MATH ALGEBRA AND FUNCTIONS

Transcription

1 Students: 1. Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations and graph and interpret their results. *1. Write and solve one-step equations with one variable. Write an equation Write the equation for the following: A number increased by 6 is 25 A number times 3 is 6 6 more than x is 18 7 decreased by n is 19 b divided by 8 is 12 5 less than a number is 8 Write the equation as you would read it. x - 28 = 54 ( a number decreased by 28 is 54) 3x = 9 x/2 = 4 x + 45 = 90 Solve equations with one variable Is each equation true for the given value of x? x - 10 = 30 where x = 20 x + 5 = 5 where x = 0 x/20 = 5 where x = 100 3x = 45 where x =

2 For an equation like x + 10 = 35, how many values of x make it true? Complete the table. Input x + 3 = 10 x - 3 = 12 Operation subtract 3 from both sides Output x = x = Complete the table. Input 3x = 9 x/3 = 9 Operation divide both sides by 3 Output x = x = Solve and graph the solution points on a number line. y - 14 = 20 x + 99 = n = 36 b/4 = 2 Find n if a) 49/21 = 14/n b) n/3 = 5/7 ( FW) 6y - 2 = 10 What is y? ( FW) 16

3 2. Write and evaluate algebraic expressions for a given situation using up to three variables. Write algebraic expressions Write in algebraic terms. 7 less than twice a number 6 more the a number divided by 4 9 times n decreased by twice m Write the following as algebraic and numerical expressions (let n be some number). 1. A number increased by The product of a number and /2 decreased by some number 4. The square of some number divided by 7 5. The sum of some number and 1/3, increased by the third power of the same number ( FW). What is the difference between an equation and an expression? 17

4 Evaluate algebraic expressions Find the value of the following expressions where a = 10, b= 5, and c = 2. a + b - c 2a + b 5a - 2c ac + 3 b Evaluate for a = 5. 5a 5 a 5(a) (5)(a) (5)a How are these terms similar? 3. Apply algebraic order of operations and the commutative, associative and distributive properties to evaluate. Order of operation Simplify numerical expressions using rules for order of operation (4 3)/ x (7 x 3) - 2 x 4 Evaluate Which of the following problems is the same as 5(6) + 5(18)? a) 5(6) + 18 b) 5 (6 + 18) c) 6(5) + 6(18) d) (5 + 6)(18) Solve. 10(5 + 22) 18

5 4. Solve problems using correct order of operations manually and by using a scientific calculator (when possible). Circle all answers that evaluate to a number greater than 35. a) 4(4 + 5) + 5 b) (4)(4) c) -1(6)(-10) d) -1(6-50) e) -1(50-6) Evaluate for: a = 5 4(a - 2) 4a - 2 Evaluate for: a = 2 and b = 3 5a + 2b 4a True or false? 6(5 + 3) = 6 x (3c) = 6 x x c (a + b) + c = a + (b + c) True or false? ( )6 =

6 Manually Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions. Use a scientific calculator (when possible) with parentheses. With division Students: 1. Convert from one unit of measurement to another (e.g., from feet to miles, from centimeter to inches) (18 6) (7-4) Use a function table to convert feet to inches. Input Output (Number of feet) (Number of inches) x 12x What is the function rule that converts feet to inches? 20

7 Make the following conversions: 2 miles to feet 21,120 feet to miles 100 centimeters to inches 7 yards to meters 6 miles to kilometers 7 gallons = qts. 64 oz = lbs. 4ft. = inches Complete the following statements: If 3 ft. = 1 yd, then 7 ft = yds. If 32 oz = 1 qt, then 6.7 qt = oz. ( FW) One British pound is worth $1.50. In London a magazine cost 3 pounds. In San Francisco the same magazine costs $4.25. Where was the magazine cheaper? ( FW) *2. Demonstrate understanding that rate is a measure of one quantity per unit value of another quantity. State if the ratio is a unit rate. 10 mi/2 hours 70 mi/hour 60 apples/1 pie Hunter earned $18 for working 3 hours. What would he earn for 1 hour of work? 21

8 Mike drove 100 kilometers in 3 hours. Use a rate to compare these numbers. Express the rate in kilometers per hour. How does the function table help determine how much money Meiko makes per hour. What does 15x represent? Hours Meiko Worked Pay in $ x 3. Solve problems involving rates, average speed, distance, and time. Set up application problems using proportions An airplane can fly 1500 kilometers in 2 hours. How long would it take to fly 3750 kilometers. Distance = kilometers Time hours 1500 km = 3750 km 2 hours x hours 22

9 A family drinks 14 gallons of milk in 7 days. How many gallons will the family drink in 10 days? Evan can run 100 meters in 12 seconds. If he continues at that pace, how long will it take him to run 1500 meters? A pump can fill a 900 liter tank in 30 minutes. How long will it take to fill a 1200 liter tank? A map is drawn so that 5 centimeters represents 5 miles. On a map two towns measure 20 centimeters apart. Find the actual distance between these towns. Denise drove 100 km on 12 liters of gasoline. How many liters will she use to drive 25 km? Jane took the rapid transit to work which is a distance of 12 miles. It took her 10 minutes. What was the average speed of the train? 23

10 Marcus took a train from San Francisco to San Jose, which is a distance of 54 miles. The train took 45 minutes for the trip. What was the average speed of the train? ( FW) 3. Students investigate geometric patterns and describe them algebraically. Students: 1. Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = 1/2 bh, C = πd), which give the perimeter of a rectangle, area of a triangle, and circumference of a circle, respectively. Evaluate Find the perimeter of a rectangle with length of 18 centimeters and width of 6 centimeters. Find the circumference of a circle with a diameter of 15 centimeters. Find the area of a triangle with a base of 15 and height of 8 feet. Write an equation and solve. The length of a rectangle is 4 times the width. Let x = the width. Write the equation for finding the perimeter. The length of a rectangle is 2 meters more than the width. The perimeter is 28 meters. Find the length and width. 24

11 A rectangle has width = w. Its length is one more than 3 times its width. Find the perimeter of the rectangle. (Your answer will be expressed in terms of w). ( FW) 2. Express simple relationships arising from geometry in symbolic form. If the sides of a square are doubled, the area is four times as large. Use the formula for area of a square to show why this is true. A triangle has a 25 degree angle and a 47 degree angle. Which equation will find the third angle? a) = x b) x = 90 c) x d) = x 25

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