District Text Guide for Math 8 – 2: 2006

 

The Math 8-2 district standards correlate with the Prentice Hall text Pre-Algebra, and the supplemental program Connected Mathematics. The course is standards-driven, rather than text-driven, thus several district objectives are referenced in more than one section of the text. The content will be tested on Math 8 CST and correlates with released items on the California High School Exit Exam. This course emphasizes the fundamental computational and procedural concepts and problem-solving strategies leading to algebra. Students, who reach mastery of concepts, may be offered topics leading to Algebra 1.

Benchmark #1: Objectives 2.5-2.6, 3.1-3.5   Benchmark #2: Objectives 5.1 – 5.3   Benchmark #3: Objectives 4.1 –4.3

Connected Mathematics: Thinking with Mathematical Models; and Say It with Symbols also -  Brad Fulton: The Pattern and Function Connection

Pattern development through warm-ups, journal writings, and other activities is essential for conceptualizing functions and algebra.

 

Standard 2: Geometry – Objective 2.5 – 2.6

Integrate geometric & algebraic concepts with a coordinate plane, Pythagorean Theorem & slope.

Standard 3: Functions & Algebra – Objective 3.1 – 3.5

Extend & connect conceptual understandings of linear relationships expressed verbally and through tables, graphs, and equations.

Standard 4: Probability – Objectives 4.1 – 4.3

Use simulations and apply basic principles of probability to make predictions and to evaluate real life situations.

Standard 5: Measurement – Objectives 5.1 – 5.3

Formulas for 2 and 3 dimensional objects: perimeter, area, volume: Determine congruence and similarity.

 

                           SS = Say it with Symbols          PH = Prentice Hall textbook;         MM = Thinking with Mathematical Models

Date

OBJECTIVE

PH

SS

Comments/Suggestions

1/9

3.1, 5.2: Similar triangles, Scale factors

6.3

 

Corresponding angles and sides

1/10

3.1, 5.2: Area of circle

10.3

 

A = pr2                         = B          (the  base!)       of a right cylinder                                              Circles 9.6 p.469. Key #7, 8, 31

1/12

3.1, 5.2: Area of quadrilateral (square or rectangle)

10.1

 

A = bh        = B (the base!)       of a right rectangular prism (or cube )            #24, 29 Use substitution.

1/17

3.1, 5.2: Area of triangle

10.2

 

A = ½ bh    = B (the base!)        of a right triangular prism                             

↓

3.1, 5.2: Area of irregular figures

10.2

 

Area of a trapezoid, p510.  #25

1/19

3.1, 5.2: Identify Space Figures

10.4

 

Nets of the right prisms #4,12,13, the cylinder #15. Key problems #16,17,18. Challenge in TG, p.523

1/23

Review 10.1 – 10.4

 

 

 

1/24

5.2, 5.3: Develop rules for scale factors

10.5

 

p.528, Surface area formulas. Test fluency #24. Critical Thinking #22, Mathematical Reasoning # 23.

1/26

5.2, 5.3: Volume of right prism (quadrilateral base)

10.7

 

V = Bh.          where       B (the base!) = A     the Area of the quadrilateral base      = bh

↓

5.2, 5.3: Volume of right prism (triangle base)

10.7

 

V = Bh.          where       B (the base!) = A     the Area of the triangular base          = ½ bh

↓

5.2, 5.3: Volume of right cylinder (circular base)

10.7

 

V = Bh.          where       B (the base!) = A     the  Area of the circular base               = pr2

↓

5.2, 5.3: Volume of pyramid (quadrilateral base)

10.9

 

V = ⅓ Bh.      where       B (the base!) = A     the Area of the quadrilateral base       = bh

↓

5.2, 5.3: Volume of pyramid (triangle base)

10.9

 

V = ⅓ Bh.      where       B (the base!) = A     the Area of the triangular base          = ½ bh

↓

5.2, 5.3: Volume of cone (circular base)

10.9

 

V = ⅓ Bh.      where         B (the base!) = A     the  Area of the circular base              = pr2

1/30

 

 

 

 

1/31

3.1: Simplify numerical expressions using properties

2.1

 

Review commutative, associative, and identity properties. Assign Exercises # 28-39

↓

3.3. Model direct variation in a one-step equation

6.3

 

p113 Direct variation between the masses of different of coins. Uses a pencil and a ruler to create a balance.

2/2

3.3: Write equations that represent equivalence

2.4

 

Vocabulary: variable, equation, solution, open sentence. Assign Exercises #20-33, 37.

↓

3.1: Error analysis in algebraic solutions

 

2.3

Key ACE problem # 20 for error analysis. Items # 4–8, 13–18 for the identification of equivalent expressions.

2/6

3.1: Simplify algebraic expressions (and evaluate)

2.3

 

Distinguish between simplifying and solving. Assign #19-30 and error analysis #40.

2/7

3.1: Simplify numerical and algebraic expressions

2.2

 

Visualize the distributive property and its application. Assign Exercises #29 – 40

↓

3.1, 3.2: Write algebraic sentences

 

2.1

Write equivalent expressions using distributive property. ACE Problems # 19, 25 as check for understanding.

↓

3.1: Simplify expressions using distributive property

 

3.1

The follow-up should provide continuing practice with commutative and distributive properties.

2/9

3.3, 3.4: Solve one-step equations by ( + & – )

2.5

 

Use visual representation of a scale to show equivalence. Practice Error Analysis #44-45.


Date

OBJECTIVE

PH

MM

Comments/Suggestions

2/13

3.3, 3.4: Solve one-step equations by ( x & Έ ) 

2.6

 

#35 – 38 provide review of definitions of absolute value.

↓

3.1, 3.2: Evaluate algebraic expressions using  Έ

 

1.2

Use 1.2 E to discuss three ways to write an equation involving division. Key ACE Problems # 29-30, 34-41

2/15

3.4: Solve two-step equations

7.1

 

Visualize the logic for each step of a two-step equation. Exercises # 11-25 routine problems, 36 (error analysis).

↓

3.3: Write quantitative algebraic sentences

 

3.2

Constructed response problem posed in real-life context. Key ACE problems # 39 – 41.

2/21

3.4: Solve multi-step equations

7.2

 

Useful Steps for Solving a Multi-Step Equation, p.342.  #30-31(contextual problems) and #32 (justify).

↓

3.4: Explain logic in solving multi-step equations

SS

4.2

Explain reasoning for steps to solve a linear equation. Key ACE #11 show equivalent forms of one equation.

↓

3.4: Explain logic in multi-step equation

SS

4.3

Key ACE #13 justify the sequence of steps in solving for an x embedded in a multi-step equation.

2/23

3.3: Write one-step inequalities

2.8

 

Vocabulary of inequality, translate a graph or description into algebraic sentence. #21–33.

↓

3.4, 3.5: Solve one-step inequalities by ( + & – )

2.9

 

Uses the procedures for solving by ( + & – ). Background p104. Assign Exercises #23, 31 

2/27

 

 

 

 

2/28

3.4, 3.5: Solve one-step inequalities by ( x & Έ )

2.10

 

Change direction of inequality symbol when dividing by a negative number. Is it reasonable? #29, 31, 33-36.

3/2

3.4: Solve two-step inequalities

7.6

 

Assign Exercises # 9 –13 (routine inequalities), #29 (error analysis) and #30 (interpreting a solution as a graph).

3/6

 

 

 

 

3/7

2.5, 3.2: Graphic representation for rate of change

 

1.1

Generate data in the context of constant rate of change. Key ACE problems #29-31

↓

3.1: Evaluate algebraic expressions using ( + & – )

SS

1.1

The meaning of the slope and the y-intercept in the context of verbal problems Key ACE Problems # 31 – 33.

3/9

2.5, 2.6: Connect rate of change to y = mx + b

 

1.4

Patterns in tables and graphs & define m & b in a linear equation. ACE problems #24, 27.

3/13

 

 

 

 

3/14

2.5, 2.6: Represent slope of earnings per week

 

1.5

“m” (slope) = rise over run, “b” = y-intercept. Key ACE problems # 4 – 19, 32-38.

3/16

3.2: Contrast non-linear with a linear relationship

 

3.1

ACE problem #7 encourages mathematical reasoning in the interpretation of graphs.

↓

3.2: Compare / contrast linear v non-linear graphs

 

2.1

Draw conclusions from tables and graphs of linear and non-linear equations.

Study                                                             INTERSESSION                                                            Study

4/17

 

 

 

 

4/18

2.6: Connect time and distance traveled to slope

 

4.2

Summarize by interpreting more graphs. It is not necessary to assign ACE problems.

4/20

3.2: Interpret linear and non-linear graphs

p384

 

Put meaning to the configurations of the graphs on the coordinate plane.

↓

3.1: Evaluate algebraic expressions

SS

4.1

Graph linear equations from t-chart. Key ACE problem #16: recognize positive / negative slope & y-intercept.

4/24

 

 

 

 

4/25

2.5: Model slope in graphic form

8.2

 

Create and organize a t-chart of (x, y) coordinates to graph the equations. Exercises #20 –29.

↓

2.6, 3.5: Convert units between systems

p396

 

Change inches to centimeters in a direct variation model. Explain what defines direct variation.

4/27

2.5: Compute slope as “rise over run”

8.3

 

This section introduces slope and y-intercept. Exercises #10-15, #22-29.]

                                   5/1 CST Review                                                                                                       5/2 – 5/5 California Standards Test

5/8

2.5: “rise over run” and y-intercept in y = mx+ b

8.4

 

y = mx + b       Work on Part 2 , Examples 2 and 3. Exercises #15 – 20.

5/9

 

 

 

 

5/11

4.1: Probabilities as fractions, decimals, or percents

6.4

 

Vocabulary: outcomes, event, and probability. Exercises # 1-4, 6-18.

5/15

 

 

 

 

5/16

4.1: Construct sample spaces

12.4

 

Develop the concept ex.1 tree diagram. Develop concept of theoretical probability ex3. Exercises # 4, 12-17.

5/18

4.2: Probabilities in independent & dependent events

12.5

 

Multiply fractions and decimals in a non-routine context. Key problems # 26-29.

5/22

4.3: Theoretical and experimental probabilities

12.7

 

Compare and contrast the meanings of theoretical and experimental probabilities. #1-4, 6-11. Key#12&16

5/24

4.3: Predict w/theoretical & experimental probability

12.8

 

Focus on Example 2 using proportional reasoning skills from Semester 1. Key problems # 10 –11.

5/25

 

 

 

 

Notes:                                             Contributor in Class are Contributors with Class