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226 • Chapter 7
Now you can see the pattern. Each time, you add the
next counting number to the term. Often a visual aid such as
creating a table helps you identify a pattern you may not no-
tice in paragraph form.
To help build spatial-relationship skills, view these num-
bers in a picture.
The triangular arrangement prompts us to name this se-
quence the triangular numbers. Looking at the pattern of
dots, decide how adding a counting number each time adds
dots to the figures.
The next exercise requires that you perform long divi-
sion. You may prefer to use a calculator, but the display may
not hold enough digits for you to recognize the pattern.
Complete the following table and then look for patterns.
Notice that the division will never end, so stop after 12 dig-
its in your answers. As soon as you recognize the pattern,
test one more number, and then fill in the Quotient block
from the pattern. Answers are at the end of this chapter.
Division Quotient
1 ÷ 7 0. _ _ _ _ _ _ _ _ _ _ _ _
2 ÷ 7 0. _ _ _ _ _ _ _ _ _ _ _ _
3 ÷ 7 0. _ _ _ _ _ _ _ _ _ _ _ _
4 ÷ 7 0. _ _ _ _ _ _ _ _ _ _ _ _
5 ÷ 7 0. _ _ _ _ _ _ _ _ _ _ _ _
6 ÷ 7 0. _ _ _ _ _ _ _ _ _ _ _ _
Notice the patterns within the quotients that relate to 7?
Examine the Quotient column. Do you see that there is a 14
and 28 in each number? That is 2 ´7 and 4 ´7. Another pat-
tern is that the first digits in the quotients are in ascending