Geometric
Patterns
Lesson 1
MINDS ON!
A LINEAR PATTERN can be
identified by a COMMON
DIFFERENCE between terms.
For example 3,5,7,9… is a LINEAR
PATTERN 3,5,8,12… is a
NON-LINEAR pattern.
20 min
MINDS ON!
Is this a LINEAR PATTERN? How would you
find the expression to represent it? How many
shapes will be in the 5th shape?
20 min
20 min
MINDS ON!
Make a table of values!
Term Number
(x)
0
Pattern Rule:
Term Value
(y)
First Difference
20 min
MINDS ON!
Let’s graph
the relation!
Why do you think this type of pattern
is called Linear?
EXPECTATION
C1.1 identify and compare a variety of repeating, growing, and shrinking
patterns, including patterns found in real-life contexts, and compare linear
growing and shrinking patterns on the basis of their constant rates and
initial values
LEARNING GOAL
Today we are learning to represent
linear growing patterns.
EXAMPLE
1,3,5,7,9,11 can be described as a
pattern that starts with 1 and
increases by 2 as it extends.
ACTION!
Make a table of values then define the pattern
rule algebraically.
Use the expression to find the perimeters
of Frames 5, 10, and 100.
ACTION!
Make a table of values then define the pattern
rule algebraically.
Use the expression to find the perimeter
of Frame 40.
CONSOLIDATION
CONSOLIDATION
Complete all questions posted on Google
Classroom.
Number
Patterns
Lesson 2
MINDS ON
MINDS ON!
MINDS ON!
Make a table of values!
Term Number
(x)
0
Pattern Rule:
Term Value
(y)
First Difference
20 min
MINDS ON!
Let’s graph
the relation!
Why do you think this type of pattern
is called Linear?
EXPECTATION
C1.1 identify and compare a variety of repeating, growing, and shrinking
patterns, including patterns found in real-life contexts, and compare linear
growing and shrinking patterns on the basis of their constant rates and
initial values
LEARNING GOAL
Today we are learning to represent
linear growing patterns.
EXAMPLE
1,3,5,7,9,11 can be described as a
pattern that starts with 1 and
increases by 2 as it extends.
ACTION!
Make a table of values then define the pattern
rule algebraically.
CONSOLIDATION
Complete all questions posted on Google
Classroom.
Tables,
Graphs, and
Equations
Lesson 3
5 min
MINDS ON
Which of the following are LINEAR?
3, 7, 11, 14, 17
1
2
2
9
3
16
4
23
5
30
MINDS ON
8, 2, -4, -10, …
Is this pattern linear? Is it growing or
shrinking? Graph this pattern and
describe it using an algebraic equation.
EXPECTATION
C1.2 create and translate repeating, growing, and shrinking patterns
involving rational numbers using various representations, including
algebraic expressions and equations for linear growing and shrinking
patterns
LEARNING GOAL
We are learning to
represent growing and shrinking patterns using tables of values
and graphs
EXAMPLE
4,6,8,10,12 can be
represented as 2x + 2
Term
Value
1
4
2
6
3
8
4
10
5
12
ACTION!
20 min
Create a table of values, a graph, and
an equation to represent this LINEAR
PATTERN.
7, 0, -7, -14, -21
CONSOLIDATION
Complete all questions posted on Google
Classroom.
Linear
Patterns
Lesson 4
MINDS ON
Ms. Noxon needs to have a LOT of pencils for her
students. Before the first day of school, she sets out 23
pencils, one for each student in the class. Every day
after, she gives out an average of four pencils.
Graph the pattern. Describe it algebraically.
How many pencils will Ms. Noxon give out after 35
days, 75 days, and 200 days?
Extension
How many days will it take for Ms. Noxon to
give out 500, 750, and 237 pencils?
EXPECTATION
C1.2 create and translate repeating, growing, and shrinking
patterns involving rational numbers using various representations,
including algebraic expressions and equations for linear growing
and shrinking patterns
LEARNING GOAL
Today we are learning to
use algebra to represent patterns.
EXAMPLE
the general term for the sequence 4, 5, 6, 7, ... can be written
algebraically as n + 3, where n represents the term number
ACTION
5 min
Shira received a $250 award for her outstanding
volunteer work in her community. She has decided to
use the money to pay for a new bike which costs $470.
If she saves $20/week, how long
will it take her to save enough
money for her new bike?
CONSOLIDATION
Ms. Noxon has to choose between two gym
membership plans.
Plan A: $50 monthly membership fee and $10
per visit.
Plan B: $25 monthly membership fee and $15
per visit.
Which plan is the better deal? Does this
change at any point?
5 min
CONSOLIDATION
Complete all questions posted on Google
Classroom.
Graphs and
Equations
Lesson 5
5 min
MINDS ON
1,4,7,10,13…
How would you find the...
8th term?
15th term?
100th term?
500th term?
MINDS ON!
Create a table of values and an
expression that correspond with the
graph.
20 min
EXPECTATION
C1.3 determine pattern rules and use them to extend patterns, make and justify
predictions, and identify missing elements in growing and shrinking patterns
involving rational numbers, and use algebraic representations of the pattern
rules to solve for unknown values in linear growing and shrinking patterns
LEARNING GOAL
Use a graph or equation to find an unknown value.
EXAMPLE
Given the graph that represents the pattern 1, 3, 5, 7, ..., find the
10th term. Given the algebraic equation that represents the pattern,
t = 2n – 1, find the 100th term.
EXTENSION!
5 min
Kelly and Gary have part-time jobs.
Kelly is paid $11/hr. How much will she earn for working
16 hours on the weekend?
Gary also worked 16 hours on
the weekend, but he earned $20
in tips. His total earnings
were $180. How much does he
earn per hour?
ACTION!
If you are given the following graph, how
can you determine the 4th term?
20 min
ACTION!
If you are given the following equation,
y = 3x - 2,
how can you find the 9th term?
ACTION!
20 min
Create the corresponding patterns (first five
values):
a) 3x + 4
b) 2x + 3
c) x -1
d) 5x -3
CONSOLIDATION
What is the 10th term?
a) y = 3x - 3
b)
5 min
PRACTICE
You are going to be using the graphs and equations you created
yesterday.
1. Using the equations you created, calculate the 10th, 15th, and
30th values for each pattern.
2. Create a new Cartesian plane and graph the lines including the
new values.
3. Confirm your findings with the members of your group.
4. Given the following pattern, identify the COMMON DIFFERENCE,
create an equation and a graph and identify the 10th, 15th, and
30th values.
2.5, 3.2, 3.9, 4.6, ...
CHALLENGES!
1. Did any of your lines have a negative slope (e.g. -3x + 2)? If not, create
a line with a negative slope and determine the 10th, 15th, and 30th
values.
Was this easier/harder than using patterns with a positive slope? What
was the difference?
2. Can you find the missing term number?
The equation for the line is y = 3x + 2 and the term value is 11. What is
the term number?
The equation for the line is y = -13x - 6 and the term value is -71. What
is the term number?
Create the corresponding pattern and graph to confirm your answers.