Download Unit 4: Equations and Inequalities

Timeline:
2nd 9 weeks
4 weeks
Vocabulary:
Addition
Property of
Equality
Algebraic
Solution
Arithmetic
Solution
Coefficients
Cross Product
Division
Property of
Equality
Unit 4: Equations and Inequalities
Activities:
New State Standards:
Expressions and Equations
7.EE
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
1. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any
form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to
calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of
answers using mental computation and estimation strategies. For example: If a woman making $25 an hour
gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50.
If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will
need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact
computation.
Concepts
and Skills:
2.
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations
and inequalities to solve problems by reasoning about the quantities.
a. Solve word problems leading to equations of the form px+ q = r and p(x + q) = r, where p, q, and r
are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution
to an arithmetic solution, identifying the sequence of the operations used in each approach. For
example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
b. Solve word problems leading to inequalities of the form px+ q >r or px+ q <r, where p, q, and r are
specific rational numbers. Graph the solution set of the inequality and interpret it in the context of
the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week
you want your pay to be at least $100. Write an inequality for the number of sales you need to make,
and describe the solutions.
Equation
Estimation
Exact
Computation
Greater Than
Greater Than
or Equal to
Inequality
Less Than
Less Than or
Equal to
Linear
Multiplication
Property of
Equality
Multi-Step
Equation
NumberLine
One-Step
Equation
Proportion
Solution Set
Subtraction
Property of
Equality
Two-Step
Equation
College Readiness:
(Range 13-15) Basic Operations and Applications: Perform one-operation computation with whole numbers and
decimals
(Range 13-15) Basic Operations and Applications: Solve problems in one or two steps using whole numbers
(Range 16-19) Basic Operations and Applications: Solve routine one-step arithmetic problems (using whole
numbers, fractions, and decimals) such as single-step percent
(Range 16-19) Basic Operations and Applications: Solve some routine two-step arithmetic problems
(Range 13-15) Numbers: Concepts & Properties: Recognize equivalent fractions and fractions in lowest terms
(Range 16-19) Numbers: Concepts & Properties: Recognize one-digit factors of a number
(Range 20-23) Numbers: Concepts & Properties: Exhibit knowledge of elementary number concepts including
rounding, the ordering of decimals, pattern identification, absolute value, primes, and greatest common factor
(Range 24-27) Numbers: Concepts & Properties: Find and use the least common multiple
(Range 13-15) Expressions, Equations, & Inequalities: Exhibit knowledge of basic expressions (e.g., identify an
expression for a total as b + g)
(Range 13-15) Expressions, Equations, & Inequalities: Solve equations in the form x + a = b, where a and b are
whole numbers or decimals
(Range 16-19) Expressions, Equations, & Inequalities: Solve one-step equations having integer or decimal answers
(Range 16-19) Expressions, Equations, & Inequalities: Combine like terms (e.g., 2x + 5x)
(Range 20-23) Expressions, Equations, & Inequalities: Solve routine first-degree equations
(Range 20-23) Expressions, Equations, & Inequalities: Perform straightforward word-to-symbol translations
(Range 24-27) Expressions, Equations, & Inequalities: Solve real-world problems using first-degree equations
(Range 24-27) Expressions, Equations, & Inequalities: Write expressions, equations, or inequalities with a single
variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using
proportions)
(Range 24-27) Expressions, Equations, & Inequalities: Solve first-degree inequalities that do not require reversing
the inequality sign*
(Range 24-27) Graphical Representations: Identify the graph of a linear inequality on the number line*
(Range 24-27) Graphical Representations: Match linear graphs with their equations*
NCTM:
Number and Operations:

Use factors, multiples, prime factorization, and relatively prime numbers to solve problems

Develop meaning for integers and represent and compare quantities with them

Use the associative and commutative properties of addition and multiplication and the distributive property of
multiplication over addition to simplify computations with integers, fractions, and decimals

Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in
their use
Algebra:

Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible,
symbolic rules

Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations

Use symbolic algebra to represent situations and to solve problems, especially those that involve linear
relationships

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Model and solve contextualized problems using various representations, such as graphs, tables, and equations
 Use graphs to analyze the nature of changes in quantities in linear relationships.
Students will:

Solve onestep
equations
with rational
numbers

Solve twostep
equations
with rational
numbers

Solve multistep
equations
with rational
numbers

Solve
equations that
involve
distributive
property

Convert
between
fractions and
decimals

Use mental
computation
and
estimation
strategies to
solve
problems or
identify
reasonable
vs. nonreasonable
answers

Check
answers to
equations
using order of
operations

Solve onestep
inequalities

Solve twostep
inequalities

Graph the
solution set
of an
inequality on
a number line

Interpret the
graph of an
inequality in
the context of
a problem

Write
equations and
inequalities
from verbal
problems

Solve word
problems
using
equations and
inequalities