Category Archives: Integers

Discovering the Pattern of Multiplying Negative Numbers

After reading Making Thinking Visible by Ron Ritchhart this summer, I knew I wanted to get students more engaged in the learning process.  I need to start talking less and have students discovering and writing more.  To be honest, this will be a challenge, so I will be taking small steps this year to accomplish this goal.

In a previous blog, I mentioned that I was making changes to my 7th grade math curriculum.  However, I noticed a spot in my 8th grade Pre-Algebra lesson plans where I could easily make a small inquiry-based task to get rid of direct instruction.  This week my 8th grade Algebra students were reviewing how to multiply real numbers.  In 7th grade we dealt mostly with multiplying only two numbers so my 8th graders were familiar with the rules that if two numbers had the same sign, their product was positive and if two numbers had different signs, their product was negative.  However, in 8th grade Pre-Algebra, this concept is extended to multiplying more than two numbers.  I wanted them to see that there is a pattern to multiplying with negative numbers. Rather than just tell them that the product of an even number of negative numbers is positive and the product of an odd number of negative numbers is negative, I wanted students to discover the pattern.  I made this handout for the students to help them come to that conclusion on their own.

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Students were given 5 minutes to work independently.  Then they got in groups of 4 and discussed their answers for another 3 – 4 minutes.  Finally, we met as a whole class, at which point we could write out the rules in our notebook.

It didn’t take a lot longer for students to work through the handout, but I know that the extra time was worth it because all students were working to find the answers, rather than just copying what I wrote down on the board.

Like I said, small steps, but with each step I hope my students will have greater understanding.

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My Favorite: Spider Match

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Today, I want to share one of my favorite games for students to play to strengthen their adding and subtracting skills with integers. It is called Spider Match.

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The object of this multi-player game is to grab as many pairs of flies that add up to the number in the middle of the spider web before your opponents see the pair.  The student with the most matches wins the round.

The game can be played with up to four people. So to start, I group my students according to ability and have them move their desks so that they are sitting near each other.  One student is in charge of setting the game up with a password and setting it up as a private game.  The person in charge then gives the password to the other students in the group so that they can enter the game.  After a few rounds, I change the groups and have all the winners play each other, the second place students play each other, etc.

Usually I have students play this game while we are studying integers.  However, this game would be great to use on the day before a break when it is hard to keep students focused.  I hope your students enjoy the game as much as mine do.

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.