Category Archives: Algebraic Expressions

Making Thinking Visible with a Card Sort

I am a firm believer that students need to practice math concepts again and again for them to become proficient.  Some students may need more practice than others, but everyone benefits from the review.  Worksheets are good when there is not a lot of time, but they can be quite boring!  However, give a student a pair of scissors and some glue and now they are engaged.  That is what I like about Jacquie’s Expanding and Simplifying Card Sort.  There are six problems for students to simplify using the distributive property and combining like terms.  The problems are similar enough that you must do the work to figure out the answers.  I wanted the pieces to be bigger so I retyped the problems in Keynote and put a border around each expression.  (Don’t worry,  I first purchased Jacquie’s set and I am not looking to sell my version.)

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I thought this would be a great activity on a day that I wouldn’t be at school.  I gave instructions for the substitute teacher to read to the students, along  with all of the materials.  Unfortunately, students seemed to glue pieces in random order.  By just looking at the papers and not knowing what went on while I was away, I’m not sure if the students did not fully understand the directions or they just didn’t want to do the work.  I do not fault the substitute teacher or the students.  Rather it got me to thinking, what could I do better to keep all students accountable for actually doing the problems and for me to see the students thinking?

So, I re-ordered the cards on the handout so that the problems were in the first two rows, the middle steps were in the next two rows, and the final expressions were in the last two rows.

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Instead of giving students all of the pieces at the start, they would only be given the initial problems to cut out and glue on their paper.  Then they would have to work out the distributing and show me their work before getting the next set of cards.  Students would be able to check their answers when they cut and glued these cards underneath their work.  Finally, they would combine like terms and show me their final expressions before getting the last of the cards.

In the end, students still get to use the scissors and the glue.  However, I can quickly glance at each student’s work to see who understands the concepts and if not, where they are making mistakes.

 

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Expanding and Simplifying Algebraic Expressions

This week, my 8th grade Algebra class will be having their first test.  Two topics that I want to review with them again before the test are the distributive property and combining like terms.  Jacquie of Mathematters has a great cutout activity that I use with my 8th grade pre-algebra class.  However, I wanted something that would take less time but still have the students engaged.  Also, I wanted the activities to make their thinking visible.  So I made a handout using the same idea, but students have to draw arrows to the correct corresponding step instead of cutting and glueing the pieces in the proper order.

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Here is an example of a student’s work:

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I was able to go around the room to see that students were showing their work with the distributive property and then circling and boxing in like terms to get the final answer.

After that, students worked in groups to figure out the errors in this free handout from Secondary Math Solutions.

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Students had to locate the mistake, as well as explain how to correct the mistake using complete sentences.

In both activities, students needed to either show their steps or write out the process to complete the problems.  Both activities allowed me to see who understood the problems and who needed more direction.  Now for the test…

The Pyramid Game or A Race to the Top

After our #eduread chat and to further explain what I can’t in 140 characters or less, I was motivated/encouraged to blog about a game that I use in my class. I have always called it “The Pyramid Game,” but I noticed that other teachers call it “A Race to the Top”. It is a very versatile game, because it can be used with many different mathematical topics. Here is a great template made by Joanne Miller of Head over Heels for Teaching. I like to use a smaller version of this when I do not have that much time.

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I have students draw five lines on the bottom row, four lines on the next row, until they have one line on the top row.

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I give the students the numbers for the bottom row. Usually, I give them every other number until we are all ready to go.

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Then I fill in the other two numbers and tell them if they are adding, subtracting, multiplying, or dividing.

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If they are adding, students add the two numbers next to each other and put the answer on the line above. They complete each row the same way until they get to the top. For incentive in my class, the first five students with the correct answer get a piece of candy. Each time, I stand in a different spot in the room to make things fair in their eyes, and students come up to me so I can see their answer.  If it’s correct, I say, “Number 1” for the first correct answer, “”Number 2” for the second correct answer, until I have five or so correct answers.  If a student has the wrong answer I tell them to try again and they go back to their seat to re-work the problem.  Ihave used this with integers and algebraic expressions with great success. Also, it is a great way to spiral back to review these concepts throughout the year. Please let me know if you use this game in another way, because I am always looking for ways to keep the students engaged in a fun and easy to prepare activity.