Lesson Title: Rational Numbers in the Real World
Date: _____________ Teacher(s): ____________________
Course: Common Core 6
Start/end times: _________________________
Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which
Mathematical Practices do you expect students to engage in during the lesson?
Apply and extend previous understandings of numbers to the system of rational numbers.
6.NS.C.7. Understand ordering and absolute value of rational numbers.
7b. Write, interpret, and explain statements of order for rational numbers in real-world contexts.
MP1: Make sense of problems and persevere in solving them.
MP2: Reason abstractly and quantitatively.
MP3: Construct viable arguments and critique the reasoning of others.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and connect
big ideas? List the questions. Provide a foreshadowing of
tomorrow.
1. Distribute or project the warm-up resource
and have students complete.
2. Have students share their answers and justify Have students complete the Illustrative Mathematics
Task: Comparing Temperatures, available at
why they chose to use specific numbers to
represent the position of the fish, water, and http://www.illustrativemathematics.org/illustrations/285
boy in the photograph.
3. Have students generate an inequality
statement to represent the comparison
between the position of the boy, water, and
fish.
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic
connections to appropriate mathematical practices.
1. Remind students that they will be using inequality statements to compare rational numbers in real- life
situations.
2. Ask students to write as many real-life situations that involve rational numbers as they can on a
separate sheet of paper. Have students think-pair-share.
3. Assign students to groups of 3-4. Distribute one scenario from Group Scenarios to each group.
4. Have each group follow the directions on the scenario to understand the real life connection to rational
numbers and to create an inequality statement based on the context of the scenario. Remind students to
use number lines, absolute value, etc.
5. Circulate around to the groups and ask, “How are you determining if the numbers are negative or
positive? How can absolute value help you write your inequality statement? Where would these
numbers be placed on a number line?” As you circulate look for evidence of MP1 and MP2.
6. After each group has had a chance to work with each scenario, assign each group to one of the
scenarios and have them share their inequality statement with the class. Discuss and have students
justify their inequality statements to the class using, number lines, absolute value, pictures, diagrams,
etc. (Look for evidence of MP2 and MP3 while listening to the class discussion.)
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student success? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened and conceptual understanding.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Rational Numbers in the Real World
Date: _____________ Teacher(s): ____________________
Course: Common Core 6
Start/end times: _________________________
Students will be able to identify the when a number should be represented as a negative or positive in a real life
situation based on the context of the problem. (Below sea level, debt, yards gained, yards lost, etc.)
Students will use knowledge of absolute value and number lines to accurately write their inequality statement.
Students will accurately write inequality statements that satisfy the context of the real world scenario.
Students will use their knowledge of inequality vocabulary words to explain their inequality statement to the class
and why it makes sense.
Student success will be measured through questioning during the group scenarios activity to see if students are able
to make math connections to the scenarios. Also, through group explanations of inequality statements during
presentations to see if students are able to use accurate reasoning for their inequality statement. Finally, through the
closure activity and homework assignment which are both independent practices for ordering rational numbers and
making an inequality statement.
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
Vocabulary: Positive number, negative number, rational number, integer, decimal, fraction, absolute
value, distance, number line, inequality, greater than, less than
Resources: What materials or resources are
essential for students to successfully complete the
lesson tasks or activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
Whiteboard/Chalkboard
Document Camera
Warm-Up
Group Scenarios
Have students create a scenario that involves rational
numbers where an inequality statement will need to be
made. Students can bring the written scenario to class
and swap with other students for a warm-up the next
day.
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson
standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
Are students able to determine the order of rational numbers by applying their knowledge of inequality vocabulary
words, such as “greater than,” “less than,” “more than,” “at least,” “at most,” “above,” “below,” etc., in order to
determine numbers on a number line?
Are students able to describe in their own words that the farther a negative number is from zero, the smaller the
value using a number line, absolute value, etc?
Are students able to write an accurate inequality statement comparing rational numbers?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this
product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.