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Overview
A further exploration of the sums of even and odd numbers
is supported by using dot numbers and the concept of pairing.
Students should now be ready to generalize about combining
odd and even numbers.
About
the Mathematics Problems 19-21 will help students
generalize the following properties of numbers:
- even
+ odd = odd,
- odd
+ odd = even.
Planning
After completing the problems on this page, many students
may be ready to generalize about adding odd and even numbers.
Decide whether you want to use problem 20 as a writing
opportunity or as an assessment. Be sure to discuss students'
answers to problem 21. Students may work in pairs
or small groups on these problems.
Comments
about the Problems
| 20.
|
Informal
Assessment This problem assesses students' ability
to reason about patterns using pairing; symmetry; even,
odd, and super-even numbers; symbols; and directions. |
| 21. |
Students
apply their understanding of the properties of odd and
even numbers in a more complex situation. If students
are having difficulty, remind them that a V-pattern
always has an odd number of objects. |
Extension
Together with students, review all the rules for the sums
of even and odd numbers. You may want to explain similar
rules for multiplying odd and even numbers. The rules for
multiplication are as follows:
- even
x even = even,
- odd
x even = even,
- odd
x odd = odd.
Writing
Opportunity Problem 20 can be used as a journal
writing assignment. Ask students to write their explanations
about dot patterns in a way that would make sense to someone
who has never heard of dot patterns.
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