Happy Holidays Everyone!

The Routty Math Teacher will be on hiatus until after the first of the year. Enjoy this time with your family and friends. Have a joyous holiday season!

Problem Solving Palooza Weekly Giveaway #2

GIVEAWAY!- The second Problem Solving Palooza giveaway will be a free item from my Teachers Pay Teachers store. Check it out- Routty Math Teacher Store.

To enter, leave a comment on this post on my Facebook page telling the Routty Math Teacher community about how you used one of the challenges I posted this week, how you plan to use the challenge in the classroom, or how your students responded to the challenge when you tried it out.

I will accept entries through Sunday at midnight (U.S. Central Time).

I will notify the winner via Facebook on Monday. Good Luck!

Disclosure- This giveaway is not hosted by or affiliated with Facebook.

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.  

Problem Solving in Santa's Workshop

Check out my new "Problem Solving in Santa's Workshop Pack." You can read a product description and see sample pages at http://bit.ly/FBSantasWorkshop. 

Through December 3rd, you can grab it for $4. Teachers Pay Teachers is offering an additional 10% discount through tomorrow, December 2nd. Check it out!

Problem Solving Palooza- Challenge #1

 "Bridge Crossing" from Coolmath.com

Today's challenge is one of my favorite web games. It's called "Bridge Crossing" 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. (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?

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 the tasks are easier than the "Bridge Crossing" task. 

• Wolf, Sheep, and Cabbage
• Penguin Families

Problem Solving Palooza Relaunch!

Problem Solving Palooza Relaunch!

Welcome to my new blog series "Problem Solving Palooza!" This series will offer ideas and strategies for integrating problem solving into your everyday mathematics curriculum. Each post of the series will include a daily challenge with tips and tricks for using the activity in the classroom. 

Each week, I will host a Facebook giveaway. I will create a post asking how you used one of the problem solving activities in your classroom. Respond to my post with how you used the activity or something cool that happened when your students interacted with the activity. I will use Rafflecopter to select a winner. The winner will receive a free item from my Teachers Pay Teachers store! Good luck and thanks for reading!

Doing Math the Routty Way: Engaging Activities from A to Z (Day 25)

Zany Problem Solving Tasks- Problem solving is a great way to get your students thinking, to emphasize critical thinking skills, and promote curricular content all at the same time. Problem solving can come in the form of games, logic problems, word problems that emphasize non-routine solution strategies, puzzles, tiling tasks, problem of the day, and stumpers (like riddles). There are many ways to integrate problem solving throughout your daily math program, through problem of the day, math stations. math menus, enrichment time, skill assessments, games, brain breaks, etc. Join me for my next series, "Problem Solving Palooza" for ideas, activities, and strategies for increasing your classroom rigor through problem solving. In the meantime, check out my freebie "Make 24," a game that promotes problem solving skills when students use four numbers to add, subtract, multiply, and divide their way to the number 24. Happy Solving!

Doing Math the Routty Way: Engaging Activities from A to Z (Day 24)

Yo-Yo Partner Work- Often times, one student tends to dominate the conversation when completing partner work.The yo-yo partner strategy is a great technique for holding partners accountable for work completed during cooperative learning so that both students have the opportunity to learn and show growth. 

When students are communicating about their mathematical thoughts, processes, and ideas, use a timer to guide discussion time. Give each student 30 seconds, longer if needed, to communicate their ideas to a partner. The listener should listen intently and then make one comment and ask one question. The students then reverse roles. 

Comments can include thoughts like, "I really like the strategy that you did. I might try that next time." Or, "Your work is easy to follow and the table that you used helps me make sense of the problem." Initially, students will need support to understand how to make informative and supportive comments. You may even want to brainstorm a list of statements/comments on chart paper for the students to refer back to when they are communicating about mathematics.  

Follow-up questions can include questions from the Open-Ended Questions Poster presented previously on my blog. 

Doing Math the Routty Way: Engaging Activities from A to Z (Day 23)

X-word Puzzles- Crossword puzzles are a fun and motivating way to practice important skills and content. There’s something about the puzzle aspect of this task that is appealing to students. Crossword puzzles can be created to assess a variety of skills. They are easy to make and the students love them! 

Check out these student created puzzles!

Resources to Get You Started: 

• The Armored Penguin Crossword Puzzle Maker is an excellent teacher resource for creating crossword puzzles. The program is free and allows you to create a puzzle as a PDF or you can copy and paste the puzzle into another document, such as Microsoft Word or PowerPoint. 
• The free puzzle maker at Discovery Education is an easy tool for students to use to create their own puzzles. Student-created puzzles can be added to math menus or used as fast finisher challenges (see the picture above). The students love creating them and seeing their classmates try to complete them!

There are many ways to use crossword puzzles. Try taking a worksheet that has numerical answers that can be represented with a single word and converting the task into a crossword puzzle. For example, in the puzzle below, students simplify each numerical expression and write the word form of each number to complete the puzzle. 

This crossword puzzle is part of my Order of Operations Pack at my Teachers Pay Teacher store. 

Doing Math the Routty Way: Engaging Activities from A to Z (Day 22)

Word Wall Activities- Make your word wall come alive! Learning math vocabulary and terms is essential to students understanding the skills and concepts necessary for mastery of the content at each grade level. As we very well know, vocabulary can make or break a student on an assessment. If they do not understand the words, they cannot make sense of the question. It's important that students interact with the vocabulary words on a regular basis in order to truly understand them.

Math word walls can be organized by topic or letter. A word wall can even be organized by both letter and topic using colored word strips. Individual word walls can also be used to highlight a specific set of words (see the picture below) or to better show connections and relationships. 

Word Wall Activity Ideas: 

• Once a week, take 5-10 minutes out of the day to review the words. Choose a word to define and say, “I’m thinking of a word wall word that means (insert the definition here).” Ask students to raise their hands to respond. Repeat the process for 5-10 words. Over time, with regular use of this activity, students will become more proficient with their math vocabulary.
• Ask two students to pick a word from the word wall. Have student groups determine how the words are related. After all student groups have had the opportunity to discuss the relationship, share out as a class. This is a great way to have students think about the relationship between words. 
• Give each student a whiteboard. Have students create a visual definition, illustration, for each word. Then, have students discuss how their visuals match the definition with a partner or classmate.

The vocabulary cards pictured above are part of Mrs. C's Classroom's Multiplication and Division Word Wall Pack from Teachers Pay Teachers. It's a freebie!

Doing Math the Routty Way: Engaging Activities from A to Z (Day 21)

Vocabulary SWAT-it!- This has been my class' favorite way to review vocabulary for years! It's a great way to get the students to learn all of their important vocabulary words. It's both engaging and fun and all of the students want to volunteer to be a swatter. 

Check out a sample Swat-it! board below!

Here's how to set it up: 
1. Use an 8.5 inch x 11 inch size paper to program a 3 x 3 unit rectangle with 9 vocabulary words.  
2. Project the rectangle onto your classroom whiteboard so that the students can reach all of the rectangles with a fly-swatter. 
3. Ask for two volunteers to come to the front of the room and stand on the left and right side of the Swat-it! board. 
4. Hand each student a fly-swatter. 
5. Read a definition. 
6. The students use the fly-swatter to swat the word that matches the definition. 
7. The first student to swat the correct word is the winner. 

Variations: Instead of vocabulary words, use numerical answers and read number sentences.

Doing Math the Routty Way: Engaging Activities from A to Z (Day 20)

Use Bulletin Boards to Promote Challenge- One of the biggest challenges for teaching mathematics in the classroom is attending to the multitude of skills and process that must be emphasized each year. One way to utilize the extra minutes that we end up with throughout the day is to use your classroom or hallway bulletin boards as learning centers. Students can complete the activity as part of a station rotation, a menu activity, or as a fast finisher challenge. Boards can be interactive and involve students contributing solutions to one problem or situation or students can use the bulletin boards to complete the problems and then submit an individual task sheet. 

Ideas for bulletin board learning centers include: 

• problem solving
• puzzles
• function tables
• real-life mysteries
• Who Am I? challenges

The picture below illustrates a Boggle Math board in use. I found this idea on Krista Wallden's Teachers Pay Teachers website. Students create number sentences using numbers that are touching in some way, i.e. sides or corners. This activity is a great way to differentiate for students because the length of the number sentences they create is based on their individual ability and understanding of the task. This activity can also be transformed into a class game where teams of students complete to create number sentences and earn points based on the length of the sentence. 

Spooky Math Problem Solving

Looking for some great problem solving to get your class in the Halloween spirit? Check out my new "Spooky Math Problem Solving Pack." You can read a product description and see sample pages at http://bit.ly/FBHalloweenPack. Check it out!

Doing Math the Routty Way: Engaging Activities from A to Z (Day 19)

Tune Time- Math songs are a great way to differentiate instruction for your auditory learners, as well as, present your math curriculum in a fun and engaging way. There are a variety of ways to integrate songs into your everyday math program: 
* teach/ reinforce a concept
* provide a brain break for the students
* encourage the memorization of a skill 
* extend a challenge for students to create their own math songs

There are many resources available for songs. A quick Google search will bring up a plethora of songs and videos. Here are a few resources that I would like to share: 

• Lory's 2nd Grade Page (Math Songs by Lory- Free Download)

• Mr. R's Math Music Videos

• Math Music- from Mathwire.com

• Kay Smitherman also has some great song books called Math Notes. You can check them out at www.amazon.com. I love her measures of central tendency song. When I assess this skill, I can see and hear some of the students singing it to themselves. 

The song below is from Lory's 2nd Grade Page. It's a great song to reinforce the different ways that we represent time. 

Doing Math the Routty Way: Engaging Activities from A to Z (Day 18)

Salute- This is one of my favorite activities! It's a great way to reinforce math facts and have some fun at the same time. 

Here's how to play: 

1. Use a set of large playing cards or create a set on large index cards. For this activity, Aces = 1, Jacks = 10, Queens = 11, and Kings = 12. The Jokers can be removed from the set or you can make them another one of the numbers. (Be sure to write the value of the face cards on the board for the students to see or take the face cards out of the deck if your students are not able to recall the values.)

2. Call two students up to the front of the room. Hand each student a playing card. 

3. Ask the students to hold the card face down in front of them. Students should not look at the card. 

4. The students then stand next to each other at the front of the room. 

5. On the teacher’s cue, the students hold the card up to their foreheads with the front of the card facing the teacher and the audience. 

6. The teacher looks at the students' cards and tells them the product of their numbers.  

7. When the teachers says, “Salute!,” both players face each other, look at the other person’s card, and try to guess the number that is on the front of their card. 

8. The first player to guess their number correctly is the winner of the round. 

Variations: 
a. Use addition for younger students. 
b. Try using three cards/digits for a multiplication or addition challenge. 

Clipart courtesy of: http://www.teacherspayteachers.com/Store/Krista-Wallden

Doing Math the Routty Way: Engaging Activities from A to Z (Day 17)

RACE and JUSTIFY Problem Solving Model- Many of our students struggle with word problems and problem solving. To better help them, I developed a more concrete structure for guiding students through this process. I have two packs available at my Teachers Pay Teachers Store to support this goal.

For more information about these models, please read below.

This problem solving model uses an acronym for the word RACE to guide students through the problem solving process. This model is designed for lower elementary students. You can find more information about this pack, as well as, a link to a sample freebie here.

This problem solving model uses an acronym for the word JUSTIFY to guide students through the problem solving process. This model is designed for use with older students. You can find more information about this pack, as well as, a link to a sample freebie here.

Doing Math the Routty Way: Engaging Activities from A to Z (Day 16)

Quiz Ball- The quiz ball is a great brain break strategy when your students need a kinesthetic movement break! 

Here's how to create one: 
1. Get a soccer ball. 
2. Label each section of the soccer ball with a computational fact or a question using blank labels. 


Here's how to play: 
1. Have students make a circle around the room. 
2. Toss the ball to a student and have him/her catch it with both hands. (The section where their right thumb lands is the question the student needs to answer.)
3. The student reads the question or problem aloud. 
4. The student answers the question or problem. 

The quiz ball works great for reinforcing many skills. Here are some ideas: 

• Program the ball with single-digit numbers. Have students add or multiply the numbers in the spaces where their thumbs land.
• Program the ball with subtraction or division facts.
• Program the ball with numbers that can be rounded to a variety of places. 
• Program the ball with vocabulary words.
• Program the ball with integer problems. 

The quiz ball below has integer addition and subtraction problems. I actually just wrote on this soccer ball with a dry-erase marker. For this activity, students could answer the problem under their right thumb or the left thumb if the right thumb is covering a black space.  

Doing Math the Routty Way: Engaging Activities from A to Z (Day 15)

Puzzle Box- We all have those fast finishers who seem to finish all of their work well before we need them to be finished. If not managed carefully, these situations can become discipline problems. One of the strategies that I use to manage this issue is called the Puzzle Box. I use a file crate with labeled file folders to maintain the puzzles and place the crate in a central location in the classroom. 

When students are finished with their work, they choose a puzzle from the box to complete. Some of the puzzles are quick; others take much longer. I always try to have a variety of different puzzles available and replace them periodically. When students finish a puzzle, they submit it to me for review, and I give them a reward of some sort, like classroom cash. I've also included the puzzles on my math menus, so students will collect the puzzle along with their other artifacts until they have completed the menu board. 

My favorite puzzles come from the AIMS website. Click here to look through their problem solving and puzzle books. I use the Solve It! book series, Puzzle Play book, and Blockout! book to fill the box. (I'm not advertising for AIMS, but they are transitioning from print materials to digital copies and are offering all of their print books for a substantially discounted rate, 60% off in most cases. Be sure to check it out!)  You can also sign up for their free newsletter here. It includes links to free activity and puzzle downloads, usually sent out once a month. 

In addition to the puzzle box, the students have access to manipulatives and other tools that may be needed to complete the puzzles. For example, for the Blockout puzzles, I provide overhead color tiles so that the students can cover the squares with the tiles to test their solution before they color the squares with markers. Some of the puzzles also require the use of toothpicks, which I make available as well. 

View examples of the puzzles in action below: 

The activity above is from the Blockout! book. This activity challenges students to create the number at the top of the page using the numbers in the large square. All numbers must belong to an arrangement of adjacent, touching, small squares that equal the number. The large squares get bigger in order to continue challenging the students. 

The activity above is from the Solve It! 4th book. This activity challenges students to complete the boxes with a designated set of numbers that match the clues below each square.