abc  
 
Solutions and Samples
   
of student work
 
14.

The figure has an even number of squares.

Explanations will vary. Possible explanations:

  • I counted the number of squares to see if it was an even or odd number. Sixteen is an even number.
  • I counted pairs to see if there was on square left over after pairing.
  • I drew a picture of the figure and rearranged the squares to show that there is an even number of squares
 

 

15.

Answers will vary. Sample student response:

 
Hints and Comments
 
   

Overview Students read the Summary, which reviews the main concepts of this section. They then analyze a configuration of squares to determine whether the total number of squares is odd or even. Students also write a description of the difference between odd and even.

Planning Have students work individually on problems 14 and 15. The Extension may be assigned as homework. After they complete Section A, you may assign appropriate activities from the Try This! section, located on pages 39-42 of the Student Book, for homework.

Comments about the Problems

14. Informal Assessment This problem assesses students' ability to recognize patterns in arrangements of objects and pictures and their ability to reason about patterns using pairing; symmetry; even, odd, and super-even numbers; and symbols. It also assesses their understanding of the concepts of pairing; even, odd, and super-even numbers; and zero as even.
15. Informal Assessment This problem assesses students' understanding of the concepts of pairing; even, odd, and super-even numbers; and zero as even. This problem evaluates students' understanding of even and odd numbers. It also shows whether they think at a concrete level by listing examples without describing generalities or are able to give more general description.

Extension Ask students: Is zero even or odd? [even] Encourage the class to think about zero, and whether it is even or odd. Have students share their reasoning. The idea of zero as even returns in Section C.

Did You Know? The V-formation is characteristic of the flight of ducks, geese, pelicans, and cranes. The "V" points in the direction of flight. In this formation, each bird behind the point can use the air that comes off of the outer wing of the bird ahead of it. This extra force of air helps a bird fly with less energy than it would need if it were flying a lone. The bird flying at the point of the V drops back when tired, and another bird takes its place. The formation probably also helps to maintain the social structure of a flock and helps young birds learn routes.

Source: The Cambridge Encyclopedia of Ornithology, edited by Michael Brooke and Time Birkhead (Cambridge, England: Cambridge University Press, 1991)

  Mathematics in Context • Patterns and Symbols
Section A   Pairing  17

MATHEMATICS IN CONTEXT - Patterns and Symbols: V-Patterns- Sections A & C
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