| NUMBER PATTERNS |
Number Patterns
Juanita drops a dime into her piggy bank every night before she goes to sleep. She started this habit on April 1st. On April 17th, she wants to know how much money she'll have at the end of the month, so she makes a table from the data of the first week, to see if she can find a pattern to help her predict the amount of money in her bank on April 30th.
| date | April 1 | April 2 | April 3 | April 4 | April 5 | April 6 | April 7 |
| money | 10¢ | 20¢ | 30¢ | 40¢ | 50¢ | 60¢ | 70¢ |
She sees that on the 5th day, she had 5 × 10¢ and on the 6th day, she had 6 × 10¢ and so on, so she concludes that the pattern is to multiply the day of the month by 10¢. Juanita then knows she'll have 30 × 10¢ or $3.00 in her piggy bank on the last day of April.
The rule for this pattern is:
multiply 10¢ by the day of the month
10¢ × day of the month
In this pattern, each value is a multiple of 10¢ so we see a multiplication sign in the rule.
With this pattern -- 1, 4, 7, 10 -- where each number is 3 more than the one before it, the rule will have a plus sign ( + ). The rule here is "number plus 3" or "number + 3".
Other patterns, like -- 24, 12, 6, 3 -- are quotients. Here, we divide each number by 2 to get the next one. The rule is "divide by 2" or "number ÷ 2"
Some patterns can have 2 different rules. We know that multiplication is repeated addition,
so the rule for this pattern -- 0, 5, 10, 15, 20, ... -- is either "number + 5" or "5 times table entries". This pattern or sequence is 5 × 1, 5 × 2, 5 × 3, 5 × 4 ...
The rule for the pattern of quotients -- 24, 12, 6, 3 -- could also be " ½ of number " since dividing a number by 2 is exactly the same as taking ½ of it.
Examples: Write the rule for these number patterns. Find the next number.
| a) 1, 6, 11, 16, ... rule: add 5 |
b) 0, 7, 14, 21, ... rule: add 7 or |
c) 20, 17, 14, 11, ... rule: subtract 3 |
d) 1, 3, 5, 7, 9, ... rule: add 2 or |
.
Now get a pencil, an eraser and a note book, copy the questions,
do the practice exercise(s), then check your work with the solutions.
If you get stuck, review the examples in the lesson, then try again.
Practice Exercises
1) Find the pattern, write the rule, fill in the blanks:
| a) 10, 20, __, 40, .. | b) 15, 13, __, 9, 7 .. | c) 4, __, 12, __, 20.. | d) 1, 4, 7, __, __, 16.. |
2) In order to study the bacteria that cause disease, mad scientists "grow" them in their labs. Some of these germs grow so quickly that every 20 minutes, there are twice as many as there were before. A mad scientist "plants" 100 grams of these bacteria at 10 a.m.
a) fill in the table of values for the weight of bacteria for every 20 minutes until noon.
| time | 10 a.m. | 10:20 | 10:40 | 11 a.m. | 11:20 | 11:40 | noon |
| bacteria | 100 g |
b) write the rule for this number pattern.
c) if the bacteria continue to grow, how much will they weigh at 12:20 p.m.?
Solutions
1) Find the pattern, write the rule, fill in the blanks:
| a) 10, 20, __, 40, .. rule: add 10; or |
b) 15, 13, __, 9, 7 .. rule: subtract 2 |
c) 4, __, 12, __, 20.. rule: add 4; (4 × table) |
d) 1, 4, 7, __, __, 16.. rule: add 3 |
2) a)
| time | 10 a.m. | 10:20 | 10:40 | 11 a.m. | 11:20 | 11:40 | noon |
| bacteria | 100 | 200 | 400 | 800 | 1,600 | 3,200 | 6,400 |
b) Start with 100, every 20 minutes, multiply by 2.
c) At 12:20 p.m. there will be 2 × 6 400 = 12 800 grams of bacteria.
