Download 9th Grade Unit 2

9th Grade Unit 2
9th Grade Math Class; Lesson Number 2 Day 3
Key Standards addressed in this Lesson: MCC9-12.A.REI.5&6
Time allotted for this Lesson: 1 day
Materials Needed:
Graph paper
Colored pencils
Key Concepts in Standards: Refer to TE
 solve linear equations in one variable.
 solve linear inequalities in one variable.
 solve a system of two equations in two variables by using multiplication and addition.
 solve a system of two equations in two variables graphically
 graph a linear inequality in two variables.
 graph a system of two linear inequalities in two variables.
Essential Question(s): Refer to TE
How do I justify the solution to an equation?
How do I prove that a system of two equations in two variables can be solved by multiplying and
adding to produce a system with the same solutions?
How do I solve a system of linear equations graphically?
How do I graph a linear inequality in two variables?
How do I graph a system of linear inequalities in two variables?
Vocabulary: (Tier) Refer to TE
Tier 1: already knows
Tier 2: needs review
Tier 1
Tier 2
Algebra
Variable
Coefficient
Equation
Expression
Inequality
Ordered Pair
Substitution
Concepts/Skills to Maintain: Refer to TE
 Interpreting a graph
 Creating a table of values
 Being able to read and write inequality symbols
 Graphing equations and inequalities on the coordinate plane
Tier 3: New Vocabulary
Tier 3
Elimination
9th Grade Unit 2
Opening: (use on the Elmo)
Give students these problems that can be solved with substitution or any method:
1. 4 x  y  17
y  1
2. y  3 x  6
y  x4
3. y  8 x  3
3 x  2 y  6
Work Session:
Worksheet: Solving Systems of Equations Using Any Method (16 problems)
See attached
Additional Resources:
Punchline Algebra Book A 8.2, 8.6, 8.7
Carnegie Coordinate Algebra Lessons 6.2-6.4
Closing:
Quiz: 4 problems (1 graphing, 1 elimination, 1 substitution, 1 any method) see attached
Corresponding Task(s) (if not in work session – there may be several tasks that fit) –
****All Tasks can be found at www.georgiastandards.org****
Highlight the Mathematical Practices that this lesson incorporates:
Make sense
of problems
and
persevere
in solving
them
Reason
abstractly
and
quantitatively
Construct
viable
arguments
and critique
the
reasoning
of others
Model with
mathematics
Use
appropriate
tools
strategically
Attend to
precision
Look for
and make
sure of
structure
Look for
and
express
regularity in
repeated
reasoning
9th Grade Unit 2
Solving Systems of Equation Using Any Method
3
1. y   x  4
4
1
y  x 1
2
4.
7.
10.
y  4 x  11
y  x4
y  7x  4
y  7x  4
y  2 x  19
y  3 x  16
2. 4 x  3 y  6
3.  9 x  5 y  27
5 x  3 y  21
5.
8.
11.
5 x  2 y  4
x  2 y  8
7x  2 y  9
9 x  9 y  0
y  5 x  12
5 x  2 y  21
 2 x  8 y  16
6.
9.
12.
3 x  2 y  20
12 x  8 y  16
x  4 y  16
3x  2 y  6
x  5 y  2
4 x  6 y  18
13. The sum of two numbers is 19. Their difference is 1. What are the numbers?
14. The difference of two numbers is 4. Their sum is 24. What are the numbers?
15. Steve and Jennifer each improved their yards by planting rose bushes and shrubs. They bought their supplies
from the same store. Steve spent $114 on 6 rose bushes and 12 shrubs. Jennifer spent $148 on 12 rose bushes
and 14 shrubs. What is the cost of one rose bush and the cost of one shrub?
16. The senior classes at Eastside High School and Northside High School planned separate trips to the local
amusement park. The senior class at Eastside High School rented and filled 12 vans and 9 buses with 312
students. Northside High School rented and filled 5 vans and 14 buses with 335 students. Each van and each
bus carried the same number of students. Find the number of students in each van and in each bus.
9th Grade Unit 2
Quiz – Solving Systems of Equations
Name ______________________________
Solve each system of equations.
1.
2.
3.
4.
The sum of two integers is 92. Their
difference is 20. Find the numbers.