Illuminations: Begin With Buttons

Begin With Buttons

Lost Buttons

In this lesson and the following one, students investigate subtraction more directly, beginning with the easier “take away” mode. They model “take away” subtraction with buttons and write subtraction sentences. They also work with the additive identity (0) as an addend and as a difference and find missing addends.

Learning Objectives
 
Students will:
  • determine the results of removing sets
  • review the term “difference”
  • investigate subtracting zero and subtracting all
  • find a missing addend

Materials
 
Number cubes
Buttons
Sums to 10 Chart
Shirts Template
Crayons

Instructional Plan

Call seven students to the front of the room and roll a number cube to decide how many will return to their seats. Have a volunteer record on the board the subtraction equation the students acted out. Repeat with different sets of seven students. Then ask zero students to sit down and call on a volunteer to record the sentence 7 – 0 = 7. Finally, ask all seven students to sit down and ask a volunteer to record the number sentence 7 – 7 = 0 where all can see it. Have the students identify the difference in each number sentence.

Ask the students whether they have ever lost a button. [At this point you may wish to read Corduroy by Don Freeman. In this story, a stuffed bear lost a button.] Now group the students in pairs and give each pair a bag of buttons, two number cubes, and a copy of one of the Shirts Template. Tell them to put six to 10 buttons on the shirt, and then take some buttons away as if the buttons had been lost. Ask them to make a record of how many they started with, how many they “lost” and how many were left.

Call attention to a chart with columns you have labeled “Number of Buttons,” “Number Lost,” and “Number Left.” Display a shirt with six buttons and roll a number cube to see how many buttons to take away, for example, two buttons. Then demonstrate how to enter this information in the chart. For example, 6 (written in purple), 2 (written in red), and 4 (written in blue).

Next ask the students to create new entries for the chart and to record them under their picture of the shirt using the colors modeled on the chart. When they are ready, help them enter their findings on the class chart. Then ask them what would be recorded if they started with 7 buttons and took 7 away. Repeat with a model for 7 – 0. Prompt them to add entries to the chart. Now call on a volunteer to write each row of the chart as a subtraction sentence.

To help the students become more familiar with the “take away” model for subtraction, ask them to choose a row of the chart and make up stories about lost buttons using the numbers in that row. [Some children may need to use manipulatives to complete this task.] Then demonstrate how to use the Sums to 10 chart to find the answer when they know the sum and one addend. [Find the red addend. Go across the row until you get to the sum. Then go up the column to find the other addend.]

At the end of the lesson, ask children to choose one of the number sentences derived from the chart. They should draw a shirt with buttons on it and cross some out to illustrate one subtraction fact. Remind the students to write the number sentence under the picture. The drawings would make an appropriate entry for their mathematics portfolio.

Questions for Students
 

What happens when we take away four buttons from seven buttons? Can you show that with these buttons?

Which difference on our chart was the greatest? If we use only 10 buttons, do you think we could get a larger difference? How?

What would be the smallest difference we could get with eight buttons? How would you get it?

Suppose you had five buttons. What would the difference be if you lost two buttons? If you lost zero buttons? How about if you lost five buttons?

Look at the chart we made. How did someone get a difference of five? Did anyone get a difference of five another way?

Can you draw a picture to show that you had seven buttons and lost three of them?

If you know there are seven buttons on a shirt and you can only see three of them, how many can’t you see?

Show me how to use the Sums to 10 chart to find the addend that’s missing when the sum is six and one addend is two.

Assessment Options
 
  1. At this stage of the unit, it is important for students to know how to:

    • model “take away” subtraction using the set model
    • identify differences and addends
    • recognize the effect of subtracting all and subtracting zero
    • find a missing addend

Teacher Reflection
 
  • Which pairs of students worked effectively together? Which pairs should be reconfigured?
  • Which students did not meet the objectives of this lesson? What caused them particular difficulty?
  • Can most of the students justify the difference when one addend is zero? Can they justify a difference of zero?
  • Can most of the children use the addition chart efficiently?
  • Which children met all the objectives of this lesson? What are appropriate next steps for them?
  • What parts of the lesson went smoothly? Which parts should I change the next time that I teach this lesson?

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. Count with understanding and recognize "how many" in sets of objects.
  4. Use multiple models to develop initial understandings of place value and the base-ten number system.
  5. Understand the effects of adding and subtracting whole numbers.
  6. Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.
  7. Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
  8. Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.
  9. Develop fluency with basic number combinations for addition and subtraction.

References
 
  • Freeman, Don. Corduroy. New York: Puffin Books, 1968.
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
© 2000 National Council of Teachers of Mathematics
Use of this Web site constitutes acceptance of the Terms of Use

The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest quality for all students. The views expressed or implied, unless otherwise noted, should not be interpreted as official positions of the Council.