Number Line Gallery Walk

My students did poorly last year on number line questions because I did not emphasize the precision and attention to detail necessary to accurately depict a set of numbers on a number line. I was determined this year to find a way to teach this topic more effectively.

This year I started out by showing the students examples of number lines:

After studying these examples, we discussed what elements these numbers lines had and from this discussion we created a number line checklist that students would use to make sure that their numbers lines contained all the elements needed for accurate numbers lines.

Here are some examples of student created number lines. There are some small errors in these number lines, which I did not correct as I circulated during class. During the Number Line Gallery Walk, I wanted students to have the chance to go through the number line check list for each number line to find any errors.

1) Draw a horizontal number line to represent the set of numbers:  Even numbers between 30 and 45.

2) Draw a vertical number line to represent the set of numbers:  Whole numbers greater than 20 but less than 27.

3) Draw a vertical number line to represent the set of numbers: Decimals between 9.4 to 10.5 with an interval of 0.1 between each pair of decimal.

4) Draw a horizontal number line to represent the set of numbers: Mixed number from 6 to 7, with an interval of 1/5 between each pair of mixed numbers.

                    

5) Draw a vertical number line to represent the set of numbers: Mixed numbers between 5 and 7, with an interval of 1/3 between each pair of mixed numbers.

After the students completed the number lines, groups displayed their number lines around the classroom and then using their number line check list did a gallery walk and evaluated each number line in small groups. There was great discussion in the groups about whether or not a number line met all the criteria for an accurate number line. 

I prepared a PowerPoint presentation for the next day by taking photographs of the number lines so they could be displayed in front for all to see and this was tremendously helpful to facilitate discussion. First, I asked the group who made the number line to decide whether their number line was accurate, and then I opened it up for class discussion.

The construction of number lines on large graph paper, small group work, the gallery walk including peer evaluation and error analysis and finally a class discussion with number lines projected for all to see, helped turn a somewhat dry and tedious topic into a very productive and engaging lesson for my students.

These see through colored dots that I found at Staples were great because it allowed students to add dots to their number lines and still see the tick marks below. The difference between tick marks and dots, has been difficult for some of my students and I think the stickers dots helped them make the distinction between tick marks and dots and why all numbers on the number line need tick marks and only some numbers get dots.

Students Make Their Own "I Have, Who Has?" Game

We play I Have, Who Has frequently in my classroom and the students always really enjoy it. I have a stopwatch and I time the class going through the whole set--competing with other classes and also against themselves for the best class time. Last year, when we started the chapter on Algebraic Expressions, I used a set of cards from Mathwire, which is great as an introduction to this topic, but it only has cards for the basic algebraic expression for sum, difference and product. I wanted a set that also included cards for quotients and combining like terms and thought about making a set myself and then decided that, instead of a review worksheet on algebraic expressions, I would ask the students to make their own set of cards for homework instead. They were thrilled and very motivated by this project.  Once the games were made, I allowed the students who wrote and created the cards to run the game in class (hand out the cards, read the first clue, help students if needed, time the class, etc) and they loved it. For about a week we played I Have, Who Has in class with a different set of student made cards each day and, each time we played, students were once again reviewing algebraic expressions by reading, translating and understanding the language of algebra.
The students certainly got a lot of good practice with algebraic expressions just by writing the cards. Unfortunately, most of the games had some errors (2 clues with the same answer, writing that was difficult to read, mathematical mistakes, etc.) in the chain of cards that should loop back to the first card after all the clues and answers have been given (the first card can be any card chosen from the set). I wanted to do this project again this year and decided to create a template for students to use to write the clues and the answers before they make the cards. I wanted the template to be very clear in terms of how the game works and how to write the cards so that each clue is on one card and the answer to that clue is on the next card. I also wanted the students to turn in their template before they make the cards allowing me to review their work and make sure the cards are correct and that the clues and responses will loop through every card correctly. Below is the first page of the template I created--the second page (not shown) has space to make 30 cards in total. I numbered the cards in the columns next to the cards in order to help students keep track of the clues and the answers, but students will need to be instructed to NOT write the card number on the cards so as to not give away the order of the cards during the game.

Here is a link to the template I created.

My Crazy Friend

I used "My Crazy Friend" for the first time in my classroom last week. "My Crazy Friend" is a teaching technique that allows the teacher to introduce a new idea or method of solving a certain type of problem without becoming the one and only authority in the classroom. It also allows students to consider the idea from My Crazy Friend along with other ideas that are generated by students in the classroom. I asked the students how to convert 2/3 into a percent. Here is a list of ideas solutions that they came up with: 66.7%, 67%, 66.6%, 66.67% and 66.66% (repeating). No one in the class came up with 66 2/3%. So I said, I have this crazy friend who says that one way to convert fractions into decimals is to multiply the fraction by 100%. The students tried it and there were some exclamations of surprise when they realized that this gave them the percent in mixed number form. We then spent some time discussing why and how this method works and one student contributed to the discussion by explaining that since 100% = 1, multiplying by 100% does not change the value of the fraction.

Here is a graphic organizer that I use to summarize how to convert from fraction to percent and from decimals to percents using this method. It also shows the opposite--converting to fractions and decimals from percents by dividing by 100. I print this out on a half sheet of paper and the students tape it into their math journals for reference.

Favorite Holiday Gifts!

Math related gifts are the best!

Thanks to my sweet daughter and my wonderful sister!

Mathles to Mathles

I was so excited to read about a new game structure designed by Kate Nowak at f(t) that can be used to practice problems in math classes. She called it Graphles to Graphles because she designed the game to give her Algebra 2 students the opportunity to practice sketching graphs given certain constraints.

But the game seems very promising for my middle school math classes, so I have been thinking about different topics sixth grade students could practice and review using this same structure.

1) Prime Factorization

2) GCF and LCM

3) Number Lines

4) Multiplying and Dividing Fractions

5) Multiplying and Dividing Decimals

6) Graphing Inequalities

7) Solving Equations

8) Area of Polygons

9) Plotting Points and finding Area and Distance on the Coordinate Plane

10) Volume and Surface Area

It really seems that you could make "Mathle" cards for any math problem or topic and then use this game structure to provide students with a fun and engaging way to practice. One thing I really like about this game is how students take turns being the referee whose role in the game is to evaluate the work of the other students in the group and then determine the winner for each round.

I think this game would be especially good for students who are just learning how to solve equations. Students can often solve simple one-step equations in their heads and have a difficult time understanding why they need to write out the steps by showing inverse operations on both sides of the equations. I try to emphasize the importance of Balance and then insist on Algebraic Style. Mathles to Mathles: Solving Equations Edition would be a great opportunity for students to not only find the solution, but also practice and be rewarded for good equation solving skills like showing inverse operations on both sides of the equation and checking solutions.

Inverse Operations Game

This is a game I call Name that Operation. I use it to help the students build on prior knowledge of inverse operations and then use that to understand the connection between squares and square roots, cubes and cube roots and then later in the year, distributive property and factoring. Here are some slides I use in class to play the game:

Students quickly see that you must add 4 to go from 5 to 9 and then subtract 4 to go from 9 to 5 and now they understand the game.

Students see +8 and -8. Then I ask for a different operation and they see *3 and /3. 

Now they see *7 and /7 and then I ask if there is another way to write 7*7 and some students know that 7^2 means 7*7. So then I ask, what would be the inverse operation for squaring a number. Usually some students are familiar with square roots. This next slide shows where the term square root might have come from.

Then I show the next slide to make the connection to geometry: the length of the side of a square squared is the area, the square root of the area of a square gets you back to the side of a square.

And this slide is used later in the year to help students see the connection between distributive property and factoring.

Algebraic Style

One of the most challenging things about teaching one-step equations is trying to convince students that they should show their work and do inverse operations on BOTH sides of the equations. Most students can solve one-step equations using mental math and see no reason to show their work on one side of the equation, let alone both sides! After working on one-step equations for a few days, I decided to create a game where groups would solve problems collaboratively and receive points by solving one-step equations "algebraic style."

I started class by playing this song that was written by students in my Pre-Algebra class from last year: Algebraic Style.
Students work in groups of four and solve one-step equations in a relay race format--each student in the group takes a turn coming to the white board in the front or back of the classroom and does one part of the problem and then passes the dry erase marker to the next person on the group. Here are the four steps that I want to see from each group:
1) Write the problem on the board
2) Show inverse operations on both sides of the equation
3) Find the solution
4) Check the solution

When all the groups completed a problem, I walked around the room and award points based on Algebraic style (inverse operations on both sides of the equation), correct solutions, cooperative group work, following directions, etc. I also awarded points to students who could find or explain errors in the student work around the room.

And then to add a twist towards the end of class, I put up a list of songs the students could choose from that offered another style they could add to their algebraic style. I chose a student randomly to select a new style and then played the accompanying song while groups solved the next equation. Here is the list of different styles I came up with:

1) Gangnam Style

2) Disco Style:  Bee Gees Stayin Alive

3) Robot Style:  Daft Punk Robot Rock

4) Mrs. Dalton’s Favorite Song Style:  Washed Out Call it Off

5) Electronic Style:  SNAP Rhythm is a Dancer 

6) Pop Style  Dynamite Taio Cruz

7) Electric Slide Style

8) Kermit Style:  Rainbow Connection

9) Harry Potter Style

10) Batman Style:  Dark Knight  Introduce a Little Anarchy

11) Video Game Style:  Mario Theme Song
12) YMCA Style
13) 70s Style: ABBA Dancing Queen
14) Star Style:  Cold Play A Sky Full of Starts

p.s. I don't show the music videos, I just use these links to play the songs.