Getting Students to Work Together in Cooperative Groups

One of my colleagues completed a Leadership Project with her ten students that I want to share with you. She had two similar 100 piece puzzles. (The puzzles are fairly inexpensive at Walmart or Dollar General.) Kay took these two similar puzzles which had alike colors/pictures on them and mixed them up. She then separated them into two baggies, and put each baggie in one of the original two boxes.

The class numbered off, 1-2-1-2...and so on, and then separated into two groups. At first, the students thought this was going to be a race to see which group could complete their puzzle first; however, each group started at the same time, writing the starting time on the board. After that, Kay didn’t say a word, and answered no questions! She simply observed the students. The students tried asking her, "Hey we don’t have all the edges; these pieces don’t match; are these the right puzzles?" Something is wrong; what's up?"

Kay waited to see who would take the lead to combine the groups, and how they joined. She wondered, "Would they join peacefully? Would they gather and form one group; two new groups; work together, or divide again?"  As she continued to observe, she began to write names on the board of those who were positive and took leadership. She then wrote the time on the board when they commenced to form one group.

When they finished, she held a Socratic Seminar (an Avid strategy) about how they felt concerning the activity. One student, who did not want to join a group in the beginning, became so involved during the project that he actually was the leader in getting the groups together.  It was one of those fantastic teacher moments!

Kay's students learned quite a bit from the activity since in reality, this is how life, social, and work environments are. She pointed out that they may not have a project that is going well, but by joining together with another group, you can problem solve, gain assistance, and acquire more pieces to your puzzle to accomplish your project.

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Since working together doesn't seem to be a skill that comes naturally, I use this activity with my college freshman as they begin their final group projects. Plus, as you think about your class and are puzzled about how you can get your students to work well in cooperative groups, keep this activity in mind.  It might just put the pieces together for you.

If your class enjoys cooperative learning, try this rubric for grading co-op groups.

Looking For and Analyzing Mathematical Patterns

Mathematics is the science of patterns.  In this post, I want to target some mathematical problems in which we investigate developing patterns.

In the first example below, you will notice we begin by multiplying one by one; then 11 by 11, and so forth. Each time we multiply, the number of digits in the multiplier and the multiplicand increases. Do you see the pattern that progresses in the answer (product)? Notice how this multiplication pattern forms a triangle? Can you figure out what kind of triangle this would be if we added a "peak" or a row at the top?

Here is another interesting pattern. In this one, instead of multiplying by 1, then 11, then 111, the answer (product) looks like the multiplier in the pattern above. Do you notice anything else significant?

Yes, we are multiplying by 9 each time. Now look at the number being added, and count the number of ones you see in each answer. Surprised? Isn’t it amazing how math is ordered, methodical and precise? Maybe that is one reason I love to teach it! Encourage your students to look for and make sense of math patterns and structure in order to deepen their mathematical understanding and retain what they learn.

Using Mathematical Patterns to Problem Solve

In this post, I will present two patterns for you to look at with the hopes that you will try to dissect them and be able to answer a few questions.  Are you ready?  Here is the first one that I call Consecutive Number Series.

What counting pattern do you see in this sequence?  How would you describe the sequence of numbers that are being added?  What pattern do you see in the answers?  Can you figure out the pattern for 8 × 8 and 9 × 9?  Notice this pattern made a triangle.  Do you know what kind it is?

My next pattern I call The Eights, and you will readily see why. It, too, forms a triangle, but a different kind. Do you recognize this triangle as isosceles?  If you take a ruler, you will find that the base is 4" while the sides are both 3".

What do you think will happen if we take this same pattern and add a 0?  Notice that this pattern does not begin with adding an eight.  Can you figure out why?

I use this type of patterns with my remedial math college students because I consider it important to do some problem solving while recognizing and describing patterns.  After all, problem solving is a part of life.  It doesn't occur in a vacuum. Because students must reason about some specific content, I think patterns are a great place to begin.  Problem solving also helps students to make connections to other parts of mathematics and find some relevance to what they are learning.  And did you know, that problem solvers are typically better test takers?  So take these patterns, and create some of your own questions for your students.  Use them in a journal or as a small group activity.  But whatever you do, have fun learning and discovering patterns in math.

Using Math Riddles to Reduce Fractions, Recognize Equivalent Fractions, Identify Basic Percents

Do you need something besides a “drill and kill” activity to practice fractions and/or percents? This fraction riddle bundle is my newest bundled resource. It is a 33 page resource that is a fun and engaging way to utilize math concepts while keeping the students actively involved. 

Specific words are provided. The students are instructed to figure out the correct fractional part of each particular word. (Example: The first ½ of WENT would be WE. Notice that WE is also 2/4 or 50% of WENT.) If each fractional part is correctly identified, when the students write the fractional parts on the lines provided, a new word is created. Each group of new words becomes a riddle or the answer to a riddle.

It is important that students understand that a fraction and a percent represent the same thing; so, in the Snow Riddles handout, 25%, 50%, 75% and 100% are introduced.

 In March Riddles, specific questions are asked to acquaint the students with fun facts about the month of March. April Riddles introduces the students to several interesting historical facts that occurred during this month.

For each month, there are between 7-11 word fraction riddles; so, there are numerous ways to practice recognizing fractional parts, understanding equivalent fractions, identifying basic percents (25%, 50%, 75% 100%), and reducing fractions to lowest terms.

Instead of completing all of the monthly riddles in one day, the puzzles may be divided up and used as a focus activity, when a student finishes early, or when there is a short amount of time left before the next class or activity. An individual puzzle may be given each day, or the riddles can be interspersed throughout the week or month. Answers are included at the end of each month’s activities. The complete resource features six months (January, February, March, April, October, December) and contains a total of 49 fraction riddles.

If you prefer, each month of fraction riddles may be purchased separately; however, this resource bundles all six months for a discounted price. Just click the title under the cover page shown above, and download the preview to take a quick look at this new item.