7th pre-algebra pacing-2010 - billings public schools - … guide - (pacing... · ·...

SEVENTH GRADE Pre-Algebra

Revised June 2010

Billings Public Schools

Correlation and Pacing Guide Math - McDougal Littell Middle School Math 2004

(Chapter Order: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13)

BILLINGS PUBLIC SCHOOLS 7th Pre-Algebra-2010 Seventh Grade-McDougal Littell Pre-Algebra 2005 Correlation/Pacing Revision

I - Introduce the learning objective, D – Develop the learning objective, E - Essential learning objective, and A – Apply the learning objective

2

Suggested Pacing Student/Teacher Edition Learning Objectives – 1st Semester

Supplemental Materials

Chapter 1 – Variable,

Expressions, and Integers

Approximately 16 days

Lesson 1.1 (1 day) Expressions and Variables

Review

Lesson 1.2 (1 day) Powers and Exponents

Review

Lesson 1.3 (1 day) Order of Operations

Review Use calculators to find solutions using the order of operations

Necessary Lesson (2 days) Comparing and Ordering Integers Or: Lesson 1.4 (2 days)

Number Sense and Operation • Solve and create problems using integers and check the

reasonableness of the answer. (I, D, E, A) • Evaluate expressions with integers and whole number

exponents with and without calculator. (I, D, E, A)

Stepping Out Integers from AIMS

Quiz (1 day) Necessary Lessons (8 days) Adding, Subtracting, Multiplying and Dividing Integers Or: Lesson 1.5, 1.6 & 1.7 (8 days)

Number Sense and Operation • Use models to represent integers. (I, D, E, A) • Use and justify the strategies and procedures for computing

with integers. (I, D, E, A) • Solve and create problems using integers and check the

reasonableness of the answer. (I, D, E, A)

Integer Addresses from AIMS What’s the Charge for Addition and Subtraction from AIMS Integer Patterns from AIMS

Review/Test (2 days)



3


Supporting Materials

Chapter 2 – Solving

Equations


Lesson 2.1 (2 days) Properties and Operations

Algebraic and Functional Reasoning • Generate equivalent forms of algebraic expressions

including those involving like terms and justify each step with properties of operations. (I, D, E, A)

Pre-Algebra with Pizzazz

Lesson 2.2 (2 days) The Distributive Property



Pre-Algebra with Pizzazz “Did You Hear About”

Necessary Lesson (2 days) Rates & Unit Analysis

Number Sense and Operation • Use rates to justify conversions between units within the

same system. (e.g., miles per hour to feet per second) (I, D, E, A)

Need a supplemental lesson for rates and unit analysis

Algeblock Lesson (3 days) Simplifying Variable Expressions OR: Lesson 2.3



Introducing Algeblocks and Variable Expression Lesson using worksheets 5-1 to 5-3 & 5-7 from the Algeblock Notebook (Lesson Plan provided in Supplement Folder)

Quiz (1 day) Lesson 2.4 (1 day) Variables and Equations

Algebraic and Functional Reasoning • Solve multi-step linear equations incorporating multiple

grouping symbols and check the reasonableness of the solution. (I, D, E, A)

Lesson 2.5 (2 days) Solving Equations Using Addition or Subtraction



Lesson 2.6 (1 day) Solving Equations Using Multiplication or Division





4



Chapter 2 – Solving

Equations


Lesson 2.7 (1 day) Decimal Operations and Equations with Decimals



Review/Testing (2 days)



5

Suggested Pacing Student/Teacher Edition Learning Objectives – 1st Semester Supporting Materials

Chapter 3 – Multi-Step

Equations and Inequalities


Lesson 3.1 (2 days) Solving Two-Step Equations



Pre-Algebra with Pizzazz 2-Step Equations “Find a Match”

Lesson 3.2 (2 days) Solving Equations Having Like Terms and Parentheses



Pre-Algebra with Pizzazz “What is the Title”

Lesson 3.3 (2 days) Solving Equations with Variables on Both Sides



Pre-Algebra with Pizzazz “Superstar”

Quiz (1 day) Lesson 3.4 (1 day) Solving Inequalities Using Addition or Subtraction

Algebraic and Functional Reasoning • Use properties of numbers and inverse operations to solve

multi-step linear inequalities in one variable, graph the solution on a number line and check the reasonableness of the solution (ie. associative, commutative, distributive, identity, and inverse). (I, D, E, A)

Lesson 3.5 (1 day) Solving Inequalities Using Multiplication or Division



Pg. 143 Mini-Lesson

Lesson 3.6 (2 days) Solving Multi-Step Inequalities






6

Suggested

Pacing Student/Teacher Edition Learning Objectives – 1st Semester Supporting Materials

Chapter 4 – Factors,

Fractions, and Exponents


Lesson 4.1 (1 day) Factors and Prime Factorization

Number Sense and Operation • Apply number theory concepts such as prime factorization,

greatest common factor, and least common multiple to solve problems. (A)

Lesson 4.2 (2 days) Greatest Common Factor





Lesson 4.3 (1 day) Equivalent Fractions





Lesson 4.4 (2 days) Least Common Multiple





Algebra With Pizzazz GCF & LCM

Quiz (1 day)



7

Suggested


Chapter 4 – Factors,

Fractions, and Exponents


Lesson 4.5 (1 day) Rules of Exponents

Number Sense and Operation • Evaluate numeric expressions including nested parentheses,

exponents, and other grouping symbols. (I, D, E, A) Algebraic and Functional Reasoning • Generate equivalent forms of algebraic expressions


Lesson 4.6 (2 days) Negative and Zero Exponents

Number Sense and Operation • Evaluate numeric expressions including nested parentheses,

exponents, and other grouping symbols. (I, D, E, A) Algebraic and Functional Reasoning • Generate equivalent forms of algebraic expressions


Lesson 4.7 (2 days) Scientific Notation

Number Sense and Operation • Compare, order, and graph rational numbers on a number

line. (E, A) • Evaluate numeric expressions including nested parentheses,

exponents, and other grouping symbols. (I, D, E, A)




8



Chapter 5- Rational

Numbers and Equations

Approximately 15 Days

Necessary Lesson (2 days) Rational Numbers

Number Sense and Operation • Recognize, model, and compare different forms of integers

and rational numbers including percents, fractions, decimals, and numbers using exponents and scientific notation. (I, D, E, A)

Classifying Number Sets Lesson

Lesson 5.1 (1 day) Rational Numbers

Number Sense and Operation • Compare, order, and graph rational numbers on a number

line. (E, A)

Lesson 5.2 (1 day) Adding and Subtracting Like Fractions

Number Sense and Operation • Compute fluently and solve multi-step problems using

integers, fractions, decimals, and numbers in exponential form. (I, D, E, A)

Algebraic and Functional Reasoning • Generate equivalent forms of algebraic expressions including

those involving like terms and justify each step with properties of operations. (I, D, E, A)

Lesson 5.3 (2 days)Adding and Subtracting Unlike Fractions





Quiz (1 day) Lesson 5.4 (1 day) Multiplying Fractions







9

Suggested


Chapter 5- Rational

Numbers and Equations


Lesson 5.5 (2 days) Dividing Fractions





Lesson 5.6 ( 1 day) Using Multiplicative Inverses to Solve Equations



Lesson 5.7 (2 days) Equations and Inequalities with Rational Numbers



• Use properties of numbers and inverse operations to solve multi-step linear inequalities in one variable, graph the solution on a number line and check the reasonableness of the solution (ie. associative, commutative, distributive, identity, and inverse). (I, D, E, A)




10

Suggested Pacing Student/Teacher Edition Learning Objectives – 1st Semester Supporting Materials

Chapter 6 – Ratio,

Proportion, and Probability


Lesson 6.1 ( 1 day) Ratios and Rates

Number Sense and Operation • Use rates to justify conversions between units of measure (e.g.,

convert miles/hour to feet/second). (E, A)

Lesson 6.2 (1 day) Writing and Solving Proportions

Number Sense and Operation • Use proportions to solve contextual problems including

similarity and congruence. (E, A)

Lesson 6.3 (1 day) Solving Proportions Using Cross Products



Quiz (1 day) Necessary Lesson (2 days) Similar and Congruent Figures & Similarity and Measurement OR: Lesson 6.4 or 6.5

Number Sense and Operation • Use appropriate tools and technology to solve problems

involving measurement in scientific and cultural situations, including those of Montana American Indians. (A)

• Use proportions to solve contextual problems including similarity and congruence. (E, A)

Geometric Reasoning • Justify similarity of figures using proportional reasoning and

angle relationships. (I, D, E, A) • Justify congruency of figures using sides and angle

relationships. (I, D, E, A)

“Finding Heights” from Navigation through Measurement p. 55-59



11

Suggested


Chapter 6 – Ratio,

Proportion, and Probability


Lesson 6.6 (1 day) Scale Drawings



• Use proportions to solve contextual problems including similarity and congruence. (E, A)

Geometric Reasoning • Justify similarity of figures using proportional reasoning and

angle relationships. (I, D, E, A) • Justify congruency of figures using sides and angle

relationships. (I, D, E, A)




12

Suggested Pacing Student/Teacher Edition Learning Objectives – 2nd Semester Supporting Materials

Chapter 7 – Percents


Lesson 7.1 & 7.3 (1 day) Percents, Fractions and Decimals

Review Page 334 Estimating with Percents

Lesson 7.2 (2 days) Percents and Proportions



Lesson 7.4 (1 day) The Percent Equation

Number Sense and Operation • Solve multi-step problems containing rational numbers

and numbers in exponential form. (I, D, E, A) Algebraic and Functional Reasoning • Generate equivalent forms of algebraic expressions


Quiz (1 day)

Lesson 7.5 (2 days) Percent of Change



Lesson 7.6 (2 days) Percent Applications



Lesson 7.7 (1 day) Simple Interest



Omit compound interest




13

Suggested Pacing

Student/Teacher Edition Learning Objectives – 2nd Semester Supporting Materials

Chapter 8 – Linear Functions


Lesson 1.8 (1 day) The Coordinate Plane

Review

Lesson 8.1 (2 days) Relations and Functions

Algebraic and Functional Reasoning • Create and use multiple representations (tables, graphs,

verbal descriptions, symbolic expressions) of data to generalize the patterns and make connections among all representations. (A)

• Determine from a set of ordered pairs, a table, graph, or a rule whether a relation is a function. (I, D, E, A)

• Compare and contrast the properties of functional and non-functional relations using technology when appropriate. (I, D, E, A)

Page 397: Technology

Lesson 8.2 (2 days) Linear Equations in Two Variables



• Determine from a set of ordered pairs, a table, graph, or a rule whether a relation is a function. (I, D, E, A)

• Generate equivalent forms of algebraic expressions including those involving like terms and justify each step with properties of operations. (I, D, E, A)



14

Suggested

Pacing Student/Teacher Edition Learning Objectives – 2nd Semester Supporting Materials



Lesson 8.3 (1 day) Using Intercepts



• Solve multi-step linear equations incorporating multiple grouping symbols and check the reasonableness of the solution. (I, D, E, A)

• Generate equivalent forms of algebraic expressions including those involving like terms and justify each step with properties of operations. (I, D, E, A)

• Determine the slope, x-intercept, and y-intercept of a line given its graph, equation, or two points on the line. (I, D, E, A)

Quiz (1 day) Necessary Lesson (4 days) The Slope of a Line and Slope-Intercept Form OR: Lesson 8.4 and 8.5

Algebraic and Functional Reasoning • Identify the properties (slope, intercepts, continuity,

and discreteness) of linear relationships using multiple representations. (I, D, E, A)


“Zap It” from AIMS Carnegie materials



15




Lesson 8.6 (2 days) Writing Linear Equations



• Create and use multiple representations (tables, graphs, verbal descriptions, symbolic expressions) of data to generalize the patterns and make connections among all representations. (A)


• Model and solve contextual problems involving linear proportions or direct variation using cultural contexts, including those of Montana American Indians. (I, D, E, A)

Lesson 8.8 (2 days) Systems of Linear Equations



• Identify the solution to a system of linear equations by determining whether the lines are parallel, intersecting, or the same line. (I, D, E, A)



16

Suggested




Lesson 8.9 (2 days) Graphs of Linear Inequalities

Algebraic and Functional Reasoning • Use properties of numbers and inverse operations to

solve multi-step linear inequalities in one variable, graph the solution on a number line and check the reasonableness of the solution (ie. associative, commutative, distributive, identity, and inverse). (I, D, E, A)

Compare Linear & Non-linear Functions (1 day)

Algebraic and Functional Reasoning • Compare and contrast the properties of linear and non-

linear relationships using technology when appropriate. (I, D, E, A)




17

Suggested


Chapter 9-Real Numbers and

Right Triangles


Lesson 9.1 (1 day) Square Roots

Number Sense and Operation • Estimate and explain the square root of any whole

number from 1-625 and simple cube roots from 1-1000. (I, D, E, A)

Lesson 9.3 (3 days) The Pythagorean Theorem

Geometric Reasoning • Use Pythagorean Theorem to find a missing side of right

triangles to calculate perimeter, area, surface area and volume, and label with appropriate units. (I, D, E, A)

• Make a logical argument for the Pythagorean Theorem and its converse. (e.g., decompose a square in two different ways). (I, D, E, A)

Students need to make a logical argument for Pythagorean Theorem

Lesson 9.4 (1 day) Real Numbers

Number Sense and Operation • Read, write, and compare numbers using integer

exponents and scientific notation. (I, D, E, A) • Compare, order, and graph rational numbers on a number

line. (E, A) • Estimate and explain the square root of any whole

number from 1-625 and simple cube roots from 1-1000. (I, D, E, A)

Lesson 9.5 (2 days) The Distance and Midpoint Formulas

Geometric Reasoning • Use Pythagorean Theorem to find a missing side of right

triangles to calculate perimeter, area, surface area and volume, and label with appropriate units. (I, D, E, A)






18


Chapter 10 – Measurement,

Area, and Volume


Lesson 10.1 (2 days) Triangles

Geometric Reasoning • Develop and justify a formula for the area of a trapezoid

(e.g., decompose a trapezoid into common polygons or use a composition of two trapezoids to create another common polygon). (I, D, E, A)

Algebraic and Functional Reasoning • Use properties of rational numbers and inverse operations

to solve multi-step equations and check the reasonableness of the answer. (I, D, E, A)

• Use properties of equality and rational numbers to rewrite an algebraic expression in multiple ways and show that the expressions are equivalent. (I, D, E, A)

Students need to make a logical argument for the sum of the angles in a triangle are 180 degrees

Lesson 10.2 (1 day) Polygons and Quadrilaterals



Algebraic and Functional Reasoning • Use properties of rational numbers and inverse operations

to solve multi-step equations and check the reasonableness of the answer. (I, D, E, A)

• Use properties of equality and rational numbers to rewrite an algebraic expression in multiple ways and show that the expressions are equivalent. (I, D, E, A)



19

Suggested



Area, and Volume


Lesson 10.3 (2 days) Areas of Parallelograms and Trapezoids



Geometric Reasoning • Determine the circumference and area of circles and

trapezoids and label with appropriate units. (I, D, E, A) • Develop and justify a formula for the area of a trapezoid

(e.g., decompose a trapezoid into common polygons or use a composition of two trapezoids to create another common polygon). (I, D, E, A)

Students need to develop and justify the area formula for a trapezoid

Area of Regular Polygons (2 days)

Geometric Reasoning • Develop and justify a formula (informal or formal) for

area of regular polygons (e.g., decompose a regular polygon into congruent isosceles triangles). (I, D, E, A)

Need a supplemental activity for determining and making a logical argument for the area formula for a regular polygon

Lesson 10.4 (2 days) Circumference and Area



Geometric Reasoning • Develop and justify the area formula of a circle (e.g.,

decompose a circle into a number of wedges and rearrange them into a shape that approximates a parallelogram). (I, D, E, A)

Students need to develop and justify the area formula for a circle

Quiz (1 day)



20

Suggested



Area, and Volume


Lesson 10.5 (2 days) Surface Areas of Prisms and Cylinders



Geometric Reasoning • Decompose a prism, pyramid and cylinder into its two-

dimensional shapes and compose its two-dimensional shapes into a cylinder. (I, D, E, A)

• Determine the surface area and volume of prisms and cylinders and label with appropriate units. (I, D, E, A)

“To the Surface and Beyond” from Navigating through measurement grades 6-8 Pages 39-42

OR “How Does Your Doughnut Measure Up?”

Lesson 10.7 (2 days) Volumes of Prisms and Cylinders



Geometric Reasoning • Determine the surface area and volume of prisms and

cylinders and label with appropriate units. (I, D, E, A)

Proportional Reasoning and Scale Factor (1 day)

Geometric Reasoning • Determine the lengths, areas, and volume using

proportional reasoning and scale factors of similar two- and three-dimensional objects. (I, D, E, A)

Need a supplemental lesson for determining length using proportional reasoning and scale factors of similar two-dimensional objects

How Scale Factor Affects Area and Volume (2 days)

Geometric Reasoning • Make a logical argument for how a scale factor affects

the area and volume of similar two- and three-dimensional objects. (I, D, E, A)

Need a supplemental lesson for determining area and volume using proportional reasoning and scale factors of similar three-dimensional objects




21

Suggested

Pacing Student/Teacher Edition Learning Objectives – 2nd Semester


Chapter 11 – Data Analysis and

Probability


Lesson 11.1 (1 day) Stem-and-Leaf Plots and Histograms

Data Analysis Mathematics • Organize and represent data using histograms and circle

graphs. (I, D, E, A) • Analyze histograms and circle graphs to solve problems

within daily life, scientific, and cultural contexts including those of Montana American Indians. (I, D, E, A)

Lesson 11.2 (2 days) Box-and-Whisker Plots

Data Analysis Mathematics • Collect, organize, and represent univariate data in box

plots. (I, D, E, A) • Describe and interpret a box plot using the 5 # summary,

the interquartile range, and percentiles. (I, D, E, A) • Compare and analyze the data represented in two or more

parallel box plots. (I, D, E, A)

Students need to create and analyze parallel box plots

Lesson 11.3 (1 day) Using Data Displays

Data Analysis Mathematics • Create and justify the appropriate visual representation

for given data sets from science, history, and culture, including those of Montana American Indians with and without technology. (A)

Review or teach line graph, scatter plot, bar graph and circle graph

Changes in Data (2 days)

Data Analysis Mathematics • Compare and analyze the strengths and limitations of

using each descriptive statistical measure and evaluate how changes in data affect those statistics. (E, A)

“Measuring Hand Spans” Lesson

Quiz (1 day) Line of Best Fit (1 day)

Data Analysis Mathematics • Estimate the line of best fit on a scatter plot to make

decisions and predictions about data within daily life, scientific, and cultural contexts, including those of Montana American Indians. (I, D, E, A)

“Exploring Relationships” from Navigating through Data Analysis grades 6-8



22

Suggested


Chapter 11 – Data Analysis and

Probability


Experimental & Theoretical Probability (3 days)

Data Analysis Mathematics • Create simple simulations and collect data to predict the

theoretical probability of the event. (I, D, E, A) • Use the experimental and theoretical probability of an

event to make a prediction for a large number of trials and justify your reasoning (e.g., probability of rolling a sum of two when rolling a pair of dice is 1/6; how many times would you expect a sum of two if you rolled the pair of dice 360 times). (I, D, E, A)

• Create and test conjectures made from the results of experiments and simulations using experimental and theoretical probabilities from scientific and cultural events, including those of Montana American Indians. (E, A)

“Cheyenne Basket Game” Lesson

Lesson 11.8 (1 day) Probabilities of Disjoint and Overlapping Events

Data Analysis Mathematics • Describe and apply the addition rule for probabilities of

events that are mutually exclusive and for events that are not mutually exclusive. (I, D, E, A)

Lesson 11.9 (1 day) Independent and Dependent Events

Data Analysis Mathematics • Describe and apply the addition rule for probabilities of

events that are mutually exclusive and for events that are not mutually exclusive. (I, D, E, A)

Misleading Presentation of Data (1 day)

Data Analysis Mathematics • Identify misleading presentations of data found in the

media and predict the effects of conclusions drawn. (E, A)

Need supplemental lesson that identifies misleading presentations of data found in the media




23

Suggested


Chapter 13- Angle Relationships and Transformations


Plane Geometry (1 day) Geometric Reasoning • Name and describe the basic objects of plane geometry.

(D, E, A)

Need a supplemental lesson for naming and describing the basic objects in plane geometry

Lesson 13.1 (1 day) Angle Relationships

Geometric Reasoning • Describe and define the angles created by intersecting

rays, intersecting lines, and parallel lines cut by transversals. (I, D, E, A)

Lesson 13.2 (1 day) Angles and Parallel Lines



• Use attributes of angles created by intersecting lines and parallel lines cut by transversals to solve problems involving missing sides or angles. (I, D, E, A)

Lesson 13.3 (2 days) Angles and Polygons



• Use attributes of angles created by intersecting lines and parallel lines cut by transversals to solve problems involving missing sides or angles. (I, D, E, A)

• Develop and justify the theorem for the sum of the interior angles of a triangle equaling 180º and the exterior angles of a triangle. (I, D, E, A)

Quiz (1 day)



24

Suggested


Chapter 13- Angle Relationships and Transformations


Lesson 13.4 (1 day) Translations

Geometric Reasoning • Define, identify and execute a translation, a rotation,

and a reflection with and without technology. (I, D, E, A)

May use IEFA Lesson Find the lesson: Native American Designs (2 days) at http://opi.mt.gov/indianed2/CurrSearch/Index.html

Lesson 13.5 (1 day) Reflections and Symmetry



Lesson 13.6 (1 day) Rotations and Symmetry



Lesson 13.7 (1 day) Dilations

Geometric Reasoning • Define, identify and execute a dilation with and

without technology. (I, D, E, A)


http://opi.mt.gov/indianed2/CurrSearch/Index.html



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