Writing Algebraic Inequalities

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SWBAT translate algebraic inequalities.

Big Idea

Students identify key words to translate inequalities.

Do Now

10 minutes

Students have previously worked on solving algebraic equations. The results of student exit tickets have shown that students have more difficulty solving equations that involve fractions and decimals.  The Do Now problems are an opportunity for students to practice these concepts.

I will encourage students to discuss the algorithms for operations with decimals and fractions with their group. 

 Do Now

1)  x + 2.75 = 15

2)   8.7x – 1.2 = 16.2

3)   1/2r - 2/5 = 3/4

I will review the Do Now problems with the class by randomly calling on students to guide me through their steps.


Inequality Symbols

5 minutes

Although students may be familiar with inequalities, I will review the symbols and their meaning.

Inequality Symbols

> Greater than

≥Greater than or equal to

<Less than

≤Less than or equal to

Students often confuse the less than and greater than signs; to clarify I will use the common reference to Pac-Man.  

Pac-Man's mouth opens to the larger number because he is hungry.

Group Work

15 minutes

I will explain to students that much like we translating algebraic expressions, we will translate algebraic inequalities.

I've given you the four inequality symbols and their meaning, however, oftentimes there are other words used to express the inequalities.  The Writing Algebraic Inequalities Chart.docx contains important words that may used instead of the typical inequality wording.  You will complete the chart with your group by restating the sample sentence in your own words and writing an algebraic inequality.

Students will have 10 minutes to discuss and complete the chart with their group. Then groups will share out their ideas and answers with the class.  If groups disagree on the algebraic inequality, it is important to discuss it as a class until an inequality symbol has been agreed on.

Independent Practice

10 minutes

The Independent Practice is an opportunity for students to apply the Writing Inequalities Chart to translating expressions.  Students may have difficulty with the 1 step inequalities. I will suggest that they underline/highlight the key words that indicate an operation and underline/highlight the key words that indicate an inequality.

Independent Practice

1)  14 is greater than a

2)   b is less than or equal to 8

3)  6 is less than the product of f and 20

4) The sum of t and 9 is greater than or equal to 36.

5)  7 more than w is less than or equal to 10

6)  19 decreased by p is greater than or equal to 2

7)  Fewer than 12 items

8)  No more than 50 students

9)  At least 275 people attended the play

 After 10 minutes, I will randomly select students to present their answers on the board.  Students will have to explain what key words helped them translate the inequality.

Lesson Summary

5 minutes

Referring to the Writing Inequalities Chart, I will ask students additional questions to assess and deepen their understanding of the concept.

 If "at most 7 students were late for class", is it possible that 10 students were late?

Students should understand that the maximum number of students is 7.

If "Tracy is at least 14 years old", could she be 2 years old?  How old could she be?

Students should understand that Tracy could be 14 or older.

How many extra credit assignments could Ms. Love possibly give to her class?

Students should understand that Ms. Love could give 0,1, or 2 assignments.

If the "average test scores is less than 85", could it be 85?

Students should understand that the average test score is less than, but does not include, 85.

If the "price of the shirt is more than $40", could the shirt have cost $40?

Students should understand that the cost of the shirt is more than, but does not include, $40.