That Equations Can Be Translated to Word Problems

Math Lesson: Problems From Equations / Grade Level: 7
Lesson Summary: Students will translate between equations and word problems. Advanced students will translate between equations and word problems involving exponents and square roots, in addition to the basic operations. Struggling students will use a table of common words and phrases to assist in translating.
Lesson Objectives:
Students will know…

that equations can be translated to word problems.
that word problems can be translated to equations.

Students will be able to…

create word problems for a given equation.
translate a given word problem to an equation.

Learning Styles Targeted:
x / Visual / x / Auditory / Kinesthetic/Tactile
Pre-Assessment:
Use this quick assessment to see if students understand the language in word problems.
1)Write an equation that could be used to solve the following problem:
The sum of what number doubled and eight is twenty?
Whole-Class Instruction
Materials Needed: paper and pencil, PowerPoint Presentation*
Procedure:
Presentation:
1)Discuss the equation for the pre-assessment (2x + 8 = 20). Ask students what words told them addition was involved (sum). Brainstorm a list on the board of other words or phrases that indicate the four basic operations, or an equal sign (usually “is”), and the variable (what number, how much, etc.)Explain that these words and phrases can help “decipher” word problems, as well as to write them.
Guided Practice:
2)Have students work in groups to write two simple (one or two operations) algebraic equations with one variable, and to write in words two such equations. Groups will exchange equations and word problems to translate.
3)Discuss strategies students used to write the problems and equations.
Independent Practice:
4)Have students work to complete the independent practice questions from the PowerPoint Presentation.
Closing Activity:
7) Read the rhyme, “As I was Going to St. Ives,” for the class to solve.
As I was going to St. Ives, I met a man with seven wives
Each wife had seven sacks,
Each sack had seven cats
Each cat had seven kits
Kits, cats, sacks, wives: How many were going to St. Ives?
There are several answers, depending on how the rhyme is interpreted.
Advanced Learner
Materials Needed: paper and pencil
Procedure:
1)Ask students to write an equation expressing the following: What number multiplied by itself is the sum of four and two times itself five times?
2)Discuss the solution with students (x2 = 4 + 25), and explain that exponent and square roots can be used in equations, and expressed in words.
3)Have students work in pairs to write equations and statements that use different operations, including exponents and/or square roots. Students will exchange equations and word problems to translate.
4)Discuss students’ solutions and strategies.
Struggling Learner
Materials Needed: paper and pencil
Procedure:
1)Provide students with the following table to use for translating mathematical statements:

2)Have students translate the following statement using the table: The product of what number and five is the sum of twelve and eight?
3)Discuss the solution with students:
4)product: times, what number: x, is: =, sum +
5)5x = 12 + 8
6)Have students work in pairs to write equations and statements that use one or two operations. Students will exchange equations and word problems to translate.
7)Discuss students’ solutions and strategies.

*see supplemental resources