Saturday, March 28, 2015

The Bank Account Game

When I first started teaching high school math, a colleague made a simple card game that the students LOVED to play. It was kind of like the Game of Life without the board and the little cars with removable blue and pink pegs.

Each student had a blank check register and they would keep track of deposits and withdrawals to their checking account by recording these amounts in the deposit or withdrawal column of the check register based on the cards that they drew and then add or subtract to find the current balance in their account. In this game, each player had a job that earned them an annual salary that was paid out to all the players every few rotations. Hence the students had practice keeping an accurate checking account balance but never had to worry about bouncing a check or having a negative balance. The student who had the highest balance in their account at the end of the game was the winner.

Throughout the school year, I found myself going to her regularly to borrow her card game for a few days and always wanted to make my own set of cards, but never found the time.

Five years later, when I started teaching sixth grade, I realized that this game structure would be a great way for my students to practice working with negative numbers. I still didn't have the time to make a set of card myself, so I got my students involved by asking them to make two deposit cards and two withdrawal cards. I told the students to only use increments of $10 with a maximum of $50 for each deposit or withdrawal. These friendly numbers allowed the students to play the game using mostly mental math by referencing a number line drawn in increments of 10. They loved playing the game with cards they had created themselves and now I have an abundance of student made cards--enough for several groups to be playing at the same time.  Here are some examples that I showed them.

And find some examples of student made deposit and withdrawal cards here.

The goal of the game was not to practice integer computation following a set of memorized rules, but instead for them to get a feeling for moving along the number line especially when the balance changes from positive to negative or vice versa.

I encouraged the students to draw number lines to work with during the game. Next year I will provide large number lines in sleeve protectors that they can draw on with dry erase markers as they calculate the balance in their account.

Here is the link to the Bank Account Game Template.

Saturday, March 21, 2015

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.