OLD Resources. The resources on this page have NOT yet been updated to align with the revised elementary mathematics TEKS. These revised TEKS were adopted by the Texas State Board of Education in 2005, with full implementation scheduled for 2006–07. These resources align with the original TEKS that were adopted in 1998 and should be used as a starting point only.

Clarifying Lessons

Grade 3: Related Number Pairs

Lesson Overview

Students use tables to organize and display related pairs of numbers, such as the relationship of the number of insects to the total number of legs.

Mathematics Overview

Students generate a table of related number pairs based on a real-life situation, identify patterns in the table, and use the patterns to extend the table to solve problems.

Set-up (to set the stage and motivate the students to participate)

  1. Begin by presenting a familiar situation from which you can create related number pairs (using counters to represent the objects in the situation): (3.7A, 3.15A) "Let's start with 1 bike. How many tires does TomÈ need? How many tires does TomÈ need with 2 bikes? If we write the number of bikes in a row such as 1, 2, 3, 4, 5, . . ., we can write the number of tires under it. [Demonstrate on the overhead or chalkboard.]

    number of bikes 1, 2, 3, 4, 5, . . .
    number of tires 2, 4, 6, 8, 10, . . .

    Or we can organize the lists into a table to show the related pairs of numbers:

    table of related pairs

    Sometimes we want to express this information in related number pairs, or what mathematicians call ordered pairs. The information in this problem can be written as {(1,2), (2,4), (3,6), (4,8), (5,10), . . .}. The number pairs show (number of bikes, number of tires)." (3.16B)

  2. Allow the groups time to discuss and explain their ideas. Each group should make sure everyone in their group understands the information. (3.15C)
  3. Ask, "If TomÈ wanted to buy 6 bikes, can we use the table to find out how many tires he needs to buy? How? Can we use the table find out how many tires he will need for 20 bikes? Can we find out without filling in the table up to 20? How?" Allow the groups time to discuss and explain their ideas. (3.15B, C, D)
  4. Ask, "Can someone use words or symbols to describe our pattern? (You add two of the number of bikes together to get the number of tires; or if you have 3 bikes, you add 3 twos together.) How can we write a description to use with the calculator to find how many tires are needed for 32 bikes? (32 + 32 or 32 x 2) How can we write a description to find the number of tires for any number of bikes?" (n + n or n x 2 where n = number of bikes). (3.6A, 3.7B, 3.16B, 3.17A)
  5. Read another situation aloud. For example, "A movie ticket costs $4.00. How much would it cost for two people to go to the movies? Three people? Four people? 10 people?" Have each group generate a table and a set of related number pairs to represent this situation and to share with the class. (3.7A)
  6. Have each group consider, "How can we describe the pattern? How can we use our description to find out how much it would cost for 40 people to go to the movies?" (3.6A, 3.7B, 3.16B, 3.17A)
  7. Continue with other related number pairs: (3.7A, B; 3.15A, B, C, D; 3.16B; 3.17A)
    • the number of sides in a shape compared to the number of angles in the shape
    • the number of feet in a measurement compared to the number of inches in that measurement
    • the number of people compared to the number of cars needed for a field trip
  8. Allow the groups time to share and discuss their lists of related number pairs. (3.16B)

Teacher Notes (to personalize the lesson for your classroom)

Guiding Questions (to engage students in mathematical thinking during the lesson)

  • How do the table and the ordered pairs help you find a pattern? (3.6A; 3.7A, B; 3.15C)
  • How are the numbers in the right-hand column of the table related to the numbers 1, 2, 3, 4, 5, . . . in the left-hand column? (3.6A, 3.7B)
  • Do the numbers increase? (3.6A)
  • Is it an addition pattern? (3.6A, 3.7B)
  • Is it a multiplication pattern? (3.6A, 3.7B)
  • Do the numbers decrease? (3.6A, 3.7B)
  • Is it a subtraction pattern? (3.6A, 3.7B)
  • Is it a division pattern? (3.6A, 3.7B)

Teacher Notes (to personalize the lesson for your classroom)

Summary Questions (to direct students' attention to the key mathematics in the lesson)

To uncover students' understanding of the relationships described by the number pairs, ask questions such as:

  • What does this set of related number pairs represent? (3.7A, 3.16B)
  • What pattern do you see in this set of number pairs? (3.6A, 3.7B)
  • How did you use the table to help you find the pattern? (3.7B; 3.15A, B)
  • How would you describe the pattern using words or symbols? (3.16B, 3.17A)
  • How can you use your description to make predictions about other number pairs that belong in the table? (3.7B, 3.17A)

Teacher Notes (to personalize the lesson for your classroom)

Assessment Task(s) (to identify the mathematics students have learned in the lesson)

  • Have students generate a set of related number pairs to fit a situation and explain its pattern. They can record their number pairs and explanation in their math journal.
  • Give students a set of related number pairs in a table and have them describe the pattern (or situation) that is represented by the numbers in the table.

Teacher Notes (to personalize the lesson for your classroom)

Extension(s) (to lead students to connect the mathematics learned to other situations, both within and outside the classroom)

  • Students can develop their own related number situations for their partners to solve.
  • Students can design a situation to fit a given set of related number pairs.

Teacher Notes (to personalize the lesson for your classroom)