Every year it approaches with a mix of excitement and trepidation, triumph and frustration. Integers. Which sometimes seem more like “integrrrrrs“. Now fortunately, my students have all seen integers by the time they get to me. Sixth graders are oh so happy to do “grown up” math…at least at first. Then the learning split happens. Some people can pick up adding, subtracting, multiplying, and dividing signed numbers in a heartbeat, but invariably I’ll have a few who are completely lost. Multiplication and Division are the easy ones. In class we call them ‘golden rules’;
1. When you multiply or divide integers with the SAME sign, your answer is positive.
2) When you multiply or divide integers with DIFFERENT signs, your answer is negative.
Understanding these two rules leads to the “A-Ha” moment when students figure out that an odd number of “negatives” means a negative solution while an even number means a positive.
Then we have addition and subtraction…
I’ve used a couple of different strategies to teach addition and subtraction of integers.
1) We make number lines that are aligned vertically with an elevation theme. Then we use http://veloroutes.org/elevation/ to look up the elevation at each student’s home address and use them to compare. We’ll find the diference between the highest and lowest, we’ll compare to our school, and in groups, students will find the mean elevation.
2) We use a number line with arrows.
3) We use tiles.Each students gets two colors of “tiles” I’ve used anything from actual 2 color counters to two different colors of construction paper. One color represents positives, the other color represents negatives. If you’ve never used tiles with integers before, I highly recommend it. I’ll post a video soon on how that strategy works.
One online tool that works really well for drilling integers is http://www.thatquiz.org/ In the computer lab, I’ll assign certain settings for the kids to stick to and practice. The kids earn a bronze level achievement for the week if they score in the 70s, a silver level achievement if they score from 80-94. And a Gold Level achievement if they score 95 and above. I love using the site because there are lots of different choices to help tailor instruction to each student’s needs. My strugglers will practice the skills that they need help with, but if a child isn’t challenged enough, I can step it up by having them work on inverted problems or triplet problems.