Writing expressions, equations, and inequalities from word problems

Writing expressions, equations, and inequalities from word problems • Let’s review our Vocabulary! • Please write all the following vocabulary words in your Math Journal for future use. Slide 1

Essential Vocabulary: Sum means addition The sum of Pat’s age and 11 equals 28 p + 11 = 28 • Difference means subtraction • The difference between my age and my younger brother’s age, who is 10 years old, is 6 years. • y – 10 = 6 Product means multiplication The product of Joe’s age and 14 is 162 14j = 162 Slide 2

Essential Vocabulary: Times means multiplication Three times Ben’s age is 45. 3b = 45 Less than means subtraction Seven less than my age equals 32. y – 7 = 32 Total means addition The total change under the couch cushion and $10 dollars is $10.43 c + 10 = 10.43 More than means addition Eleven more than the Principal’s age is 55. 11 + p = 55 Slide 3

Other Vocabulary words • Variable: A variable is a symbol that represents a number. Usually letters are used such as x, y, n, or t. • Expression: An expression is a mathematical statement that may use numbers, variables or both. An expression does not have an equal sign. Example: x + 2. • Equation: An equation is a mathematical statement that two numbers or expressions are equal. An equation always has an equal sign. Example: x + 2 = 8 • Inequality: A mathematical sentence that contains <, >, (insert a greater than or less than symbol), (insert a less than or greater than symbol), (insert a non equal symbol). Example: x + 2 > 8 Slide 4

Examples of expressions: 8 X 3 + 4 2y + 5 3 + 5(4-3) An expression is a mathematical statement that may use numbers, variables or both. An expression does not have an equal sign. Writing expressions from word sentences Slide 5

Writing expressions from word sentences • Bart weighs 60 kilograms, and Maggie weights k kilograms. Write an expression for their combined weight. • Four books more than b books • The quotient of p and 8 Slide 6

Examples of equations: 3 = 3 18 = 15 + 3 x = 28 t + 4 = 9 4n + 5 = 25 An equation is a mathematical statement where two numbers or expressions are equal. Equations do have equal signs. Writing equations from word sentences. Slide 7

Writing equations from word sentences. Translate the following into an equation: • The sum of 8 and a number is equal to 30 • Thirty-seven more than a number is 8 • Eight fewer than a number is 10 Slide 8

Examples of inequalities: 3 ≠ 5 80 > 15 + 3 x < 28 27 ≤y t ≥ 9 = 1 An inequality is a mathematical statement that contains <, >, ≤, ≥ Writing inequalities from word sentences. Slide 9

Writing inequalities from word sentences. Translate the following into inequalities: • My favorite song is less than 5 minutes long. • To drive a car you must be at least 14 years old. • The truck can carry more than 650 pounds. Slide 10

Translate into an expression: The cost of a candy bar divided among 3 friends. Application #1 Writing expressions Write and solve this in your Journal. Slide 11

Translate the following word problem into an equation: Suppose you have $32.00 to spend at Joyland. Admission cost $4.00. If ride tickets are $2.00 per ticket, how many tickets can you buy? Application #2 Writing equations Write and solve this in your Journal. Slide 12

Translate the following word problem into an inequality: My locker shelf can hold at most 50 pounds. Application #3 Writing inequalities Write and solve this in your Journal. (Do not try this on your locker!) Slide 13

Step-by-Step #1 Demonstration Nine cards fewer than c cards Who would like to write this on the board? Slide 14

Step-by-Step #2 Demonstration Who would like to write this one on the board? The sum of 45 and a number is 68 Slide 15

Demonstration Step-by-Step #3 The dog’s age is over 10 years. Who would like to write this on the board? Slide 16

Show us what you can do! • Write your own word problem. Then write the algebra problem that goes with this word problem and explain it to the class. • You will need to be able to defend your answer if needed. Slide 17

Do these on your own and we will check them together. • Write an expression, equation, or inequality for each word phrase. • 1. Seven times your quiz score q. • 2. The sum of 7 and a number is 40. • 3. The temperature is over 100 F.

Quiz time Write an expression, equation, or inequality for each word phrase. • Divide the total points p by 4 • Seventeen more than a number is 6 • To enter the movie, you must be 18 years old. • 8 less than d dollars.

5. Seven fewer than a number is 12. • You can walk there in 20 minutes or less. • You plan to read 500 pages of a book in one week. You have read 142 pages so far this week. Set up an equation to find out how many more pages you must read? • The sum of s students and 9 students.

Twenty-seven is 4 less than a number. • Each prize is worth over $1758. • In a pet store the number of fish is 120 more than three times the number reptiles. The pet store has 210. Set up an equation to find out how many reptiles does it have?

Writing expressions, equations, and inequalities from word problems