How Many of Each?

Both the first and second graders are exploring "How Many of Each?" problems in math. At the first grade level, this looks at a number of objects from 5-12 that may come in two types. For example, I have 9 peas and carrots - how many of each could I have?. The students need to deconstruct and rebuild the target number using a different combination of peas and carrots (1+8, 2+7, 3+6, 4+5). It is tricky to generate all solutions as 1 pea and 8 carrots is not the same spoonful of vegetables as 8 peas and 1 carrot. This brings some algebraic thinking into the mix - x+y=9. What could the values of x and y be? We give the kids the context of peas and carrots or apples and bananas instead of the abstract entities of "x" and "y" but the thinking work is the same. They have many tools to use in their strategy work including orange and green cubes, ten frames (or, 9 frames in this case) and kids have the opportunity to work on their own, with a buddy or with a teacher led group. 

On the second grade level, this work focuses around place value using a sticker context. These stickers come in strips of 10 and singles, representing the 10s and 1s in two digit numbers. Looking at a target 2 digit number as the quantity of stickers, such as 35, how many strips and how many singles could I have? (3 strips and 5 singles, 2 strips and 15 singles, 1 strip and 25 singles, or 35 singles) Here again, kids are tasked with this algebraic thinking that pushes them beyond simple addition or subtraction as there are multiple possibilities and how do you know if you've found them all? The tools available to help make this abstract thinking more concrete include base 10 blocks and snap cubes. 

Wrap up shares, posters and discussions help to grow everyone's thinking as we look at multiple approaches to the same problem. These big questions will continue to be explored in both grade levels in the weeks to come. Check out the pictures below of our young mathematicians!