Download CCSS.Math.Content.HSA.REI.A.1

Reasoning with Equations: Solving One Variable Equations
Name: ____TEACHER COPY ______ _______
CCSS.Math.Content.HSA.REI.A.1
Date: ______________________ Period: _____
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the
assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Lesson on Solving Multi-Step Equations:
1. Warm-up (last page)
2. Intro: Solving equations is all about keeping things balanced. Who here has been on a see-saw? What happens if the person on the other side
of the see-saw is much lighter or tinier than you? What happens when they are much bigger? What happens when you weigh the same? To keep
an equation (balanced see-saw) and not an inequality (like an unbalanced see-saw), we need to add the same weight (or number) to both sides.
3. Graphic Organizer: This graphic organizer shows all the concepts covered in this strand of the common core standards, creating equations.
Reasoning with
Equations &
Inequalities
Addition &
Subtraction
Solve Multi-step
Equations
Solve Equations w/
Coefficients
Represented by
Letters
Multiplication &
Division
Multiply by
Reciprocal
Inspection/Graphing
Taking Square
Roots
Solve Quadratic
Equations
System of Equations
& Inequalities
Completing the
Square
Quadratic Formula
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Factoring
4. Examples
1.
If we knew the value of a, what two operations will we do and in what order?
𝑎
6= 4+2
To isolate the variable, we must undo these operations and solve for a.
If we knew the value of x, what two operations will we do and in what order?
6.
−1 =
5+𝑥
6
To isolate the variable, we must undo these operations and solve for a.
If we knew the value of x, what two operations will we do and in what order?
12.
144 = −12(𝑥 + 5)
To isolate the variable, we must undo these operations and solve for a.
5. Exit Slip
A. What type of operations "undo" each other? Give an 2 step example. (Inverse operations: 10 - 7 = 3, 3 + 7 = 10)
B. If you do the same thing to both sides of the = sign, you've ______________ the equation. (balanced)
C. To isolate the variable, get it _____________ on one side of the = sign. (by itself)
D. The __________ of an equation is the answer. (solution)
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All Rights Reserved by NewMathTeacher.Net
Reasoning with Equations: Solving One Variable Equations
Name: ____TEACHER COPY ______ _______
CCSS.Math.Content.HSA.REI.A.1
Date: ______________________ Period: _____
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the
assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Graphic Organizer: Today, we are focusing on the far left side of the organizer, solving multi-step equations.
Reasoning with
Equations &
Inequalities
Addition &
Subtraction
Solve Multi-step
Equations
Solve Equations w/
Coefficients
Represented by
Letters
Multiplication &
Division
Multiply by
Reciprocal
Inspection/Graphing
Taking Square
Roots
Solve Quadratic
Equations
System of Equations
& Inequalities
Completing the
Square
Quadratic Formula
Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
All Rights Reserved by NewMathTeacher.Net
Factoring
Reasoning with Equations: Solving One Variable Equations
Name: ____________________ ______ _______
CCSS.Math.Content.HSA.REI.A.1
Date: ______________________ Period: _____
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the
assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Answer each of the following.
1.
What is the inverse operation of subtraction?
2. If you add 5 to the right side of an equation, how do you keep the equation balanced?
3. How do you isolate the variable in the equation p - 4 = 12 ?
Properties Used for Solving Equations
General Rule
Specific Example
Addition Property of Equality
Subtraction Property of
Equality
Multiplication Property of
Equality
Division Property of Equality
*Using Multiplicative Inverses (Reciprocals) reduces the number of steps you must perform when solving equations.
Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
All Rights Reserved by NewMathTeacher.Net
Warm-up
Name: ______________________
Simplify the following expressions.
1
1
A. 4 (2 𝑥 + 3) − (−7)
3 2 2
4
9
3 2 2
4
9
B. ( ) ∙
B. ( ) ∙
8
8
C. √2 + 3
C. √2 + 3
Name: ______________________
Simplify the following expressions.
1
A. 4 (2 𝑥 + 3) − (−7)
3 2 2
B. (4) ∙ 9
8
2
C. √ + 3
Name: ______________________
Simplify the following expressions.
A. 4 (2 𝑥 + 3) − (−7)
Warm-up
Warm-up
Warm-up
Name: ______________________
Simplify the following expressions.
1
A. 4 (2 𝑥 + 3) − (−7)
3 2 2
B. (4) ∙ 9
8
2
C. √ + 3
Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
All Rights Reserved by NewMathTeacher.Net