Teaching Notes 1.9: Identifying Patterns by Considering
All of the Numbers
Identifying patterns and recognizing the relationship between numbers is an important skill.
Students frequently make a quick decision based on examining only a few numbers in a pattern
instead of all of them, which, of course, leads to mistakes.- Explain that the numbers in any pattern are related in some way.
- Emphasize that students must consider all, not merely some, of the numbers of a pattern
before they can identify the relationship between the numbers in the pattern. - Provide your students with the following example: 2, 4, 8,...
- Ask them to consider only the first two numbers. Explain that two relationships for the num-
bers are possible:- Each number is two more than the previous one.
- Each number is two times the previous one.
- Direct your students to now consider the third number. Explain that the third number proves
that the only correct relationship is that each number is two times the number before it. - Review the information and examples on the worksheet with your students.
EXTRA HELP:
All numbers in a pattern must be related.ANSWER KEY:
(1)3 is subtracted from the previous number. (2)8 is added to the previous number.
(3)The second number is found by adding 10,
the third is found by adding 1, and this
pattern continues.
(5)Each number is the square of the previous
number.
(7)Each number is 3 more than the previous
number.
(9)Each number is a multiple of 4.(4)Numbers are found by adding 3, then
adding 4, adding 5, and so on.
(6)Each number is one-third of the previous
number.
(8)Each number is found by subtracting 1,
then adding 1, and so on.
(10)Each number is found by dividing the
previous number by 5.
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(Challenge)The missing number is 11. Each number is the sum of the two preceding numbers.
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