Base 10 blocks can make abstract ideas like place value and regrouping visible and tangible for your primary school students when the time comes to teach subtraction.
Subtraction is not the easiest idea for second and third graders to grasp. When you confine the process to problems like eight minus two or six minus three, the relatively concrete idea of counting backwards works. But the larger the numbers, the greater the degree of abstraction involved. And eventually the child bumps into regrouping...
Overcoming Abstraction
In the struggle to teach math to elementary grade kids, the real enemy is Piaget's stages of development. Teachers are stuck with the job of finding a way to get relatively abstract mathematical ideas across to children who haven't yet developed much capacity for abstract thought. The simplest solution is to find a way to represent those abstract ideas in a tangible, concrete manner that kids can see and touch. Base 10 blocks (image 1) are a powerful tool for doing just that.
Working With Base 10 Blocks
Hopefully you've already been using base 10 blocks to teach place value. If you've succeeded at that, students should be able to model numbers at least as large as 1,232 (image 2). Your students are really limited to working with numbers under 2,000 when using base 10 blocks; but that's only because of the limited number of available blocks. If you combine sets, you can come up with enough of the large "blocks" (for the thousands place) to make larger numbers, but students usually don't need number that large to master the skills involved.
If students have a place value mat that they can lay on their work surface, the process is a little easier. Such a mat gives them a labeled space to put the ones "cubes" in, the "longs" that represent tens in, the "flats" that represent hundreds in, and the large "blocks" that represent thousands in. Students also get a spot over each space where they can use a dry erase marker to write the digit associated with the amount of blocks in each of those spaces.
Subtraction Without Regrouping
Begin teaching subtraction with problems that don't involve any regrouping. With an example like 47 minus 12, students create the number 47 with base 10 blocks on their place value mat and then create the number 12 nearby on their work surface by removing the blocks they need for 12 from the blocks they used to make 47. After they've made 12, ask them to look at the blocks on their place value mat and decide what number those remaining blocks make. The answer should be 35; they should have removed one "long" and two "cubes" from the 47 on their place value mat to make 12 with.
Practice problems like these until students are competent with subtraction problems that do not require regrouping.
Subtraction With Regrouping
Eventually you will want to try problems that involve regrouping. Images 3 thru 5 illustrate the process of solving such a problem. The problem is 37 minus 19.
Go through the following steps below with your students. You probably want to use an ELMO or overhead projector to model working the problem yourself for students to see.
- Begin by having students use the base 10 blocks to make the number 37 (image 3).
- Tell them that you want them to subtract 19.
- Ask the students if they have enough of the small "cubes" in the ones place to make 19. The answer should be "no."
- Tell them you have a solution to that problem, and that you're going to take one of your "longs" out of the tens place and trade it in for 10 of the small "ones" cubes. After you do that to model it, let them do it.
- Once yuo've placed the new cubes in your ones spot, you should now have 17 "cubes" and two "longs" on your work surface (image 4). Check and make sure that's the case.
- Ask the students if they can subtract 19 now. Most will say "yes." Let them do it (most will be able to), and then show them how you would do it. (Take one "long" from the tens place and nine "cubes" from the ones place and move them to another part of your work surface to form 19.)
You should have 18 displayed on your work surface. And your students should be on their way to understanding regrouping...
