Illuminations: Comparing Connecting Cubes

Comparing Connecting Cubes


Using the Number Line to Compare

In this lesson, students determine differences using the number line to compare lengths. Because this model is based on linear measurement, it is a distinctly different representation from the models presented in the previous two lessons. At the end of this lesson, children are encouraged to predict differences and answer puzzles involving subtraction.

Learning Objectives
 
Students will:
  • use the number line model to find differences by comparing lengths
  • solve and create puzzles using the number line

Materials
 
Chalk
Connecting cubes in two or more colors
Crayons
Group Short and Long Trains Activity Sheet
Sample Number Line

Instructional Plan

Make a chalk number line on the floor. Children will find differences on a number line by hopping from a given number toward 0. Inform the students that they will now use the number line to compare lengths. Ask one student to hop to the “5,” and another to hop to the “3.” Then ask, “Who hopped farther? How much farther?” Repeat with other students.

 

 

Next draw a number line with the spaces one cube apart and construct a train with 9 connecting cubes and another with 5 cubes. (This part of the lesson explores the meaning of “how many more?” by encouraging students to model trains and towers with different numbers of cubes.) Ask the following questions:

  • How many more connecting cubes are in the train with 9 cubes?
  • How can we find out using the number line?

 

Encourage the students to align the longer train with the left end of the number line. Then place the shorter train on top of it. Demonstrate how to “hop” a counter from 9 backward to 5, counting the hops aloud. Have the children record the comparison using the equation notation [9 – 5 = 4] on a copy of the Group Short and Long Trains Activity Sheet.

To forestall any misconceptions, highlight the fact that in this model, the spaces are counted, not points on the number line. After several trials, show the children that they do not need to place the trains on the number line but can mark the length with a crayon or marker that is same color as is the train.

Then put the students into pairs and give each pair connecting cubes in two colors as well as crayons and one number line. Ask each partner to make a train in a different color, draw its length on the same number line in the appropriate color, and then compare the lengths on the number line to find the difference. Ask the students to record the comparison in pictures and in equation form. After allowing time for exploration, call the students together to read their equations and share their number line illustrations.

As a concluding activity, pose puzzles such as “I am thinking of two numbers on the number line that have a difference of 5. The larger number is 6. What is the other number?” If the students are ready for a challenge, you might say only “I am thinking of two numbers on the number line that have a difference of 5. What are the two numbers?” You may wish to have the students create and share similar problems.

Questions for Students
 

How would you use the number line to compare two trains, one of which is 5 cubes long and the other 3 cubes long?

What numbers have a difference of 2? Can you find some of them on the number line?

What would be the difference of two trains that were the same length?

How would you explain to a friend how to compare lengths on the number line?

Assessment Options
 
  • Although the guiding questions above may assist you in understanding your children’s level of knowledge, others may suggest themselves as you watch the children at work. You may find it helpful to add to your recordings on the Class Notes Sheet that you began earlier in this unit. This data may be helpful as you plan strategies for regrouping children and for remediation or extension activities.

    • Teacher Reflection
     
    • Which similarities did students notice?
    • Which differences did students notice?
    • What other learning experiences would enable students to compare properties of concrete objects and would also be important to the students?
    • What additional learning experiences do students need?

    NCTM Standards and Expectations
     
    Number & Operations Pre-K-2
    1. Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.
    2. Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections.
    3. Understand the effects of adding and subtracting whole numbers.
    4. Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.
    5. Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
    6. Develop fluency with basic number combinations for addition and subtraction.
    This lesson prepared by Grace M. Burton.
      
    1 period   

    NCTM Resources

    Principles and Standards for School Mathematics
    National Council of Teachers of Mathematics Thinkfinity Verizon Foundation
    More and Better Mathematics for All Students
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