Decimal Inequalities – Addition and Subtraction


Decimal Inequalities – Addition and Subtraction introduces students to solving inequality equations that contain decimal values. Students will apply their knowledge about inequalities with whole numbers to this lesson. They will learn to simplify numbers by either adding or subtracting before comparing two numbers. By the end of the lesson, they will be able to compare decimal inequalities correctly.

There are several suggestions listed in the “Options for Lesson” section of the classroom procedure page. One option is to review inequalities with whole numbers before starting decimals. If you have students who are struggling, you can let those students use a place value chart to help them figure out problems.

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What our Decimal Inequalities – Addition and Subtraction lesson plan includes

Lesson Objectives and Overview: Decimal Inequalities – Addition and Subtraction teaches students how to solve inequality expressions that involve adding and subtracting. Students will apply their knowledge of inequalities to decimal values. They will learn to simplify decimals by adding or subtracting them. Then they can determine which inequality symbol makes a statement true. This lesson is for students 4th grade and 5th grade.

Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the blue box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand. The only supplies you will need for this lesson are colored pencils. To prepare for this lesson ahead of time, you can gather the colored pencils and copy the handouts.

Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. If your students have trouble comparing numbers, you can allow them to use a place value chart. You can also review how to compare whole numbers before comparing decimals. If you have more advanced students, you can have them practice problems with smaller numbers first. Finally, your students can use graph paper to keep the decimal points aligned.

Teacher Notes

The teacher notes page includes lines that you can use to add your own notes as you’re preparing for this lesson.


The Decimal Inequalities – Addition and Subtraction lesson plan includes three pages of content. The lesson begins by explaining that inequalities are mathematical sentences that show the relationship between two values. We use three different symbols to show these relationships: > for greater than, = for equal to, and < for less than. An easy way to remember these symbols is to think about an alligator eating the numbers. Alligators want to eat the largest amount so their mouths are always open to the larger number. Decimal inequalities have place values that are less than one. The lesson includes a place value chart for reference.

The lesson then goes over a few inequalities. In order to solve them, you first have to add or subtract the decimals on one side of the inequality. You can then compare the values. The first example is 4.1 + 5.6 ? 10.3. The first step is to simplify the left side of the inequality by adding the decimals. 4.1 + 5.6 = 9.7. The new inequality is now 9.7 ? 10.3. 9.7 is less than 10.3, so the inequality is 9.7 < 10.3. The lesson then includes an example where you have to subtract decimals. The process to solve the inequality is the same.

Some inequalities require you to add or subtract decimals on both sides of the equation. The lesson includes an example: 10.75 – 3.5 ? 7.15 + 0.13. First, you need to simplify both sides of the inequality.  The inequality becomes 7.25 ? 7.28. Next, you can compare the sides. 7.25 is less than 7.28, so the inequality is 7.25 < 7.28. Make sure to line up the decimal points when adding or subtracting with decimals!


The Decimal Inequalities – Addition and Subtraction lesson plan includes four worksheets: an activity worksheet, a practice worksheet, a homework assignment, and a quiz. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.


You can have students work alone, in partners, or in small groups for the activity. Students will have to solve four or more problems and illustrate the addition or subtraction on 10 x 10 grids. They will then write in sentence form how to solve the inequality. Finally, they will solve the problem numerically. There is space next to the four problems on the worksheet for students to write their sentences and show their work.


For the practice worksheet, students must solve 10 inequality equations. They will first need to add or subtract the decimals depending on the question. Once they figure out the simplified numbers, they can write the correct inequality symbol that makes the statement true.


The homework assignment mimics the practice worksheet. Students must simplify the decimals and figure out which inequality symbol makes 10 statements true.


The quiz contains a table with three columns and then two inequality statements. Students must draw the correct symbol that represents less than, equal to, and greater than in the table. Then they will have to figure out which symbol makes the two statements true.

Worksheet Answer Keys

This lesson plan includes answer keys for the practice worksheet, the homework assignment, and the quiz. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.

Additional information


4th Grade, 5th Grade



State Educational Standards


Lessons are aligned to meet the education objectives and goals of most states. For more information on your state objectives, contact your local Board of Education or Department of Education in your state.