Algebra One Plus
Algebra One Plus
REMEMBER THE BELLRINGERS ON TEACHER SHARE
Unit 1: Connections to Algebra & Properties of Real Numbers
Algebra 1 text – Chapters 1 & 2
Timeline: 8-11 days
Common Core Standards
N.RN.3
A.SSE.1
A.SSE.3
F.IF.1
Outline:
• 1.5: Translating Words into Mathematical Symbols (1 to 2 days)
o Discuss vocabulary from 1.4 “Equations and Inequalities”
o Translating words into mathematical symbols.
o Focus on vocabulary: evaluate, simplify, solve
▪ Use function notation here. i.e. f(2) = 2x + 7
• Add as needed - 2.3, 2.4, & 2.5: Adding, Subtracting, and Multiplying Real Numbers (1 day)
o Add real numbers using a number line.
o Add real numbers using the rules of addition
o Subtract real numbers using the subtraction rule.
o Multiply real numbers using the rule for the sign of a product.
• 2.8: Dividing real Numbers (1 day)
o Divide real numbers and use division to simplify algebraic expressions.
• 2.6 & 2.7: The Distributive Property and Combining Like Terms (1 to 2 days)
o Use the distributive property.
o Simplify an expression by combining like terms.
• Core and Application: Utilize problems that require the use of concepts taught in this unit (2 to 3 days)
o 1.3: Order of Operations
▪ Amp up difficulty by using problems that utilize order of operations, distributive property & combining like terms
▪ Use the order of operations
o Perimeter and area of rectangles and squares
o Perimeter of polygons
o Other application problems
o Look for PSAT and smarter balanced problems, could use parking lot problem here
• Review & Assessment (2 days)
• Miscellaneous
o Discuss functions more
▪ when doing input/output tables
▪ use function notation when asking students to evaluate a function
o Discuss domain and range
o Put in some application problems that require CCSS N.Q.1-3
▪ Seans snow vs cars on football field problem
Unit 2: Solving Linear Equations
Algebra 1 text – Chapter 3
Timeline: 11 - 14 days
Common Core Standards
A.REI.1
A.REI.2
A.REI.3
A.CED.4
F.IF.1
F.LE.5
Outline:
• 3.1 & 3.2: Solving Equations Using Addition, Subtraction, and Multiplication (1 day)
o Solve a linear equation using addition.
o Solve a linear equation using subtraction.
o Solve a linear equation using multiplication.
o Solve a linear equation using division.
o Solve a linear equation using the reciprocal.
• 3.3: Solving Multi-Step Equations (1 day)
o Use two or more steps to solve a linear equation.
• 3.4, 3.5, and 3.6: Solving Equations with Variables on Both Sides of the Equal Symbol, More on Linear Equations, and Solving Decimal Equations (1 to 2 days)
o Solve equations that have variables on both sides of the equal symbol.
o Solve more complicated linear equations.
o Use problems from 1.6: Solving Decimal Equations as a ticket out the door or warm-up
• 3.7: Extend to solving formulas for a variable (1- 2 days)
• 6.1, 6.2, and 6.3: Solving Inequalities Using Addition, Subtraction, Multiplication, Division and Multi-Steps (2 days)
• Core and Application: Area, perimeter, and Pythagorean theorem (3 - 4 days)
o Area and perimeter of triangles
o Pythagorean theorem (see p. 724)
o Lisa gave an open-ended application problem for this unit
o We can also revisit the parking lot problem and put in a value for the perimeter and have students solve for the variable
o Look for PSAT and smarter balanced problems, could use parking lot problem here
o CHECK SMARTER BALANCED
• Review & Assessment (2 days)
Unit 3: SLOPE-INTERCEPT FORM ONLY Graphing Linear Equations and Functions AND Writing Linear Equations
Algebra 1 text – Chapters 4, 5, & 6
Timeline: 13 – 15 days
Common Core Standards:
A.CED.1
A.CED.2
A.CED.3
A.REI.10
A.REI.11
A.REI.12
Outline:
• 4.1 & 4.2: The Coordinate Plane and Graphing Linear Equations (1 day)
o Plot points in the coordinate plane
o Graph a linear equation using a table of values.
• 4.5: The Slope of a Line (1 day)
o Be sure to also use the terminology “rate of change” to describe slope
o Find the slope of a line from a graph.
o Find the slope of a line using the slope-formula.
• 4.7: Graphing Lines Using Slope-Intercept Form (2 days)
o Graph a linear equation using the slope-intercept form.
o Be sure to discuss direct variation
o Show how y = mx + b can also be written f(x) = mx + b
• 5.1, 5.2, & 5.3: Writing an equation of a line in Slope-Intercept Form and Writing Linear Equations Given Two Points
(2 days) Use slope-intercept form to write an equation of a line.
o Write an equation of a line given two points. (point-slope is covered here)
• 6.8: Graphing Linear Inequalities in Two Variables (1 - 2 days)
o Graph linear inequalities in two variables.
• Core and Application: All problems are dealing with slope-intercept form (5 - 6 days)
o Relationship between tables, equations, and graphs
o Linear regression – need to find problems that only do y = mx + b
o Utilize problems like those in section 12.7
o Linear Inequalities - need to find problems that only do y = mx + b
o Look for PSAT and smarter balanced problems, could use parking lot problem here
• Review & Assessment (2 days)
o Need to change
• Miscellaneous
o Give the students Ax + By = C and have them put it in slope-intercept (function) form to help them make connections with slope and y-intercept.
Unit 4: Graphing Linear Equations and Functions AND Writing Linear Equations
Algebra 1 text – Chapters 4, 5, & 6
Timeline: 11 - 14 days
Common Core Standards:
F.IF.4
F.IF.7A
A.CED.2
A.REI.10
A.REI.12
S.ID.6
Outline:
• 4.3 & 4.4: Graphing Horizontal and Vertical Lines and Graphing Lines Using Intercepts (1 – 2 days)
o Graph horizontal lines.
o Graph vertical lines.
o VUX - HOY
o Find the x-intercept of a linear equation.
o Find the y-intercept of a linear equation.
o Make a quick graph of a linear equation using its x and y intercepts.
• 5.4: Standard Form (1 day)
o Write an equation of a line in standard form.
• 5.6: Perpendicular Lines (1 day)
o Write equations of perpendicular lines.
o Review parallel lines and coordinate geometry
• 6.8: Graphing Linear Inequalities in Two Variables (1 - 2 days)
o Graph linear inequalities in two variables.
• Core and Application: (5 - 6 days)
o Discuss determining the type of polygon on a coordinate plane using parallel and perpendicular concepts and properties of polygons
o Solve real-life application problems
o Linear Regression
▪ Use function notation
o Inequalities
o Look for PSAT and smarter balanced problems, could use parking lot problem here
• Assessment (2 days)
Unit 5: Systems of Linear Equations and Inequalities
Algebra 1 text – Chapter 7
Timeline: 8 - 10 days
Common Core Standards:
A.REI.5
A.REI.6
A.CED.1
A.CED.2
A.CED.3
+A.REI.8
+A.REI.9
+A.REI.12
Outline:
• Show how to use graphing calculators to check answers
• 7.1 & 7.2: Graphing Linear Systems and Solving Linear Systems by Substitution
(1 day)
o Estimate the solution of a system of linear equations by graphing.
o Solve a linear system using the substitution method.
• 7.3: Solving Linear Systems Using the Elimination Method (1 day)
o Solve a linear system using the elimination method.
• Practice with all three methods (1 day)
o Add in problems that push students to think about which method is the best way to solve
• + Show students how to use matrices to solve (use graphing calculators)
• + 7.6 Systems of Linear Inequalities
• Core and Applications (1 day)
o Use linear systems to solve real-life problems.
• Assessments (2 days)
o May want to add in a problems for matrices and systems of linear inequalities
Unit 6: Exponents and Exponential Functions
Algebra 1 text – Chapter 8
Timeline: 9 -11 days
Common Core Standards:
A.SSE.3C
A.CED.1
F.IF.7E
F.IF.8B
F.LE.1
F.LE.5
S.ID.6A
N.RN.2
Outline:
• 8.1, 8.2, & 8.4: Multiplication/Division Properties of Exponents and Zero/Negative Exponents (3 - 4 days)
o May want to discuss concepts from 1.2
o Use multiplication properties of exponents.
o Evaluate powers that zero exponents.
o Evaluate powers that have negative exponents.
o Use division properties of exponents.
• Core and Applications
o Exponential Growth Functions (1 day)
▪ Write, graph, and apply exponential growth functions.
o Exponential Decay Functions (1 day)
▪ Write, graph and apply exponential decay functions.
o Compound Interest (1 day)
▪ Write, graph, and apply compound interest functions
o Exponential Regression (1 - 2 days)
▪ Use graphing calculators
o Assessment (2 days)
• Miscellaneous
o Add in problems that require the use of function notation and f(#)
o Touch on CCSS N.R.N. 1 &2: working with radicals and rational exponents
o Add in problems that require a student to look at a graph on an exponential and a linear model
Unit 7: Quadratics
Algebra 1 text – Chapter 9
Timeline: 9 - 12 days
Common Cores Standards:
A.CED.1
A.CED.2
A.REI.4B
F.IF.7A
S.ID.6A
A.REI.7
+F.IF.7B
Outline:
• 6.6: Solving Absolute Value Equations (1 day)
o Solve absolute value equations in one variable.
o Discuss what the graph looks like
• 9.2: Solving Quadratic Equation by Finding Square Roots (1day)
• + 9.3 Simplifying Radicals
• 9.4: Graphing Quadratic Functions (1day)
• 9.5: Solving Quadratic Equation by Graphing (1 day)
o Utilize graphing calculators
• 9.6: Solving Quadratic Equations by the Quadratic Formula (1 day)
o Use only problems with perfect square discriminants
• + Solving Systems of Quadratic and Linear Functions
• + 9.8 Graphing Quadratic Inequalities
• Core and Applications (2 day)
• Assessment (2 days)
o Include solving a quadratic using all methods
o F.IF.6 Calculate and interpret the average rate of change of a function
(presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★
o Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
o Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Renee suggested doing 10.2, 10.4, and 10.5 instead of 9.3 & 9.8. What do we think?
Things to work on for entire course:
• Use of terminology for functions
• Use of function notation
• Scatter the concept of (text 3.7) rearranging a formula for a variable throughout the course, especially in application problems
• Be sure to discuss correlation coefficient
Miscellaneous
• Pearson website
o
o login: CommonCore2012
o PW: pearsonmath
Additions/Discussions/Things To Do:
• Need to think about the best place for a formative assessments or quick check in each unit. Maybe a warm-up or something.
• Lesson Plans
• Stats and probability unit
o need to work on getting resources for this
o NVLM manipulative are available online
o Use Compass Learning to cover Stats?
• Operations with matrices
o Core materials may work for this
o Use grade calculations as examples to teach these concepts
• Functions and function notation
• Need to find more modeling problems
• Modeling (we need resources for this)
o Bellringers
o Lianne found some textbooks
o CCSSMath:
o DOE:
• Starred standards are modeling items
• + standards are expected to be covered in higher level or 4th year courses
Common Core State Standards Not Covered in 2013-2014 outline for Algebra 1
Appendix A: Algebra 1 Unit 1
N.Q.1-3:
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S.ID.1-3 & 5 & 9: Can we cover using Compass Learning?
[pic]
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Currently in Algebra 2, but in the future will need to add to Algebra 1
Appendix A: Algebra 1 Unit 2
N.RN.1- 2:
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F.IF.4-7: [pic]
A.SSE.2-3:
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A.REI.4
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Other items that need to be covered before senior year
Geometric Sequences
Trig Functions
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