solving equations
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Solving Equations. Chapter 2. 2.1 Solving One-Step Equations. Pg. 81 – 87 Obj : Learn how to solve one-step equations in one variable. Content Standard: A.CED.1 and A.REI.3. 2.1 Solving One-Step Equations. Equivalent equations – equations that have the same solution(s) - PowerPoint PPT PresentationTRANSCRIPT
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