## More and More Buttons

Pre-K-2
1

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

To review rational counting and to prepare for the exploration of addition, distribute a bag of buttons and one number cube to each student. Ask the students to roll their number cube and then make a set with as many buttons as the number of spots showing on the number cube. Ask for volunteers to say the number in their set of buttons and then write it. Now tell the students to make a set of one more and one less button than the set they first made.

Group the students into pairs and give each pair two number cubes, a bag of buttons, and a strip of paper. Ask them to fold the strip in half, and then color one side of the paper red and the other side blue.

Display a class chart that is labeled “Number of Buttons on the Red Side,” “Number of Buttons on the Blue Side,” and “Number of Buttons in All.” Now ask the students to each roll a number cube and make a set containing the same number of buttons as there are spots showing on the number cube, with one student placing his or her set of buttons on the red side of the chart and the other student placing his or her set on the blue side. Then ask them to determine how many buttons they have when they join the two sets together.

To make the joining action more obvious, assign one student in each pair to place his or her hands around the two sets and say “whoosh” while bringing both sets of buttons together. On scrap paper, the other student writes in red the number of buttons on the red side, in blue the number of buttons on the blue side, and in purple the number of buttons in all. Then have the students switch roles. Repeat several times.

When they have identified several sums, help each group to enter two or three of their findings on a class chart. After the students have made their entries, ask them to give examples of the terms “addend” and “sum.” Call on a volunteer to read one row of the chart. Then call on other volunteers to read other rows. Next demonstrate how to write the entries on the chart as addition sentences. Encourage the students to record a few of their “whooshes” as addition sentences.

3 + 4 = 7

Now ask the students to put three buttons on the red side of their paper and four buttons on the blue side. Ask them to whoosh them together and record the addition sentence that tells what they did, using red and blue numerals for the addends and purple for the sum. Next, ask them to put four buttons on the red side and three buttons on the blue side and to predict how large the set will be when they whoosh the two sides together. Ask them to use red, blue, and purple numerals to write the addition sentences.

3 + 4 = 7     4 + 3 = 7

Repeat with other number pairs until the students are comfortable with the idea that order does not matter when they are joining two sets and recording the results.

Ask the students to choose one of the rows from the chart and draw a picture illustrating that number fact, writing under it the addition sentence that the picture illustrates.

Then distribute a copy of the Sums to 10 Chart to each student and ask the students to find the addends they just used, putting one finger on each addend. Demonstrate how they can bring their fingers together on the sum. [Note that the addends and sum are color coded to match the chart they worked with earlier.] Now ask them to find the same addends in the other color and see if they get the same sum. Now have several children use their drawings and the Sums to 10 chart to explain the commutativity property in their own words. You may wish to display the drawings in the classroom or in a more public place before adding the records to their portfolio.

• Buttons
• Number cubes
• Scrap paper
• Strips of paper
• Sums to 10 Chart
• Red, blue, and purple crayons or markers

Assessment Options

1. At this stage of the unit, it is important for students to know how to:
• model addition using the set model
• recognize and use the order principle
2. Because young children often have difficulty putting their understandings into words, encourage them to demonstrate what they are thinking with objects and pictures first. The guiding questions listed above may assist you in understanding your students' level of knowledge, but others may suggest themselves as you talk with your students.
Extension
Move on to the next lesson, Numbers Many Ways.

Questions for Students

1. How can you show you are joining two sets?
2. How many buttons are on the red side of this sheet? On the blue side? How many in all?
3. Which sum on the classroom chart was listed first? What addends were used to get it?
4. Which sum on the Sums to 10 chart was the greatest? Which pairs of addends were used to get it?
5. Which pairs of addends on the Sums to 10 chart were used to get 8? 5?
6. Look at this row. Does any other row have the same sum? Are the addends the same?
7. Would you get the same sum if you had two buttons on the blue side and five on the red side as you would if five were on the blue side and two were on the red side? Can you show why?

Teacher Reflection

• Were all students able to model the addition of sets?
• Could they record the addition in a number sentence?
• Did they use the terms “addend” and ‘sum” correctly?
• Are all students able to explain in their own words the commutative property of addition?
• Did some students exhibit special strengths? Did some students exhibit reluctance to participate? Why?
• Which students met all the objectives of this lesson? What extension activities are appropriate for these students?
• Which students did not meet the objectives of this lesson? What misconceptions did they demonstrate?
• What parts of the lesson went smoothly? Which parts would I change the next time that I teach this lesson?

### Button Trains

Pre-K-2
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.

### Many Sets of Buttons

Pre-K-2
Students classify buttons and make disjoint and overlapping Venn diagrams. In an extension, they make and record linear patterns.

### How Many Buttons?

Pre-K-2
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.

### Numbers Many Ways

Pre-K-2
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.)

### Lost Buttons

Pre-K-2
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.

### Shirts Full of Buttons

Pre-K-2
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.

### Looking Back and Moving Forward

Pre-K-2
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:
• Model the addition of set.
• Use the terms “addend” and “sum.”
• Explore the Commutative Property of Addition.

### NCTM Standards and Expectations

• Connect number words and numerals to the quantities they represent, using various physical models and representations.
• 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.
• 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.

• CCSS.Math.Content.1.OA.B.3
Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

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

• 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.

• 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.

### Common Core State Standards – Practice

• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.
• CCSS.Math.Practice.MP8
Look for and express regularity in repeated reasoning.