Topic/Unit: The Number System Big Ideas/Enduring Understandings: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers Essential Questions: Why do I need mathematical operations? How are common fractions, decimals and percents alike and different? How can fractions be modeled, compared and ordered? How is computation with rational numbers similar and different to whole number computation? How do the four operations of mathematics relate to one another? How do I know which mathematical operation (+, -, x,, exponents, etc.) to use? PA Academic Standards (PA Common Core): CC.2.1.7.E.1 Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with Mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Tier 3 Vocabulary: Opposite, absolute value, additive inverse, distributive property, integer, rational numbers, terminating decimals, repeating decimals, complex fractions Concepts: Competencies: Instructional Practices: Assessments: Students will know that: Students will be able to: KWL chart of terms White boards Rational numbers can be added, subtracted, multiplied and divided. Describe situations in which opposite quantities combine to make zero. Word walls Videos Thumbs up/down Tests Addition and subtraction can be represented on both vertical and horizontal number lines. subtract rational numbers by adding the inverse. Quizzes Practice packets Page 1
Division of rational numbers either terminate or repeat. Absolute value can be represented graphically on the number line. Division by zero is impossible. the decimal form of a rational number terminates or eventually repeats. Multiply using the distributive property. Convert a rational number to a decimal using long division. Solve real world and mathematical problems involving the four operations with rational numbers. Explain how to use the distributive property. Independent Practice www.brainpop.com www.studyisland.com www.mangahigh.com www.thatquiz.com www.ixl.com www.mathplay.com www.bidideasmath.com www.quizlet.com Notebook presentations Presentations and lessons Interactive virtual worksheets and practice Graded Assignments Probes Study/Core benchmarks Study Island Core Practice Mangahigh Challenges Thatquiz.com Exit cards Quizlets Cloud sheet checks Classroom discussions and discoveries Think pair share Rally couch Four corners Dice partners Group collaboration Page 2
Topic/Unit: Ratios and Proportional Relationships Big Ideas/Enduring Understandings: Analyze proportional relationships and use them to solve real-world and mathematical problems Essential Questions: What is the repeating and/or increasing unit? Is the constant of proportionality the same? When and why do I use proportional comparisons? How does comparing quantities describe the relationship between them? PA Academic Standards (PA Common Core): CC.2.1.7.D.1 Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with Mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Tier 3 Vocabulary: Ratio, rate, unit rate, proportion, proportional, constant of proportionality, simple interest, principal, tax, percent mark down, percent markup, tip, commission, percent of change, percent of increase, percent of decrease, percent error Concepts: Competencies: Instructional Practices: Assessments: Students will know that: Students will be able to: KWL chart of terms White boards Unit rate is applicable to finding quantities such as predictions of price, length and area. Proportionality is a direct concept of slope. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like and different units. Word walls Videos Independent Practice www.brainpop.com www.studyisland.com Thumbs up/down Tests Quizzes Practice packets Page 3
Y is a direct relation dependent of x in the form y= mx. Proportions are used to solve problems containing percents. Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship by testing for equivalent ratios in a table or graph on a coordinate plane and observing whether the graph is a straight line through the origin. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. Explain how a point (x.y) on the graph is a proportional relationship in terms of the situation, with special attention to the points (0,0) and (1,r) where r is the unit rate. www.mangahigh.com www.thatquiz.com www.ixl.com www.mathplay.com www.bidideasmath.com www.quizlet.com Notebook presentations Presentations and lessons Interactive virtual worksheets and practice Classroom discussions and discoveries Think pair share Rally couch Four corners Dice partners Group collaboration Graded Assignments Probes Study/Core benchmarks Study Island Core Practice Mangahigh Challenges Thatquiz.com Exit cards Quizlets Cloud sheet checks Page 4
Use proportional relationships to solve multistep ratio and percent problems. Page 5
Topic/Unit: Expressions and Equations Big Ideas/Enduring Understandings: Use Properties of operations to generate equivalent expressions Essential Questions: In what ways can numbers and expressions be expressed? How is an equation like a balance scale? How can relationships be expressed mathematically? Why are variables used? What strategies can be used to solve for unknowns? How does finding the common characteristics among similar problems help me to be a more efficient problem solver? How is thinking algebraically different from thinking arithmetically? How do I use algebraic expressions to analyze or solve problems? How do the properties contribute to algebraic understanding? What is meant by equality? How do I know when a result is reasonable? What is the relationship between solving problems and computation? Why is the ability to solve problems the heart of mathematics? When is it appropriate to use estimation and/or approximation? How important are estimations in real life situations? How do I make a reasonable estimate? PA Academic Standards (PA Common Core): CC2.1.7.E.1, CC.2.2.7.B.1, CC.2.2.7.B.3 Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with Mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Tier 3 Vocabulary: Expression, variable, linear expression, equivalent expression, equation, model, strategy, inequality Page 6
Concepts: Competencies: Instructional Practices: Assessments: Students will know that: Combining like terms is a procedure that is used to simplify expressions. The distributive property is a procedure that results from multiple addition of like expressions. That the process for solving multi-step equations and inequalities follow that same procedures and mathematical relationships. Students will be able to: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Rewrite expressions in different forms in a problem. Solve multi-step real-life and mathematical problems containing negative and positive rational numbers in a form. Analyze the reasonableness of an answer. Use variables to represent quantities in real-world or mathematical problem, and construct equations and inequalities to solve problems. KWL chart of terms Word walls Videos Independent Practice www.brainpop.com www.studyisland.com www.mangahigh.com www.thatquiz.com www.ixl.com www.mathplay.com www.bidideasmath.com www.quizlet.com Notebook presentations Presentations and lessons Interactive virtual worksheets and practice Classroom discussions and discoveries Think pair share Rally couch White boards Thumbs up/down Tests Quizzes Practice packets Graded Assignments Probes Study/Core benchmarks Study Island Core Practice Mangahigh Challenges Thatquiz.com Exit cards Quizlets Cloud sheet checks Four corners Dice partners Group collaboration Page 7
Topic/Unit: Geometry Big Ideas/Enduring Understandings: Draw, construct, and describe geometric figures and describe the relationships between them Solve real-life and mathematical problems involving angle measures, area, surface area, and volume Essential Questions: How can a plane and solid shapes be described? How are geometric figures constructed? What are strategies can be used to verify similar figures and or congruency? How do geometric models describe spatial relationships? How are geometric shapes and objects classified? Why do I need standardized units of measurement? What is the difference between sketching a geometric figure, drawing a geometric figure, and constructing a geometric figure? What is the difference between a pair of supplementary and a pair of complementary angles? If two parallel lines are cut by a transversal, which angle pairs are congruent? What are the types of angles and their relationships? What are perimeter, circumference, area, volume, and surface area and how do you calculate them? How do we translate and solve real world situations/problems using algebra and geometry? How will I use perimeter, area, surface area, and volume in my life? PA Academic Standards: CC.2.3.7.A.2, CC.2.3.7.A.1 Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with Mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Tier 3 Vocabulary: Scale drawing, geometric shape, polygon, regular polygon, Triangle Inequality Theorem, solid figure, cross section, diameter, radius, circumference, pi, area, complementary angles, supplementary angles, adjacent angles, vertical angles, congruent, volume, prism, surface area Page 8
Concepts: Competencies: Instructional Practices: Assessments: Students will know that: Students will be able to: KWL chart of terms White boards Scale drawings of geometric figures can be used to find missing lengths and areas of similar figures. Triangles can be classified by sides and by angles measures. Triangles can only be formed if the angles sum to 180 degrees and the sides comply with the Triangle Inequality Theorem. Two-dimensional figures are result of slicing threedimensional figures. Use supplementary, complementary, adjacent, and multi-step problems to write and solve for an unknown. Two parallel lines cut by a transversal form sets of equivalent angles. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing at a different scale. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane section of right rectangular prisms and right rectangular pyramids. Use formulas for the area and circumference of a circle to solve problems. Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle is a figure. Word walls Videos Independent Practice www.brainpop.com www.studyisland.com www.mangahigh.com www.thatquiz.com www.ixl.com www.mathplay.com www.bidideasmath.com www.quizlet.com Notebook presentations Presentations and lessons Interactive virtual worksheets and practice Classroom discussions and discoveries Think pair share Rally couch Thumbs up/down Tests Quizzes Practice packets Graded Assignments Probes Study/Core benchmarks Study Island Core Practice Mangahigh Challenges Thatquiz.com Exit cards Quizlets Cloud sheet checks Four corners Page 9
Area and circumference can be calculated for geometric shapes. Area, volume, and surface area of two-and threedimensional objects can be used to solve real-world and mathematical problems. Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Dice partners Group collaboration Page 10
Topic/Unit: Statistics and Probability Big Ideas/Enduring Understandings: Use random sampling to draw inferences about a population Draw informal comparative inferences about two populations Investigate chance processes and develop, use and evaluate probability models Essential Questions: How does the type of data influence the choice of display? What aspects of a graph help people understand and interpret the data easily? What kinds of questions can and cannot be answered from a graph? How is probability of an event determined and described? Why is data collected and analyzed? How do people use data to influence others? How can predictions be made based on data? How can I use probability to make wise decisions in my life? What is probability? How do we determine probability? How do we use probability in real-life situations? How can dats be described and interpreted? How can estimation of likelihood be made for random events? How reliable or useful are the statistical outcomes in decision making? PA Academic Standards: CC.2.4.7.B.1, CC.2.4.7.B.2, CC.2.4.7.B.3 Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with Mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Page 11
Tier 3 Vocabulary: Population, survey, sample, random sample, biased sample, proportion, percents, measures of variation, box-andwhisker plot, median, range, lower quartile, upper quartile, measure of central tendency, mean, mode, probability, outcomes, sample space, theoretical probability, experimental probability, compound events, independent events, dependent events, table, tree diagram Concepts: Competencies: Instructional Practices: Assessments: Students will know that: Students will be able to: KWL chart of terms White boards Predictions can be made from random samples of real-world situations. Two numerical collections of data can be compared based on their centers and variability s. Some outcomes are certain, more likely, less likely, equally likely or impossible. Probabilities can be calculated for simple and compound events from tables, tree diagrams, lists and frequency. The value of a probability is between 0 and 1 inclusive. use statistics to gain information about a population by examining a sample. Use measures of center and measure of variability for numerical data from random samples to draw informal comparative inferences. Use probabilities to expresses the likelihood of the event occurring. Approximate the probability of chance event by collecting data. Find probabilities of compound events using organized lists, tables, and tree diagrams. Word walls Videos Independent Practice www.brainpop.com www.studyisland.com www.mangahigh.com www.thatquiz.com www.ixl.com www.mathplay.com www.bidideasmath.com www.quizlet.com Notebook presentations Presentations and lessons Interactive virtual worksheets and practice Classroom discussions and discoveries Thumbs up/down Tests Quizzes Practice packets Graded Assignments Probes Study/Core benchmarks Study Island Core Practice Mangahigh Challenges Thatquiz.com Exit cards Quizlets Cloud sheet checks Think pair share Page 12
Rally couch Four corners Dice partners Group collaboration Page 13