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Transcript
Livingston County Schools Eighth Math Unit 2 One Variable Equations, Exponents, Scientific Notation Unit Overview Students solve single variable equations using the properties of equality. Students use positive and negative exponents, and use scientific notation in a real world context. Length of unit: 25 days KY Core Academic Standard 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² x 3-5 = 3-3 = 1/33 = 1/27. 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational. 8.EE.3 Use numbers expressed in the form of a single digit times an Learning Target K I can explain the properties of integer exponents to generate equivalent numerical expressions. For example, 3² x 3-5 = 3-3 = 1/33 = 1/27. X I can apply the properties of integer exponents to produce equivalent numerical expressions. I can use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. X X X I can evaluate square roots of small perfect squares. X I can evaluate cube roots of small perfect cubes. X I can understand that the square root of 2 is irrational. I can express numbers as a single digit times an integer power of 10. X R S P Critical Vocabulary Texts/Resources/Activities integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger. 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. 8.EE.7a Solve linear equations in one variable: a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these X I can use scientific notation to estimate very large and/or very small quantities. X I can compare quantities to express how much larger one is compared to the other. I can perform operations using numbers expressed in scientific notations. X X I can use scientific notation to express very large and very small quantities. X I can interpret scientific notation that has been generated by technology. X I can choose appropriate units of measure when using scientific notation. 33. I can give examples of linear equations in one variable with one solution and show that the given example equation has one solution by successively transforming the equation into an equivalent equation of the form x = a. X Coefficient, inverse operation, isolate the variable, like terms, linear equation, multiplication Crosswalk Lesson 9 Lesson 1-7 & 1-8 p. 34-43 Solving Equations using all operations Lesson 2-7 Solving Equations with Rational Numbers Lesson 2-8 p. 98 Solving Two-Step Equations possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). 8.EE.7b Solve linear equations in one variable: b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 34. I can give examples of linear equations in one variable with X infinitely many solutions and show that the given example has infinitely many solutions by successively transforming the equation into an equivalent equation of the form a = a. 35. I can give examples of linear equations in one variable with no solution and show that the given example has no solution by X successively transforming the equation into an equivalent equation of the form b = a, where a and b are different numbers X 36. I can solve linear equations with rational number coefficients. 37. I can solve equations whose X solutions require expanding expressions using the distributive property and/ or collecting like terms. Common Assessments Developed (Proposed Assessment Dates): HOT Questions: property of equality, rate of change, relation, variable Coefficient, inverse operation, isolate the variable, like terms, linear equation, multiplication property of equality, rate of change, relation, variable Crosswalk Lesson10 Lesson 11-1 p. 584 Simplifying Algebraic Expressions Lesson 11-2 p. 588 Solving Multi-Step Equations Lesson 11-3 p. 593 Solving Equations w/Variables on Both Sides