## Looking Back and Moving Forward

Pre-K-2
1

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.

To prepare, find a free graphing tool on the web that will allow you create a bar chart. A simple web search should return multiple viable results. Set up five activity stations. Divide the class into groups of four students and assign groups to stations. Encourage them to visit each of the stations during class time. [If you need more than five stations, you might choose to have more than one of any of the stations.] Since students will need more direction at Station 3, you may wish to introduce this to the whole class before beginning station exploration time.

Each student should roll one die and make a set with as many buttons as there are dots on the die. Then the group should work together to compare the sets and write all the subtraction sentences that are indicated by the four sets. Ask them to record the comparisons in pictures and in number sentences.

Provide each pair with two dice and twelve buttons. The children work in pairs to roll dice, make a set with that many buttons, and compare the sets. The pair with the most buttons in their set makes a tallying mark. After 10 rounds, the children compare their tallies; the one with the most tallies wins the game.

Help the students find a graphing tool. Using the class button data from Lesson 7, ask the students to make a bar chart. [You may want to describe the difference between labeling the chart and labeling the vertical axis.] Allow them to choose the colors for each bar. [When the chart is displayed, the number of students who wore each number of buttons appears at the top of each bar.] Ask the students to print their graph after they are satisfied that it displays the data correctly. Then ask them to compare the computer-generated graph with the graph they made with the sticky notes.

Distribute 10 buttons and a brightly colored sheet of paper to each pair of students. Have one student in each pair drop the buttons and count those that land on the paper. The other student will count those that land off the paper. After they compare the numbers, the student whose number is greater records the difference between the buttons that landed on the paper and the buttons that landed off the paper as his or her score for that round. The play continues until one player has 25 points.

Provide buttons and a Button Bingo Grid Activity Sheet to the players. Remind the players how to play the game (see Lesson 3). Then designate one player as caller.

After the children have had time at the stations, call them together and ask them to record in their journals what happened at their station.

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Teacher Reflection

• Which students met all the objectives of this unit? What extension activities are appropriate for those students?
• Which students did not meet the objectives of this unit? What additional instructional experiences do they need?
• Given a sum, can all students discover several sets of addends for that sum?
• Can students explain the commutative property in their own words?
• Can students model finding differences using both the “take way” and the comparison mode?
• Can students identify the three (or two) members in a fact family?
• Can students explain in their own words the role of zero in addition and in subtraction?
• Can students answer comparison questions using a bar graph?
• What were the greatest challenges for the students?
• Which portions of this unit plan were the students most motivated to complete? Why?
• How can I help students to continue to focus on the important ideas in this set of lessons?
• What other learning experiences or manipulatives will help students explore addition and subtraction?
• How might I connect the ideas of this unit with lessons with similar mathematics content?
• What learning experiences would help students not yet comfortable with these concepts?
• What did I learn about the students while I taught this unit?
• When should I revisit or extend the key ideas of this unit?

### 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.

### More and More Buttons

Pre-K-2
Students use buttons to create, model, and record addition sentences. They also explore commutativity in addition contexts.

### 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.

### Learning Objectives

Students will:

• Review the models for subtraction.
• Practice subtraction in a variety of formats.

### 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, Counting & Cardinality

• CCSS.Math.Content.K.CC.A.2
Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

-Kindergarten, Counting & Cardinality

• CCSS.Math.Content.K.CC.A.3
Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).

-Kindergarten, Counting & Cardinality

• CCSS.Math.Content.K.CC.C.6
Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.

-Kindergarten, Counting & Cardinality

• CCSS.Math.Content.K.CC.C.7
Compare two numbers between 1 and 10 presented as written numerals.

-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.

-Kindergarten, Algebraic Thinking

• CCSS.Math.Content.K.OA.A.5
Fluently add and subtract within 5.

-Kindergarten, Measurement & Data

• CCSS.Math.Content.K.MD.B.3
Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

• 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.B.4
Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.

• 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.OA.C.6
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

• CCSS.Math.Content.1.OA.D.7
Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

• CCSS.Math.Content.1.OA.D.8
Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _.

• CCSS.Math.Content.1.NBT.B.3
Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

• 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.OA.B.2
Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

• CCSS.Math.Content.2.NBT.A.4
Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

• 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.

• CCSS.Math.Content.2.MD.B.6
Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

• 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.

• CCSS.Math.Content.3.OA.B.5
Apply properties of operations as strategies to multiply and divide. Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative property of multiplication.) 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication.) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56. (Distributive property.)

• CCSS.Math.Content.3.MD.B.3
Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step ''how many more'' and ''how many less'' problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.