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Shirts Full of Buttons

Number and Operations
Grace M. Burton
Location: unknown

Students explore subtraction in the comparative mode by answering questions of “How many more?” and “How many less?” as they match sets of buttons. They also make and discuss bar graphs based on the number of buttons they are wearing.

Ask the students to count the number of buttons they are wearing, and write that number on a small sticky note. Then draw on the board the outline of a bar graph, with the vertical axis labeled in numbers up to twelve, and the horizontal axis labeled “Number of Buttons.” Label the graph “Number of Buttons We Wore Today.” Call on students to place their sticky notes in the column that shows the number of buttons they are wearing. [As they place the notes, be sure the first note in each column lies on the horizontal axis and that the bottom of each succeeding note touches the top of the last note in that column.]

299 Histogram

When the students are ready, encourage them to pose questions that can be answered from the graph, such as how many of us had on five buttons? How many more students had on six buttons than had on three buttons today? How many fewer of us had on four buttons than had on two buttons today? Ask the students to make a copy of the graph. [It will be used in Lesson 8, Looking Back and Moving Forward.]

pdficonShirts Template

Next display two copies of the Shirt Template and put six buttons on one shirt and four buttons on the other shirt. Ask the students how the number of buttons on the shirts could be compared. Repeat with other addend pairs. Then model a subtraction problem in which two sets are compared. For example, if Joan’s shirt has five buttons and Sue’s shirt has three buttons, how many more buttons does Joan’s shirt have? How many fewer buttons are on Sue’s shirt?

Display a large piece of chart paper where all the students can see it. Point out the columns you have labeled “Buttons on the Smiley Face Shirt,” “Buttons on the Starburst Shirt,” and “Difference.” Call on a volunteer to enter the sum, one addend, and the difference on the chart.

Next give each pair of students the template with two shirts, buttons, and a piece of paper for a work mat. Now have the students pose and answer comparison questions.

Begin by helping students model a comparison in which a set of three and a set of four are compared. [If students have difficulty comparing, have them add buttons to the shirt with less buttons until the shirts have the same number of buttons. Then suggest that the students circle the added buttons and count them.]

Next, encourage the students to make up other comparison situations using any numbers they wish. Call on students to share their problems. Finally, ask what would be recorded if both shirts had seven buttons [7, 7, 0]. Prompt the students to add other such entries.

You may wish to suggest that the students record in pictures and in equation form one of the comparing problems for their portfolios.

Assessment Options

  1. At this stage of the unit, it is important for students to know how to:
    • model comparison subtraction using the set model
    • identify differences and addends
    • recognize the effect of subtracting all and subtracting zero
    • construct and make inferences from a bar graph
  2. The Questions for Students may assist you in understanding your students’ level of attainment of the concepts in this lesson.
  3. As you reach the final lesson in this unit, it may be useful to consider how much individual students have grown, and to use this information to plan strategies for remediation and extension activities. This would also be a good time to ask individual students to talk with you about the entries in their unit portfolios.
Move on to the last lesson, Looking Back and Moving Forward.

Questions for Students 

  1. Can you show how to compare the number of buttons on two shirts? 
  2. Which difference on our chart shows that one shirt had five buttons and the other had three buttons? 
  3. If you compared a shirt with seven buttons and another with seven buttons, what would be the difference? 
  4. If you compared a shirt with seven buttons and another with zero buttons, what would be the difference? 
  5. If you had a shirt with four buttons, how would you make a shirt with three more buttons? With three less buttons? 
  6. Suppose you had a shirt with five buttons. How many buttons would have to be on another shirt so that there is a difference of two? Is there another answer?

[7 and 3 are equally valid answers.]

Teacher Reflection 

  • Which students are able to compare sets and record the differences?
  • Which students need additional instruction and practice on the objectives of this lesson?
  • Can most of the students find the difference when one addend is zero? Can they find it when the addends are the same?
  • 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?
ButtonTrains ICON
Number and Operations

Button Trains

In this lesson, students describe order by using vocabulary such as before, after, and between. They also review and use both cardinal and ordinal numbers.
Number and Operations

Many Sets of Buttons

Students classify buttons and make disjoint and overlapping Venn diagrams. In an extension, they make and record linear patterns.
HowManyButtons ICON
Number and Operations

How Many Buttons?

In this lesson, students review classification, make sets of a given number, explore relationships between numbers, and find numbers that are one more and one less than a given number. They apply their knowledge of classification as they play a game similar to bingo.
MoreAndMoreButtons ICON
Number and Operations

More and More Buttons

Students use buttons to create, model, and record addition sentences. They also explore commutativity in addition contexts.
NumbersManyWays ICON
Number and Operations

Numbers Many Ways

Students work with subtraction at the intuitive level as they explore number families and ways to decompose numbers to 10. They will also identify members of fact families. (A fact family is a set of three [or two] numbers that can be related by addition and subtraction, for example: 7 = 4 + 3, 7 = 3 + 4, 7 - 4 = 3, and 7 - 3 = 4. When the number is a double, there are only two members of the fact family. An example would be 10 - 5 = 5, and 5 + 5 = 10.)
LostButtons ICON
Number and Operations

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.
Number and Operations

Looking Back and Moving Forward

This final lesson of the unit reviews the work of the previous lessons through a variety of activity stations, one of which involves using an interactive graphing tool. Students model with buttons and record addition and subtraction.

Learning Objectives

Students will:

  • Explore the results of comparing sets.
  • Review the term “difference.”
  • Construct and make inferences from a bar graph.

NCTM Standards and Expectations

  • Count with understanding and recognize "how many" in sets of objects.
  • Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.
  • Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections.
  • Use multiple models to develop initial understandings of place value and the base-ten number system
  • Understand the effects of adding and subtracting whole numbers.
  • Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.
  • Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
  • Develop fluency with basic number combinations for addition and subtraction.
  • Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.

Common Core State Standards – Mathematics

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.1
    Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.2
    Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Grade 1, Algebraic Thinking

  • CCSS.Math.Content.1.OA.C.5
    Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

Grade 1, Number & Operations

  • CCSS.Math.Content.1.NBT.C.4
    Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

Grade 1, Measurement & Data

  • CCSS.Math.Content.1.MD.C.4
    Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Grade 2, Number & Operations

  • CCSS.Math.Content.2.NBT.B.7
    Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Grade 2, Measurement & Data

  • CCSS.Math.Content.2.MD.D.10
    Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

Common Core State Standards – Practice

  • CCSS.Math.Practice.MP4
    Model with mathematics.
  • CCSS.Math.Practice.MP5
    Use appropriate tools strategically.