Why Combining Numbers Is Important in Common Core Math
In order to solve Common Core math problems later, kindergarten students must first learn to play with the properties of numbers. Among these properties are that numbers can be combined, and that — correspondingly — any number can be taken apart into smaller bits.
Children need practice noticing and thinking about these combinations. For example, combinations to make 10 are significant. Mental math (that is, figuring out computations in your head) and paper‐and‐pencil algorithms in first and second grades require knowing combinations to make 10. When students see the number 1, they should think about 9 as the other half of the combination to make 10. When they see 4, they should think about 6, and so on.
Being fluent with these facts helps students find their way around the number system. If they learn in kindergarten that 4 and 6 make 10, then adding 14 + 16 in second grade is easy. You have one 10 from the 14, another 10 from the 16, and then a third 10 from the 4 and the 6, so 14 + 16 = 30.
You can also use the idea of making tens when you add 7 + 4. If you know that 7 and 3 make 10, then you may see that 7 and 4 make 1 more than 7 and 3 do. Therefore, 7 + 4 = 11. Because the number system is based on 10, being able to combine numbers to make tens — and being able to break 10 apart — is a skill that pays dividends for years to come.
But notice how the 7 + 4 computation was handled: the 4 was broken apart so you could think about 4 as 1 more than 3. Nothing in the statement of the problem 7 + 4 = tells you to break apart the 4 (and you could just as easily have broken apart the 7, because 6 + 4 is another combination to make 10). Breaking numbers apart is a habit of mind that comes from counting, playing, talking, and listening to lots of different ways of thinking about numbers. All are important activities for kindergarteners to engage in on a daily basis.