Transformation Tuesday: Cooperative Learning- Fact or Fib

This month, I will be focus on engaging instructional strategies that incorporate cooperative learning structures. For this first full week of October, I want to feature a strategy I just recently learned about while creating an activity for some teachers with whom I work. The activity is called "Fact or Fib" and is an adapted Lead4ward instructional strategy. 

What I love about "Fact or Fib" is how the structure of the activity focuses on students' understanding and justification of a standard or skill. Students must have an example, or even better, a counterexample, to illustrate their answers. 

Here's how it works: 

1. Group students in group of 3 or 4.

2. Give each student the "Fact or Fib" desk tent or have students write "fact" and "fib" on individual index cards. 

3. Give the students a statement based on the current standard or skill. For example, "When you multiply two numbers together, the product is greater than the two factors that were multiplied together*." 

4. Give each student think time to determine whether the statement is a fact or a fib. Then have students create examples or counterexamples to justify their response on a whiteboard. 

5. Once all students have written justifications, each student displays his/her desk tent to show whether they believe the statement to be a fact or a fib. 

6. In turn, each student states whether the statement is a fact or a fib and gives his/her justification.

7. After all students have shared, the group should come to a consensus and have several examples or counterexamples to support the group's decision. 

8. Each group shares their consensus with the class. 

9. After all groups have shared, verify and/ or clarify student responses addressing misconceptions where needed. 

10. Repeat the process with another statement. 

Click here to download a copy of the desk tent.

The picture below is an example of how "Fact or Fib" can be used as an assessment tool. It was a bonus to the September "Transformation Tuesday" blog series included in the October edition of "Teaching Tidbits," my monthly newsletter. Click the banner at the bottom of this post to get your copy of "Teaching Tidbits."

Sound Off! How will you adapt this activity in your classroom? Write about it in the comments below!

* CCSSM- 5.NF.B.5.B

Introducing The Routty Math Teacher's Teaching Tidbits Monthly Newsletter

Sign-up here or click the banner below.

Solve It! Friday- Task #5

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:

#RMTSolveItWeek5: The numbers are 18, 20, and 22. 

Thursday Tool School: Critical Thinking with Pattern Blocks

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 for the September series is called, "What's the Whole?" (shown below) 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. In addition, the activity addresses the following Common Core Math Standard: 

3.NF.A.1- Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

Here's how to use it: 

1. Review the students' understanding of a 'part' and a 'whole.' Note: Students need to have some experience with the notion of part and whole before completing this activity.  

2. Give each group of students several sets of pattern blocks. For example, give each student one set of pattern blocks but allow students to work together so that they have access to more than one of each shape. 

3. Allow students an opportunity to explore with the pattern blocks. Students should have some understanding of the relationships that exist among the pattern blocks. If students do not readily note the relationship between the yellow hexagon, red trapezoid, blue rhombus, and green triangle, be sure to bring it to their attention. This will support their work during the activity later. 

4. Give each student a "What's the Whole?" activity sheet (shown below).

5. Allow students an opportunity to work through each problem with a partner. You may want to have students draw a picture of each whole on another sheet of paper with the parts drawn and labeled on the inside. Note: The first few problems are based on the relationships students were exposed to earlier. They are meant to help students understand the idea of the 'part' and the 'whole.' 

6. Review the students' solutions. Discuss how to use the known part to discover the whole. Be sure to discuss whether or not students' views of a whole have changed and any thoughts or "wonderings" they may now have.

Extension: Have students create their own "What's the Whole?" example, exchange it with a partner, and make a small poster illustrating and explaining their solution. 

Free Resource Alert! Click here for a free download of the "What's the Whole?" activity page shown above.

Share your thoughts, opinions, and experiences of this activity in the comments section below. 

Transformation Tuesday: Assessment Strategies- Kahoot!

Today's "Transformation Tuesday" assessment strategy is actually a tech tool. It's called Kahoot!, an online quiz system. What I love about Kahoot! is how easy the assessments are to create. It's very similar to the clickers that many teachers have available to them; however, the Kahoot! format is very colorful (as you can see from the picture) and engaging for students to use. The best part-- students can participate in the assessment from a variety of devices, including laptops, netbooks, tablets, and smart phones. 

Here's how it works:

1. Create a free account at www.getkahoot.com. 

2. Choice the kind of Kahoot! you want to create, i.e. quiz, discussion, or survey. 

3. Create your assessment tool by entering questions or statements and response options. Like graphics? You can insert a graphic of your choice as well. 

4. Add a cover picture and put the finishing touches on the assessment tool. 

5. Launch the assessment.

6. Invite students to join using the game pin on their own devices. 

7. Have fun using Kahoot! and watch your students' results as you go. See the example below. 

Learn more at getkahoot.com

Share your thoughts, opinions, and experiences of this activity in the comments section below. 

Solve It! Friday- Task #4

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:

#RMTSolveItWeek4: The question specifically asks for the amount raised by fourth grade. However, I will provide all of the amounts for your reference: Third Grade- $700, Fourth Grade- $500, Fifth Grade- $400

Thursday Tool School: Critical Thinking with Pattern Blocks

The final pattern block activity I want to share with you is called "Pattern Block Line-Ups." In this activity, 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. 

Here's how it works: 

1. Determine how many shapes to use. Note: Using a smaller amount of shapes may better support the learning of young mathematicians or students who need a more accessible problem to begin. In addition, deciding to give students the entire 6-piece set to choose from is a way to make the task more challenging because students will need to select which shapes to place in the line-up. 

2. Write the clues. Due to the versatility of pattern blocks, there are lots of options for the clues. Besides using sides and angles, think about using color, length of the shape names, or size. Note: You may want to provide students with a work mat. You can find a blank work mat for 3- and 4-box problems here. 

3. Double-check the solution. Sometimes, there may be more than one correct solution based on the way the clues are written. This is a great opportunity to think about ways to encourage your students to check their strategies. Note: I personally like to place the shapes where I think that they go and then re-read the clues to be sure each shape is in the correct place.

4. Use the strategy with the class. You may want to demonstrate this activity by having the students act it out with large shape cut-outs. This provides a terrific opportunity to use a think-aloud strategy while modeling. After students are comfortable with the activity, move to using the work mats. 

Examples of Pattern Block Line-Ups   

Note: The term 'corners' was used intentionally to make the task more accessible to a younger group of learners.

Note: After your students have had the chance to get comfortable with this activity, get creative! Use money, counting bears, number tiles, etc. to mix things up.

Free Resource Alert: Get a copy of a blank 3- and 4-box work mat here. 

Share your thoughts, opinions, and experiences of this activity in the comments section below. 

Transformation Tuesday: Assessment Strategies- Vocabulary Dominoes

For a blank copy, click here. 

Today's strategy is based an activity I recently learned about from Lead4ward. The activity is called "Vocabulary Dominoes". It's one of their high-yield instructional strategies because it allows teachers to provide instruction for specific standards-based content, as well as, stress the mathematical process/ practice standards. Used intentionally, this activity requires students to compare and contrast terms, as well as, look for, analyze, justify, and communicate about relationships. While I may blog about this activity for another "Transformation Tuesday," today's strategy will focus on the end result. 

Here's how this assessment tool works:

1. Program a set of vocabulary dominoes with content-specific math terms. See the picture at the right for an example. Note: I intentionally placed words whose relationships were easily identifiable on the same domino so that students have to explore other relationships.

Domino ends that touch show connections. 

2. Decide in advance whether you want students to create their own arrangement or if you will create one for them to use. Note: There are advantages to both approaches. The first approach allows you to gain knowledge regarding individual student's understanding of the terms; whereas the second method forces the students to make judgments and find relationships based on someone else's thinking. In addition, the second method may take less time because students will not need time to create their layout. 

3. If students are creating their own arrangement, provide them time to cut-out and arrange their dominoes based on the relationships they found between the words. If you are using a teacher-created arrangement, provide students think time to review the layout and placement of the words. 

4. Ask students to write 3 - 4 statements regarding the relationship of the terms based on the connections made. See the picture below for an example. 

5. Review the students' work to support your understanding of where you class is in the learning process and next steps for instruction. In addition, this activity makes for a great formative assessment tool and would fit well in a journal. 

Free Resource Alert: Download an editable copy of the "Vocabulary Dominoes" here. 

To use: Insert the image into a word document. Just add a text box with each word you want to add and place it in the center of each half of the domino. 

Share your thoughts, opinions, and experiences of this assessment tool in the comments section below. 

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. 

Thursday Tool School: Critical Thinking with Pattern Blocks

Today's pattern block activity is called "Odd One Out." In this activity, 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. 

Here's how it works: 

1. Determine which four shapes to use. Note: I find it easiest to choose the four shapes and go through the set to be sure there is a reason for each shape to be the "odd one out". 

2. Display the four shapes. 

3. Have students determine which shape is the "Odd One Out." 

4. After students have had an opportunity to determine an answer, use the "Four Corners" strategy to discuss the students' responses. 

    a.  Assign each shape a corner. Note: Create a 8.5" x 11" size paper to make a poster illustrating each shape on cardstock. Laminate them for durability. 

    b. Ask students to go to the corner which represents their chosen shape. 

    c. Once assembled, have the students in each corner discuss their reasoning to determine if they all had the same idea or if other ideas exist. Each corner should determine which ideas are true for the set to share with the group. 

    d. One group at a time, have each corner share their thinking with the class. 

Variation: Assign each student a letter. Have students determine a reason why their shape is the "Odd One Out." Then have students go to their designated corner and continue with the Four Corners strategy from above. 

Note: For the "Odd One Out" example above, here is my thinking. 

A. The hexagon is the only shape that does not have acute or right angles.

B. The trapezoid is the only shape with unequal sides or unequal angles.

C. The triangle is the only shape without at least one pair of parallel sides.

D. The square is the only shape with right angles.  

Like this activity? Check out this website-- Which One Doesn't Belong?

Transformation Tuesday: Assessment Strategies- Exit Tickets with Understanding

Today's assessment strategy is a kicked-up version of the exit ticket strategy called Exit Tickets with Understanding*. You may be familiar with traditional exit tickets where students complete a problem or write about a skill or concept on a small slip of paper at the end of class. The kicked-up version of this uses the same concept except that students write about their understanding of the lesson objectives. This allows the teacher an opportunity to get a glimpse of where each student is in their thinking about and development of the objectives of a targeted concept or skill.

Here's how it works: 

1. Post the lesson objectives in specific, kid-friendly language. (See the picture above.)

2. Give each student a small slip of paper. Note: I always collect extra copies, unused activity pages and handouts, or papers from the school in a container by the front door. Students are encouraged to use this paper as scrap paper to show work or for drawing. This paper collection is a great way to recycle paper. Just cut it into half-page pieces for the exit tickets. 

3. Students choose an objective, or one suggested by you, and provide evidence of their understanding. For example, ask students to share their thoughts in pictures, words, or numbers. (See the picture below.) 

4. Collect the students' responses. Sort the student responses based on levels of student understanding. Use the feedback to determine the next steps of instruction. 

Want more Fraction Relationship and Comparison Strategy resources? Check out: http://bit.ly/RMTCompareFractionsPreview. 

Free Resource Alert! Grab a copy of my newest freebie, Comparing Fractions with the Same-Size Whole pack from my Teachers Pay Teachers Store!

* Adapted from Lead4ward

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).

Thursday Tool School: Critical Thinking with Pattern Blocks

Today's activity is 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. 

Free Resource Alert: Download a copy of this resource here. 

The Task: 
1. Present the pattern block task. Read the task together and answer any initial questions the students may have before beginning.  

2. Allow student groups time to work through the questions. Note: Students will need more room for question #3. You may want to provide each group with poster paper so that they can illustrate and display their solutions. 

3. Conduct a math talk session to discuss the students' responses. Note: This does not need to be lengthy; just be sure that students have an opportunity to share their work and make connections between solutions. 

4. Use the following questions to encourage high-level thinking and the development of mathematical processing skills: 
* How can you determine the price of each blue rhombus and the orange square?
* What process did you use to determine if there were other price combinations that would work? Are their some processes that are more efficient than others?
* How can you verify if you have found all of the possible price combinations? 
* How can you represent your solutions? 
* Compare your solution to another group's solution. How are they alike and different?
* Do you notice any patterns in your group's price combinations? If so, what are they? How could understanding the pattern help you find all of the price combinations? 

Extension: Create similar tasks with additional designs. Assign a total cost and repeat the activity. 

Reference: 
Fuentes, S. Q. & Quebec, R. (2015). How much do the tiles cost? Teaching Children Mathematics, 22(1), 8 - 11.

Transformation Tuesday: Assessment Strategies- Rock and Roll Math Problems

Today's engaging assessment tool is called "Rock 'n' Roll Math Problems*." This assessment tool encourages student groups to explore various parts of the problem solving process. Here's how it works:

1. Pair students and assign them to be Partner A or Partner B.  
2. Provide each pair with a number cube (die). 
3. Provide each pair with a concept-based word problem or multiple-choice item. 
4. Partner A rolls the number cube and then uses the Rock and Roll activity page to determine which task to complete. 
5. Partner B completes the activity indicated on the number cube using the word problem or multiple-choice item.
6. If Partner A does not understand Partner B's response, Partner A should ask clarifying questions until the response is understood. 
7. Pairs should continue alternating rolls and rolling the number cube until all of the tasks have been completed or for the allotted amount of time. 
8. As a class, have pairs discuss their responses to each of the tasks. Be sure to highlight any responses which reveal essential understandings or new strategies. 
9. Begin the process again with a new problem if available. (Note: Sometimes, one well-developed question is more effective than several basic ones. Be sure to choose a task that will give you the most bang for your buck.)

Free Resource Alert: Download a copy of "Rock and Roll" Math Problems here. 

* Adapted from Lead4ward