7th pre-algebra pacing-2010 - billings public schools - … guide - (pacing... · ·...
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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)
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
3
Suggested Pacing Student/Teacher Edition Learning Objectives – 1st Semester
Supporting Materials
Chapter 2 – Solving
Equations
Approximately 17 days
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
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 “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
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)
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
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 2.6 (1 day) Solving Equations Using Multiplication or Division
Algebraic and Functional Reasoning • Solve multi-step linear equations incorporating multiple
grouping symbols and check the reasonableness of the solution. (I, D, E, A)
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
4
Suggested Pacing Student/Teacher Edition Learning Objectives – 1st Semester
Supporting Materials
Chapter 2 – Solving
Equations
Approximately 17 days
Lesson 2.7 (1 day) Decimal Operations and Equations with Decimals
Algebraic and Functional Reasoning • Solve multi-step linear equations incorporating multiple
grouping symbols and check the reasonableness of the solution. (I, D, E, A)
Review/Testing (2 days)
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
5
Suggested Pacing Student/Teacher Edition Learning Objectives – 1st Semester Supporting Materials
Chapter 3 – Multi-Step
Equations and Inequalities
Approximately 13 days
Lesson 3.1 (2 days) Solving Two-Step 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)
Pre-Algebra with Pizzazz 2-Step Equations “Find a Match”
Lesson 3.2 (2 days) Solving Equations Having Like Terms and Parentheses
Algebraic and Functional Reasoning • Solve multi-step linear equations incorporating multiple
grouping symbols and check the reasonableness of the solution. (I, D, E, A)
Pre-Algebra with Pizzazz “What is the Title”
Lesson 3.3 (2 days) Solving Equations with Variables on Both Sides
Algebraic and Functional Reasoning • Solve multi-step linear equations incorporating multiple
grouping symbols and check the reasonableness of the solution. (I, D, E, A)
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
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)
Pg. 143 Mini-Lesson
Lesson 3.6 (2 days) Solving Multi-Step 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)
Review/Test (2 days)
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
6
Suggested
Pacing Student/Teacher Edition Learning Objectives – 1st Semester Supporting Materials
Chapter 4 – Factors,
Fractions, and Exponents
Approximately 14 days
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
Number Sense and Operation • Apply number theory concepts such as prime factorization,
greatest common factor, and least common multiple to solve problems. (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 4.3 (1 day) Equivalent Fractions
Number Sense and Operation • Apply number theory concepts such as prime factorization,
greatest common factor, and least common multiple to solve problems. (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 4.4 (2 days) Least Common Multiple
Number Sense and Operation • Apply number theory concepts such as prime factorization,
greatest common factor, and least common multiple to solve problems. (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)
Algebra With Pizzazz GCF & LCM
Quiz (1 day)
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
7
Suggested
Pacing Student/Teacher Edition Learning Objectives – 1st Semester Supporting Materials
Chapter 4 – Factors,
Fractions, and Exponents
Approximately 14 days
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
including those involving like terms and justify each step with properties of operations. (I, D, E, A)
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
including those involving like terms and justify each step with properties of operations. (I, D, E, A)
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)
Review/Test (2 days)
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
8
Suggested Pacing Student/Teacher Edition Learning Objectives – 1st Semester
Supporting Materials
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
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)
Quiz (1 day) Lesson 5.4 (1 day) Multiplying 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)
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
9
Suggested
Pacing Student/Teacher Edition Learning Objectives – 1st Semester Supporting Materials
Chapter 5- Rational
Numbers and Equations
Approximately 15 Days
Lesson 5.5 (2 days) Dividing 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 5.6 ( 1 day) Using Multiplicative Inverses to Solve 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 5.7 (2 days) Equations and Inequalities with Rational Numbers
Algebraic and Functional Reasoning • Solve multi-step linear equations incorporating multiple
grouping symbols and check the reasonableness of the solution. (I, D, E, A)
• 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)
Review/Test (2 days)
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
10
Suggested Pacing Student/Teacher Edition Learning Objectives – 1st Semester Supporting Materials
Chapter 6 – Ratio,
Proportion, and Probability
Approximately 9 days
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
Number Sense and Operation • Use proportions to solve contextual problems including
similarity and congruence. (E, A)
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
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
11
Suggested
Pacing Student/Teacher Edition Learning Objectives – 1st Semester Supporting Materials
Chapter 6 – Ratio,
Proportion, and Probability
Approximately 9 days
Lesson 6.6 (1 day) Scale Drawings
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)
Review/Test (2 days)
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
12
Suggested Pacing Student/Teacher Edition Learning Objectives – 2nd Semester Supporting Materials
Chapter 7 – Percents
Approximately 12 days
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
Number Sense and Operation • Use proportions to solve contextual problems including
similarity and congruence. (E, A)
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
including those involving like terms and justify each step with properties of operations. (I, D, E, A)
Quiz (1 day)
Lesson 7.5 (2 days) Percent of Change
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 7.6 (2 days) Percent Applications
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 7.7 (1 day) Simple Interest
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)
Omit compound interest
Review/Test (2 days)
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
13
Suggested Pacing
Student/Teacher Edition Learning Objectives – 2nd Semester Supporting Materials
Chapter 8 – Linear Functions
Approximately 20 days
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
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)
• Generate equivalent forms of algebraic expressions including those involving like terms and justify each step with properties of operations. (I, D, E, A)
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
14
Suggested
Pacing Student/Teacher Edition Learning Objectives – 2nd Semester Supporting Materials
Chapter 8 – Linear Functions
Approximately 20 days
Lesson 8.3 (1 day) Using Intercepts
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)
• 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)
• 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)
“Zap It” from AIMS Carnegie materials
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
15
Suggested Pacing Student/Teacher Edition Learning Objectives – 2nd Semester Supporting Materials
Chapter 8 – Linear Functions
Approximately 20 days
Lesson 8.6 (2 days) Writing Linear Equations
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)
• 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 the slope, x-intercept, and y-intercept of a line given its graph, equation, or two points on the line. (I, D, E, 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
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)
• 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)
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
16
Suggested
Pacing Student/Teacher Edition Learning Objectives – 2nd Semester Supporting Materials
Chapter 8 – Linear Functions
Approximately 20 days
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)
Review/Test (2 days)
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
17
Suggested
Pacing Student/Teacher Edition Learning Objectives – 2nd Semester Supporting Materials
Chapter 9-Real Numbers and
Right Triangles
Approximately 9 days
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)
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)
Review/Test (2 days)
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
18
Suggested Pacing Student/Teacher Edition Learning Objectives – 2nd Semester Supporting Materials
Chapter 10 – Measurement,
Area, and Volume
Approximately 19 days
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
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)
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)
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
19
Suggested
Pacing Student/Teacher Edition Learning Objectives – 2nd Semester Supporting Materials
Chapter 10 – Measurement,
Area, and Volume
Approximately 19 days
Lesson 10.3 (2 days) Areas of Parallelograms and Trapezoids
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)
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
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)
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)
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
20
Suggested
Pacing Student/Teacher Edition Learning Objectives – 2nd Semester Supporting Materials
Chapter 10 – Measurement,
Area, and Volume
Approximately 19 days
Lesson 10.5 (2 days) Surface Areas of Prisms and Cylinders
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)
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
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)
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
Review/Test (2 days)
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
21
Suggested
Pacing Student/Teacher Edition Learning Objectives – 2nd Semester
Supporting Materials
Chapter 11 – Data Analysis and
Probability
Approximately 18 days
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
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
22
Suggested
Pacing Student/Teacher Edition Learning Objectives – 2nd Semester Supporting Materials
Chapter 11 – Data Analysis and
Probability
Approximately 18 days
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
Review/Test (2 days)
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
23
Suggested
Pacing Student/Teacher Edition Learning Objectives – 2nd Semester Supporting Materials
Chapter 13- Angle Relationships and Transformations
Approximately 12 Days
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
Geometric Reasoning • Describe and define the angles created by intersecting
rays, intersecting lines, and parallel lines cut by transversals. (I, D, E, A)
• 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
Geometric Reasoning • Describe and define the angles created by intersecting
rays, intersecting lines, and parallel lines cut by transversals. (I, D, E, A)
• 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)
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
24
Suggested
Pacing Student/Teacher Edition Learning Objectives – 2nd Semester Supporting Materials
Chapter 13- Angle Relationships and Transformations
Approximately 12 Days
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
Geometric Reasoning • Define, identify and execute a translation, a rotation,
and a reflection with and without technology. (I, D, E, A)
Lesson 13.6 (1 day) Rotations and Symmetry
Geometric Reasoning • Define, identify and execute a translation, a rotation,
and a reflection with and without technology. (I, D, E, A)
Lesson 13.7 (1 day) Dilations
Geometric Reasoning • Define, identify and execute a dilation with and
without technology. (I, D, E, A)
Review/Test (2 days)