Students: 1. Use letters, boxes, or other symbols to stand for any number in simple expressions or equations. 1. Students use and interpret variables, mathematical symbols and properties to write and simplify expressions and sentences. Review properties Given the equation 7 + 9 = 16, are the following statements true? Explain. 16-7 = 9 9 + 7 = 16 16-9 = 7 Use the associative property to complete the number sentences. (7 + 5) + 4 = 7 + ( + ) 9 x (8 x 7) = (9 x 8) x Use the commutative property to complete the number sentences. 3 + 8 + 7 = 7 + + 3 x 8 x 7 = 7 x x Is 6 x 8 the same as 8 x 6? Will reversing the factors always result in the same product? 23
A letter can be used to name the variable until the value is determined Tanya read the first 78 pages of a 130 page book. Which number sentence could be used to find the number of pages left in the book? ( FW) 130 + 78 = - 78 = 130 130-78 = Expressions Write the following expressions using y instead of a number. Three times a number (3 x y) A number divided by 3 A number minus 15 A number increased by 5 (y + 5) Equations Rewrite the following equations using y for the unknown number. + 10 = 24 (y + 10 = 24) 15 = 3 3 x = 27 What is n representing in the following equations? 6 x 7 = n n + 13 = 23 n - 7 = 3 n 5 = 2 24
MATH ALGEBRA AND FUNCTIONS *2. Interpret and evaluate mathematical expressions that use parentheses. Solve. 40 (5 + 3) = 24 (6 2) = (7 x 4) + 6 = (5 x 12) - (2 x 9) = ( FW) (28-10) - 8 = ( FW) 28 - (10-8) = ( FW) (3 x 12) - [(24/6) + 8] = ( FW) ([(18 + 31)/7] + 5) x 9 = *3. Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations. List all the different answers you can find by putting parentheses in different places to solve for n. 5 + 4 x 3 = n 2 x 10 2 = n Which operation do you perform first to evaluate these expressions? 5 + (3 x 9) (7 + 3) - 10 Use the associative property to recombine the terms and solve the equation for y. (y + 7) + 10 = 19 (y x 6) x 2 = 24 25
4. Use and interpret formulas (e.g., Area = length times width or A = lw) to answer questions about quantities and their relationships. Evaluate simple expressions using substitution A variable can vary with every problem. List two different ways to write three times x. [ 3x 3 x 3(x) (3)(x) (3)x ] What does 5a mean? Evaluate the following expressions for a = 8 and b = 5 a + 7 a + b a - b 3a - b a 2 Use the formula A = lw to find the area of a rectangle with length equal to 5 in. and width equal to 3 in. What are the variables in the formula A = lw? Why are they called variables? What happens if the length changes to 7 in.? The length of a rectangle is 15 cm. and the width is 7 cm. Use the formula P = 21 + 2w to find the perimeter. What happens if the width changes to 10? 26
*5. Understand that an equation, such as y = 3s + 5 is a prescription for determining a second number when a first number is given. Review patterns and relationships What number comes next? 18 14 10 6 Complete the table. in 6 12 18 22 out 3 6 8 11 Determine function rules Suppose you put 4 into a function machine and 20 comes out. What is the function rule? Is there more than one rule? Write two possible function rules for each function. 1. 4 ---- ---- 8 2. 10---- ---- 20 3. 3---- ---- 21 4. 1---- ---- 1 5. 15---- ---- 30 6. 1---- ---- 0 27
Evaluate the function rule to complete the table. n Function rule n + 3 Out 2 2 + 3 5 3 4 5 100 A function machine has output of 100, 95, 90, 85. What is the rule? What is the next number? Use the table to write the function rule. in 1 2 3 4 out 5 10 15 20 There is a rule to get from Column A to Column B. Can you say what it is? ( FW) Column A Column B 10 2 15 3 45 9 50 10 28
Use an equation to determine a second number when a first number is given Use and find the value of the variable for the output of a function machine. Input Rule Output 7 +4 y therefore y = 16-4 y therefore y = 16 4 y therefore y = Find the values of the variable y when y = x + 3 If x is 3 what is y? y = If x is 5? y = If x is 100 y = *2. Students know how to manipulate equations. Students: *1. Know and understand that equal added to equals are equal. Use inverse operations to solve simple equations Use the function machine to find the value of x. input rule output x +4 10 x -4 10 x x2 2 x x5 10 x 2 1 x 2 6 29
Given 10 + 3 = 13. Is each side of the equation equal? If I add 5 to both sides of the equation is it still equal? Explain. Know how to manipulate equations What operation do you use to keep both sides of the equation equal (balanced) in solving for x? x + 6 = 15 (subtract 6) n - 13 = 25 3x = 93 x/6 = 12 *2. Know and understand that equals multiplied by equals are equal. Given 3 x 2 = 6. If I multiply both sides by 3 is the equation still equal? Explain. 30
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