# Introduction to Combining Like Terms

Last week my 7th grade students looked at combining like terms.  As a visual introduction, I handed each student one of three different colored  “tickets” to a Giants game.  I presented the students with this scenario: “An anonymous donor bought tickets for the entire class to go to a Giants game.  Unfortunately, not all the seats are in the same area.”  I put a map of MetLife stadium on the board showing the different seating areas. The different colored tickets showed the seat number, level, and the price of the ticket.   Green tickets were seats in the upper level, yellow tickets were seats in the mezzanine level, and orange tickets were seats in the lower level.  After getting in groups of four, I had the the students find out how much the donor paid for all of the tickets.  Each group had to write their answer on a small whiteboard.  After about 4 minutes, I had each group put their whiteboard on the front ledge so that we could discuss it as a whole class.

The conversation went something like this:

Me:  What did the donor pay for all of the tickets?

Student: \$4200.

Me:  How did you come up with that amount?

Student:  The oranges tickets cost \$2400, the yellow tickets cost \$1200, and the green tickets cost \$600.

Me:  What do you mean?

Student:  There are 6 orange tickets, 4 yellow tickets, and 6 green tickets.  Orange tickets cost \$400, so \$400 times 6 is \$2400.  Yellow tickets cost \$300, so \$300 times 4 is \$1200.  Green tickets cost \$100, so \$100 times 6 is \$600.

Me:  Why didn’t you just add the total number of tickets and multiply that number by \$400? or 300? or \$100?

Student:  Because the different colored tickets are worth different amounts.

Me:  So, why can you only combine the yellow tickets with other yellow tickets?

Student:  Because they are all worth the same amount.

Me:  And why can you only combine the green tickets with other green tickets?

Student:  Because they are all have the same value.

Me:  And what about the orange tickets?

Student: You can add the orange tickets together because they have the same value.

At this point I introduced combining like terms with variables and constants.  Each time a student tried to add something like 3x + 5 + 2x to get 10x, I reminded them of the different colored tickets.  For instance, the 3x and the 2x are like the green tickets and the 5 is like the yellow ticket.

After we worked on a few problems in our interactive notebook, students worked with a partner to play a Combining Like Terms Dice Activity.  I put stickers on a pair of wooden dice.  On one die were different coefficients (positive and negative)  with the variable x and on the other die were different coefficients (positive and negative) with the variable y.  Students had to roll the pair of dice twice and write down the terms in the squares on the handout and then combine like terms.  After completing four problems like this, they had to combine the answers of #1 and #2 together, and the answers for #3 and #4.

Partners would work on the problems independently and then check answers with each other.  If they got different answers and could not agree, they could raise their hands to ask me for help.

After these two activities, I felt students were ready to tackle similar problems for homework.  I wish I could incorporate visuals and games with every new concept!

I would love to hear about anyone else’s way to introduce combining like terms.  Please share!

# My Favorite: Spider Match

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.

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.

# Slope and Scavenger Hunts

It’s been a long time since I’ve written a post.  However, the MTBos 2016 Initiative has gotten me inspired to get back into blogging.  I was also encouraged by Kate Novak’s blog to write about the basic stuff.  These types of posts appeal to me especially since I am more of a small projects type of teacher.

I like activities that have little preparation and get students out of their seats.  Scavenger hunts fit the bill on both counts.  The most recent scavenger hunt that I have done with my 8th grade pre-algebra class is Finding the Slope of Two Points on a Graph – Scavenger Hunt.  All I had to do was print off the cards, laminate them so I could use them again, hang them up around my classroom, and print a copy of the recording sheet for each student.

Sure, students could just count the number of spaces up/down and to the right/left to find the slope.  However, I told students that I wanted them to give me the two ordered pairs that corresponded with the points on the graph and then to find the slope by using the change in y over the change in x.

To help with organization, I printed off a 4 x 3 blank table on the back of the recording sheet so they had a spot to to complete each problem.  When students got stuck, they or I could easily go box by box to see where they made a mistake.

This year I bought enough clipboards for each student.  This has made a big difference in the neatness of their work.  Now, instead of students using the wall or several students trying to cram their papers on one small desk, students have their own work space.

What a great way to get students to do 12 problems while being able to move about the room!

# 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.

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.

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

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

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.