Lesson 13

Tables and Double Number Line Diagrams

Lesson Narrative

In this lesson, students explicitly connect and contrast double number lines and tables. They also encounter a problem involving relatively small fractions, so the flexibility of a table makes it preferable to a double number line. Students have used tables in earlier grades to identify arithmetic patterns and record measurement equivalents. In grade 6, a new feature of working with tables is considering the relationship between values in different rows. Two features of tables make them more flexible than double number lines:

  • On a double number line, differences between numbers are represented by lengths on each number line. While this feature can help support reasoning about relative sizes, it can be a limitation when large or small numbers are involved, which may consequently hinder problem solving. A table removes this limitation because differences between numbers are no longer represented by the geometry of a number line.
  • A double number line dictates the ordering of the values on the line, but in a table, pairs of values can be written in any order. 5 pounds of coffee cost \$40. How much does 8.5 pounds cost? You can see in the table below how being able to skip around makes for more nimble problem solving:
weight of coffee (pounds) cost (dollars)
5 40
1 8
8.5 68

At this point in the unit, students should have a strong sense of what it means for two ratios to be equivalent, so they can fill in a table of equivalent ratios with understanding instead of just by following a procedure. Students can also always fall back to other representations if needed.

Learning Goals

Teacher Facing

  • Compare and contrast (orally) double number line diagrams and tables representing the same situation.
  • Draw and label a table of equivalent ratios from scratch to solve problems about constant speed.

Student Facing

Let’s contrast double number lines and tables.

Required Preparation

Make 1 copy of the The International Space Station blackline master for every 4 students, and cut them up ahead of time.

Learning Targets

Student Facing

  • I can create a table that represents a set of equivalent ratios.
  • I can explain why sometimes a table is easier to use than a double number line to solve problems involving equivalent ratios.
  • I include column labels when I create a table, so that the meaning of the numbers is clear.

CCSS Standards

Building On


Print Formatted Materials

For access, consult one of our IM Certified Partners.

Additional Resources

Google Slides

For access, consult one of our IM Certified Partners.

PowerPoint Slides

For access, consult one of our IM Certified Partners.