Mod 1 Ratios and Proportional Relationships Number of Days: Key Learning(s): Determine if two quantities are in a proportional relationship, identify constants of proportionality, and represent the relationship by equations How can we use proportionality represented through models of and models for ratio tables, factor-of-change (scale factor), a unit rate, and cross-multiplication Unit : to solve real world problems? Apply a variety of strategies for proportional reasoning and use them to solve real world problems, including problems dealing with similarity and rates of change. Recognize problem situations in which two or more variables have a linear relationship to each other. Understand the connections between linear equations and the patterns in the tables and graphs of those equations: rate of change, slope, and y-intercept. Lesson # A = Acquisition ET = Extended Thinking Materials Tier 2 Vocabulary Tier 3 Vocabulary rates and ratios How do rates and ratios help you describe real-life problems pg. 98-100 rate, ratio CC. 2.1.7.D.1 Analyze proportional relationships and use them to model and solve real-world and mathematical problems unit rates Comparing two rates graphically proportionally related Why are unit rates so important? How can we tell from a graph of a line what the unit rate is? How do you compare two rates graphically? What does the slope of a line mean? how can proportions help you decide when things are fair? How can we tell if two quantities are proportionally related? How can we tell from looking at a graph if two quantities are proportionally related? pg., 100-103 pg. 104-109 pg. 110-115, extra worksheets for graphing part unit rate slope proportion, proportional, cross products,
Module 2 Rational Numbers Number of Days: Key Learning(s): Addition, Subtraction, Multiplication and Division of Rational Numbers Unit : How is computation with rational numbers similar and different to whole number computation? Compute fluently and solve problems using positive and negative rational numbers (including integers). Solve real-world problems involving the four operations with rational numbers. CC.2.1.7.E.1 Apply and extend previous understandings of adding integers(review) operations with fractions to operations with rational numbers CC.2.2.7.B.3 Model and solve real-world and mathematical problems by using and connecting subtracting integers(review) numerical, algebraic, and/or graphical representations Lesson # A = Acquisition ET = Extended Thinking Is the sum of two integers positive, negative or zero? How can you tell? How do you add more than two integers? How do we represent addition on a number line? How are addition and subtraction of integers related? How do we represent subtraction on a number line? pg. 8-13 pg. 14-19 Materials Tier 2 Vocabulary Tier 3 Vocabulary sum, positive, negative, opposites, difference integer, additive inverse multiplying integers(review) Is the product of two integer s positive, negative or zero? How can you tell? How do you multiply more than two integers? pg. 22-27 product dividing integers(review) Is the quotient of two integers positive, negative or zero? How can you tell? How is dividing integers related to multiplying integers? pg. 28-33 quotient order of operations(review) How does using order of operations help me evaluate expressions while use multiple operations? [ET] pizazz sheets PEMDAS
fraction to decimals, decimals to fractions How do we know if a number is rational based on its decimal form? How do we convert between decimals and fractions to test for rationality? pg. 52-55 improper fraction, mixed number, terminating decimal, repeating decimal, rational number, adding & subtracting rational numbers How does adding and subtracting rational numbers compare with adding and subtracting integers? pg. 56-61 rational number multiplying & dividing rational numbers How is multiplying and dividing rational numbers compare to pg. 64-67B multiplying and dividing integers? product, quotient Reiterates above named concepts. Concept Formative Assessments Summative Assessments Instructional Specific activity to measure degree of student learning and ability to apply concept. Provides enrichment, acceleration, and/or remediation for learner. Provides enrichment, acceleration, and/or remediation for learner.
Module 3 Algebra, Equations, & Inequalities Number of Days: Key Learning(s): Identify and use algebraic properties to simplify expressions and solve multi-step equations and inequalities. Unit : When are algebraic and numeric expressions used? Model and solve real world and mathematical problems using multiple representations such as algebraic, graphical and using tables. Solve multi-step equations or inequalities with one variable. Solve and interpret multi-step real life and mathematical problems posed with positive and negative rational numbers. apply properties of operations to generate equivalent expressions CC.2.2.7.B.3 Model and solve real-world and mathematical problems by Addition & Subtraction Oneusing and connecting Step Equations numerical, algebraic, and/or graphical representations Lesson # A = Acquisition ET = Extended Thinking How do you use inverse operations to solve an equation? Materials pg. 70-75 Tier 2 Vocabulary Tier 3 Vocabulary equivalent equations, inverse operations, MP.1, MP.2, MP.3, MP.4, MP.5, MP.6 Multiplication and Division One-Step Equations How do you use multiplication and division to solve an equation? pg. 76-81 coefficient Distributive Property How do we distribute rational numbers? pizazz sheets Simplifying Expressions How do we combine like terms, including rationales? like terms, simplest form, Solving two-step equations In a two step-equation, which step should you do first? pg. 82-87 Multi-Step Equations In multi-step equations, which operations should you perform first? pizazz
one-step addition/subtraction inequalities one-step multiplication/division inequalities & graph multi-step inequalities & graph How are one-step addition and subtraction inequalities related to onestep addition and subtraction equations? What's the difference? How are one step multiplication and division inequalities related to one step multiplication and division equations? When is there an exception? How do we graph inequalities? How are multi-step inequalities related to multi-step equations? When is the exception? pg. 87A greater than, less than inequality, pg. 87B-87C pg. 87D Reiterates above named concepts. Concept Formative Assessments Summative Assessments Specific activity to measure degree of student learning and ability to apply concept. Provides enrichment, acceleration, and/or remediation for learner. Suggested Instructional Activities Students apply new learnings working independently.
Mod 4 Percents and Proportional Relationships Number of Days: Key Learning(s): Parallel on Mod 1 with a concentration on percent. Unit : How can proportions be used to solve percent problems? Use proportional relationships to solve multistep ratio and percent problems Lesson # A = Acquisition ET = Extended Thinking Materials Tier 2 Vocabulary Tier 3 Vocabulary CC.2.1.7.D.1 Analyze proportional relationships and use them to model and solve real-world and mathematical problems Solving for a variable in a proportion How can you write a proportion that solves a problem in real-life pg. 116-127 cross products Using the percent equation How do you use the percent equation to find the missing variable in a percent question? pg. 160-163 percent percent increase & percent decrease What is a percent of increase? What is a percent of decrease? pg. 164-169 percent of change, percent of increase, percent of decrease markups, markdowns, discounts How do you find discounts and markups efficiently? pg. 172-177 discount markup Gratuities & commissions How do we use percents to find gratuities and commissions? extra worksheets gratuity, commission tax How do we find the amount of tax of an item? extra worksheets
simple interest fees How can you find the amount of simple interest earned on a savings account? How can you find the amount of interest owed on a loan? How are interest rates related to percents? pg. 178-183 interest rate interest, principal, simple interest,
Mod 5 Statistics and Probability Number of Days: Key Learning(s): Drawing inferences about populations through random samples, use probability models to predict results Unit : How does the collection, organization, analysis, and interpretation of data help us answer real life questions? What kind of questions can and cannot be answered from the data set and its display? How do we make predictions based on the outcomes of a probability experiment? Answer questions regarding a data set using measures of center and spread and interpreting the graphical representation (including box-and-whisker plots) of the data set. Determine the sample space for one-stage experiments and determine, when possible, the theoretical probabilities for events defined in the sample space. Lesson # A = Acquisition ET = Extended Thinking Materials Tier 2 Vocabulary Tier 3 Vocabulary CC.2.4.7.B.2 Draw informal comparative inferences about two populations experiment, outcomes & events, probability How can you predict results? pg. 386-389 experiment, outcomes, events, probability CC. 2.4.7.B.1 Investigate chance processes and develop, use, and evaluate probability models Theoretical & Experimental Probability What is the difference between theoretical and experimental probabilities? pg. 390-403 theoretical probability, experimental probability, equally likely, fair, Independent vs. dependent events, multi-stage experiments What is the difference between independent and dependent events? How can we show probabilities for multi-stage experiments both mathematically pg. 404-411 independent event, dependent event Replacement/nonreplacement What is the difference between replacement and nonreplacement? pg. 404-411 Random sampling Determine if a sample is random given a real-world situation? How can you use a survey to make a conclusion about the general population? pg. 368-373 population, sample mean absolute deviation How do we use samples to compare populations? pg. 373B-374 & extra worksheets mean, median, mode, range mean absolute deviation
Mod 6 Geometry Number of Days: Drawing and constructing informal geometrical figures. Revisit unknown angles, volumes and surface area problems, which now include problems involving Key Learning(s): percentages of areas or volumes. How can the decomposition of 3-dimensional shapes aid in the understanding of surface areas and volumes? How can we use the relationship between surface Unit : area and volume to help us draw, construct, model, and represent real situations and/or solve problems of surface area and volume? How can we use Extend previous understandings of the characteristics of 3d-shapes to develop an understanding of, and use formulas to determine surface areas and volumes. CC. 2.3.7.A.2 Visualize and represent geometric figures scale drawings and describe the relationships between them Lesson # A = Acquisition ET = Extended How can you use a scale drawing to estimate real quantities? pg. 212-218 Materials Tier 2 Vocabulary Tier 3 Vocabulary scale drawing, scale model CC.2.3.7.A.1 Solve realworld and mathematical problems involving angle measure, area, surface area, circumference and volume triangle classification How do we classify triangles by the lengths of their sides? How do we classify triangles by the measures of their angles? additional worksheets acute triangle, obtuse triangle, scalene triangle, isosceles triangle, equilateral triangle, equiangular triangle triangle inequality theorem How can we use drawing triangles based on side lengths to interpret the triangle inequality theorem? pg. 424-425 triangle inequality theorem Angle classification What additional ways are there to classify angles? pg. 422-423 & additional worksheets parallel lines, perpendicular lines transversal, adjacent angles, vertical angles, congruent angles, complimentary angles, supplementary angles, corresponding angles, exterior angles, interior angles, alternate exterior angles, alternate interior angles
slices of three dimensional figures What shapes will result from plane slices through 3D figures? pg. 427 Circle measurements How do we find the circumference and area of a circle? pg. 261B pi, radius, diameter, chord, circumference Surface Area How do we find surface area of pg. 250-261, 262-288 cylinders and rectangular prisms? Volume How do we find volume of cylinders and rectangular prism pg. 298-321 net