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Which number is greater? Which number is less? How do you know?


Alignments to Content Standards: K.CC.C.6

Task

Action:

This task should be done as a whole group. * The teacher will show the class two groups of objects or drawings of objects. 6_and_9_f491690b99466ac24d049e2bf0c3ae20 * The class will chorally count the two groups and the teacher or a student can record the number below the group. * The teacher will then ask the class to chorally say which number is greater and which number is less. * The teacher will then instruct students to turn to their talking partner and tell them how they know which number is greater or less than the other number. It can be helpful if students have preassigned "talking partners." This is not necessary, but will make the lesson go more smoothly as students will quickly know who they should turn and talk with.

IM Commentary

The purpose of this task is for students to explain how they know one quantity is greater or less than another quantity. Students will easily be able to identify which number is greater or less. However, explaining their reasoning will help them solidify their number sense skills. The teacher should sometimes ask "which number is greater?" and sometimes "which number is less?" so that students gain skill with the concept of less than. Greater than is an easier concept to master for young children, as it connects to their very intrinsic sense of "more," but less than can be tricky.

Solution

“When I count it goes 1, 2, 3, 4, 5, *6*, 7, 8, than *9*. I know that six is less than nine because I say six before I say nine.”

“I know that nine is greater than six because my brother is nine years old and I'm six years old, and he’s older than me.”

“Okay, you have six. One more is seven. One more is eight. One more is nine. So nine is greater than six. Okay?”

“Well, when I see the number line I see six comes before nine.” “

This many fingers is six (shows six fingers). This many fingers is nine (shows nine fingers). I have to put up more to show you nine.”

Any answer which includes the child correctly explaining why one number is greater or less than the other is acceptable. The teacher should encourage students to use the words greater than/less than. The first few times this activity is done the answers may be long and full of extra information that is not relevant to the problem such as, “You know my brother Jayovanni. He’s in third grade. He used to be in kindergarten with you Mrs. Wood. He loved kindergarten! Well now he’s in Ms. Martin’s class. My mama got him new blue Jordans, but I didn't get new ones because my feet are still the same size as when I got these shoes. Well Jayovonni is nine. And I’m five. Five is less then six. Jayovonni is older then me. I know that nine is more then six because Jayovonni is nine and he is older then me.” If this happens the teacher should paraphrase the relevant math information back to the student.

The answer of “nine is bigger than six” is not a sufficient answer. The students need to explain why they know nine is greater than six, or six is less than nine. If students use the words bigger/smaller, the teacher should help the students connect this language to the more precise words (greater than/less than) and help the students use this language.

redbaron says:

over 3 years

Doesn't the second solution only establish that 9 is greater than 5? Perhaps if the student verbalized that he/she would turn 6 in a year or less, but that 9 was a more distant milestone, that would be a valid explanation. Alternatively, if we wanted to make the kindergartener 7 years old, the transitive property would hold: "He's older than me and I'm older than 6, so 9 must be greater than 6."

Cam says:

over 3 years

Good catch, as always. Thanks! I've taken the simplest way out, and simply made it a direct age comparison.

alyce mcmenimen says:

over 5 years

I am very happy to see the additional notes for teachers. It is all about the math language that the students use to get to a real understanding of 'more or less'. The earlier and more we make them use the math language to explain their thinking, the more they will own the concept. Children experiencing difficulties will benefit from seeing and hearing their peers explain the concept. alycemac48