SEVENTH GRADE PreAlgebra Revised June 2010


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1 SEVENTH GRADE PreAlgebra Revised June 2010 Billings Public Schools Correlation and Guide Math  McDougal Littell Middle School Math 2004 (Chapter Order: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13)
2 Chapter 1 Variable, Expressions, and Integers 16 days Student/Teacher Edition Learning Objectives 1 st Semester Supplemental Materials Lesson 1.1 (1 day) Expressions and Variables Lesson 1.2 (1 day) Powers and Exponents Lesson 1.3 (1 day) Order of Operations Necessary Lesson (2 days) Comparing and Ordering Integers Or: Lesson 1.4 (2 days) Quiz (1 day) Necessary Lessons (8 days) Adding, Subtracting, Multiplying and Dividing Integers Or: Lesson 1.5, 1.6 & 1.7 (8 days) Review/Test (2 days) Review Review Review 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) 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) Use calculators to find solutions using the order of operations Stepping Out Integers from AIMS Integer Addresses from AIMS What s the Charge for Addition and Subtraction from AIMS Integer Patterns from AIMS 2
3 Chapter 2 Solving Equations 17 days Student/Teacher Edition Learning Objectives 1 st Semester Supporting Materials Lesson 2.1 (2 days) Properties and Operations Lesson 2.2 (2 days) The Distributive Property Necessary Lesson (2 days) Rates & Unit Analysis Algeblock Lesson (3 days) Simplifying Variable Expressions OR: Lesson 2.3 Quiz (1 day) Lesson 2.4 (1 day) Variables and Equations Lesson 2.5 (2 days) Solving Equations Using Addition or Subtraction Lesson 2.6 (1 day) Solving Equations Using Multiplication or Division including those involving like terms and justify each step with properties of operations. (I, D, E, A) including those involving like terms and justify each step with properties of operations. (I, D, E, A) Use rates to justify conversions between units within the same system. (e.g., miles per hour to feet per second) (I, D, E, A) including those involving like terms and justify each step with properties of operations. (I, D, E, A) Solve multistep linear equations incorporating multiple grouping symbols and check the reasonableness of the solution. (I, D, E, A) Solve multistep linear equations incorporating multiple grouping symbols and check the reasonableness of the solution. (I, D, E, A) Solve multistep linear equations incorporating multiple grouping symbols and check the reasonableness of the solution. (I, D, E, A) PreAlgebra with Pizzazz PreAlgebra with Pizzazz Did You Hear About Need a supplemental lesson for rates and unit analysis Introducing Algeblocks and Variable Expression Lesson using worksheets 51 to 53 & 57 from the Algeblock Notebook (Lesson Plan provided in Supplement Folder) 3
4 Chapter 2 Solving Equations 17 days Student/Teacher Edition Learning Objectives 1 st Semester Supporting Materials Lesson 2.7 (1 day) Decimal Operations and Equations with Decimals Review/Testing (2 days) Solve multistep linear equations incorporating multiple grouping symbols and check the reasonableness of the solution. (I, D, E, A) 4
5 Student/Teacher Edition Learning Objectives 1 st Semester Supporting Materials Chapter 3 Lesson 3.1 (2 days) PreAlgebra with Pizzazz MultiStep Solving TwoStep Equations Solve multistep linear equations incorporating multiple 2Step Equations Find a Equations and grouping symbols and check the reasonableness of the Match Inequalities solution. (I, D, E, A) 13 days Lesson 3.2 (2 days) Solving Equations Having Like Terms and Parentheses Lesson 3.3 (2 days) Solving Equations with Variables on Both Sides Quiz (1 day) Lesson 3.4 (1 day) Solving Inequalities Using Addition or Subtraction Lesson 3.5 (1 day) Solving Inequalities Using Multiplication or Division Lesson 3.6 (2 days) Solving MultiStep Inequalities Review/Test (2 days) Solve multistep linear equations incorporating multiple grouping symbols and check the reasonableness of the solution. (I, D, E, A) Solve multistep 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 multistep 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) Use properties of numbers and inverse operations to solve multistep 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) Use properties of numbers and inverse operations to solve multistep 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) 5 PreAlgebra with Pizzazz What is the Title PreAlgebra with Pizzazz Superstar Pg. 143 MiniLesson
6 Chapter 4 Factors, Fractions, and Exponents 14 days Student/Teacher Edition Learning Objectives 1 st Semester Supporting Materials Lesson 4.1 (1 day) Factors and Prime Factorization Lesson 4.2 (2 days) Greatest Common Factor Lesson 4.3 (1 day) Equivalent Fractions Lesson 4.4 (2 days) Least Common Multiple Quiz (1 day) Apply number theory concepts such as prime factorization, greatest common factor, and least common multiple to solve problems. (A) Apply number theory concepts such as prime factorization, greatest common factor, and least common multiple to solve problems. (A) including those involving like terms and justify each step with properties of operations. (I, D, E, A) Apply number theory concepts such as prime factorization, greatest common factor, and least common multiple to solve problems. (A) including those involving like terms and justify each step with properties of operations. (I, D, E, A) Apply number theory concepts such as prime factorization, greatest common factor, and least common multiple to solve problems. (A) including those involving like terms and justify each step with properties of operations. (I, D, E, A) Algebra With Pizzazz GCF & LCM 6
7 Chapter 4 Factors, Fractions, and Exponents 14 days Student/Teacher Edition Learning Objectives 1 st Semester Supporting Materials Lesson 4.5 (1 day) Rules of Exponents Lesson 4.6 (2 days) Negative and Zero Exponents Lesson 4.7 (2 days) Scientific Notation Review/Test (2 days) Evaluate numeric expressions including nested parentheses, exponents, and other grouping symbols. (I, D, E, A) including those involving like terms and justify each step with properties of operations. (I, D, E, A) Evaluate numeric expressions including nested parentheses, exponents, and other grouping symbols. (I, D, E, A) including those involving like terms and justify each step with properties of operations. (I, D, E, A) 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) 7
8 Chapter 5 Rational Numbers and Equations 15 Days 8 Student/Teacher Edition Learning Objectives 1 st Semester Supporting Materials Necessary Lesson (2 days) Rational Numbers Lesson 5.1 (1 day) Rational Numbers Lesson 5.2 (1 day) Adding and Subtracting Like Fractions Lesson 5.3 (2 days)adding and Subtracting Unlike Fractions Quiz (1 day) Lesson 5.4 (1 day) Multiplying Fractions 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) Compare, order, and graph rational numbers on a number line. (E, A) Compute fluently and solve multistep problems using integers, fractions, decimals, and numbers in exponential form. (I, D, E, A) including those involving like terms and justify each step with properties of operations. (I, D, E, A) Compute fluently and solve multistep problems using integers, fractions, decimals, and numbers in exponential form. (I, D, E, A) including those involving like terms and justify each step with properties of operations. (I, D, E, A) Compute fluently and solve multistep problems using integers, fractions, decimals, and numbers in exponential form. (I, D, E, A) including those involving like terms and justify each step with properties of operations. (I, D, E, A) Classifying Number Sets Lesson
9 Chapter 5 Rational Numbers and Equations 15 Days Student/Teacher Edition 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 Review/Test (2 days) Learning Objectives 1 st Semester Compute fluently and solve multistep problems using integers, fractions, decimals, and numbers in exponential form. (I, D, E, A) including those involving like terms and justify each step with properties of operations. (I, D, E, A) Solve multistep linear equations incorporating multiple grouping symbols and check the reasonableness of the solution. (I, D, E, A) Solve multistep 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 multistep 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) Supporting Materials 9
10 Chapter 6 Ratio, Proportion, and Probability 9 days Student/Teacher Edition Learning Objectives 1 st Semester Supporting Materials Lesson 6.1 ( 1 day) Ratios and Rates Lesson 6.2 (1 day) Writing and Solving Proportions 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 Use rates to justify conversions between units of measure (e.g., convert miles/hour to feet/second). (E, A) Use proportions to solve contextual problems including similarity and congruence. (E, A) Use proportions to solve contextual problems including similarity and congruence. (E, A) 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) 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
11 Chapter 6 Ratio, Proportion, and Probability 9 days Student/Teacher Edition Learning Objectives 1 st Semester Supporting Materials Lesson 6.6 (1 day) Scale Drawings Review/Test (2 days) 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) 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) 11
12 Student/Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Chapter 7 Lesson 7.1 & 7.3 (1 day) Review Page 334 Percents Percents, Fractions and Estimating with Percents Decimals 12 days Lesson 7.2 (2 days) Percents and Proportions Lesson 7.4 (1 day) The Percent Equation 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 Review/Test (2 days) Use proportions to solve contextual problems including similarity and congruence. (E, A) Solve multistep problems containing rational numbers and numbers in exponential form. (I, D, E, A) including those involving like terms and justify each step with properties of operations. (I, D, E, A) including those involving like terms and justify each step with properties of operations. (I, D, E, A) including those involving like terms and justify each step with properties of operations. (I, D, E, A) including those involving like terms and justify each step with properties of operations. (I, D, E, A) Omit compound interest 12
13 Student/Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Chapter 8 Lesson 1.8 (1 day) Review Linear Functions The Coordinate Plane 20 days Lesson 8.1 (2 days) Relations and Functions Lesson 8.2 (2 days) Linear Equations in Two Variables 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 nonfunctional relations using technology when appropriate. (I, D, E, 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 from a set of ordered pairs, a table, graph, or a rule whether a relation is a function. (I, D, E, A) including those involving like terms and justify each step with properties of operations. (I, D, E, A) Page 397: Technology 13
14 Chapter 8 Linear Functions 20 days Student/Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Lesson 8.3 (1 day) Using Intercepts Quiz (1 day) Necessary Lesson (4 days) The Slope of a Line and SlopeIntercept Form OR: Lesson 8.4 and 8.5 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 multistep linear equations incorporating multiple grouping symbols and check the reasonableness of the solution. (I, D, E, A) including those involving like terms and justify each step with properties of operations. (I, D, E, A) Determine the slope, xintercept, and yintercept of a line given its graph, equation, or two points on the line. (I, D, E, A) Identify the properties (slope, intercepts, continuity, and discreteness) of linear relationships using multiple representations. (I, D, E, A) Determine the slope, xintercept, and yintercept of a line given its graph, equation, or two points on the line. (I, D, E, A) Zap It from AIMS Carnegie materials 14
15 Student/Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Chapter 8 Lesson 8.6 (2 days) Linear Functions Writing Linear Equations 20 days Lesson 8.8 (2 days) Systems of 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) 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, xintercept, and yintercept 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) 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) 15
16 Student/Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Chapter 8 Linear Functions 20 days Lesson 8.9 (2 days) Graphs of Linear Inequalities Compare Linear & Nonlinear Functions (1 day) Review/Test (2 days) Use properties of numbers and inverse operations to solve multistep 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 and contrast the properties of linear and nonlinear relationships using technology when appropriate. (I, D, E, A) 16
17 Chapter 9Real Numbers and Right Triangles 9 days Student/Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Lesson 9.1 (1 day) Square Roots Lesson 9.3 (3 days) The Pythagorean Theorem Lesson 9.4 (1 day) Real Numbers Lesson 9.5 (2 days) The Distance and Midpoint Formulas Review/Test (2 days) Estimate and explain the square root of any whole number from and simple cube roots from (I, D, E, A) 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) 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 and simple cube roots from (I, D, E, A) 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) including those involving like terms and justify each step with properties of operations. (I, D, E, A) Students need to make a logical argument for Pythagorean Theorem 17
18 Student/Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Chapter 10 Lesson 10.1 (2 days) Students need to make a Measurement, Triangles Develop and justify a formula for the area of a trapezoid logical argument for the Area, and (e.g., decompose a trapezoid into common polygons or sum of the angles in a Volume use a composition of two trapezoids to create another triangle are 180 degrees common polygon). (I, D, E, A) Use properties of rational numbers and inverse operations to solve multistep 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 19 days Lesson 10.2 (1 day) Polygons and Quadrilaterals the expressions are equivalent. (I, D, E, A) Use appropriate tools and technology to solve problems involving measurement in scientific and cultural situations, including those of Montana American Indians. (A) Use properties of rational numbers and inverse operations to solve multistep 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) 18
19 Chapter 10 Measurement, Area, and Volume 19 days Student/Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Lesson 10.3 (2 days) Areas of Parallelograms and Trapezoids Area of Regular Polygons (2 days) Lesson 10.4 (2 days) Circumference and Area Quiz (1 day) Use appropriate tools and technology to solve problems involving measurement in scientific and cultural situations, including those of Montana American Indians. (A) 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) 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) Use appropriate tools and technology to solve problems involving measurement in scientific and cultural situations, including those of Montana American Indians. (A) 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 trapezoid Need a supplemental activity for determining and making a logical argument for the area formula for a regular polygon Students need to develop and justify the area formula for a circle 19
20 Chapter 10 Measurement, Area, and Volume 19 days Student/Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Lesson 10.5 (2 days) Surface Areas of Prisms and Cylinders Lesson 10.7 (2 days) Volumes of Prisms and Cylinders Proportional Reasoning and Scale Factor (1 day) How Scale Factor Affects Area and Volume (2 days) Review/Test (2 days) Use appropriate tools and technology to solve problems involving measurement in scientific and cultural situations, including those of Montana American Indians. (A) Decompose a prism, pyramid and cylinder into its twodimensional shapes and compose its twodimensional 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) Use appropriate tools and technology to solve problems involving measurement in scientific and cultural situations, including those of Montana American Indians. (A) Determine the surface area and volume of prisms and cylinders and label with appropriate units. (I, D, E, A) Determine the lengths, areas, and volume using proportional reasoning and scale factors of similar twoand threedimensional objects. (I, D, E, A) Make a logical argument for how a scale factor affects the area and volume of similar two and threedimensional objects. (I, D, E, A) To the Surface and Beyond from Navigating through measurement grades 68 Pages OR How Does Your Doughnut Measure Up? Need a supplemental lesson for determining length using proportional reasoning and scale factors of similar twodimensional objects Need a supplemental lesson for determining area and volume using proportional reasoning and scale factors of similar threedimensional objects 20
21 Chapter 11 Data Analysis and Probability 18 days Student/Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Lesson 11.1 (1 day) StemandLeaf Plots and Histograms Lesson 11.2 (2 days) BoxandWhisker Plots Lesson 11.3 (1 day) Using Data Displays Changes in Data (2 days) Quiz (1 day) Line of Best Fit (1 day) 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) 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) 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) 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) 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) Students need to create and analyze parallel box plots Review or teach line graph, scatter plot, bar graph and circle graph Measuring Hand Spans Lesson Exploring Relationships from Navigating through Data Analysis grades
22 Chapter 11 Data Analysis and Probability 18 days Student/Teacher Edition Experimental & Theoretical Probability (3 days) Lesson 11.8 (1 day) Probabilities of Disjoint and Overlapping Events Lesson 11.9 (1 day) Independent and Dependent Events Misleading Presentation of Data (1 day) Review/Test (2 days) Learning Objectives 2 nd Semester 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) 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) 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) Data Analysis Mathematics Identify misleading presentations of data found in the media and predict the effects of conclusions drawn. (E, A) Supporting Materials Cheyenne Basket Game Lesson Need supplemental lesson that identifies misleading presentations of data found in the media 22
23 Chapter 13 Angle Relationships and Transformations 12 Days Student/Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Plane Geometry (1 day) Lesson 13.1 (1 day) Angle Relationships Lesson 13.2 (1 day) Angles and Parallel Lines Lesson 13.3 (2 days) Angles and Polygons Quiz (1 day) Name and describe the basic objects of plane geometry. (D, E, A) Describe and define the angles created by intersecting rays, intersecting lines, and parallel lines cut by transversals. (I, D, E, A) 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) 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) Need a supplemental lesson for naming and describing the basic objects in plane geometry 23
24 Chapter 13 Angle Relationships and Transformations 12 Days Student/Teacher Edition Learning Objectives 2 nd Semester Supporting Materials Lesson 13.4 (1 day) Translations Lesson 13.5 (1 day) Reflections and Symmetry Lesson 13.6 (1 day) Rotations and Symmetry Lesson 13.7 (1 day) Dilations Review/Test (2 days) Define, identify and execute a translation, a rotation, and a reflection with and without technology. (I, D, E, A) Define, identify and execute a translation, a rotation, and a reflection with and without technology. (I, D, E, A) Define, identify and execute a translation, a rotation, and a reflection with and without technology. (I, D, E, A) Define, identify and execute a dilation with and without technology. (I, D, E, A) May use IEFA Lesson Find the lesson: Native American Designs (2 days) at d2/currsearch/index.htm l 24
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