Lesson Plans

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Number Types: Where Vocabulary Meets Numbers

Lesson Question:

How can students use the Visual Thesaurus to evaluate different numbers according to type?

Applicable Grades:

6-12

Lesson Overview:

Who knew there were so many words to describe numbers? In this math lesson, students use the VT to define vocabulary words that are often used to label numbers. Then, students will evaluate different numbers according to their features and decide how they can categorize them according to number type.

Length of Lesson:

One hour to one hour and a half

Instructional Objectives:

Students will:

  • define different number types using the Visual Thesaurus
  • learn how to complete a Semantic Feature Analysis grid
  • work collaboratively to classify different numbers according to type
  • analyze patterns from a Semantic Feature Analysis grid regarding number type

Materials:

  • student notebooks
  • white board
  • computers with Internet access
  • "Analyzing Numbers According to Type" sheets (one per student) [click here to download]

Links:

*Note: This lesson models the vocabulary instruction technique of using Semantic Feature Analysis grids. Traditionally, SFA grids are used to help students distinguish between closely related words by considering which features they share or don't share, but this lesson uses the technique to extend to students evaluating numbers according to number type categories.

Warm-up:

Introducing the concept of "natural numbers":

  • Ask students to reflect back on their first math lessons – at home, in preschool or in kindergarten. What did they learn? What did they "do" with numbers back then?
  • Elicit students' responses to the reflection prompt. Students most likely remember learning to count, beginning with the number one. They might also remember counting physical objects like blocks or beads.
  • Explain to students that the numbers children are first introduced to are considered "natural numbers."

Instruction:

Defining natural number with the Visual Thesaurus:

  • On the white board, display the Visual Thesaurus word map for "natural number" and point out its definition as "the number 1 and any other number obtained by adding 1 to it repeatedly."
  • Explain that natural numbers make up the most simplistic category of numbers; that is why young children are first introduced to this concept of numbers. As students get older, they learn about more complicated types of numbers – numbers like zero, negative numbers, fractions, etc.
  • In the VT word map display for  "natural number," follow the dashed "type of " line toward the word "number" and hover the cursor over the definition of number as "a concept of quantity involving zero and units." Click on that red meaning bubble in order to make that meaning the center of a map that reveals all the types of numbers the VT contains in its database:

Introducing a sample Semantic Feature Analysis grid (see Note above):

  • If students are unfamiliar with a Semantic Feature Analysis grid, model creating a simple one based on a set of related math terms. For example, you could analyze the features of different geometric shapes.
  • Ask students to brainstorm a list of features or attributes that are commonly used to classify or describe geometric shapes (e.g., round, symmetrical, acute angles, parallel sides, number of sides, right angles, two-dimensional, three-dimensional, number of vertices, etc.).
  • On the board, choose three or four of shape features to act as column titles for a Semantic Feature Analysis Grid for shapes. Then, create three or four rows in the grid, each listing a different shape.
  • For example, here is a sample Semantic Feature Analysis grid that has students distinguish between different types of shapes based on four different features.

Shapes

   Characteristics or Features

Contains right-angles

Two-dimensional

Three-dimensional

Contains curved lines

cube

 

 

 

 

square

 

 

 

 

cone

 

 

 

 

circle

 

 

 

 

  • Explain that each empty box should be filled in with either a plus sign (to indicate that the shape has that particular feature) or a minus sign (to indicate that the shape does not have that attribute or feature).

Sample completed SFA grid:

shapes

   Characteristics or Features

Contains right-angles

Two-dimensional

Three-dimensional

contains curved lines

cube

+

-

+

-

square

+

+

-

-

cone

-

-

+

+

circle

-

+

-

+

Defining Number Types:

  • Explain that just as shapes can be analyzed according to different features, numbers can also be analyzed in a similar way – according to type.
  • Provide each student with an "Analyzing Numbers According to Type" worksheet (download here).
  • Have students define each number type (i.e., natural number, integer, rational number, irrational number, real number) using the Visual Thesaurus. Note: students should enter two words into the search box as they define each two-part terms – e.g., search for "real number" not just for "real."

Completing Number Type grids:

  • Organize the class in partners or small groups, depending on the availability of computers.
  • Ask students to analyze each number listed in the far left column of the grid to determine how many Number Type categories it fits in. (If it fits in a number type category, students should draw a plus sign (+) in the box that corresponds to the number's row and that Number Type column. If the number does not fit into a Number Type category, students should draw a minus sign (-) in the appropriate box.)
  • If students are unsure about whether or not a particular number fits a number type, they can consult the VT definition for the number type and/or right-click on the number type in the word map display to do an Internet search to find additional information.

Wrap-up:

Discussing patterns on the Number Analysis grid:

  • Display the "Analyzing Numbers According to Type" grid on the board and discuss how students completed each box.
  • What patterns do students see in the grid? What conclusions can they make based on these patterns? For example, each number is either marked with a + as being "rational" or "irrational," but never both.  (Therefore, students can conclude that numbers cannot be both rational and irrational.)

Extending the Lesson:

  • Challenge students to create original Semantic Feature Analysis grids to distinguish between another set of related math terms.
  • For advanced students, you could extend this lesson to include complex numbers.

Assessment:

  • Check groups' completed "Analyzing Numbers According to Type" sheets to assess whether or not students accurately identified the different number types for each number listed on the grid.

Educational Standards:

Mathematics

Standard 2. Understands and applies basic and advanced properties of the concepts of numbers

Level III (Grades 6-8)
1. Understands the relationships among equivalent number representations (e.g., whole numbers, positive and negative integers, fractions, ratios, decimals, percents, scientific notation, exponentials) and the advantages and disadvantages of each type of representation 
2. Understands the characteristics and properties (e.g., order relations, relative magnitude, base-ten place values) of the set of rational numbers and its subsets (e.g., whole numbers, fractions, decimals, integers)
3. Understands the role of positive and negative integers in the number system
7. Understands the concepts of ratio, proportion, and percent and the relationships among them 

Level IV (Grades 9-12)
1. Understands the properties (e.g., relative magnitude, density, absolute value) of the real number system, its subsystems (e.g., irrational numbers, natural numbers, integers, rational numbers), and complex numbers (e.g., imaginary numbers, conjugate numbers)


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