Summer PD

Check out my new 8-week Summer PD series beginning Wednesday, June 1st! 

Solve It Friday!- Task #35

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:

#RMTSolveItWeek35: There were 20 red fish, 10 green fish, and 6 yellow fish.  

Thursday Tool School: Critical Thinking Tools- Games

Thank you for reading my "Thursday Tool School" series. Today's post marks the last "Thursday Tool School" 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 one of my favorite critical thinking games. It is sure to keep your students engaged in these last few days as it is open-ended and can meet the individual needs of your students. "Make 24" is a game that promotes problem solving skills when students use four numbers to add, subtract, multiply, and divide their way to the number 24. 

Freebie Alert! Grab a free copy of this game here. 

Sound Off! What are your favorite critical thinking games?  

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 #34

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:

#RMTSolveItWeek34: There are 7 ways for the girls to spend exactly $2 on candy and chips: 20 candies and 0 chips, 17 candies and 2 chips, 14 candies and 4 chips, 11 candies and 6 chips, 8 candies and 8 chips, 5 candies and 10 chips, or 2 candies and 12 chips.  

Transformation Tuesday: Critical Thinking Tools- Pattern Blocks

In September 2015, my Thursday Tool School series titled, "Critical Thinking with Pattern Blocks" introduced using pattern blocks as a critical thinking tool. (Read the original post here.) Today, I would like to rewind to that series and take another look at how pattern block activities can be used to increase your students' critical thinking skills. 

Click the image to read the post!

Here's a short summary of the purpose of pattern blocks. A set of pattern blocks contains six basic shapes: a yellow hexagon, a red trapezoid, a blue rhombus, a green triangle, an orange square, and a beige rhombus. The pieces are proportional to each other which extends the number of ways in which they can be used. 

My favorite activity from my "Critical Thinking with Pattern Blocks" series is "What's the Common Attribute?" This activity can be used year-round and makes a great starter activity, especially during that your geometry unit. The only prerequisite skills needed are some basic vocabulary terms related to shapes, i.e. sides, angles, congruent, equal, etc. I created a freebie pack of tasks to accompany this activity. You can find a copy of the freebie pack with the original post!

Click the image to read the post!

The next activity was inspired by an article in the August 2015 edition of Teaching Children Mathematics. It involves having students determine the cost of each element of a pattern block design given the total cost. This task provides the foundation for essential algebraic thinking skills and offers a high-level problem solving task with multiple solutions. You can find a copy of the activity page with the original post. 

Click the image to read the post.

The next activity is similar to the common attribute task above. For "Odd One Out," you display four of the pattern blocks. Students study each figure and determine which shape is the "Odd One Out." The caveat-- there isn't necessarily one right answer. In fact, the name of this game is critical thinking. The goal is for students to scrutinize each shape and use discrimination to isolate one shape 

from the group.

Click the image to read the post.

The next activity emphasizes logical reasoning to determine in what order to place a collection of shapes. For "Pattern Block Line-Ups," students try to place pattern blocks in the correct position using a set of clues to find the correct placements. This activity is a great way to integrate vocabulary and build critical thinking skills at the same time! You can find a free set of frames with the original post!

Click the image to read the post.

Pattern blocks. Fractions. No way! Yes, way! My favorite way to use pattern blocks in the classroom is to teach fractions. The red trapezoid, blue rhombus, and green triangle all fit proportionally inside of the yellow hexagon, which makes them great tools to use to model fractions.

The last activity is called, "What's the Whole?" and supports students' understanding of the 'whole' when compared to the 'part'. Specifically, this activity requires students to view a whole as more than the area inside of a single space, such as the hexagon; it helps them understand a whole to be a unit, as defined by the size of each part. You can grab a free copy of this activity sheet with the original post!

Freebie Alert! Be sure to check out the series link here for freebies and printables to accompany this series! 

Sound Off! How do you use pattern blocks in the classroom? 

Transformation Tuesday: Engaging Critical Thinking Activities- The Puzzle Box

Throughout the month of May, I am highlighting my favorite critical thinking activities to help keep your students engaged during these last few weeks of school. Today's activities are critical thinking puzzles and have been among my students' favorite activities. While I tend to find puzzles everywhere, my favorite source for puzzles is AIMS Education's Puzzle Corner. Check it out here. 

I use puzzles in many different ways, such as for fast finisher activities and menu work. I keep them in a file box that I call The Puzzle Box. The box has hanging files inside where I store all of the puzzles. Storing the puzzles this way serves several purposes. First, it keeps all of the puzzles in a convenient location. Second, it allows students to search for a task that matches their ability level. For this reason, I keep the puzzle box at the back of the room on a shelf with a variety of manipulatives, like centimeter cubes, toothpicks, and pattern blocks, students can use to support them while they are working through the puzzle tasks. 

During this time of year, puzzles can be a great whole-class challenge where students work with a partner to complete the tasks, or they can be used as individual or fast finisher challenges. Because understanding the puzzles can initially be a challenge for students, you can remove this barrier by introducing one or two puzzles at a time and giving the students time to play with the task before placing them in the box. Students can then determine whether or not to continue with the challenge or to try another puzzle. I typically introduce two or three new puzzles during each grading period and then add them to the box for students to complete throughout the year. 

The students love the puzzles and when they find the right "fit," they are willing to invest the time to complete the task. After students complete a puzzle, I review the work and provide a reward of some sort, such as extra credit, classroom cash, etc, for correct solutions.

Below are two examples of the puzzles I include in my Puzzle Box. 

This puzzle came from an AIMS book called Solve It! 4th where students use the clues
 to complete the boxes with specific numbers. 

The picture below shows a Blockout Puzzle from AIMS where students shade adjacent boxes 
whose sum equals the number above the large square, i.e. 9a, 9b, 9c, or 9d.

Here are some of my favorite AIMS puzzles: 

• Goalpost Puzzle

• The Frustrated Farmer

• Linking Bridges

• How Many Squares?

• The Eight-Digit Puzzle

• Flipping Fish

• Penny Pinning Puzzle

Note: To use them, copy and paste the problem into a word processing document or print the downloadable activity sheet. 

Freebie Alert! You can also find a variety of activities to include in your puzzle box using the "Problem Solving and Critical Thinking" link my file cabinet. Click here to check it out!

Sound Off! Which puzzle is your favorite? Why?

Solve It! Friday- Task #33

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:

#RMTSolveItWeek33: The pattern is add five and subtract three. There will be 31 people in line at 6:00. 

Thursday Tool School: Critical Thinking Tools- Dominoes

This month, I am highlighting critical thinking activities to keep your students engaged during these last weeks of the school year. There are many ways to infuse critical thinking into your everyday curriculum, including through games. Today's critical thinking tool is a set of dominoes-- a versatile tool that has many purposes. Dominoes may not be a standard math tool, but they are great to have laying around. If you don't have any in your classroom, you can pick some up at the dollar store (usually one dollar per set). 

I'm sharing two domino activities with you today. The first one was featured on my blog back in October and is called "Boneyard Numbers." (Read the original post here.) This activity is oozing with critical thinking and can be adapted to meet the needs of all students. 

Here's how it works: 

1. With a partner, spread-out one set of face-down dominoes. This is called the boneyard.

2. The tallest player goes first.

3. In turn, each player grabs two dominoes from the boneyard. 

4. Using the four numbers indicated on the dominoes, create a number sentence using addition, subtraction, multiplication, and/ or division with a final result of any number from 0 to 12. Note: Students can use one operation or any combination of the four. 

5. Once a target number is reached, cover the number on the game board with your marker. 

6. Continue playing until someone covers four numbers in a row, column, or diagonal. 

Note: Some students will ask if they can use exponents. This is completely up to you. I sometimes tell students that they can only square numbers. Squaring a number does not affect the four digits on the dominoes and can be used even if the student's set of dominoes does not include a two. 

Free Resource Alert! Grad a copy of this game here. 

The second activity was featured in the November 2016 edition of my newsletter "Teaching Tidbits" and is called "Balance the Bones. In this domino game, partner duos use their critical thinking skills to create equivalent expressions with the numbers on four dominoes. This game emphasizes the use of the equal sign as an indicator that both sides have the same value instead of as a directional symbol to show that one set of operations leads to a single-number value. This game supports students' understanding that the equal sign shows balance between the expression on the left and the one on the right. 

Here's how it works: 

1. With a partner, spread-out one set of face-down dominoes. This is called the boneyard.

2. In turn, each player grabs one domino from the boneyard. 

3. Using the eight numbers indicated on the four dominoes, teams create two equivalent numerical expressions using addition, subtraction, multiplication, and/ or division. See the example below. Note: Students can use one operation or any combination of the four. 

4. Teams record their expressions on their whiteboard and the round is won when a team correctly records a set of equivalent expressions. 

5. Continue playing until a team is able to create the most sets of equivalent numerical expressions after five rounds.

Free Resource Alert! Grad a copy of this game here. 

Both of these domino games make great station and fast finisher activities while infusing critical thinking into your curriculum. 

In addition, they can both be modified to meet the needs of a variety of students because students choose which operations to use based on their own abilities. 

Sound Off! What are your favorite domino activities?

Transformation Tuesday: Critical Thinking Activities- Math Boggle Board

As we inch closer and closer to the end of the year, it’s important to keep our students engaged. The more engaged they are in tasks that are both developmentally appropriate and challenging, the less off-task behavior they will display. With these two goals in mind, today’s activity is called Boggle Math. It’s similar to the traditional Boggle game except that students create number sentences instead of words. 

I originally found this idea on Krista Wallden's Teachers Pay Teachers website. 

Here's how it works: 

1. Create a Boggle board with an empty bulletin board space or on poster board. See the picture below for an example. (Depending on the needs of your students, a larger or smaller square can be created as needed.)

2. Students look for and create number sentences using numbers that are touching in some way, i.e. sides or corners. 

3. Students earn points based on the difficulty and length of their number sentence, such as one point for each unique operation, one point for each additional number after the first three, and one point for each number that is squared. See the solutions below for an example.   

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 then earn points based on the length of the sentence. 

Note: I originally wrote about Boggle Math as part of my "Doing Math the Routty Way: Engaging Activities from A to Z. See the post here. 

Sound Off! What number sentences can you make using the Boggle Math board above? 

Solve It! Friday- Task #32

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:

#RMTSolveItWeek32: The value of each symbol is as follows: flip flop = 1; sun with popsicles = 2; sunglasses = 4; beach ball = 6

Thursday Tool School: Critical Thinking Tools- Tiling Tasks

As you may have seen from this week's Transformation Tuesday post, the theme for this month is critical thinking. Using critical thinking activities is an awesome way to keep the students engaged at this point in the school year. It's also a great way to enhance grade level content without reaching into the next grade level's content and skills. Therefore, Thursday Tool School will feature some of my most favorite critical thinking tools. Today's tool for this Thursday Tool School (on a Friday) is tiling tasks.

I first introduced tiling tasks in my "Doing Math the Routty Way: Engaging Activities from A to Z series. (Read the series here.) Tiling task cards make great menu activities or fast finisher challenges. Using tiling tasks in the classroom offers you an opportunity to increase the critical thinking skills of your students because they must use their strategic knowledge in order to determine where to place each tile. 

Here's how to use them: 

1. Give each student a set of number tiles, a set of numbered tiles 0-9, to complete each task card. 

2. Students use their reasoning skills to complete the task cards. Each tile belongs to one space and only one space. As you can see in the task below, there can be more than one way to represent each problem, but only one combination of numbers will work. 

Free Resource Alert! Grad a copy of this tiling task here. 

Note: A set of tiles can be downloaded here. Copy them on card stock for easy use.

This tiling task is included in my Order of Operations: Activities and Games After Math Pack in my Teachers Pay Teachers Store. 

Want More? Marcy Cook's Tiling Task Cards are some of my favorite resources! She has a whole collection of these cards for a variety of skills. In addition, here are some free tiling task resources that I discovered from Teachers Pay Teachers. Check them out! 

• Number Tiles: Free Sampler of 5 Puzzles
• Math Tiles: Free

Sound Off! What are your favorite tiling tasks resources?

Transformation Tuesday: Critical Thinking Activities- Weight Logic

Click the picture to see the pack in my store.

It's Transformation Tuesday on a Thursday! I've been buried this week trying to finish the first draft of my dissertation proposal. It's finally done and I've been singing, "Celebrate good times, com'on," since pushing the send button earlier this week! 

This month for Transformation Tuesday, I will feature problem solving and critical thinking activities to keep your students engaged during these last weeks of school. Managing student behavior at the end of the school year can be a challenge for even our most experienced teachers. Trust me when I say that keeping them engaged is how to win the battle. 

With that in mind, today's activity has been a class favorite for my students over the years! It's called Weight Logic. Logic puzzles help students develop solid critical thinking and problem solving skills in the early grades. This is essential to support higher-level mathematics in the later ones. Problem solving and critical thinking activities can be infused in a variety of ways. The most important thing is to get our students thinking and communicating about their thinking as often as we can. 

To complete the weight logic puzzles, students use the sum of the symbols shown on the scale to determine the value of each symbol. For many students, this task seems simple. You guess and check the values until you find a combination that works. But that level of thinking is just the beginning. The real critical thinking comes in when students use strategies, other than guess and check, to determine the value of each fruit. 

For example, on puzzle #5 (to the top right), if students recognize that the watermelon and two strawberries on the left side are included in the two pieces of watermelon and two strawberries on the right side, they can subtract the 10 on the left from the 12 on the right to see that the leftover watermelon slice has a value of 2. Once they know that, they can determine the value of the strawberry. How's that for fostering algebraic thinking in elementary school!

For puzzle #6 (to the bottom right), students recognize that there are three watermelon slices on the right whose total value must be a multiple of three. The only multiple of three that is less than five is 3. If students subtract 3 from 5, then you discover the value of the bunch of grapes is 2 and the value of the lemon slices is 1. Students can then double-check their values using the left side to see if their solution works. 

How awesome would our students be if they could articulate that level of thinking? It will take time for students to arrive at these solutions, but once they've mastered guess and check, encourage them to look for other ways to solve the problem. Be sure to have students share their solution strategies with other classmates as well. 

Freebie Alert! Click here to see the pack in my store and download your own copy. 

Like this pack? 
Check out my Valentine's Day Freebie and save it for next year!

Click the picture to see the pack in my store!

Sound Off: What strategies would your students use to solve these types of problems?