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8th Grade Math Suggested Duration: 20 Days Unit 5: Algebraic Representation and Applications (13 Days) Unit 6: Irrational Numbers and Pythagorean Theorem (7 days) TEKS CONCEPTS GUIDING QUESTIONS UNIT 5: Algebraic Representation and Applications 8.2A Select appropriate operations to solve problems involving rational numbers and justify the selections. 8.2B use appropriate operations to solve problems involving rational numbers in problem situations 8.3A compare and contrast proportional and nonproportional linear relationships 8.4 Generate a different representation of data given another representation of data (such as table, graph, equation, or verbal description). 8.5A Predict, find and justify solutions to application problems using appropriate tables, graphs, and algebraic equations. 8.5B Find and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change). Identify rational numbers, irrational numbers, and real numbers. Algebraic Relationships using proportionality Algebraic Reasoning in expressions, equations, and representations Relationships among quantities expressed in different representations Different representations of data generated by one given form of representation Solving equations involving a plan of strategy to keep values on What is the difference between a rational number and an irrational number? Identify a proportional and non-proportional relationship. How can comparing and contrasting proportional and nonproportional assist in linear relationships? Identify an arithmetic sequence. What are the characteristics of an equation? Do algebraic equations or expressions yield the same solution or values? Identify an expression. Could an expression consist of symbols, operations, and/or variables to indicate the application of order of operations? 3rd Six Weeks CLOSING TASKS The students will create a list of rational and irrational numbers and explain why they are considered rational and irrational numbers. The students will set up a table identifying the position and term of a sequence and insert the appropriate values in each column/row The students will write an equation on a notecard and label the parts of an equation. The students will write in two or more sentences the difference between an equation or an expression. FORMATIVE ASSESSMENT Yes, No Cards Red Cup, Green Cup Small Whiteboards Foldable Journal Entry Quiz Peer/Self Assessment Teacher-Student Conference Journal Rubric Exit Ticket Demonstration Questioning Think Pair Share Graphic Organizer Discussion Four Corners Observation Data Appointment Clock Thumbs Up, Thumbs Down RESOURCES CScope TEKSING Towards STAAR Teacher Tube BrainPop Discovery Education (United Streaming) at mydiscoveryeduca tion.com Khan Academy website www.mathisfun.co m sfdrcisd.curriculumloft. com 8th Grade Math 8.7D Locate and name points on a coordinate plane using ordered pairs of rational numbers. 8.9B use proportional relationships in similar twodimensional figures or similar three-dimensional figures to find missing measurements. 8.14A Identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics. 8.14B use a problemsolving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness 8.14Cselect or develop an appropriate problemsolving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem 8.14D select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. 3rd Six Weeks both sides equally balanced utilizing reasonableness for solution Using geometry in a coordinate system by plotting ordered pairs on a coordinate plane Using arithmetic sequence to identify patterns by finding the common difference between each pair of consecutive numbers Generating different representations of data given one form of representation Validating and analyzing sequences or tables to determine algebraic expressions and finding the terms in a sequence Describe the nth term. Identify some different representations (i.e. concrete models, tables, graphs, verbal descriptions, and algebraic expressions/equations) How do we identify the value of a variable that makes the equation true? (solution) What is the process of finding the values of a variable that makes an equation true? Identify a variable. (symbol, usually a letter, used to represent an unknown value) Identify the quadrants in a coordinate plane. The variable “x” is on which axis? Variable “y”? What are twodimensional figures? How can you find the missing value of a twodimensional figure? The students will be given an equation and they will write a verbal description, draw a graph, and create a table to correlate with the equation. The students will identify how position and term will allow to find the nth term. The students will generate a table, graph, equation, and verbal description after being given a set of data. The students will draw a coordinate plane and label the quadrants of the plane. The students will draw a twodimensional figures and label appropriately. Students will create a number line utilizing real, rational, and irrational numbers. 8th Grade Math 8.15A communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models 8.15B Evaluate the effectiveness of different representations to communicate ideas. 8.16A make conjectures from patterns or sets of examples and nonexamples 8.16B validate his/her conclusions using mathematical properties and relationships Unit 6: Irrational Numbers and Pythagorean Theorem 8.1C Approximate (mentally [and with calculators]) the value of irrational numbers as they arise from problem situations 8.1E Compare and order real numbers with a calculator. 8.2B Use appropriate operations to solve problems involving rational numbers in problem situations. 3rd Six Weeks Using a plan of strategy to analyze patterns to find and evaluate an algebraic expression in an arithmetic sequence Locate and name ordered pairs on a coordinate using rational numbers. Use irrational numbers to find the value of square roots that is not considered to be a perfect square root. Use pictures or models to represent the Pythagorean Theorem. Use the Pythagorean Theorem to solve real-life problems. Identify what are square roots? How are they different from perfect square roots? How can the value of an irrational number approximation be graphed on a number line between integers? What are the characteristics of a right triangle? What does the Pythagorean Theorem variables represent? How are the sums of the areas of the squares drawn on the legs of the right triangle equal to the area of the square drawn on the hypotenuse? The students will create a number line and graph irrational number between integers. Students will graph a set of data of ordered pairs on a coordinate plane. The student will draw and label a right triangle to include the hypotenuse of the triangle. Students will solve the areas of the legs of the right triangle. Students will solve the area of the hypotenuse of the right triangle. Students How can you utilize the will then sum the Pythagorean Theorem areas of the legs to determine the size and compare to of your television? the area of the hypotenuse. Students will then compare their findings with the Pythagorean Theorem formula. 8th Grade Math 8.7B use geometric concepts and properties to solve problems in fields such as art and architecture 8.7C Use pictures or models to demonstrate the Pythagorean Theorem. 8.9A Use the Pythagorean Theorem to solve real-life problems. 8.14A identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics 3rd Six Weeks Students will measure the diagonal section of a television set to find the hypotenuse.