Wethersfield Public Schools Course Outline

Course Name: Pre-Algebra Grade 8 Department: Math Grade(s): 8 Level(s): 2 Course Number(s): N/A Credits: N/A Wethersfield Public Schools Course Outline Course Description: Pre-Algebra incorporates the following units: Integers and Algebraic Expressions Rational Numbers Basic Algebraic Equations Ratios, Rates, and Proportions Application of Percents Geometry: area, volume, surface area Probability Graphing and the Coordinate Plane Multi-step Equations Irrational Numbers Required Instructional Materials: Mathematics Course 3, Prentice Hall, 2008 Online Interactive Textbook Revised/Approval Date: Administrative Team 9/14/11 Approved Student Programs and Services Committee October 20, 2011 Approved Board of Education October 25, 2011 Authors/Contributors: Pat Krzesicki Pat Stratton Pre Algebra Grade 8 Page 1

Overarching Skills Students will engage in tasks for which the solution method is not known in advance and build new mathematical knowledge through problem solving. Students will reason and think analytically to make and investigate mathematical conjectures. Students will learn from and work collaboratively with others in a spirit of mutual respect and open dialogue. Students will be able to express their understanding orally, in writing, and with models. Students will deepen their understanding by connecting mathematical ideas to each other and to real world applications of those ideas. Students will learn to use representation to understand and communicate mathematical ideas. Students will use technology as a tool to research, organize, evaluate and communicate information. Numeric reasoning involves fluency and facility with numbers. Spatial sense and geometric relationships are a means to solve problems and make sense of a variety of phenomena. Measurement is a tool to quantify a variety of phenomena. Algebra provides language through which we communicate the patterns in mathematics. Reading, understanding, interpreting, and communicating data are critical in modeling a variety of real-world situations, drawing appropriate inferences, making informed decisions, and justifying those decisions. Probability quantifies the likelihood that something will happen and enables us to make predictions and informed decisions. A problems solver understands what has been done, knows why the process was appropriate, and can support it with reasons and evidence. The ability to solve problems is the heart of mathematics. How can counting, measuring, or labeling help to make sense of the world around us? How do operations affect numbers? How can we decide when to use an exact answer and when to use an estimate? How do spatial and geometric relationships help to solve problems and/or make sense of phenomena? How can measurements be used to solve problems? How can patterns, relations, and functions be used as tools to best describe and help explain real-life situations? How can the collection, organization, interpretation, and display of data be used to answer questions? How can experimental and theoretical probabilities be used to make predictions or draw conclusions? How do I decide what strategy will work best in a given situation? How does explaining my process help me to understand a problem s solution better? Why is the ability to solve problems the heart of mathematics? Objectives (skills) The student will: S.1. Solve problems involving variables, integers, reciprocals, percents, exponents and mathematical operations; S.2. Compare, order, add, subtract, multiply and divide integers; S.3. Solve problems addressing square roots and the Pythagorean theorem; S.4. Apply graphing skills and complete algebraic equations; S.5. Recognize and apply basic geometric concepts with an emphasis on area and volume; S.6. Use probability, ratios and percents; S.7. Write and communicate mathematically; S.8. Apply of technology in solving math problems; S.9. Interpret three-dimensional objects in our world by developing spatial visualization skills Pre Algebra Grade 8 Page 2

Instructional Support Materials Prentice Hall Course 3 Textbook Access to Interactive Online Text Kuta Software (for differentiated worksheets / assessments) Graphing calculators Excel program Suggested Instructional Strategies Modeling Guided practice Problem solving in context Differentiated tasks Use of manipulatives Vocabulary reinforcement Cooperative activities/games Suggested Assessment Methods Pre-assessments Quizzes Chapter tests Common assessments (at the end of each term) Math application problems Pre Algebra Grade 8 Page 3

Unit 1: Integers and Algebraic Expressions Time Frame: September Length of Unit: 10-12 days Mathematics is a language consisting of symbols and rules. Numbers can be used to count, label, order, identify, measure, and describe things and experiences. Coordinate geometry can be used to represent and verify geometric relationships. How is mathematics a universal language? What is a symbol? What is a rule? What couldn t we do if we didn t have / use numbers? How can geometric relationships best be represented and verified? Objectives (knowledge and skills) (Show link to standards in parenthesis after objective) The student will: 1.1 Write algebraic expressions and evaluate them using order of operations. (1.1.1 & 1.3.10 & 1.2.5) 1.2 Find the absolute value of integers and use absolute value to compare integers. (2.1.1) 1.3 Perform basic operations with integers and solve problems involving integers. (2.2.5) 1.4 Identify integers as ordered pairs on the coordinate plane. (2.1.1) Grade Level Expectations (March 2010) 1.1.1 Generalize the relationships in patterns in a variety of ways, including recursive and explicit descriptions. 1.3.10 Evaluate and simplify algebraic expressions, equations and formulas, including those with powers, using algebraic properties and the order of operations. 2.1.1 Compare and order rational and common irrational numbers and locate them on number lines, scales and coordinate grids. 2.2.5 Compute using addition, subtraction, multiplication and division; solve problems with positive and negative rational numbers. 1.2.5 Represent linear and nonlinear mathematical relationships with verbal descriptions, tables, graphs and equations when possible. CMT Correlation 22A. Identify the missing terms in a pattern or identify rules for a given pattern using numbers and attributes. 22B. Extend or complete patterns and state rules for given patterns using numbers and attributes. 23E. Write an expression or equation to represent a situation. 23C. Evaluate expressions or solve equations and use formulas. 23D. Represent situations with algebraic expressions or equations. 4D. Locate points on number lines and scales, including fractions, mixed numbers, decimals and integers. 8C. Add or subtract positive and negative integers. 18C. Locate and draw points on four-quadrant coordinate grids. Instructional Support Materials Number lines and visual aids to model integers. Graph paper Pre Algebra Grade 8 Page 4

Suggested Instructional Strategies Modeling Guided practice Web based models and videos Interactive math Problem solving in context Differentiated tasks Cooperative activities / games Vocabulary reinforcement Suggested Assessment Methods Pre-assessment to evaluate student s prior knowledge Quick Hits to check understanding Common formative assessment mid-point Common summative assessment at end of unit Pre Algebra Grade 8 Page 5

Unit 2: Rational Numbers Time Frame: September / October Length of Unit: 15-17 days The same value can be shown in different ways. The use of exponents and scientific notation offer efficient ways of representing large numbers How does the context of a problem help determine the best representation of a number? Objectives (knowledge and skills) (Show link to standards in parenthesis after objective) The student will: 2.1 Identify prime and composite numbers and find the greatest common factor. (2.2.5) 2.2 Show an understanding of equivalent fractions and decimals. (2.1.4) 2.3 Use least common denominators, decimals and number lines to compare and order rational numbers. (2.1.1) 2.4 Apply basic operations involving rational numbers and solve problems involving rational numbers.(2.2.5) 2.5 Write, simplify, and evaluate expressions involving exponents (1.3.10 & 2.2.11) 2.6 Convert numbers between standard form and scientific notation. (2.1.3 & 2.2.12 & 2.2.7) Grade Level Expectations (March 2010) 2.2.5 Compute using addition, subtraction, multiplication and division; solve problems with positive and negative rational numbers. 2.1.4 Represent fractions, mixed numbers, decimals and percentages in equivalent forms. 2.1.1 Compare and order rational and common irrational numbers and locate them on number lines, scales and coordinate grids. 1.3.10 Evaluate and simplify algebraic expressions, equations and formulas, including those with powers, using algebraic properties and the order of operations. 2.2.11 Use rules for exponents to multiply and divide with powers of 10 and extend to other bases. 2.1.3 Read and represent whole numbers and those between zero and one in scientific notation and vise versa and compare their magnitudes. 2.2.7 Develop and use strategies for multiplying and dividing with numbers expressed in scientific notation using the commutative and associative properties. 2.2.12 Estimate answers to problems in context containing numbers expressed in scientific notation. CMT Correlation 7C. Multiply and divide whole numbers and decimals by 10, 100, 1,000, and 0.01. 11A. Determine a reasonable estimate and describe the strategy used to arrive at the estimate. 8A. Add and subtract fractions and mixed numbers with reasonable and appropriate denominators. 8B. Multiply whole numbers and fractions by fractions and mixed numbers. 9B. Solve multistep problems involving whole numbers, fractions, mixed numbers, decimals or money amounts, and explain how the solution was determined. 3A. Rename fractions and mixed numbers as equivalent decimals and vise versa.4a. Order fractions and decimals including mixed numbers in context. 5A. Identify the appropriate operation or equation to solve a story problem. 5B. Write a story problem from and equation. 23E. Write an expression or equation to represent a situation. 23C. Evaluate expressions or solve equations and use formulas. 1A. Identify alternative forms of expressing numbers using scientific notation. 11A. Determine a reasonable estimate, and describe the strategy used to arrive at the estimate. Pre Algebra Grade 8 Page 6

Instructional Support Materials Scientific / Graphing calculators Suggested Instructional Strategies Modeling Guided practice Problems presented in context Vocabulary reinforcement Suggested Assessment Methods Ongoing review with warm-ups and exit slips Common formative assessment mid-unit Common summative assessment end of unit Pre Algebra Grade 8 Page 7

Unit 3: Basic Algebraic Equations Time Frame: October Length of Unit: 10 12 days Equations depict patterns of change A variable represents an unknown that will change in different setting Why use algebraic equations? What kinds of things in life can equations help us do? Are there relationships for which equations can t be used? Objectives (knowledge and skills) (Show link to standards in parenthesis after objective) The student will: 3.1 Identify the properties of numbers and use the properties to solve problems. (1.3.10) 3.2 Write and solve 1-step equations using addition, subtraction, multiplication, and division. (1.3.10 & 1.3.12 & 2.2.5) 3.3 Determine the correct answer, through substitution, for 2-step equations. (1.3.12) 3.4 Use formulas to solve problems and to solve a formula for a variable. (1.3.10) Grade Level Expectations (March 2010) 1.3.10 Evaluate and simplify algebraic expressions, equations and formulas, including those with powers, using algebraic properties and the order of operations. 1.3.12. Write and solve multi-step equations using various algebraic methods, including the distributive property, combining like terms, and properties of equality and justify the solutions. 2.2.5 Compute using addition, subtraction, multiplication and division; solve problems with positive and negative rational numbers. CMT Correlation 23A. Solve simple equations, including two-step equations 23E. Write an expression or equation to represent a situation 23C. Evaluate expressions or solve equations and use formulas. 5A. Identify the appropriate operation or equation to solve a story problem. 5B. Write a story problem from an equation. Instructional Support Materials Scientific / graphing calculators Suggested Instructional Strategies Modeling Guided practice Scaffold tasks with graphic organizers Cooperative problem solving Problem solving in context Vocabulary reinforcement Suggested Assessment Methods Ongoing review with warm-ups and exit slips Formative assessments (quick hits) Common formative assessment mid-unit (with strand 25 problems) Common summative assessment end of unit (with strand 25 problems) Pre Algebra Grade 8 Page 8

Unit 4: Ratios, Rates, and Proportions Time Frame: November / December Length of Unit: 12 14 days Numbers are inventions that represent quantities, rates, sequence and characteristics of things and experiences. Proportional relationships express how quantities change in relationship to each other. How do rates and proportions help us solve everyday problems? When and why do I use proportional comparisons? Objectives (knowledge and skills) (Show link to standards in parenthesis after objective) The student will: 4.1 Calculate unit rates. (2.2.9) 4.2 Use rates to solve problems (2.2.9) 4.3 Convert units within and between the customary and metric systems (2.2.9 & 3.3.10) 4.4 Identify and solve proportions (2.2.9 & 1.1.3) 4.5 Use proportions to find the missing measurements in similar figures (2.2.9 & 3.1.2) Grade Level Expectations (March 2010) 1.1.3 Write and solve problems involving proportional relationships using linear equations. 2.2.9 Use proportional reasoning to write and solve problems in context. 3.3.10 Solve customary or metric measurement problems using Dimensional Analysis (unit rate factor model) and justify the results in writing. 3.1.2 Make and test conjectures about angle and side relationships to illustrate that similar figures have congruent angles and corresponding sides and congruent figures have congruent angles and sides. CMT Correlation 12A. Solve problems involving ratios. 12B. Solve problems involving proportions in context. 12C. Solve multistep problems involving ratios or proportion, and explain how the solution was determined. 16C. Solve problems involving conversions and/or operations within customary or metric units of measure. Instructional Support Materials Number lines Calculators Manipulatives Suggested Instructional Strategies Modeling Guided practice Problems embedded in context Interactive math Differentiated tasks Vocabulary reinforcement Pre Algebra Grade 8 Page 9

Suggested Assessment Methods Formative assessments (Quick Hits in CMT like format) Common formative assessment mid-unit Common summative assessments end of unit Pre Algebra Grade 8 Page 10

Unit 5: Application of Percents Time Frame: December Length of Unit: 10 12 days The same value can be shown in different ways. Parts of a whole can be represented with different mathematical forms such as fractions, decimals, and percents How does the context of a problem help determine the best representation of a number? How do we show a part of something? Objectives (knowledge and skills) (Show link to standards in parenthesis after objective) The student will: 5.1 Convert between fraction, decimals, and percents (2.1.4 & 2.2.8) 5.2 Order and compare fractions, decimals, and percents (2.1.1) 5.3 Use proportions and equations to find part of a whole, a whole amount, or a percent (2.2.10) 5.4 Calculate mark-ups and discounts by applying percents (2.2.10) 5.5 Calculate percent of change (2.2.10) Grade Level Expectations (March 2010) 2.1.4 Represent fractions, mixed numbers, decimals and percentages in equivalent forms. 2.1.1 Compare and order rational and common irrational numbers and locate them on number lines, scales and coordinate grids. 2.2.8 Estimate reasonable answers and solve problems in context involving rational and common irrational numbers, ratios, and percentages, including percentage of increase and decrease, and justify solutions in writing. 2.2.10 Solve a variety of problems in context involving percents, including the following: Percentage of a number The percentage one number is of another number The percentage of a missing amount Percentage increase / decrease CMT Correlation 3A. Rename fractions and mixed numbers as equivalent decimals and vise versa. 3B. Rename fractions and decimals as equivalent percents and vise versa. 3C. Identify and/or shade decimals, fractions, or percents or regions or sets. 4A Order fractions and decimals including mixed numbers in context. 4B Describe magnitude or order of mixed numbers, fractions and decimals in context. 4C. Round mixed numbers, fractions and decimals in context. 11B. Given an estimate as a solution for problems involving whole numbers, mixed numbers, decimals and percents, judge its reasonableness and justify the decision. 13A. Find percents of whole numbers or the percent a given number is of another number. 13B. Solve problems involving percents in context. Instructional Support Materials Scientific / graphing calculators Interactive textbook Pre Algebra Grade 8 Page 11

Suggested Instructional Strategies Modeling Guided practice Differentiated tasks Cooperative problem solving Suggested Assessment Methods Problems embedded in context o Asking Does your answer make sense? o Math Application Problems (MAP) written explanation Common formative assessment mid-unit Common formative assessment end of unit Pre Algebra Grade 8 Page 12

Unit 6: Geometry Time Frame: January / February Length of Unit: 18-20 days Measurement helps us understand and describe our world Measurement of distance is fundamentally different from measurement of area Both the real and man-made world are designed using geometric figures The properties of geometric figures determine how the figures can be used How does what we measure influence how we measure? Where can you find geometry in the real world? How does changing one dimension (or measure) on a geometric figure impact other measurement such as area or volume? Objectives (knowledge and skills) (Show link to standards in parenthesis after objective) The student will: 6.1 Identify and classify two-dimensional polygons. 6.2 Classify triangles and quadrilaterals. 6.3 Calculate the perimeter and area of triangles and quadrilaterals. (3.1.1) 6.4 Calculate area and circumference of a circle (3.1.1) 6.5 Calculate the area of irregular figures (3.1.1 & 3.3.8) 6.6 Identify congruent figures (3.1.2) 6.7 Identify and draw transformations such as reflections, rotations, and slides (3.2.5) 6.8 Calculate the volume of rectangular prisms, triangular prisms, and cylinders (3.2.6) 6.9 Calculate the surface area of a prism (3.2.6 & 3.3.9) 6.10 Create nets to analyze relationships between the surface area of 2-dimensional nets and 3- dimensional solids (3.2.6) Grade Level Expectations (March2010) 3.1.2 Make and test conjectures about angle and side relationships to illustrate that similar figures have congruent angles and corresponding sides and congruent figures have congruent angles and sides. 3.1.1 Determine the effect of scale factors (resulting from similar figures) on the perimeters and areas of two-dimensional shapes and on the surface areas and volume of three-dimensional solids. 3.2.6 Develop and use formulas to determine the surface areas of rectangular prisms, cylinders and pyramids. 3.2.5 Use the coordinate plane to make and test conjectures about the changes in the coordinates of the vertices of polygons as a result of a transformation and describe the result in writing. 3.3.8 Understand and describe in writing the measurement tools, measurements and estimates of measures are not precise and can affect the results of calculations. 3.3.9 Use estimation and measurement strategies, including formulas, to solve surface area and volume problems in context. CMT Correlation 15A. Estimate lengths, areas, volumes and angle measure. 17A. Identify, describe and classify two and three-dimensional geometric shapes and figures. 17B. Draw, describe and classify two and three-dimensional geometric shapes and figures. 18A. Identify congruent and similar figures. 18B. Draw, classify, describe and / or explain why figures are similar. 16A. Measure and determine perimeters, areas and volumes. Explain or show how the solution was determined. 16B. Determine perimeters, areas and volume. 18D. Identify geometric transformations (reflections, rotations and translations) Pre Algebra Grade 8 Page 13

18E. Draw geometric transformations. 18F. Relate two- and three- dimensional representations and vise versa. 25A. Solve extended numerical and statistical problems. Instructional Support Materials Geometric manipulatives Interactive online models Suggested Instructional Strategies Modeling Hands on manipulatives Guided practice Web based models / videos Cooperative problem solving Vocabulary reinforcement o Flash cards o Crossword puzzles Suggested Assessment Methods Pre-assessment Problems embedded in context Math Application Problems (MAP) to explain thinking and understanding Common formative assessment Common summative assessment Pre Algebra Grade 8 Page 14

Unit 7: Probability Time Frame: February Length of Unit: 10-12 days Probability describes the likelihood of phenomena occurring in a population. Sometimes sampling is better than counting everything. A larger sample generally provides more reliable information about the probability of an event than a smaller sample. How well can we predict the outcomes of some future events? When should we sample? How much (of a sample) is enough? Objectives (knowledge and skills) (Show link to standards in parenthesis after objective) The student will: 7.1 Find theoretical probability, experimental probability, and odds.(4.2.6) 7.2 Make predictions based on theoretical and experimental probabilities. (4.2.6 & 4.2.7) 7.3 Identify random samples and biased questions and to judge conclusions based on survey results. (4.2.8) 7.4 Find the probabilities of independent and dependent events. 7.5 Find the number of permutations of a set of objects. (4.3.9 & 4.3.10 & 4.3.11) 7.6 Find the number of combinations of a set of data using lists and combination notation. (4.3.9 & 4.3.10 & 4.3.11) Grade Level Expectations (March 2010) 4.2.6 Make observations and inferences and evaluate hypotheses based on collected and / or experimental data. 4.2.7 Describe in writing the accuracy of statistical claims such as four out of five dentists prefer Brand X toothpaste by recognizing when a sample is biased or when data is misrepresented. 4.2.8 Explain the effects of sample size and sampling techniques (convenience sampling, voluntary sampling, systematic sampling and random sampling) on statistical claims. 4.3.9 Determine when a situation is a permutation (changing the order results in a different outcome) or a combination (changing the order does not result in a different outcome). 4.3.10 Use tree diagrams. Lists or the counting principle to determine all possible outcomes in permutations and combinations. 4.3.11 Apply permutations and combinations to predict possible outcomes and find probabilities to solve problem in a variety of contexts. CMT Correlation 24B. Sort or classify objects, and draw logical conclusions from data including Venn diagrams, combinations, permutations and transitive reasoning questions. 25A. Solve extended numerical and statistical problems. 24A. Solve problems involving the organization of data. 20B. Draw reasonable conclusions from data in tables, graphs, and charts. 21A. Identify correct solutions to problems involving elementary notions of probability and fairness expressed as fractions, decimals or percents. 21B. Solve problems involving elementary notions of probability and fairness expressed as fractions, decimals or percents and justify solutions. 21C. Solve problems involving expected outcomes or predictions and justify solutions. Pre Algebra Grade 8 Page 15

Instructional Support Materials Manipulatives Suggested Instructional Strategies Cooperative problem solving Vocabulary reinforcement Problems embedded in context Suggested Assessment Methods Written explanations (Math Application Problems) Common formative assessment mid unit Common summative assessment end of unit Pre Algebra Grade 8 Page 16

Unit 8: Graphing and the Coordinate Plane Time Frame: March Length of Unit: 16-18 days Mathematical ideas can be represented numerically, graphically, or symbolically. Changes can be represented mathematically and graphically. How can we best show and describe changes? How do graphs help us visualize solutions to problems? Objectives (knowledge and skills) (Show link to standards in parenthesis after objective) The student will: 8.1 Use tables, equations and graphs to solve problems. (1.1.2) 8.2 Interpret and sketch graphs that represent real-world situations. (1.1.2 & 1.1.4) 8.3 Represent functions with equations, tables, and function notation. (1.1.2 & 1.1.4) 8.4 Find the slope of a line from a graph or table. (1.2.9 & 1.2.6) 8.5 Use tables and equations to graph linear functions. (1.1.2 & 1.2.8 & 1.2.7) 8.6 Display and analyze data using scatter plots and a line of best fit (4.1.1 & 4.2.5) Grade Level Expectations (March 2010) 1.1.2 Determine whether relationships are linear or nonlinear. 1.1.4 Examine and make comparisons in writing between linear and nonlinear mathematical relationships using a variety of representations. 1.2.6 Determine the constant rate of change in a linear relationship and recognize this as the slope of a line. 1.2.9 Interpret and describe slope and y-intercept from contextual situations, graphs and linear equations. 1.2.8 Compare and contrast the slopes and graphs of lines to classify lines as parallel, perpendicular or intersecting. 1.2.7 Compare and contrast the slopes and graphs of lines that have a positive slope, negative slope, zero slope, undefined slope, slopes grater than one, and slopes between zero and one. 4.1.1 Collect and organize data using an appropriate representation (including box and whisker plots, stem and leaf plots, scatter plots, and histograms) based on the size and type of data and the purpose for its use. 4.2.5 Make predictions from scatter plots by using or estimating a line of best fit. CMT Correlation 23E. Write an expression or equation to represent a situation. 19B.. Create graphs from data in tables and charts. 20A. Draw reasonable conclusions from data in tables, graphs, and charts. 20B. State a conclusion and explain why an answer is or is not reasonable based on the data. Instructional Support Materials Graphing calculators Graph paper Interactive online models Suggested Instructional Strategies Cooperative problem solving Partner tasks Problems embedded in context Pre Algebra Grade 8 Page 17

Modeling Guided practice Suggested Assessment Methods Ongoing review Common formative assessments Common summative assessments Pre Algebra Grade 8 Page 18

Unit 9: Multi-step Equations Time Frame: April / May Length of Unit: 18-20 days Equations depict patterns of change A variable represents an unknown that will change in different setting Why use algebraic equations? What kinds of things in life can equations help us do? Are there relationships for which equations can t be used? Objectives (knowledge and skills) (Show link to standards in parenthesis after objective) The student will: 9.1 Solve two-step equations and use two-step equations to solve problems (1.3.12) 9.2 Combine like terms and use the distributive property to simplify algebraic expressions (1.3.12 & 1.3.10) 9.3 Write and solve multi-step equations (1.3.12) 9.4 Write and solve two-step equations from word problems (1.3.12) 9.5.Explore systems of equations (1.3.11) Grade Level Expectations (2010) 1.3.12 Write and solve multistep equations using various algebraic methods, including the distributive property, combining like terms, and properties of equality and justify the solutions. 1.3.10. Evaluate and simplify algebraic expressions, equations and formulas, including those with powers, using algebraic properties and the order of operations. 1.3.11 Examine systems of two linear equations and formulas, including those with powers, using algebraic properties and the order of operations. CMT Correlation 23A. Solve simple equations, including two-step equations. 23B. Solve multi-step problems using algebraic concepts. 23C. Evaluate expressions or solve equations and use formulas. 23E. Write an expression or equation to represent a situation 25A. Solve extended numerical and statistical problems. Instructional Support Materials Graphing Calculators Suggested Instructional Strategies Cooperative problem solving Partner tasks Problems embedded in context Modeling Guided Practice Suggested Assessment Methods Ongoing review (warm-ups / exit slips) Common formative assessment mid-unit Common summative assessment end of unit Pre Algebra Grade 8 Page 19

Unit 10: Irrational Numbers Time Frame: May / June Length of Unit: 14-16 days Mathematical rules, functions, formulas and algorithms depict mathematical relationships. How does a theorem differ from rule? Objectives (knowledge and skills) (Show link to standards in parenthesis after objective) The student will: 10.1 Find and estimate square roots and classify numbers as rational or irrational. (2.1.2 & 2.2.6 & 2.2.1) 10.2 Use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle. (3.1.3 & 3.1.4) 10.3 Use the Pythagorean Theorem to find the missing measurements of right triangles. (3.1.3 & 3.1.4) Grade Level Expectations (March 2010) 2.1.2 Identify perfect squares and their square roots and use these relationships to estimate other square roots. For example: squares 1, 4, 9, and 16 correspond to 1, 2, 3 and 4. 2.2.1. Compare and order rational and common irrational numbers and locate them on number lines, scales and coordinate grid. 2.2.6 Calculate the square roots of positive rational numbers using technology 3.1.3 Construct and/or examine right triangles, make and test conjectures about the relationships of angles and sides and develop the Pythagorean Theorem. 3.1.4 Apply side and angle relationships in geometric figures to solve problems, including the Pythagorean Theorem and similar figures. CMT Correlation none Instructional Support Materials Scientific / Graphing calculators Suggested Instructional Strategies Cooperative problem solving Problems embedded in context Modeling and guided practice Interactive models Suggested Assessment Methods Math application problems Common formative assessment mid unit Common summative assessment end of unit Pre Algebra Grade 8 Page 20