Download 2nd Quarter – Math

2nd Quarter – Math
Domain: Expressions and Equations
Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations.
Standard: MAFS.EE.3.7 Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the
case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a
and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive
property and collecting like terms.
Understand
“Essential understandings,” or generalizations, represent ideas that are transferable to other contexts.

There can be multiple approaches to solving a multi-step equation, and some approaches may be more appropriate than
others.
Know
Do
Declarative knowledge: Facts,
Procedural knowledge: Skills, strategies and processes that are transferrable to other
vocabulary, information
contexts.
• How to solve multi-step linear
equations
• Know key vocabulary such as:
Linear
equation, rational number, coefficients,
equation, expression, distributive
• Solve multi-step linear equations with rational coefficients
• Expand expressions in linear equations using the distributive property
• Collect like terms in linear equations
property, like terms
Prerequisite skills:
What prior knowledge (foundational skills) do students need to have mastered to be successful with this standard?
• Solve one and two step linear equations
• Know the difference between an expression and an equation
• Know the difference between like and unlike terms
• Simplify using the Distributive property
• Apply integer rules
• Know operations with fractions and decimals
• Apply inverse operations to solve equations
Standard: MAFS.EE.3.7 Solve Linear Equations in One Variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is
the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results
(where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive
property and collecting like terms.
Score Learning Progression
I can…
4.0
• Construct a viable argument to
Sample Tasks
1. Construct a viable argument to correct an error on a
multi-step linear equation below:
2. Solve this multi-step equation using
at least two different solution
methods, and justify your reasoning.
correct an error on a multi-step linear
2(x + 3) + 8 = 10
equation. Solve a multi-step equation
using at least two different solution
methods, and justify my reasoning.
3.5
I can do everything at a 3.0, and I can demonstrate partial success at score 4.0.
I can…
• Solve linear equations in one
variable, with or without a real world
context.
pays $7.50. They spend a total of $40 for the shark exhibit.
no solution, one solution or infinitely
The total cost is $70. Solve 7.5x + 40 = 70 to find how many many solutions.
people went to the aquarium.
• 3x = 3x + 4
• 3x + 4 = 3x + 4
one variable with one solution,
• 3x + 4 = 4x + 3
solutions.
2. Solve
1/4(8x – 12) = 5x + 9
• Solve linear equations with rational
number coefficients, including
equations whose solutions require
expanding expressions using the
distributive property and collecting
like terms.
2.5
3. Select whether each equation has
• Give examples of linear equations in
infinitely many solutions, or no
3.0
1. Some friends decide to go to the aquarium. Each person
I can do everything at a 2.0, and I can demonstrate partial success at score 3.0.
I can…
1. Solve -2( x + 3) = 12
like terms:
• Solve one and two-step equations.
a. x, x2
• Identify and combine like terms.
2.0
• Expand an expression using the
distributive property.
3. Identify the pair(s) that have/has
2. Solve 7 + 5x
= 42
• Recall key vocabulary such as: Linear
b. 4x, 4y
c. x, 7x
d. x2, -2x2
equation, rational number,
coefficients, equation, expression,
distributive property, like terms
1.0
I need prompting and/or support to complete 2.0 tasks.
Domain: Expressions and Equations
Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations.
Standard(s): MAFS.8.EE.3.8
Analyze and solve pairs of simultaneous linear equations.
1. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of
their graphs, because points of intersection satisfy both equations simultaneously.
2. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the
equations. Solve simple cases by inspection.
3. Solve real-world and mathematical problems leading to two linear equations in two variables (ie. Given coordinates
for two pairs of points can determine whether the line that passes through the first pair of points intersects the line
that passes through the second pair of points.)
Understand
“Essential understandings,” or generalizations, represent ideas that are transferable to other contexts.

The intersection of two lines in a coordinate plane is the solution to the system of linear equations.

A system of linear equations can be solved algebraically, using substitution or elimination.

The algebraic solution of a linear system can be estimated by graphing.

A system of linear equation can have one solution, no solution or infinitely many solutions.

A linear system can represent a real world problem.
Know
Do
Declarative knowledge: Facts,
Procedural knowledge: Skills, strategies and processes that are transferrable to
vocabulary, information
other contexts.
Vocab: Proportional/non-proportional
relationship, unit rate, slope, y-intercept,
similar triangle, rate of change, initial

Graph a system of two linear equations.
value, linear function, systems of

Find the point of intersection of two linear equations.
equations, substitution, elimination,

Solve a linear system using substitution or elimination.
point of intersection,

Estimate the algebraic solution by graphing.
independent/dependent variables,

Determine how many solutions there are to a linear system.
domain/range

Write and solve a linear system to model a real world situation.

Can solve by graphing or using
algebra.

Can recall the multiplication
property of equality.

Can identify the solution(s) of the
system.
Prerequisite skills:
What prior knowledge (foundational skills) do students need to have mastered to be successful with this standard?

Graphing ordered pairs.

Using slope, y-intercept and a table of values to graph a linear equation.

Writing and solving equations.

Using substitution to check the solution with each equation.
Math Florida Standard(s): MAFS.8.EE.3.8
Analyze and solve pairs of simultaneous linear equations.
1. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of
their graphs, because points of intersection satisfy both equations simultaneously.
2. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the
equations. Solve simple cases by inspection.
3. Solve real-world and mathematical problems leading to two linear equations in two variables (ie. Given coordinates
for two pairs of points can determine whether the line that passes through the first pair of points intersects the line
that passes through the second pair of points.)
Score Learning Progression
4.0
I can…
Sample Tasks

Elias is trying to choose between two bike companies.
Rent-A-Bike charges a $25 initial fee and an additional $5

for each hour rented. Crusin’ Bikes charges an $18 initial
Solve a linear system that is represented in different
fee and an additional fee $6 for each hour rented.
forms (ie. table and an equation).

Create a system from a real world situation.
For how many hours of rental is the amount charged by the
two companies the same?
What is the cost, in dollars, of renting a bike from either
company when the hours and costs are both the same?
3.5
I can do everything at a 3.0, and I can demonstrate partial success at score 4.0.
I can…

Use the graphs of two linear equations to estimate
the solutions of a system.

Solve a linear system by graphing.

Solve a linear system by using algebra.

Check the algebraic solution by graphing the two
linear equations.
3.0


Solve the system by graphing.
y=x+4
y = -2x - 2

Solve the system algebraically.
Show that there are systems of equations that have
one solution, no solution or infinitely many
solutions.

Apply my knowledge of system of equations to real
world situations.
m5+ 1.5 = 2
7m + n = 17.5

Given the following equations, students can solve the 4.0
word problem:
Rent-A-Bike: y = 5x + 25
2.5
I can do everything at a 2.0, and I can demonstrate partial success at score 3.0.
I can…
2.0

of linear equations given a graph.

1.0
Use mathematical reasoning to solve simple systems
Use a table to find the solution.
I need prompting and/or support to complete 2.0 tasks.
Cruisin’ Bikes: y = 6x + 18