Using Arithmetic Racks for Doubles and Near Doubles

Two summers ago I attended an Inquiry Math Workshop at Purdue University Calumet.  I learned SO much about how kids' mathematical concepts develop and how inquiry math can foster this growth.  Basically inquiry is all about discovering rules and concepts, rather than just having them be told.  Kids come up with their own strategies and definitions and they are so much more meaningful.

Last week I used arithmetic racks to help kids visually see doubles facts.  We talked about twins (we have 4 sets of twins in first grade and I have one sibling from each set), and that doubles are like identical twins.  The arithmetic rack lends itself to this with its two rows.  We used the arithmetic racks to help fill out our fact cards.

While doing mClass, I discovered that students were not using all the strategies we had learned to solve math facts.  Instead, students were relying on counting all and counting on, which isn't very efficient when you are trying to solve 8+7!  The students who were counting all didn't have enough fingers, and the students who were counting on were susceptible to mistakes with all that counting!  They'd count the seven fingers, then go back and have to remember that they started with 8 and count on.  Needless to say, my students didn't solve very many facts in 60 seconds!  I had to reteach the strategies and try to get them to stick.

We took an extra day on Monday to work on doubles +1 and doubles +2 facts.  In the past, I presented the strategies to the class.  I just simply told them that a fact like 6+7 was a doubles plus 1 fact and showed them how the doubles fact could help them.  I wanted to find a way to make it more meaningful to really help the students see the connection between the types of facts.

What I ended up doing was reviewing doubles facts and then studying the patterns.  We did the doubles facts in order and the students noticed that the sums went up by 2.  I asked students to talk about why this pattern occurred.  I love seeing how excited they get when they discover and understand patterns!  So now I had them right where I wanted them... I wrote 6+7 up on the chart paper and asked what they thought the sum would be and why.  Could they use the doubles facts to help them?   Lo and behold, I had volunteers for how to use 6+6 and how to use 7+7... AND how to use them both, which I didn't think they'd see!  Since they saw the pattern with the sums going up by 2s with the doubles, one pair of smarties realized the sum of 6+7 would be between 12 and 14, the sums of the 6 and 7 doubles facts!  YAY!

Now obviously not all students saw these patterns and relationships, so we busted out the arithmetic racks.  We made doubles plus one facts on the racks and looked to see which doubles facts they were close to.  We paid close attention to how we changed the near doubles to the doubles facts.  I realized that I needed to stop calling them doubles +1 facts when some students were using the larger number to double and then subtracting 1!