CGI Problem solving as a vehicle

First grade math curriculum and standards have changed so much since I began teaching! The CCSS require first graders to:

Use place value understanding and properties of operations to add and subtract.
CCSS.MATH.CONTENT.1.NBT.C.4Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

I like to use problem solving as a vehicle to help students grasp this concept. The way this works is by carefully selecting the numbers you use in your problem-solving tasks.  Rather than introducing a strategy and giving students a problem to solve using the strategy, I give students a problem and help them discover more efficient strategies.

My average students are very efficient with counting up from a number and using a hundreds chart. They are also getting proficient with adding multiples of 10 to a given number. Now I'm going to introduce them to adding two digit numbers that are not multiples of 10. My first problems are:

When I introduce a problem, I read it several times. We talk about what is happening in the problem. These problems are very straight forward because I want to focus on the complex number work. Then I might ask the students what they notice about the number selections. When someone notices that all the numbers end in 3 or 1, I will be very surprised and make some sort of comment about how I can't believe I did that. The students work on these problems individually. I have them divide their notebook page into 4 sections and solve the problem using all 4 of the number selections.

I just spent a couple weeks working on join-change-unknown (unknown addend) and compare problems. You can read a little about it and get an old freebie here. The problems I will be using the next couple weeks are almost all basic addition or part-part-whole. To start out I made the numbers pretty high because I want to discourage drawing pictures. If   When I see someone drawing bunches of circles, I will remind them how much faster it is to draw large numbers using base 10 pictures. As students work I circulate and look for interesting strategies, I try to talk to as many students as possible. I choose 1-4 students to share their math. After 10-15 minutes of work time, everyone cleans up except the kids who were asked to share.

I have the student with the most basic strategy share first, and the most complex strategy solve last. When I present these problems the first few times, I expect a large number of students will count on by ones, hopefully they will start with the bigger number! If I can find anyone who starts with the bigger number and counts on by 10s, then adds the ones, I will ask that person to share. The goal is to find a student who breaks the problem apart into 10s and 1s to solve. I know some of my students will, but they probably won't demonstrate that in their work, I'll need to pull it out of them. I show them how to record their thinking in a way that is efficient, but still shows me what they did. Some students will just write an equation because they added 10s and 1s mentally. Once the students have shared, I will write the 4 equations and give them another chance to tell what they notice. Before I introduce the next problem, I often refer back to the strategies used in the previous problem and encourage students to try "Danny's strategy" of adding tens and ones.

The first few days of this series of problems have number selections where the numbers in the ones place stays the same in each selection. Then I start using more number variety. Once students are pretty comfortable with adding tens and ones separately, I have a few problems where the numbers in the ones place make 10.Finally, I give the students some problems where the numbers in ones place add up to 12. When I got to this point, I went back to keeping the number in the ones place the same.

I am sharing this sample from my series with everyone. If you are interested in the whole 12 problem set, please like my Not very fancy Facebook page.

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I would love to hear about how problem solving looks in your class!