# Comparing Numbers

One of the critical concepts in math is understanding which numbers represent "more" and which numbers represent "less."

As with counting and ordering numbers, some students compare numbers easily and naturally. Other students need a lot of practice.

When students have a hard time comparing numbers, use manipulatives. If a student cannot abstractly determine if 5 or 7 is greater, have the student count out 5 objects and then 7 objects and compare the groups.  If necessary, have the student pair up objects from each group, to see which group has some objects left over.

When students start to outgrow manipulatives, try "thought manupulatives."  Ask the student to name something that he or she likes. Let's say it's cookies. Then, ask which is greater 300 or 350? What would the child prefer, 300 cookies or 350 cookies?

When manipulatives don't work, sometimes it helps to count (if the student can count by 10s, that can be a more efficient way to deal with larger numbers than counting by 1). Let the student see, as you count, which number is higher -- or takes longer to get to. Sometimes it helps to write the numbers out on a number line, so that the student can see that the "higher" number is farther down the number line.

The following "Compare numbers 1-10" worksheets provide some drawn manipulatives that young students can use to help them compare.

When students can circle the greater number, they show that they can compare numbers.

Also teach students to use the greater than (>) and less than (<) signs.  These symbols can be hard for students.  Most students learn that the "mouth" of the symbol always wants to eat the larger number. Some students also learn that the arrow points to the smaller number.  We usually just teach "mouth"=greater.