Equations & Inequalities (excerpt from Pre-Algebra Out Loud)
Content
Activity 6.3 Translating Words into Algebra
2x − 5x + 6x = 3x A(B + C) = AB + AC 4 × 5 = 5 × 4 2(3 + 5)2 + (−1)2 y = mx + b
WHAT? Description
This lesson asks students to translate English phrases or sentences into algebraic expressions or equations. This activity is best used as a precursor to activity 2.4, in which students create their own word problems. To be successful at this activity, pre-algebra students must work with their knowledge of basic ideas and concepts of algebra or use their textbooks or concept circles to find definitions and descriptions of math and algebra concepts.
WHY? Objectives
During this activity, pre-algebra students: • Practice translating algebraic symbols into words • Learn more about how linear applications are constructed and solved • Practice deciphering mathematical word problems • Practice using and translating algebra concepts into real-world problem solving • Write out the definitions of the terms expression, equation, and inequality and identify the differences among them
HOW? Examples
Here are three examples of translations: • Five times a number plus six → 5x + 6 is an expression. • One-half of 10 times a number and 3 is twice that number → 1 2 (10x + 3) = 2x is an equation. • A number is at most 13 times 2 . The number → x ≤ 13 ( 2 x) is an 3 3 inequality.
126
Pre-Algebra Out Loud
Worksheet 6.3 Translating Words Into Algebra
NAME DATE
2x − 5x + 6x = 3x A(B + C) = AB + AC 4 × 5 = 5 × 4 2(3 + 5)2 + (−1)2 y = mx + b
Directions: Translate each of the following phrases or sentences into algebraic terms. Label each problem as an expression, equation, or inequality by circling the correct term. There is no need to solve any of the equations or inequalities. Use as many numbers and symbols as possible in your translation. If you feel there is more than one way to translate your phrase, choose one way and write it out in numbers and symbols. 1. The product of 13 and a number, all divided by 2 = Circle one:
Copyright © 2013 by John Wiley & Sons, Inc.
Expression
Equation
Inequality
2. The sum of five times a number and 2 = Circle one: Expression Equation Inequality
3. The opposite of a negative 3 minus 2 times a number = Circle one: Expression Equation Inequality
4. Seven times the quantity of 2 and a number is at least 4 = Circle one: Expression Equation Inequality
5. A number is at most the quotient of 40 and negative 4 = Circle one: Expression Equation Inequality
6. Write an example like the ones above of your own and translate it into algebra. Label it an expression, equation, or inequality.
Equations and Inequalities
127
2x − 5x + 6x = 3x A(B + C) = AB + AC 4 × 5 = 5 × 4 2(3 + 5)2 + (−1)2 y = mx + b
WHAT? Description
This lesson asks students to translate English phrases or sentences into algebraic expressions or equations. This activity is best used as a precursor to activity 2.4, in which students create their own word problems. To be successful at this activity, pre-algebra students must work with their knowledge of basic ideas and concepts of algebra or use their textbooks or concept circles to find definitions and descriptions of math and algebra concepts.
WHY? Objectives
During this activity, pre-algebra students: • Practice translating algebraic symbols into words • Learn more about how linear applications are constructed and solved • Practice deciphering mathematical word problems • Practice using and translating algebra concepts into real-world problem solving • Write out the definitions of the terms expression, equation, and inequality and identify the differences among them
HOW? Examples
Here are three examples of translations: • Five times a number plus six → 5x + 6 is an expression. • One-half of 10 times a number and 3 is twice that number → 1 2 (10x + 3) = 2x is an equation. • A number is at most 13 times 2 . The number → x ≤ 13 ( 2 x) is an 3 3 inequality.
126
Pre-Algebra Out Loud
Worksheet 6.3 Translating Words Into Algebra
NAME DATE
2x − 5x + 6x = 3x A(B + C) = AB + AC 4 × 5 = 5 × 4 2(3 + 5)2 + (−1)2 y = mx + b
Directions: Translate each of the following phrases or sentences into algebraic terms. Label each problem as an expression, equation, or inequality by circling the correct term. There is no need to solve any of the equations or inequalities. Use as many numbers and symbols as possible in your translation. If you feel there is more than one way to translate your phrase, choose one way and write it out in numbers and symbols. 1. The product of 13 and a number, all divided by 2 = Circle one:
Copyright © 2013 by John Wiley & Sons, Inc.
Expression
Equation
Inequality
2. The sum of five times a number and 2 = Circle one: Expression Equation Inequality
3. The opposite of a negative 3 minus 2 times a number = Circle one: Expression Equation Inequality
4. Seven times the quantity of 2 and a number is at least 4 = Circle one: Expression Equation Inequality
5. A number is at most the quotient of 40 and negative 4 = Circle one: Expression Equation Inequality
6. Write an example like the ones above of your own and translate it into algebra. Label it an expression, equation, or inequality.
Equations and Inequalities
127
