When teaching math in kindergarten, it is so important to provide students with a variety of math strategies and tools they can use to solve addition and subtraction problems. By providing different strategies for students to choose from, you can naturally differentiate math. Students are able to choose different strategies as their skill levels change, and they become more abstract math thinkers.
Concrete Math Strategies
At the beginning of the year, kindergarten students have very concrete math thinking. Your math strategies for kindergarten require something physical for them to manipulate in order for them to make sense of math problems. In addition problems like 2 + 3, this can look like setting out a group of 2 counting bears, and a group of 3 counting bears. Then students can count all the bears together to figure out the solution.
Concrete math strategies for kindergarten look similar for a subtraction problem. For example, if you give students the problem 5-1, students count out 5 cubes. Then, they remove 1 cube from their group and be able to count again to see the answer is 4.
In these examples, students used counting bears and cubes as strategies to solve math problems. There are also many other tools they can use, depending on what you have in your classroom. They can manipulate counters, rekenreks, and ten frames with moveable pieces to solve math problems. Even fingers are a great tool to use when students need those concrete math strategies in order to solve problems!
Transitional Math Strategies
As students become more comfortable with solving math problems, they begin transitioning towards more abstract thinking. They still need something to represent the problem, but now it does not have to be something that they can touch and move. Instead, it can look more like drawings that can represent the tools they use.
For example, instead of using physical cubes to represent a problem, students may draw cubes. Rather than using a physical ten frame, students may draw a ten frame to help them solve a math problem. In a subtraction problem like 8-3, this would look like a student first drawing 8 circles within a ten frame. Then, they can erase or cross out 3 of those circles to show that there are now only 5 left.
I think it is important to note that while we do want students to be able to draw these quicker pictures to solve problems, that probably won’t be the case in the beginning. As in, if you give students a word problem that involves 4 flowers plus 6 more flowers, you should fully expect to see 10 beautiful flowers drawn out on your students' paper!
Our transitional math thinkers can also use drawn strategies, such as number lines, tally marks, and even classroom tools like dominos and dice in their problem solving.
Abstract Math Strategies
When students move on to abstract math thinking, they are ready for more complex strategies. With these types of strategies, students can represent things with numbers rather than pictures or physical objects. Also, many of these strategies rely on using some mental math and prior math knowledge to solve problems.
For example, later in the year (and earlier in the year for some of our more advanced students) students can begin using strategies like doubles facts that they have memorized. When given a problem like 2+2, many students just know that 2+2=4 without having to give it much thought.
Students at this stage might also be ready to use strategies like counting on from the first number in an addition problem, and counting backward from the beginning number in a subtraction problem. Students can even think about composing and decomposing numbers as a way to solve problems when they are at this stage, so they can see what smaller numbers come together to make up larger numbers.
Depending on what stage of math thinking students are in, the math strategies that they can effectively use will be vastly different. That is why it is so important to present students with a variety of strategies that they can pull from as they need them. You can even keep the strategies you have taught on display using Math Strategies Posters. This way, students have a choice in what strategies they use, and math is naturally differentiated as students solve problems in their own way and according to their own skill level.
You can find many of these strategies used in this 100th Day of School set too! Happy teaching!