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Page 1: Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8 · Interdisciplinary: NJCCCS Technological Literacy 8.1A, ... • Adding and subtracting real numbers . ... Holt Algebra Tl-83

HADDONFIELD PUBLIC SCHOOLS Curriculum Map for Algebra 1

September Targeted Standard(s): NJCCCS 4.1.A.1, 4.1.B.1, 4.3.C.1 Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B Enduring Understandings (The big ideas): Algebraic representation can be used to generalize patterns and relationships Essential Questions: How can we compare and contrast numbers? How do operations affect numbers?

Core Content/Objectives Instructional Actions Concepts

What students will know Skills

What students will be able to do Activities/Strategies

Learning Activities/ Differentiation Interdisciplinary Connections

Assessment How learning will be assessed

Chapters I & 2 Patterns of Algebra

• Indentifying Patterns • Variables, Expressions, &

Equations • Order of Operations • Graphing with coordinates

Operations in Algebra

• Real Numbers and Absolute Numbers

• Adding and subtracting real numbers

The students will: 1. Use differences to find patterns

in expressions and equations. (This guides them slowly into concept of slope and y-intercept.)

2. Identify variables, expressions, & equations

3. Simplify expressions using the order of operations .

4. Identify quadrants of a graph, the origin, the x & y axes.

5. Graph points on a coordinate plane.

The student will: 1. Identify natural numbers, whole numbers.

2. Identify & use absolute value. 3. Add & subtract real numbers

using ‘intuitive thinking’ as well as lists of rules.

An order of operations group activity where the groups simplify expressions and check with a calculator. This shows discrepancies with their answers, thus leading the students toward the use and need of the order of operations.

Weekly quizzes and a Chapter Test Weekly quizzes

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HADDONFIELD PUBLIC SCHOOLS Resources/Technology: Holt Algebra Tl-83

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HADDONFIELD PUBLIC SCHOOLS

October Targeted Standard(s): NJCCCS 4.1.A.1, 4.1.B.1, 4.3.C.1 Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B Enduring Understandings (The big ideas): Computational fluency includes understanding the meaning and the appropriate use of numerical operations. Essential Questions: How do operations affect numbers?

Core Content/Objectives Instructional Actions Concepts

What students will know Skills

What students will be able to do Activities/Strategies

Learning Activities/ Differentiation Interdisciplinary Connections

Assessment How learning will be assessed

Chapters I & 2 Patterns of Algebra

• Indentifying Patterns • Variables, Expressions, &

Equations • Order of Operations • Graphing with coordinates

Operations in Algebra

• Real Numbers and Absolute Numbers

• Adding and subtracting real numbers

The students will: 1. Multiply & divide real numbers using the rules for mult and div two signed numbers. 2. Identify & use the identity

property for multiplication. 3. Identify & use the

Multiplicative inverse property 4. Identify & use the properties

of zero. 5. Identify & use the properties of equality. 6. Combine like terms The students will: 1. Solve one-step equations using addition, subtractions, multiplication, or division.

Combine like terms using m&m’s Weekly quizzes and a Chapter Test. Weekly quiz

Resources/Technology: Holt Algebra TI-83

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HADDONFIELD PUBLIC SCHOOLS

November Targeted Standard(s): NJCCCS 4.1.A.1, 4.1.A.3, 4.3.B.1, 4.3.D.2 Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B Enduring Understandings (The big ideas): Algebraic and numeric procedures are interconnected and build on one another to produce a coherent whole. Essential Questions: What makes an algebraic algorithm both effective and efficient?

Core Content/Objectives Instructional Actions Concepts

What students will know Skills

What students will be able to do Activities/Strategies

Learning Activities/ Differentiation Interdisciplinary Connections

Assessment How learning will be assessed

Equations (continued from Oct.) • Solving two-step equations • Solving multi-step equations • Using the distributive property • Using formulas & literal

equations

Proportional Reasoning & Statistics • Using proportional reasoning • Percent problems • Introduction to Probability • Measures of Central Tendency

The students will: 1. Solve equations in the form

ax+b=c. 2. Solve equations with variables on

each side. Ex: 3x-7=2x+5. 3. Solve multi-step equations which

require simplification on each side of the equations. Ex: 2x-7+3x=7-4+9

4. Solve multi-step equations with fractions. 5. Solve equations which contain parentheses. Beginning with parentheses on both sides. Ex: 3-(4x+5)=2(5x-1). 6. Solve literal equations

The students will: 1. Determine if a given proportion is true. 2. Solve proportions. 3. Convert decimals to percents &

vice-versa. 4. Solve percent sentences (by

translating the sentence into an algebraic equations: is=,of x).

5. Be exposed to basis statistics

We do numerous activities in this chapter:

1. Purchase furniture with no interest or payments until 200?, and find the ‘catches’.

2. Basic experiments flipping coins & rolling dice.

Multiple quizzes per week and a Chapter Test. NOTE: This chapter requires numerous quizzes! Weekly quizzes and a Chapter Test.

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HADDONFIELD PUBLIC SCHOOLS

experiments using dice & coins. 6. Identify and fine mean, median

and more

Resources/Technology: Holt Algebra Tl-83

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HADDONFIELD PUBLIC SCHOOLS

December Targeted Standard(s): NJCCCS 4.1.B.4, 4.3.B.2, 4.4.A.1 Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B Enduring Understandings (The big ideas): Patterns and relationships can be represented graphically, numerically, symbolically or verbally. Essential Questions: What is the meaning of linear? How can a linear equation be used? How are patterns of change related to the behavior of functions?

Core Content/Objectives Instructional Actions Concepts

What students will know Skills

What students will be able to do Activities/Strategies

Learning Activities/ Differentiation Interdisciplinary Connections

Assessment How learning will be assessed

Chapter 4 & 5 Proportional Reasoning & Statistics (Continued from November)

• Percent Problems • Measures of Central Tendency

Linear Functions

• Linear Functions & Graphs

The students will: 1. Convert decimals to percents and vice-versa.

2. Solve Percent Sentences (by translating the sentence into an algebraic equations:

‘is’=,’of’- multiplication. 3. Identify and find mean,

Median and mode. The students will: 1. Determine whether a relation is a function.

2. Describe the domain & range of a function

3. Calculate the slope of a line given two points on a line.

4. Identify and Sketch lines positive, negative, no and zero slope.

When covering percents, we do numerous authentic problems involving, but not limited to: sales, tax, interest rates, and financing. Each year, the activities change to better fit the dynamic of the class. For instance, this year we (the class) did a learning-through-discovery activity using snow-boarders to introduce slope, and to assist the students with a real-life representation of the slope concepts. In years past, we’ve used play racecars, ramps, handicap ramps, and even videos of students in the class performing tricks with their bicycles.

Multiple quizzes per week and a Chapter Test Weekly quizzes and a Chapter Test (in January) NOTE: Obviously the concept of graphing is critical, and the foundation needs to be solid. This chapter always tends to take longer than anticipated. Take it slow…it’s worth it! Mid-Term Exam

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HADDONFIELD PUBLIC SCHOOLS Resources/Technology: Holt Algebra Tl-83

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HADDONFIELD PUBLIC SCHOOLS

January Targeted Standard(s): NJCCCS 4.1.A.1, 4.1.A.3, 4.3.B.1, 4.3.D.2 Enduring Understandings (The big ideas): Algebraic and numeric procedures are interconnected and build on one another to produce a coherent whole. Essential Questions: What makes an algebraic algorithm both effective and efficient?

Core Content/Objectives Instructional Actions Concepts

What students will know Skills

What students will be able to do Activities/Strategies

Learning Activities/ Differentiation Interdisciplinary Connections

Assessment How learning will be assessed

Chapters – 1-5 Linear Functions (Continued from December)

• Defining Slope • Rate of Change • The Slope-Intercept Form

A week is spent preparing for the midterm.

The students will: 1. Find the rate of change from a

Graph 2. Identify, define, & interpret

the components of y=mx + b 3. Use the slope –intercept form

to graph a line 4. Use the slope-intercept form

To write the equations of a given line by identifying the slope and y-intercept.

The students will make review sheets for each chapter and do problem sets as a review for the upcoming midterm

As an introduction to the slope-intercept form, the students will do a white-boarding activity. Each group will graph a line in the form y=mx+b using ordered pairs. After the groups have successfully completed the task, all of the white boards are displayed simultaneously at the front of the room. The students are then guided to identify the slope of each line, and the y-intercept. After purposeful questioning, the students are given time to find patterns/similarities with the slope they computed with the equations of each line, as well as the y-intercepts and the equations of each given line. This activity, leaning-through-guided discovery, allows the student to interpret the components of an equation in the form y=mx+b. The students will do an activity that graphs one line using three different techniques:

1. Ordered Pairs (t-chart) 2. Slope-Intercept Method 3. Intercepts Method

This review consists of group work, board work, and independent study.

Multiple quizzes per week and a Chapter Test None

Resources/Technology: Holt

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HADDONFIELD PUBLIC SCHOOLS TI-83

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HADDONFIELD PUBLIC SCHOOLS

February Targeted Standard(s): NJCCCS 4.3.C.1, 4.2.C.1, 4.3.D.2 Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B Enduring Understandings (The big ideas) Algebraic and numeric procedures are interconnected and build on one another to produce a coherent whole. Essential Questions: What is a system of equations? How can a system of equations be solved algebraically? What makes an algebraic algorithm both effective and efficient?

Core Content/Objectives Instructional Actions Concepts

What students will know Skills

What students will be able to do Activities/Strategies

Learning Activities/ Differentiation Interdisciplinary Connections

Assessment How learning will be assessed

Chapters 6 – 7 Inequalities and Absolute Value

• Solving & Graphing Inequalities

• Multi-Step Inequalities • Write & Graph Compound

Inequalities • Solve Absolute Value

Equations Systems of Equation & Inequalities

• Graphing systems of equations • Solving systems of equations

using: 1. The Substitution Method 2. The Elimination Method 3. The Graphing Calculator

The students will: 1. State & use symbols of inequality. 2. Graph inequalities on a number

line. 3. Solve & graph inequalities using

addition & subtraction 4. Apply the Multi. & Div Properties of

inequalities to solve and graph inequalities.

5. Solve & graph multi-step inequalities in one variable.

6. Graph compound inequalities (using and/or)

7. Solve basic absolute-value equations.

The students will: 1. Graph systems of equations. 2. Solve systems of equations though

inspection of the coordinate plane 3. Solve systems of equations using

the substitution method 4. Solve a system of equations using

the Elimination Method.

There is a considerable amount of board work with this chapter. The class is lead using ‘learning through discovery’ questioning techniques to guide them into thinking about number lines representing answers. This tends to be a fairly easy chapter for the students. For the first few days, we graph two lines on one coordinate plane & discuss the similarities & differences. After the point of intersection is observed, we analyze just what an intersection represents. The students are asked to write these ideas out for hw and share them with the class the next day. We will then discuss the concept of ‘human error’ and conclude that solving a system using graphing isn’t the best/most accurate approach. At this point the substitution and elimination methods are

Two quizzes: 1. Sections 6.1 through 6.3 2. Sections 6.3 through 6.5

Chapter Test

Quiz #1 on solving a system by graphing by hand Quiz #2 on using the Substitution and Elimination Methods

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HADDONFIELD PUBLIC SCHOOLS introduced. Resources/Technology: Holt Tl-83

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HADDONFIELD PUBLIC SCHOOLS

March Targeted Standard(s): NJCCCS 4.2.C.1, 4.3.B.2, 4.5.C.2 Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B Enduring Understandings (The big ideas): Patterns and relationships can be represented graphically, numerically, symbolically or verbally Essential Questions: What is a system of equations? How can a system of equations be solved algebraically?

Core Content/Objectives Instructional Actions Concepts

What students will know Skills

What students will be able to do Activities/Strategies

Learning Activities/ Differentiation Interdisciplinary Connections

Assessment How learning will be assessed

Chapter 7 (continued from January) Systems of Equations and Inequalities

• Graphing systems of equations • Solving systems of equations

using : 1. The Substitution Method 2. The Elimination Method 3. The Graphing Calculator

The student will: 1. Graph systems of equations 2. Solve systems of equations

though inspection of the coordinate plane

3. Solve systems of equations using the substitution method.

4. Solve a systems of equations using the Elimination Method

For the first few days, we graph two lines on one coordinate plane and discuss the similarities and differences. After the point of intersection is observed, we analyze just what an intersection represents. The students are asked to write these ideas out for hw and share them with the class the next day. We will then discuss the concept of ‘human error’ and conclude that solving a system using graphing isn’t the best/most accurate approach. At this point the substitution and elimination methods are introduced.

Quiz #1 on solving a system by graphing by hand Quiz #2 on using the Substitution and Elimination Methods Chapter 7 Test

Resources/Technology: Holt Tl-83

Date completed/revised August 2009 Reviewed 9/09 Page 12

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HADDONFIELD PUBLIC SCHOOLS

April Targeted Standard(s): NJCCCS 4.1.B.2, 4.1.B.4 Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B Enduring Understandings (The big ideas): Mathematical models can be used to describe and quantify physical relationships. Essential Questions: What are the properties of exponents? How do we use the properties of exponents?

Core Content/Objectives Instructional Actions Concepts

What students will know Skills

What students will be able to do Activities/Strategies

Learning Activities/ Differentiation Interdisciplinary Connections

Assessment How learning will be assessed

Chapter 8 Exponents and Exponential Functions

• Laws of Exponents: Multiplying Monomials

• Laws of Exponents: Powers and Products

• Laws of Exponents: Dividing Monomials

• Negative and Zero Exponents

The students will: 1. Define exponents and

powers 2. Find products of powers 3. Simplify products of

monomials 4. Find the power of a power 5. Find the power of a product 6. Simplify quotients of powers 7. Simplify powers of fractions 8. Understand the concepts of

negative and zero exponents

9. Simplify expressions containing neg and zero exponent

This is a VERY misleading chapter to teach…the students grasp on the laws of individually, but as soon as the rules combine, they get confused and lessons need to be reinforced. All laws are introduced by expanding powers into products, performing the given operation (mult/div,etc) and then ‘condensing’ once again. Ex: x When students do get confused, they tend to go back to the basics of expansion and work through the problems. Again, a somewhat frustrating chapter to instruct. Constant spiraling and reinforcements are required.

Numerous quizzes Chapter Test

Resources/Technology:

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HADDONFIELD PUBLIC SCHOOLS Holt TI-83

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HADDONFIELD PUBLIC SCHOOLS

May Targeted Standard(s): NJCCCS 4.1.A.1, 4.3.D.1, 4.4.D.2 Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B Enduring Understandings (The big ideas): Using sound algebra, one can rearrange an expression to make it more manageable. Essential Questions: How can you rewrite an algebraic expression as the product of two exponents?

Core Content/Objectives Instructional Actions Concepts

What students will know Skills

What students will be able to do Activities/Strategies

Learning Activities/ Differentiation Interdisciplinary Connections

Assessment How learning will be assessed

Chapter 9 Polynomials and Factoring

• Adding and subtracting polynomials

• Multiplying polynomials (box method, double/multiple distribution method)

• Greatest Common Factors • Factoring trinomials in the form

x +bx + c • Factoring binomials; difference

of squares and sum of squares

The students will: 1. Add & subtract polynomials 2. Multiply binomials &

polynomials using distribution & the box method

3. Find products of binomials using the FOIL method

4. Factor a polynomial by using the greatest common factor

5. Factor the sum and difference of squares

6. Factor trinomials in the form x + bx+c

Adding and subtracting polynomials is a fairly simple concept for the students to master. Multiplying polynomials is another topic that is accepted rather easily by the students. The FOIL method and/or the ‘double distribution’ method work but using the box method is what leads students to a conceptual understanding of multiplying areas together. This box method has proven to be successful when working with accelerated students as well as with students who struggle. For factoring trinomials in the form x + bx + c, it is easiest for the students when the problem is broken down into two manageable steps: 1) find two numbers when multiplied result in “c” and 2) when combined result in “b”. Surprisingly this is well received by the students and it leads them toward success in an otherwise ‘dreaded’ algebra topic.

Numerous quizzes: 1. Adding and subtracting

polynomials 2. Multiplying polynomials 3. Factoring the GCF 4. Factoring binomials 5. Factoring trinomials

** As the quizzes progress it is helpful to include one or two of the previous topics. Chapter Test

Resources/Technology:

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June

Targeted Standard(s): NJCCCS 4.1.A.1, 4.3.D.1, 4.4.D.2 Interdisciplinary: NJCCCS Technological Literacy 8.1A, 8.1B Enduring Understandings (The big ideas): Using sound algebra, one can rearrange an expression to make it more manageable. Essential Questions: How can you rewrite an algebraic expression as the product of two expressions.

Core Content/Objectives Instructional Actions Concepts

What students will know Skills

What students will be able to do Activities/Strategies

Learning Activities/ Differentiation Interdisciplinary Connections

Assessment How learning will be assessed

Chapter 9

• Finish any content not covered in May

Final Exam Review for the remainder of the month

The students will: (complete any content from May)

After Chapter 9, if there is any extra time, students can begin factoring trinomials in the form ax +bx + c. It is important to draw the students’ attention to the leading coefficient “a”. Learning through discovery works well here, with students working in small groups, finding methods to factor these trinomials.

Quizzes Chapter Tests EOC Exam Final Exam

Resources/Technology: Holt