs to approach the task and discuss ways to meet the goal together. 

This applet makes a great fast finisher activity. It can also be included on a math menu or used on a menu of problem solving station options. 

Variations: The two websites below are more suited for younger elementary students. They are similar to the challenge above but include special conditions, such as a small penguin cannot be left alone on a side with an unrelated adult penguin. The special conditions add an additional element of challenge, but these tasks are easier than the "Bridge Crossing" task. 

• Wolf, Sheep, and Cabbage
• Penguin Families

The second challenge is another one of my favorite web games. It's called "Water Jars." See the screenshot and game details below. 

Grade Level: This website is more suited to the reasoning skills of upper elementary/ middle school students.

Objective: Measure 6 liters of water from a 5-liter jug and a 7-liter jug

Task: Fill-up the jars and use them to measure 6 liters of water. The jugs can be emptied, refilled, and transferred to the other container multiple times until the goal is achieved. 

For example, if you fill up the 5-liter jug and then pour it into the 7-liter jug, you can refill the 5-liter jug and pour it into the 7-liter jug leaving 3 liters in the 5-liter jug. You've just measured 3 liters. 

Students will need to make moves like the one above to measure 6 liters. 

Note: This is a challenging task, but it is possible. I've had students master this task in the past! 

Ways to Utilize the Activity: This website is a great way to get your student thinking about how to solve problems such as these. Consider displaying the website to the class and review the directions. Then, as a class, discuss ways to approach the task. Ask questions such as: 

• What is the task asking us to do?
• What special conditions do we need to consider?
• How can we measure different amounts, other than 5 liters or 7 liters, using these two jugs? Let's try to measure 3 liters. 
• What's the purpose of being able to fill the jug and transfer it to the other jug?

You may also want to consider allowing students to work in pairs to approach the task and discuss ways to meet the goal together. 

This applet makes a great fast finisher activity. It can also be included on a math menu or used on a menu of problem solving station options. 

Variations: This activity can be simulated in the classroom with actual jugs of water. Set the situation up by saying that you need to measure ____ liters of water but you only have a ____-liter jug and a ____-liter jug. Try using this model to support the students' understanding of the task before using the website for struggling or younger students. 

Sound Off! What websites do you like to use to challenge your students' critical thinking? 

Solve It! Friday- Task #3

Here's how Solve It! Friday works:
1. Each Friday morning (at 12:00 AM Central Time), I will post one problem-solving task. Note: In some cases, I may post more than one version of the task to reach a wider variety of grades. 
2. Before the next Friday, use the task with your students. 
3. Have students solve the problems individually or with a group. 
4. Individual students or student groups create posters using numbers, pictures, and words to illustrate the solutions. Note: The blank backs of old book covers make great poster paper! 
5. Either via a math talk session or a gallery walk, be sure to have students share their responses with other students. 

I would love to see your students' responses and showcase them on social media. Please post your students' responses to Twitter using the hashtag #RMTSolveIt(week number). For privacy, please be sure that students' names and other identifying information is located on the back of the poster. Be sure to check out other classes' solutions using the same hashtag to filter the Twitter results. 

I look forward to seeing your students' work! Thanks for sharing! 

Solution: The real beauty of this task is in the process. Please emphasize that with your students. It may take some time to solve this problem. Validate their efforts and ask questions to move them in a different direction if needed. For your convenience, I have provided the solution below:

#RMTSolveItWeek3: There are 23 four-leg desks and 26 two-leg chairs. 

Solve It! Friday- Task # 2

Here's how Solve It! Friday works:
1. Each Friday morning (at 12:00 AM Central Time), I will post one problem-solving task. Note: In some cases, I may post more than one version of the task to reach a wider variety of grades. 
2. Before the next Friday, use the task with your students. 
3. Have students solve the problems individually or with a group. 
4. Individual students or student groups create posters using numbers, pictures, and words to illustrate the solutions. Note: The blank backs of old book covers make great poster paper! 
5. Either via a math talk session or a gallery walk, be sure to have students share their responses with other students. 

I would love to see your students' responses and showcase them on social media. Please post your students' responses to Twitter using the hashtag #RMTSolveIt(week number). For privacy, please be sure that students' names and other identifying information is located on the back of the poster. Be sure to check out other classes' solutions using the same hashtag to filter the Twitter results. 

I look forward to seeing your students' work! Thanks for sharing! 

Note: Students should have prior experience with Venn Diagrams before completing these problems. If this is new for your students, create a few opportunities to use Venn Diagrams, maybe even using the same premise of getting to know each other, in advance. Be sure that students understand how to read and understand Venn Diagrams, especially the overlapping portion, before moving on to the tasks below. 

In addition, be sure students understand that  the total number of participants should equal the sum of the sections of the Venn Diagram. For today, assume that all students made a selection. There are no students outside of the diagram. However, for an extra challenge, ask students to re-solve the problem assuming a specific number of students did not make a selection-- they choose neither option. 

Using small objects to help find the solutions below will support the understanding of some of your more tactile students. The action of moving the objects may also help students who are still developing the understanding of how Venn Diagrams work. 

Solutions: The real beauty of these tasks is in the process. Please emphasize that with your students. It may take some time to solve these problems. Validate their efforts and ask questions to move them in a different direction. For your convenience, I have provided the solutions below:

#RMTSolveItWeek2A: Have Brothers- 2, Have Sisters- 1, Have Both- 2
#RMTSolveItWeek2B: Have Dogs- 1, Have Cats- 4, Have Both- 5

#RMTSolveItWeek2C: Likes Pepperoni- 9, Likes Peppers- 5, Likes Both- 1

Are there other solutions that will work? Please post your students' responses to Twitter using the hashtag #RMTSolveIt(week number).

Solve It! Friday- Task #1

The ability to solve problems using multiple methods is an essential skill students need to be successful mathematicians. NCTM (2014) advocates that "teachers must regularly select and implement tasks that promote reasoning and problem solving" so that students have opportunities to engage in "high-level" thinking (p. 17). In fact, research shows that "student learning is greatest in classrooms where the tasks consistently encourage high-level student thinking and reasoning" (NCTM, 2014, p. 17). 

The weekly Solve It! problem is designed to help meet these goals and provide teachers with an engaging task that will provide opportunities for students to reason about math and engage in high-level thinking. Additionally, students will strengthen their communication skills and learn to evaluate the mathematical thinking of others.  

Here's how Solve It! Friday works:
1. Each Friday morning (at 12:00 AM Central Time), I will post one problem-solving task. Note: In some cases, I may post more than one version of the task to reach a wider variety of grades. 
2. Before the next Friday, use the task with your students. 
3. Have students solve the problems individually or with a group. 
4. Individual students or student groups create posters using numbers, pictures, and words to illustrate the solutions. Note: The blank backs of old book covers make great poster paper! 
5. Either via a math talk session or a gallery walk, be sure to have students share their responses with other students. 

I would love to see your students' responses and showcase them on social media. Please post your students' responses to Twitter using the hashtag #RMTSolveIt(week number). For privacy, please be sure that students' names and other identifying information is located on the back of the poster. Be sure to check out other classes' solutions using the same hashtag to filter the Twitter results. 

I look forward to seeing your students' work! Thanks for sharing! 

Solutions: The real beauty of these tasks is in the process. Please emphasize that with your students. It may take some time to solve these problems. Validate their efforts and ask questions to move them in a different direction. For your convenience, I have provided the solutions below:

#RMTSolveItWeekIA: Jendi's supplies weigh 7 ounces. The pencil box weighs 4 ounces.
#RMTSolveItWeekIB: Kingston's school supplies weigh 4 pounds, therefore Cassie's school supplies weigh 12 pounds. The backpack weighs 3 pounds.

Reference: 
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. The National Council of Teachers of Mathematics, Inc.: Reston, VA. 

Kick Start Your School Year with Problem Solving

One of my favorite activities in the classroom is problem solving. It's such an important skill! We use it many times throughout our day without even thinking about it. In fact, this is a great introduction to problem solving-- make a list of all of the problems in your world you solved today or this week, such as what time to set the alarm clock for or how much time is needed to walk to school each day. Then have students discuss the strategies they used to make a decision. Create an anchor chart for these ideas and refer to them as they reappear in future discussions. Hopefully, students will begin to notice that they use some of the same strategies to solve problems outside of math class as they do inside it. 

I like to get started using problem solving in the classroom during the first days of the school year so that students understand the importance of it and that it will be a part of what we do every day. During math time, my problem solving component has two goals:

Click the picture for a free download.

• Understand How to Analyze Story Problems- While the situations are not always authentic and the problems are generally more routine, I consider this to be a form of problem solving because the students learn how to analyze the problem for the parts needed to begin solving it. This not only supports the work we do to prepare for our state assessment, but it also provides a training ground for the more non-routine problems that I like to use. Depending on the grade level of the students, I use my RACE or J.U.S.T.I.F.Y. problem solving models to accomplish this goal.  
• Solve Non-Routine Problems- These are my favorite type of problems to use in the classroom; however, they do require more time to allow the students to understand and then solve them. The understanding piece is aided by the initial process that I mentioned above. Non-routine problems are ones that cannot be solved by simply adding, subtracting, multiplying, or dividing to find the answer. They require students to develop and execute a plan of action and can often have more than one solution. 

With these two goals in mind, I try to integrate problem solving into what we do on a daily basis. Using this strategy, my students have multiple opportunities to use and expand their problem solving toolboxes, as well as, communicate with others about their thinking using math talk. 

This school year, I challenge you to integrate problem solving into your program at least three times a week. Increasing the amount of problem solving your students do on a regular basis will provide a great return on your investment. 

Here are some resources to get you started: 

• File Cabinet: Problem Solving- Follow the link for free resources.
• Problem Solving & Critical Thinking Packs at my Teachers Pay Teachers Store- There are a variety of resources here, including some holiday-themed packs. 
• The Routty Math Teacher Problem Solving & Critical Thinking Pinterest Board- This board is a collection of ideas and resources that can be used in the classroom. I do add to it regularly. 
• Textbook Problems- Don't disregard this useful tool; however, be sure to remove the answer choices and add extra information to help students practice critically analyzing the problem. 

If you have great problem solving resources to share, please include them in the comments below. 

Have a fantastic school year!

TpT Seller Challenge: Problem Solving on the Farm with a Brand New Cover!

Hello Again! This TPT Seller Challenge has me going makeover crazy! I just updated the cover of my best-selling product- Problem Solving on the Farm. This pack encourages you to expand your students' problem solving toolboxes while they become familiar with strategy terminologies and procedures, as well as, explore and evaluate multiple methods to solve problems. Check it out athttp://bit.ly/RMTProblemSolvingontheFarm. ‪

#TPTSellerChallenge

Math with Ms. Routt- Problem Solving

The fourth component of my math block is problem solving. This component of "Math with Ms. Routt" generally takes about 15 - 20 minutes. While I am a big proponent of authentic problem solving, that which arises naturally through the content that we teach, I also realize that those opportunities do not always arise at the time they are needed. Therefore, I use this time to both model and reinforce how to solve problem solving tasks and the strategies we use to attain this goal. In addition, I also hold a word problem workshop throughout the week to model/ reinforce how to analyze and successfully attack word problems. 

During this time, I either model how to address the task with a think-aloud or I ask the

Solution Strategy Poster

students to work individually, in pairs, or small groups, depending on the difficulty of the task, to complete the work. If the students complete the task without my help, we debrief the task before moving on. I have students share their work by creating a solution strategy poster (see picture to the right), review their work with the document camera, or talk through the steps they used to solve the problem. A copy of my "Open-Ended Questions Poster" can be found here. 

I use a variety of resources to find problems. Great problem solving tasks can be found via the web, in supplemental materials, or in your textbook series. For word problems, the best tasks are the ones that include extra information or include a lot of information that could be used to answer multiple questions. 

I have posted a few resources to share with you in the the "Problem Solving" section of my "File Cabinet." There is a problem solving strategies pack to expand your students' problem solving toolboxes, two packs which include a structure for analyzing word problems, and a problem solving task from one of my holiday packs (Note: you can make this an everyday task by changing the holiday words to everyday words). Click here to check out my file cabinet!

Problem Solving Palooza- Challenge #6

Magic Square

Grade Level: This activity is suitable for students in grades 2 - 8  

Objective: Get the value of each row, column, and diagonal to equal 15

Task: Place one of the digits (1-9) in each square until each row, column, and diagonal equals the number 15. Each number is only used once. 

Ways to Utilize the Activity: This is a great starter activity. Display this on your projector or give each student a copy and let them go to work. Then, as a class, discuss ways to approach the task. Ask questions such as: 

• Where do you start?
• What problem solving strategy can you use to solve this problem?
• Are there certain numbers that must be located in a specific box? If so, which ones? Why?
• Is there more than one solution? If so, what is it?

This magic square can be included on a math menu or used on a menu of problem solving station options. 

Solutions: See the solution below: 

Variation: Allow students to work with foam numbers or numbers written on sticky notes or index cards so that they can easily manipulate the number placements.  

Learn More: Have students research how Benjamin Franklin created the magic square.  

Note: You can download this freebie here.  

Problem Solving Palooza- Challenge #5

 "Water Jars" from Coolmath.com

Today's challenge is another one of my favorite web games. It's called "Water Jars" from www.coolmath.com. See the screenshot below. 

Grade Level: This website is more suited to the reasoning skills of upper elementary/ middle school students.

Objective: Measure 6 liters of water from a 5-liter jug and a 7-liter jug

Task: Fill-up the jars and use them to measure 6 liters of water. The jugs can be emptied, refilled, and transferred to the other container multiple times until the goal is achieved. 

For example, if you fill up the 5-liter jug and then pour it into the 7-liter jug, you can refill the 5-liter jug and pour it into the 7-liter jug leaving 3 liters in the 5-liter jug. You've just measured 3 liters. 

Students will need to make moves like the one above to measure 6 liters. 

Note: This is a challenging task, but it is possible. I've had students master this task in the past! 

Ways to Utilize the Activity: This website is a great way to get your student thinking about how to solve problems such as these. Consider displaying the website to the class and review the directions. Then, as a class, discuss ways to approach the task. Ask questions such as: 

• What is the task asking us to do?
• What special conditions do we need to consider?
• How can we measure different amounts, other than 5 liters or 7 liters, using these two jugs? Let's try to measure 3 liters. 
• What's the purpose of being able to fill the jug and transfer it to the other jug?

You may also want to consider allowing students to work in pairs to approach the task and discuss ways to meet the goal together. 

This applet makes a great fast finisher activity. It can also be included on a math menu or used on a menu of problem solving station options. 

Variations: This activity can be simulated in the classroom with actual jugs of water. Set the situation up by saying that you need to measure ____ liters of water but you only have a ____-liter jug and a ____-liter jug. Try using this model to support the students' understanding of the task before using the website for struggling students or younger students. 

Problem Solving Palooza- Challenge #4

Mrs. Claus's Cookies

Grade Level: This activity is suitable for students in grades 3 - 6. 

Objective: Determine the amount of chocolate chip and sugar cookies on the plate

Task: Use the information given to determine the number of chocolate chip and sugar cookies on the plate. Task A only includes one condition and has multiple solutions. Task B has two conditions and has one solution. 

Ways to Utilize the Activity: This is a great problem solving activity to emphasize identifying key information. Display this on your projector for optimal quality. Provide each student with a printer-friendly copy. Read the problem situation together. If this is your students' first exposure to this type of problem, you may want to help the students determine the objective and identify key information before beginning. Allow students to work with a partner to complete the task. Then, as a class, discuss ways to approach the task. Ask questions such as: 

• What information do you need to help you complete this task?
• What question are you trying to answer?
• What do we know about the chocolate chip cookies? 
• What do we know about the sugar cookies?
• How many chocolate chips and sprinkles are on the plate?
• If there was only one chocolate chip and one sugar cookie on the plate, how many chocolate chips and sprinkles would be on the plate?
• What strategy did you use to find a solution? Explain. 
• Would drawing a picture help you? If so, how?
• What tool can we use to organize our information?

This activity can be included on a math menu or used on a menu of problem solving station options. 

Solutions: Task A: 2 sugar and 9 chocolate chip; 4 sugar and 6 chocolate chip; or 6 sugar and 3 chocolate chip; Task B: 8 sugar and 12 chocolate chip. 

Challenge: Create an additional problem with a larger number of cookies. 

Note: You can download this freebie here.  

Problem Solving Palooza- Challenge #3

Number Clue Puzzlers

Grade Level: This activity is suitable for students in grades 3 - 6. However, second graders should be able to complete the first puzzler. 

Objective: Determine the mystery number

Task: Write down the numbers 0-9. Read each clue. Use the clues to eliminate numbers until the mystery number is found. 

Ways to Utilize the Activity: This is a great starter activity that emphasizes important math terms. Display this on your projector for optimal quality and allow students to determine the mystery number. Then, as a class, discuss ways to approach the task. Ask questions such as: 

• How do you determine what numbers to eliminate with each new clue? 
• What is another way to say, "not an odd number"?
• What does it mean to be "more than" or "less than" a number? Is the endpoint included or not included? Explain. 
• What does it mean to be between two numbers? Are the endpoints included? Explain. 
• What vocabulary do you need to know to eliminate numbers after reading this clue? (indicate a specific clue)

This number puzzler can be included on a math menu or used on a menu of problem solving station options. 

Solutions: Puzzler 1 = 6, Puzzle 2 = 7, Puzzle 3 = 4

Challenge: Have students create their own puzzlers. Increase the challenge by giving students the mystery number in advance and having them develop a puzzler to arrive at the mystery number. 

Note: You can download this freebie here.  

Problem Solving Palooza- Challenge #2

Holiday Logic

Grade Level: This activity is suitable for students in grades 3 - 5. 

Objective: Determine the value of each symbol. 

Task: Each symbol has a numerical value. The sum of each row and column is shown on the outside of the table. Use the clues to determine the value of each symbol. 

Ways to Utilize the Activity: This is a great starter activity. Display this on your projector or give each student a copy and let them go to work. Then, as a class, discuss ways to approach the task. Ask questions such as: 

• Where do you start? Why?
• How do you determine the value of a symbol? 
• In what order do you need to determine the value of the symbols? 
• In the last column, if you know the value of the elf and the gift box, how can you find the value of the cupcake?
• What problem solving strategy did you use?

Note: Some students will use the guess and check strategy to solve the puzzle; however, it is beneficial to discuss the relationships among the symbols in the puzzle as well. For example, if 3 cookies and a gift box equal 24 and the gift box equals 9, then 24 - 9 = 15. Therefore, the 3 cookies must equal 15 and 15 divided by 3 equals 5. The sugar cookie must be worth 5. Encourage students who use the guess and check strategy and achieve the solution quickly to discover some of these relationships. 

You may also want to consider allowing younger students to work in pairs to approach this task and then discuss ways to approach the task together. 

This logic puzzle makes a great fast finisher activity. It can also be included on a math menu or used on a menu of problem solving station options. 

Solution: Santa hat (7), sugar cookie (5), cupcake (6), elf (8), gift box (9)

Challenge: Have students create their own puzzles with stickers, basic shapes, or letters.  

Note: You can download this freebie, including a printer-friendly version, here.