A Closer Look…
Comparing numbers is a student’s skill to determine whether one number is more than, less than, or the same amount as another number. Or, whether the number of objects in a set has more, less, or the same as another.
Ordering numbers is a student’s skill to arrange a group of numbers from largest to smallest, or smallest to largest. To do this, a student first has to be able to compare amounts, so one part of this skill really builds on the other.
In order to compare and order amounts, children need to understand some key concepts:
1. Understanding language used to compare and order
2. Knowing how to use counting to compare and order numbers
3. Using “number after” knowledge
1. In order to make comparisons and order things, children have to be familiar with the language we use to do this. When a student sees two groups of objects, they need to know words like “more”, “less”, “larger”, “smaller”, “greater than”, and “less than”. When it comes to ordering numbers, students have to be familiar with what we call “ordinal words”, which is just a fancy way of saying words that represent position or rank in a sequential order, like “first”, “second”, and “third”.
2. To compare and order, students also need to use counting. Students need to understand that as we count higher the number words later in the sequence represent larger quantities. It sounds logical but without being able to count the objects in two groups and know that, for example, seven represents a greater quantity than five, we can’t successfully compare and determine which one has more or less.
3. To compare numbers more quickly and efficiently, students need to apply the third key concept, using “number after” knowledge. All this means is that a student can enter the counting sequence at any point and specify the next number instead of counting from one. So, when we ask a student “What comes after 8”, the student can immediately say “9”, instead of having to count from the beginning.
Students who understand these three concepts can efficiently answer the question, “Which is more, six or nine?” They know what more means, they know that 9 represents a greater quantity than 6, and they can do it quickly if they know nine comes after six in the counting sequence.
Supporting Students’ Comparing Skills
Some students will be able to compare groups of objects simply by subitizing, or quickly looking at each group, and knowing how many there are in them, and then use their knowledge of the number sequence to determine which group has more or less. Click here to see a video of a student with a solid understanding of number comparison. Notice in the first example, how he subitizes the number of blocks the teacher has, and quickly makes a set with the same number. Later, he is even able to tell the teacher how many more blocks she has than him.
Early on, children are able to visually compare two groups of objects and determine which has more. But, this only works when the groups are small (e.g., 1 apple versus 2), or really different from each other (e.g., a pile with 1 toy truck and a pile with 10 toy trucks).
However, sometimes students will need to compare two groups that are more similar in size (e.g., a group of 7 and 8), or, groups that are both large (e.g., a group of 12 and 15).
One way to support students’ ability to compare is to encourage students to use matching – pairing one object from one group to one object in the other group until all the objects in one of the groups has been matched. Now students can see that the group with objects left over has more. As students’ skills grow, they will be able to tell you how many more or fewer one group has than another, as the student in the video did. These are students’ early addition and subtraction skills at work.
Click here for additional strategies to support students’ understanding of Comparing and Ordering numbers!
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