Learning Activity

Using Number Lines to Model Real-World Problems

Subject Area

Mathematics
Digital Literacy and Computer Science

Grade(s)

7

Overview

In this activity, students will compute real-world problems with rational numbers while using a digital number line. Students are provided a sample problem to work through to become familiar with the digital number line. Since problems can be solved using multiple methods, students are asked to provide a number sentence to represent their number line model as well as the solution to the problem. Through the online digital tool, students can also share a link to their work with their teacher or classmates. This provides a great opportunity for students to investigate how to solve problems using multiple methods.

Using Number Lines to Model Real-World Problems Student Response Page

Digital Literacy and Computer Science (2018) Grade(s): 7

DLCS18.7.30

Apply the problem-solving process to solve real-world problems.

Unpacked Content

UP:DLCS18.7.30

Vocabulary

  • problem-solving process

Knowledge

Students know:
  • the steps to the problem-solving process.

Skills

Students are able to:
  • select and dissect a problem.
  • seek solutions.
  • select a best alternative.

Understanding

Students understand that:
  • often there are multiple solutions to real
  • world problems.
Mathematics (2019) Grade(s): 7

MA19.7.4

Apply and extend knowledge of operations of whole numbers, fractions, and decimals to add, subtract, multiply, and divide rational numbers including integers, signed fractions, and decimals.

Unpacked Content

UP:MA19.7.4

Vocabulary

  • Integers
  • Rational numbers
  • Additive inverses
  • opposite quantities
  • Absolute value
  • Terminating decimals
  • Repeating decimals

Knowledge

Students know:
  • a number and its opposite have a sum of 0.
  • A number and its opposite are called additive inverses.
  • Strategies for adding and subtracting two or more numbers.
  • Absolute value represents distance on a number line, therefore it is always non-negative.
  • Strategies for multiplying signed numbers.
  • Every quotient of integers (with non-zero divisor) is a rational number.
  • If p and q are integers, then -(p/q) = (-p)/q = p/(-q).
  • The decimal form of a rational number terminates or eventually repeats.

Skills

Students are able to:
  • add rational numbers.
  • Subtract rational numbers.
  • Represent addition and subtraction on a number line diagram.
  • Describe situations in which opposite quantities combine to make 0.
  • Find the opposite of a number.
  • Interpret sums of rational numbers by describing real-world contexts.
  • Show that the distance between two rational numbers on the number line is the absolute value of their difference.
  • Use absolute value in real-world contexts involving distances.
  • Multiply and divide rational numbers.
  • Convert a rational number to a decimal using long division.

Understanding

Students understand that:
  • finding sums and differences of rational numbers (negative and positive) involves determining direction and distance on the number line.
  • Subtraction of rational numbers is the same as adding the additive inverse, p - q = p + (-q).
  • If a factor is multiplied by a number greater than one, the answer is larger than that factor.
  • If a factor is multiplied by a number between 0 and 1, the answer is smaller than that factor.
  • Multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers.
  • Integers can be divided, provided that the divisor is not zero.
Mathematics (2019) Grade(s): 7

MA19.7.8

Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.

Unpacked Content

UP:MA19.7.8

Vocabulary

  • Rational numbers
  • Integers
  • Estimation

Knowledge

Students know:
  • techniques for converting between fractions, decimals, and percents.
  • Techniques for estimation, mental computations, and how to assess the reasonableness of their answers.

Skills

Students are able to:
  • convert between different forms of a rational number.
  • Add, subtract, multiply and divide rational numbers.-translate verbal forms of problems into algebraic symbols, expressions, and equations.
  • Use estimation and mental computation techniques to assess the reasonableness of their answers.

Understanding

Students understand that:
  • One form of a number may be more advantageous than another form, based on the problem context.
  • Using estimation strategies helps to determine the reasonableness of answers.

Phase

During/Explore/Explain
Learning Objectives

Learning Objectives

The student will solve real-world problems involving rational numbers.

The student will use a digital number line to solve real-world problems.

Activity Details

Students will explore using a digital number line to solve real-world problems that include rational numbers. The digital number line offers many settings that include negative values, decimals, integers, and fractions. Students will work through an example problem with detailed instructions to become familiar with how to change the settings on the number line. Students are then provided five additional problems to complete. Optional number line settings are included for each problem. Have each student complete the first problem independently. At this point, the teacher should conduct a Think-Pair-Share with the class. Each student should have a partner. Ask the students to work with their partners to compare their two number lines to determine if the models and number sentences are the same or different. Allow each group to share their results and reasoning with the rest of the class. Students can then answer the remaining questions using their digital number line. Since the digital tool can create a link to share their number lines, the students can easily send this information to the teacher. For an extension or additional practice, students can be asked to write their own real-world problems and then create a model for their problem. The problems could also be exchanged with other classmates.

Assessment Strategies

Assessment Strategies

Have students complete an exit slip explaining if they found the digital number line helpful while solving the word problems.

Through the link provided from the student, evalute the student's digital number line used to solve the real-world problem.

Variation Tips

During the Think-Pair-Share the teacher can display the number line models the students designed and allow them to explain the different ways they built their number lines. 

The teacher can also allow students to write their own word problems with given parameters and allow students to exchange problems to solve.

Background and Preparation

Background / Preparation

Visit the Digital Number Line Tool to become familiar with how to use the tool. 

Students will need online access to the digital number line.

Copy the “Using Number Lines to Model Real-World Problems” student response page.

Digital Tools / Resources

Math Learning Digital Number Line
https://apps.mathlearningcenter.org/number-line/

Approved Date

Owner (Author)

kdockery
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