Advanced Math 8 Friday, January 13, 2017, 4:27PM

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Advanced Math 8 Friday, January 13, 2017, 4:27PM Unit Content (Understings) Essential Questions Skill Objective s Assessments Learning Activities Modifications Resources Basic Real Number Operation s

1 Advanced Math 8 Friday, January 13, 2017, 4:27PM Unit Content (Understings) Essential Questions Skill Objective s Assessments Learning Activities Modifications Resources Basic Real Number Operation s (Week 1, 3 Weeks) Positive negative numbers are used to represent reallife situations. The set of numbers is closed under all operations while the set of ir numbers is not. 1. What is a real number what kind of number do I get when I add, subtract, multiply, or divide? 2. How are real numbers used in verbal algebraic models to represent real-life situations? completion of this unit, be able to : 1. Evaluate write variable expressions. 2. Evaluate expressions containing exponents. 3. Use the order of operations to evaluate algebraic expressions. 4. Check solutions solve mental math. Basic real number operation s test Written Test create their own word exchange them with partners create of Venn Diagram of set of Real Numbers colored pencils use algebra tiles in groups to model variable expression s virtual algebra tiles Reinforcement Skills (Special Needs): in Math Lab as needed Tablet Two-sided chips 5. Translate verbal phrases into algebraic

2 Unit Content (Understings) Essential Questions Skill Objective s Assessments Learning Activities Modifications Resources expressions. 6. Use tables of organized data. 7. Identify a function make an input-output table for a function. 8. Graph compare real numbers a number line. 9. Add, subtract, multiply, divide real numbers. 10. Use the distributive property. Solving Linear Equations are solved by 1. What are techniques for completion Solving Equation use

3 Unit Content (Understings) Essential Questions Skill Objective s Assessments Learning Activities Modifications Resources Equations (Week 4, 2 Weeks) creating a series of equivalent equ ations designed to isolate the variable. solving systematically? 2. How are ratios, rates, percents applied? 3. How is an equation written in function form? of this unit, be able to : 1. Solve addition subtraction. 2. Collect variables on one side of an equation. 3. Use tables graphs to check answers. s test Written Test to look at tables of values. use two sided chips to model distributive property. use algebra tiles to model. virtual function machine,virtual scale Reinforcement Skills (Special Needs): Tablet Virtual scale Virtual function machine 4. Solve a formula or literal equation for one of its variables. 5. Rewrite an equation in function form. 6. Use percents to model solve reallife

4 Unit Content (Understings) Essential Questions Skill Objective s Assessments Learning Activities Modifications Resources. Linear Equations Functions (Week 6, 3 Weeks) A relationship is if its rate of change remains constant. Linear relationships can be represented any or all of the following equivalent methods: words, table, graph, equation. 1. How are graphed? 2. What are two ways to graph quickly? 3. When does a graph or an equation represent a function? completion of this unit, be able to: 1. Plot points in a coordinate plane. 2. Graph a equation a table or a list of values. 3. Find the intercepts of the graph of a equation. test Written Test equation poster Group Project graph lines graph paper graph lines calculator graph lines postit easel graph paper use gizmo that graphs distancetime of runners. Reinforcement Skills (Special Needs): Tablet Geometer's Sketchpad 4. Find the slope of a line two of its points. distance-time graph gizmo 5. Write that represent direct

5 Unit Content (Understings) Essential Questions Skill Objective s Assessments Learning Activities Modifications Resources variation. 6. Graph a equation in slopeintercept form. 7. Solve a equation graphically. 8. Identify when a relation is a function. Solving Linear Inequalities (Week 9, 2 Weeks) Linear inequalitie s absolutevalue inequalitie s are represent ed by shaded regions rather than a 1. How are inequalities solved graphed? 2. How are absolutevalue inequalities solved graphed? 3. How are measures completion of this unit, be able to: 1. Graph inequalities in one variable. 2. Solve multistep inequalities. 3. Write, solve, inequalities test Written Test Use calculator s to draw box whisker plots Graph absolute value graphs graph paper calculator the week Reinforcement Skills (Special Needs): Tablet

6 line. of central tendency statistical plots used? graph compound inequalities. 4. Solve absolute-value. 5. Solve absolute-value inequalities. s. Use calculator s to graph inequality. 6. Graph a inequality in two variables. 7. Make use a stem-leaf plot to put data in order. 8. Find the mean, median, mode of data. 9. Draw a box-whisker plot to organize reallife data. Writing Linear Equations (Week 11, 3 Weeks) Linear can be written used in many forms including stard form, slopeintercept form, 1. What are the three forms of a? 2. Given a slope a point, or given two points, how is a completion of this unit, be able to: 1. Use the slopeintercept form to write an equation writing test Written Test calculator regression Technology Project use to create a line of best fit determine a correlation coefficient. Reinforcement Skills Tablet Two-sided chips

7 point-slope form. equation written? 3. Given the equation of a line, how is the equation of the perpendicular line written? of a line. 2. Use slope any point on a line to write an equation of the line. 3. Write an equation of a line given two points on the line. 4. Find a equation that approximates a set of data points. 5. Use the point-slope form to write an equation of a line. 6. Write a equation in stard form. are encouraged to learn how to perform a regression. This skill leads to data analysis professions that translate into high income/qualit y of life. They enter data into calculator, create scatter plot choose appropriate regression. They then graph line of bests fit the results of the regression determine correlation coefficient. draw a line of best fit by h graph paper. in groups tie knots in ropes of different thicknesses graph the length of the rope vs the number of knots. (Special Needs): 7. Determin e whether a model is appropriate. 8. Use the various forms of a equation to

8 model reallife situations. Systems of Linear Equations Inequalities (Week 14, 2 Weeks) A system of in two variables contain two with two different variables in each. A solution of a system of in two variables is an ordered pair (x, y) that satisfies each equation in the system. 1. What are three methods for solving a system of? 2. How are the number of solutions of a system determined? 3. How is a system of inequalities graphed solved? completion of this unit, be able to: 1. Solve a system of by. 2. Use substitution to solve a system. 3. Use combinations to solve a system. Systems of test Written Test graph systems of. create poster of system of postit easel graph paper. Reinforcement Skills (Special Needs): Tablet Two-sided chips 4. Choose the best method to solve a system of.

9 5. Identify systems as having one solution, two solutions, no solution, or infinitely many solutions. 6. Solve a system of inequalities by. Midterm Review (Week 16 2 Weeks) Exponents Exponential Functions (Week 18, 3 Weeks) The properties of exponents scientific notation can be used to solve functions. 1. How are expressions with exponents simplified, multiplied, divided? 2. How is scientific notation used in olving? 3. How are growth decay models used to solve real-life completion of this unit, be able to: 1. Use properties of exponents to multiply expressions. 2. Evaluate powers that have zero negative exponents. exponents test Written Test Compound Interest Project Technology Project create two accounts on excel or google sheets. The two accounts involve saving early vs saving late. After use to graph functions. use Excel spreadshee ts to compare compound interest accounts created given parameters. Reinforcement Skills (Special Needs): Tablet Two-sided chips

10 ? 3. Graph functions. 4. Use division properties of exponents to evaluate powers simplify expressions. 5. Use scientific notation to represent numbers perform operations with them. 6. Write use models for growth. 7. Graph models for growth. 8. Write use models for decay. 9. Graph models for decay. programming the spreadsheets, they write about the results, comparing contrasting the impact of compounding interest over time on one's financial well being.

11 Polynomial s Factoring (Week 21, 3 Weeks) A Polynomial is a number, a variable, or the product of a number variable. A Polynomial must have variabl es with nonnegative integer exponents. 1. How are polynomials added, subtracted, multiplied, divided? 2. How are polynomials factored? 3. How are polynomial solved by factoring? completion of this unit, be able to: 1. Add subtract polynomials. 2. Multiply two polynomials. 3. Use special product patterns for the product of a sum a difference for the square of a binomial. polynomials factoring test Written Test use algebra tiles to model factoring. use to find intercepts of function. Reinforcement Skills (Special Needs): Tablet Two-sided chips 4. Solve a polynomial equation in factored form. 5. Factor a expression. 6. Solve by factoring. 7. Use

12 special product patterns to factor polynomials. 8. Use the distributive property to factor a polynomial. Quadratic Equations Functions (Week 24, 3 Weeks) Quadratic are seconddegree which usually have two solutions. A function has a U-shaped graph called a parabola. 1. How are square roots evaluated approximated? 2. How are radicals simplified? 3. How are solved? 4. How are functions graphed? completion of this unit, be able to: 1. Evaluate approximate square roots. 2. Solve a equation by finding square roots. 3. Use properties of radicals to simplify radicals. 4. Sketch the graph of a function. equation test Written Test use algebra tiles to model factoring. use to graph look at tables. drop a ball from the roof time how long it takes to hit the ground after having calculated same. Reinforcement Skills (Special Needs): Tablet CBR unit

13 5. Use the formula to solve a equation. 6. Use models in real-life s. 7. Use the discriminant to find the number of solutions to a equation. Rational Equations Functions (Week 27, 4 Weeks) A expression is a fraction whose numerator denominator are both polynomials. 1. How are solved? 2. How are expressions added, subtracted, multiplied, divided? 3. How are proportions percent examples of completion of this unit, be able to: 1. Solve proportions. 2. Use to solve percent. 3. Use direct inverse variation. test Written Test graph hyperbolas. solve by h several methods. Reinforcement Skills (Special Needs): Tablet Two-sided chips 4. Simplify a

14 ? expression. 5. Multiply divide expressions. 6. Add subtract expressions that have like denominators. 7. Add subtract expressions that have unlike denominators. 8. Divide a polynomial by a monomial or by a binomial factor. 9. Use polynomial long division. 10. Solve. 11. Graph

15 . Radicals Connection s to Geometry (Week 31, 4 Weeks) A radical equation is any equation where the variable occurs under a radical sign. Radical are prevalent in the study of geometry. 1. How are radical functions solved graphed? 2. How is the Pythagorean Theorem applied? 3. How are the midpoint of distance between two points calculated without? completion of this unit, be able to: 1. Evaluate graph a square root function. 2. Add, subtract, multiply, divide radical expressions. 3. Solve a radical equation. radicals test Written Test graph square root functions. use geometers sketchpad to derive distance formula the Pythagorea n Theorem. Reinforcement Skills (Special Needs): Tablet 4. Solve a equation by completing the square. 5. Find the distance between two points in a coordinate plane. 6. Find the midpoint between two

Algebra IA. Unit 1 Connections to Algebra

Algebra IA. Unit 1 Connections to Algebra A Unit 1 Connections to Algebra Time: 20 days Objectives: 1, 2, 8 and 9 Translate verbal into mathematical Write using exponents Use the order of operations to evaluate open sentences by performing arithmetic