Lesson 3

Circle Pieces: Red, Pink, Orange, Aqua

Est. Class Sessions: 2–3

Developing the Lesson

Part 4. Fractions Equal To or Greater Than One

Begin this part of the lesson by asking students to discuss these questions with a partner:

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  • Is there a fraction that means one whole?
  • Can a fraction be greater than a whole?

Have a few students share their thoughts. Then direct students' attention to the Fractions Equal To or Greater Than One section in the Student Guide. Read the paragraphs and discuss the examples that precede Question 20. Use a display set of 3 pink fraction circle pieces to illustrate the examples given. Show students the notation for fractions equal to one and for fractions greater than one using improper fractions (3/2) and using mixed numbers (11/2).

Assign Questions 20–22 to student pairs to introduce notation for fractions greater than or equal to one. Encourage students to first find the circle piece that is the unit whole and then to place the other pieces onto the whole. This shows that the pieces either fully cover the whole or are greater than the whole. They essentially begin another whole. Ask students to write either mixed numbers or improper fractions for each question.

After students have completed the questions, have them share answers using circle pieces.

Tell students to use the pink piece for the unit whole and ask:

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  • What fraction describes 1 aqua piece? (1/3)
  • What fraction describes 3 aqua pieces (Question 21A)? (3/3)
  • What is another way to say three-thirds? (1 or 1 whole)
  • Write a fraction for 5 aqua pieces. (5/3)
  • What is another way to say that? (one and two-thirds)

Revisit the questions you posed in the beginning of Part 4. Students should agree that a fraction like 3/3 equals one whole, and that fractions can be greater than one, such as 5/3 or 12/3.

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Fractions. A mathematical definition of a fraction: Any number that can be written as a/b where a and b are whole numbers and b is not zero. In everyday language, we think of a fraction as part of a whole. However, using this definition 2/1, 2/2, and 3/2 are fractions, since the numerators and denominators are whole numbers and zero is not in the denominator. They are called improper fractions because the numerator is equal to or greater than the denominator. Although they are called improper, they are still fractions and quite useful in many situations, especially in computation. See Mathematics in this Unit for more information on fractions.

Student Guide: 256 257
Answers
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