MATH ALGEBRA AND FUNCTIONS 5 Performance Objective Task Analysis Benchmarks/Assessment Students:

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1 Students: 1. Use information taken from a graph or Which table, a or b, matches the linear equation to answer questions about a graph? problem situation. y 1. Students use variables in simple expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results x a. Ordered Pair 1 2 (1,2) 2 4 (2,4) 3 6 (3,6) 4 8 (4,8) b. Ordered Pair 1 1 (1,1) 2 2 (2,2) 3 3 (3,3) 4 4 (4,4) Find the function rule and use it to complete the tables

2 As altitude increases, does snow depth increase, decrease, or stay the same? y Depth of Snow Altitude The forestry service kept track of the number of employees and the number of trees they planted. Use the graph to estimate how many employees would be needed to plant 2,000 trees. Trees Planted x Employee s Trees *2. Use a letter to represent an unknown number, write and evaluate simple algebraic expressions in one variable by substitution. Use a letter to represent an unknown number Number of Employees Use a variable to write the following expressions. 22

3 5 increased by a number a a number b increased by 5 n marbles in 4 equal groups c rows of desks with 5 desks in each row 3 decreased by a number n 4 less than a number g 7 more than a number a z less b a number increased by 5 twice a number a number divided by 7 a number decreased by 2 6 divided by a number c Write an algebraic expression for the total area of both rectangles b Write an algebraic expression for n rows of 5 stamps. Write and evaluate simple algebraic expressions in one variable by substitution Find the value of the expressions when x = 10. 5x 4x + 3 3x + x 3x + 2x 2 5 8x

4 Complete the function tables. 3. Know and use the distributive property in equations and expressions with variables. n n n n n n n 3n 2 6 Solve multiplication problems using the distributive property. 3 x 97 = 3(90 + 7) 4 x 16 = 4(10 + 6) 38 x 59 = (30 + 8)59 Evaluate the following expressions for x = 3, y = 4, and z = 5. 6(x + y) 5 + 7(x + z) 3(x + 2) + 7(5 + y) Translate into an algebraic expression. Twice the sum of two and y. Three times the difference of x and 2. Know and use the order of operation Simplify each expression using the order of operations x 6-1 (32 + 8) (4-2)

5 *4. Identify and graph ordered pairs in the four quadrants of the coordinate plane. Label quadrants Label (I, II, III, IV) the four quadrants in the coordinate plane. y x Which quadrant has (-x, -y) as the ordered pair? Are the y-coordinates above the x- axis positive or negative? What do you know about the x- coordinates to the right of the y-axis? Write points of a graph as ordered pairs Name the ordered pairs for each point. B C -3 A D 25

6 Graph ordered pairs Graph the following ordered pairs and tell the quadrant in which the points fall. (1,5) (-3, -4) (-3,2) (1/2, -4) Find the ordered pairs from the information in the table and graph the points *5. Solve problems involving linear functions with integer values, write the equation, and graph the resulting ordered pairs of integers on a grid. Evaluate function tables Use the function table below to graph the function of y = 3x. Record the ordered pairs in the table. Graph the points that correspond to the ordered pairs. Draw the line that contains the points. Explain how the table, graph, and equation are related. 26

7 Complete the function table and graph the function y = x Make a function table for the rule x - 2 = y using 2, 5, and 8 as the input. Using the function y = 2x + 1, complete the table and graph the ordered pairs

8 Write an equation and graph the ordered pairs Write an equation to represent the values in the table and graph the ordered pairs x x 28

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