Algebra One Plus - Polytech High School



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?

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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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