Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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Reasoning and ProofSession 04 Overviewtab atab bTab ctab dtab eReference
Part C

Defining Reasoning and Proof
  Introduction | Pattern Recognition | Repeating Patterns | Reasoning About Repeating Patterns | Growing Patterns | Classification | Your Journal
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Classification involves making decisions about how to categorize things. It is a fundamental element of developing reasoning skills in data analysis. Classification begins by sorting or grouping items with common characteristics.

For young children, classification takes the form of informal sorting -- identifying items that go together based on a common characteristic. As children begin to sort and classify items, they start with two simple questions: What's the same? What's different? They communicate and justify their reasoning by describing how the items in a group are alike or different. Seeing common characteristics, making conjectures, and explaining their thinking are all important elements of reasoning in young children.

Different Sorted Buttons

As students move through the primary grades, they will begin to sort objects by more than one attribute or characteristic. For example, sorting buttons by color and size is a more sophisticated skill than sorting by color.

Classification activities can extend beyond sorting. So far in this session, the emphasis has been on classifying with concrete materials; however, it's also important for students to develop reasoning about numbers. The game "What's My Rule?" can be useful in this regard. In this game, a group of items with a common characteristic is selected; students use reasoning to identify other objects with the same characteristic and then identify the common characteristic of all of the selected items. The items can be physical objects, but they can also be numbers.

Let's take a look at second graders playing "What's My Rule?" using numbers.

The teacher wrote the following numbers on the board:

Numbers on the Board

Teacher: All of the numbers on the board have something in common. There are other numbers that fit my pattern or rule. Can you name a number that belongs on the board?
Sarah: I think 25 goes on the board.

Teacher: (adds 25 to the board) Any others?
Pat: Thirty-five?

Teacher: Thirty-five fits my rule. Any more?
Peg: Thirty-six.

Teacher: Thirty-six does not fit my rule.
Jacob: Five?

Teacher: Five fits my rule.
Marty: Fifty-five?

Teacher: Fifty-five fits my rule.
Caleb: One hundred?

Teacher: What do you think about 100? Does it fit my rule?
Sarah: I don't think so, because all of the other numbers have two digits.
Caleb: What about 5? It doesn't have two digits.
Sarah: That's right -- so I guess 100 fits the rule.

Teacher: (adds 100 to the board) What is my rule?
Peg: All of the numbers end in 0 or 5.

Teacher: Does anyone have another rule for my numbers?
Jacob: You say them when you count by fives.

The activity continues with the students taking turns thinking of a rule and writing their numbers on the board for the others to add to and then guess the rule.

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