Solving EquationsChapter 2

2.1 Solving One-Step EquationsPg. 81 – 87Obj: Learn how to solve one-step

equations in one variable.Content Standard: A.CED.1 and

A.REI.3

2.1 Solving One-Step EquationsEquivalent equations – equations

that have the same solution(s)Isolate – get the variable with a

coefficient of one alone on one side of the equation

Inverse Operation – an operation that undoes another operation

2.1 Solving One-Step EquationsMethod for solving one-step equations

◦Goal: Isolate the variable◦Use the inverse operation to get the

variable by itself Addition – Subtraction Subtraction – Addition Multiplication – Division Division – Multiplication

◦Whatever you do to one side of the equation, you must do to the other (balanced)

2.2 Solving Two-Step EquationsPg. 88 – 93Obj: Learn how to solve two-step

equations in one variable.Content Standards: A.REI.3,

A.CED.1, and A.REI.1

2.2 Solving Two-Step EquationsMethod for solving two-step

equations◦Goal: Isolate the variable◦Use the reverse of the order of

operations Addition or subtraction Multiplication or division

◦Use the inverse operations◦Keep the equation balanced

2.3 Solving Multi-Step EquationsPg. 94 – 100Obj: Learn how to solve multi-

step equations in one variable.Content Standards: A.CED.1,

A.REI.1, and A.REI.3

2.4 Solving Equations With Variables on Both SidesPg. 102- 108Obj: Learn how to solve

equations with variables on both sides and identify equations that are identities or have no solution.

Content Standards: A.CED.1, A.REI.1, and A.REI.3

2.4 Solving Equations With Variables on Both SidesIdentity – an equation that is true

for every possible value of the variable

2.4 Solving Equations With Variables on Both SidesSolving Equations

◦Use the Distributive Property to remove grouping symbols

◦Combine like terms on each side of the equation

◦Get the variable terms on one side of the equation

◦Use the inverse operations to solve for the variable

◦Check you solution in the original equation

2.5 Literal Equations and FormulasPg. 109 – 114Obj: Learn how to rewrite and

use literal equations and formulas.

Content Standards: A.CED.4, N.Q.1, A.CED.1, A.REI.1, A.REI.3

2.5 Literal Equations and FormulasLiteral equation - an equation

that involves two or more variables

Formula – an equation that states a relationship among quantities

2.5 Literal Equations and Formulas

Formula Name Formula Definitions of VariablesPerimeter of a Rectangle

P=2l + 2w P=perimeter, l=length, w=width

Circumference of a circle

C=2πr C=circumference, r=radius

Area of a Rectangle

A=lw A=area, l=length, w=width

Area of a Triangle A=½bh A=area, b=base, h=height

Area of a Circle A=πr² A=area, r=radiusDistance Traveled d=rt d=distance, r=rate,

t=timeTemperature C=5/9(F-32) C=degrees Celsius,

F=degrees Farenheit

2.6 Ratios, Rates, and ConversionsPg.116 – 121Obj: Learn how to find ratios and

rates and convert units and rates.Content Standards: N.Q.1 and

N.Q.2

2.6 Ratios, Rates, and ConversionsRatio – compares two numbers by

divisionRate – a ratio that compares quantities

measured in different unitsUnit Rate – a rate with a denominator of

1Conversion Factor – a ratio of two

equivalent measures in different unitsUnit Analysis – using the units in

calculations to help determine the units for the answers

2.7 Solving ProportionsPg. 124 – 129Obj: Learn how to solve and

apply proportions.Content Standards: A.REI.3,

N.Q.1, and A.CED.1

2.7 Solving ProportionsProportion – an equation that

states that two ratios are equalCross Products Property

. then ,0 and 0 where If bcaddbdc

ba

2.8 Proportions and Similar FiguresPg. 130 – 136Obj: Learn how to find missing

lengths in similar figures and use similar figures when measuring indirectly.

Content Standards: A.CED.1 and A.REI.3

2.8 Proportions and Similar FiguresSimilar Figures – have the same

shape but necessarily the same size

Scale Drawing – a drawing that is similar to an actual object or place

Scale – the ratio of any length on the drawing to the actual length

Scale Model – a 3D model that is similar to the 3D object

2.9 PercentsPg. 137 – 143Obj: Learn how to solve percent

problems using proportions and the percent equation.

Content Standard: Prepares for N.Q.3

2.9 PercentsThe Percent Proportion

100%

ofis

2.9 PercentsSimple Interest Formula

◦I = Prt I = interest P = Principal r = rate (as a decimal) t = time (in years)

2.10 Change Expressed as a PercentPg. 144 – 150Obj: Learn how to find the

percent of change and to find the relative error in linear and nonlinear measurements.

Content Standard: N.Q.3

2.10 Change Expressed as a PercentPercent of Change – expresses an

amount of change as a percent of an original amount

Percent Increase – if a new amount is greater than the original amount

Percent Decrease – if a new amount is less than the original amount

2.10 Change Expressed as a PercentPercent of Change

100%

originalchange

2.10 Change Expressed as a PercentRelative Error – the ration of the

absolute value of the difference of a measured value and an actual value compared to the actual value

Percent Error – when relative error is expressed as a percent

2.10 Change Expressed as a PercentRelative Error

valueactual valueactual - valueestimatedor measured

error relative