How Children Compare Numbers in Common Core Math
In Common Core math, many important questions require comparing numbers to decide which number is greater, or whether the numbers are equal. A kindergarten student who can count to 20 may still need to think hard to decide whether 8 is more than 5.
Questions that require comparing numbers include the following ones:

You have 7 crackers. Your friend has 5. Who has more?

Your class has 25 children. You have 17 copies of a favorite book. Do you have enough for everyone, or will you need to share?
Thinking about these everyday kinds of questions focuses children’s attention on the important ideas that numbers can be compared and that numbers can help you make good choices and treat everyone fairly.
Kindergarteners refine their knowledge of comparisons. Young children may think that the word more has to do with how much space the objects take up, so a dinner plate with peas dispersed all over it has more than a plate with the same number of peas in a neat pile, even though the number of peas is equal in these two situations. Kindergarteners explore and play with this idea.
Finally, equal means is the same as is an important idea in kindergarten. When children see many problems of this form: 3 + 4 =, they may develop the idea that the equal sign means and now write the answer. This second meaning is a common misconception that often lingers into middle school or even high school math and can be a source of trouble when students study algebra.
You can encourage your child both to understand the idea of equality and to correctly use the equal sign by talking about problems such as 3 + 4 = _ + 2. Ask what number fills in the blank. If your child says 7 (which is a common reply), you can say, “Well, 3 + 4 are two parts that make 7, yes. But we want to make the same amount as 3 and 4 using 2 as one part and some number as the other part.” Ask how your child can figure out what would make the same amount.
Try using beans to help your child think things through. Say, “If you have 3 beans and 4 more, and if your friend has 2 beans — how many more do you need so you both have the same number?” You can point out that 3 + 4 and 5 + 2 are different ways to make the same number: 7.