So I didn't just up and quit teaching, like one may have thought (with my lack of attendance in the blog-isphere). So hopefully you caught my last blog post on Addition Strategies, or if you are new here, WELCOME!
So I have been blessed with being able to have the experience of teaching first grade for 4 years and am in my 3rd year in 2nd grade. The progression and the growth in conceptual understanding with number sense and being able to start to add and subtract is a beautiful thing to watch unfold! When students have grasped the value of digits and have a solid number sense, you can then move onto introducing some addition strategies! Which then leads us here to subtraction!
Continuing with another great read-aloud The Cheese Feast by Strategic Educational Tools is a sequel, or spinoff of The Good Neighbors Store an Award. Another great read aloud for subtraction is The Action Of Subtraction by Brian Cleary. My students really enjoyed The Good Neighbors books though!
I generally spend 1-2 days on each strategy. I model the strategy, then we do some work together, then they independently practice the strategy, leading to me quickly assessing them to make sure they got the concept. Many students will find a strategy that makes sense to them, however, I encourage them during these strategy learning days to use the strategy that we are practicing on that day, and then after I introduce each strategy, they can choose how they problem solve from there on out.
So the first strategy we use in subtracting is using our base ten blocks. Literally everything hands on. We don't even write. I write the equation, and then I have them focus strictly on building using their manipulatives (base ten blocks) and then counting their tens and counting their ones ones, for their start number, and then taking away the amount they are subtracting. This is more of a concrete way for the students to solve, so many of them can pick up on this almost immediately. When I feel that they are ready, I then have them use their whiteboards and I have them draw sticks and dots (tens and ones) to take the place of the base ten blocks. We then spend the next day talking about what to do when we subtract our ones, but we don't have enough to take away what we need and they will have to make a trade of one ten for ten ones (regrouping).
The next strategy, because, to me, they are doing this strategy with subtracting with base ten blocks, is expanded form. I follow the same kind of direct instruction, I model, we do some together, with them working on their whiteboard, and also some shared solving (on the front whiteboard, a student comes up and solves), and then I have them independently solve some. This strategy also makes sense to them if they have grasped subtracting with base ten blocks. If they haven't grasped place value and don't have a strong number sense, they will struggle with expanded form. I suggest still introducing this strategy to them, but encourage them to build with base ten blocks and writing the value underneath---also pulling them into small groups to reteach place value and value of digits within numbers. After they've grasped subtracting with expanded form without regrouping, we then do some work with regrouping as well.
So number bonds was introduced to me about 2 years ago. The thought behind using number bonds, supports many of the math practices--such MP2--thinking about numbers in multiple ways. From the beginning of the school year, I try to teach my students to think of numbers flexibly.In the problem shown above, I broke the subtrahend down into 1 and 36 (from 37). Doing this allows me to easily subtract 1 from 51 to get 50. I then continue with this thinking, subtracting 30 from 50, and finally 6 from 20, leaving me with my answer of 14. Some kids refer to it as subtracting in chucks, whatever works for them!
So out of the 4 strategies I introduce, the open number line is the most abstract. The student has to be able to visually see numbers in sequential order on a number line. The student has to have a strong number sense, as well as understand greater than and less than and where numbers would go on a number line. I start by telling them on the number line, the bigger number (the start) goes all the way to the right, while the smaller number (the subtrahend) goes all the way to the left. They start with the smaller number, and then add in chunks--if that works for them adding in 10s, or adding to get to a friendly number--whatever works for them to get to that bigger number. Then they have to count their hops and that is the difference (answer). Again this one is very abstract, but some of my kiddos prefer it!
I do not spend much time at all on teaching the standard algorithm. In fact, I just show the students how to solve and I say, "This is probably the way your parents, and most old people, solve addition and subtraction problems." The kids always find that hilarious and laugh about it--I tell them I'm old too and that's how I learned to add and subtract by solving algorithms, but I also tell them I didn't understand or have a good number sense. I again hit the point that numbers are flexible and if you can see numbers flexibly you can solve any problems! Check out the FREEBIE, by clicking the image below!
If you have any different ideas for teaching addition, leave in the comments below!
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