Patterns and Relations!!!
In this unit we have started by reviewing patterns!
In this unit we have started by reviewing patterns!
In the shapes pattern above you can guess what the pattern is to find out what the shape is after the square.
1 2 3 4 5 1 2 3 4 5 _______
You can see that after the square would be another triangle.
You can see that after the square would be another triangle.
Addition Rules
What is the pattern that is taking place in this picture?
1, 4, 7, 10, 13, ___, ____, ____
Step 1. Draw the Jumps!!!!!
1, 4, 7, 10, 13, ___, ____, ____
Step 1. Draw the Jumps!!!!!
Each shape is growing by 3 dots each time.
We can make rules to figure out the other numbers!
The pattern starts with 1 dot, so our rule will too.
Then because the number increases by three each time, we will say add 3.
Rule:
Start at 1. Add 3 each time.
We can make rules to figure out the other numbers!
The pattern starts with 1 dot, so our rule will too.
Then because the number increases by three each time, we will say add 3.
Rule:
Start at 1. Add 3 each time.
Subtraction Rules
In this pattern, the number is decreasing by 4 each time. The pattern starts with 14, so will our rule.
Start at 14 then minus 4 each time.
Start at 14 then minus 4 each time.
Addition and Subtraction Rules
In this pattern the number increases by 3 and then decreases by 1.
Start at 1 then alternate adding 3 then subtracting 1.
Start at 1 then alternate adding 3 then subtracting 1.
Other Rules
Increasing Pattern
In this pattern, the number that is added increases by 1 each time.
Start at 5, add 1, then increase the amount you add by one each time.
Start at 5, add 1, then increase the amount you add by one each time.
2 Patterns in One or Alternating
Some patterns can have multiple rules.
Using Patterns to Solve Problems
One puzzle book costs $17. How many would 5 cost?
Step 1. Make a T chart like the one on the left.
Step 2. Make the titles. We know that 1 book has a total of $17 dollars. So as the number of books increase, so will the total. Step 3. If we were to buy 2 books at $17 each, the total would be 34. I can do that by adding 17 up twice or multiplying it by 2. Step 4. Complete the chart by finding the total cost by multiplying the number of books bought by $17. Formula: Tn X 17The x stands for the number of books that someone might want.
The T stands for the number of books column. The 17 stands for the $17. We can now figure our any number in the pattern. I would like to buy 103 puzzle books. What would that cost? Tn X 17 = T103 X 17 =$1751 |
Johnny has $32 dollars in his bank account. Each week he buys a new album on iTunes which costs $4.50. How many weeks can Johnny buy album before he runs out of money? How many albums can he buy and how much money will he have left?
Solving Equations with a Letter Variable
5 + 6 = 11
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9 X 3 = 27
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n + 6 = 11
(11 - 6 = n ) n = 5 5 + n = 11
(11 - 5 = n) n = 6 |
n X 3 = 27
(27 divided by 3 = n) n = 9 9 X n = 27
(27 divided by 9 = n) n = 3 |
Using Variables to Write a Formula
Andy buys 1 book each week. He already owns 7. How many will he have in 6 weeks?
7 , 8 , 9 , 10 , 11 , ___
T1 , T2 , T3 , T4 , T5 , T6
The pattern rule for this pattern is:
Start at 7 and add 1 each time
Start at 7 and add 1 each time
We are now going to take this information to write an equation to solve for other problems.
7 is in the T1 position. We are going to subtract 7 and T1. 7 - 1 = 6 8 is in the T2 position. We are going to subtract 8 and T2. 8 - 2 = 6 With this information we can create a formula. n stand for any number in the term position. Tn = Tn + 6 |
Mike bought 40 boxes of Kleenex. Each week he uses one. How many Kleenex boxes will Mike have left after 17 weeks?
Rule: Start at 40 and subtract 1 each time.
show_what_you_know.docx | |
File Size: | 174 kb |
File Type: | docx |
show_what_you_know_solutions.docx | |
File Size: | 185 kb |
File Type: | docx |
Program of Study
Patterns: Awareness of patterns supports problem solving in various situations.
How might representation of a sequence provide insight into change?
Students relate terms to position within an arithmetic sequence.
Knowledge
A table of values representing an arithmetic sequence lists the position in the first column or row and the corresponding term in the second column or row.
Points representing an arithmetic sequence on a coordinate grid fit on a straight line. An algebraic expression can describe the relationship between the positions and terms of an arithmetic sequence. |
Understanding
Each term of an arithmetic sequence corresponds to a natural number indicating position in the sequence.
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Skills and Procedure
Represent one-to-one correspondence between positions and terms of an arithmetic sequence in a table of values and on a coordinate grid.
Describe the graph of an arithmetic sequence as a straight line. Describe a rule, limited to one operation, that expresses correspondence between positions and terms of an arithmetic sequence. Write an algebraic expression, limited to one operation, that represents correspondence between positions and terms of an arithmetic sequence. Determine the missing term in an arithmetic sequence that corresponds to a given position. Solve problems involving an arithmetic sequence. |