Download Patterns, Functions, and Algebra

Patterns, Functions, and Algebra
DAY 1
PFA5.6
You can use a graph to show the relationship
between two quantities.
Points of the graph are located by using
ordered pairs of numbers. The first number of
an ordered pair tells the number of spaces you
move to the right or left. (x) The second
number tells the number of spaces to move up
or down. (y)
Example: Joe walk at the rate of 3 kilometers
per hour. The table below shows the
relationship between d, the distance he walks,
and t, the time it takes him to walk this
distance. What does the graph look like?
Time t
(h)
0
1
2
3
Distance
d (km)
0
3
6
9
Ordered
Pair
(0,0)
(x, 3)
(2,6)
(3,y)
Function Rule:
d =3 x t
Use the data in the table to graph this relation.
Step 1: Label the axes. Write time (h) to
label the horizontal axis. Write Distance
(km) to label the vertical axis.
Step 2: Plot the points.
Step 3: Connect the points.
As distance increases, time
The graph shows a line that
What does the graph look like?
Day 2
You probably recognize the relationships
between variables and their affect on each other
in real life. For example:
1) The more your puppy eats, the more or
less he weighs?
2) As the temperature decreases in the
winter, do you need to wear more layers of
clothing or less?
Example: Using the data from the table,
describe the relationship between the amount of
days left before summer break and the number
of passes sold to the Zoo.
Days left Before
Summer Break
30
25
20
15
10
5
* As one variable
variable
# of Zoo Passes
Sold
100
125
175
300
400
525
, the other
.
Is the rate of change constant?
Day 3
A sequence is a set of numbers arranged in a
pattern.
2, 5, 8, 11, 14,….
Example: Esther wrote the number sequence
below on a piece of paper. She asked her friend
Marsha to find the next two terms in the
sequence. What are the next two terms?
1, 3, 6, 10, 15, …
Day 4:
A function is a relation in which one quantity
is dependent on the other. A function can be
described in words or by using an equation
where variables are used to represent each
quantity.
Example: Julia used toothpicks to make the
triangles below. Describe the toothpick function
in words and with an equation. Based on the
function, how many toothpicks are needed to
make 8 triangles?
Step 1: Complete the function table to help.
Number of
triangles (t)
Number of
toothpicks (p)
1 2 3 4
3 5 X W
Step 2: Determine how you could change
each number in the top row to get the
number in the bottom row.
X2 +1
Step 3: Describe the function. The number of
toothpicks is equal to twice the number of
triangles plus
.
p=
xt+
Step 4: Use the function to find p when t = 8.
Day 5
Step 1: Study the diagram. Look for a
pattern.
Step 2: Apply the pattern.
How many blocks will there be on the seventh
step?
The total number of blocks is equal to the sum
of
.
Step 3: Check your answer.
Draw a seven-step staircase.
Count all the blocks.
How many were needed?
Day 6
Remember an unknown number may be
represented by a letter or other symbol called a
variable.
An algebraic expression is an expression that
contains one or more variables.
Example: Jalise had some pencils. Mary Kate
gave her 4 more pencils. Write an expression to
determine how many pencils Jalise has now.
Use p for pencils. Since we do not know the
amount she started or ended with, we can write
an expression, but not an equation.
P+4
An equation is a mathematical sentence that
states that two expressions are equal.
Each number in a sequence is called a term.
You can find any term in a sequence of
numbers if you have an algebraic expression for
the nth term of the sequence.
Step 1: Identify the rule that the pattern
follows. Make a table that lists the given terms
and the value of each term.
1st
Term
Value of Term 1
2nd 3rd
3 6
4th 5th
10 15
Step 2: Note how the values change from
term to term.
First term:1
Second Term: 3=1+2
Third Term: 6=3+3
Fourth Term: 10=6+4
Fifth Term: 15=10+5
The number being added to each term increases
by
.
Step 3: Use the pattern rule to find the sixth
and seventh terms.
Sixth:
Seventh:
Day 7
Inequality: a mathematical sentence that states
that two expressions are not equal!
Two symbols are commonly used:
< means less than
> means greater than
Inequalities are solved the same as equations,
ONLY, the solution (answer) may be more than
one number.
Example: Gabby had a greater number of
spelling words to learn than her sister who is in
second grade. Gabby’s sister had 15 words on
her list. Write an inequality to represent the
number of spelling words (N) Gabby could
have.
Solution: Gabby’s sister had 15. Gabby could
have any number greater than 15. So: N >15
N > 15, not = to 15, because the word problem
stated that Gabby had more than her sister and
her sister had 15. The variable N represents any
number greater than 15 (16, 17, 18, 19, 20, etc)
Example: Put in the correct symbol (<, >)
below. 20 + 15
45 + 5