Lesson Title: Equality Grade Level: 1st Brief description of you classroom: My classroom has 11 students with various special needs. There are no aides or paraprofessionals in the classroom. The students range in both age and grade. The grade levels in my class are between 1st-3rd. Of the 11 students, 6 have autism, 1 student has cerebral palsy, and the other 4 students have dyslexia, or other phonological disorders.

Learning Central Focus

Central Focus

What is the central focus for the content in the learning segment?

The central focus of this lesson is to have the students gain a better understanding of the equal sign. In order to do this, the students will be challenged in their knowledge of the equal sign, and put in a position to challenge their existing conceptions of the equal sign. This is an important skill to learn because often student’s misconceptions of the equal sign “limit students’ ability to learn basic arithmetic ideas with understanding” (Carpenter, 2003, p.9). The student will be challenged to answer true/false number sentence questions as well as general number sentence questions to develop their conceptions of equality. An example of the problems that will be solved in this lesson is 8+4=[ ]+5

Content Standard

What standard(s) are most relevant to the learning goals?

CCSS.MATH.CONTENT.1.OA.B.3Apply properties of operations as strategies to add and subtract.2 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.)

Student Learning Goal(s)/ Objective(s)

Skills/proceduresWhat are the specific learning goal(s) for students in this lesson?

Concepts and reasoning/problem solving/thinking/strategies

Skills/Procedures The students will be able to compare two sides of the equal sign by carrying out the calculations on each side of the equal sign.

Concepts and reasoning/problem solving/thinking/strategies The students will be able to recognize that the equal sign represent a relationship between two equal numbers. The students will be able to understand the Commutative property of Addition.

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What are the specific learning goal(s) for students in this lesson?

Prior Academic Knowledge and Conceptions

What knowledge, skills, and concepts must students already know to be successful with this lesson?

What prior knowledge and/or gaps in knowledge do these students have that are necessary to support the learning of the skills and concepts for this lesson?

The prior academic knowledge that these students will need for this lesson is basic addition skills. The students should have already mastered the following common core standard:

CCSS.MATH.CONTENT.1.OA.A.1Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Some of the students may need manipulatives during this lesson to solve some of the addition problems with larger sums. These gaps will be address by providing each table with paper, pencil, and manipulatives so that the students have variety in the ways they would like to some the addition problems.

Common Errors, Developmental Approximations, Misconceptions, Partial Understandings, or Misunderstandings

What are common errors or misunderstandings of students related to the central focus of this lesson?How will you address them for this group of students?

There are many common errors and misconceptions that will be addressed throughout this lesson. The first misconception that will be address in this lesson is that a+b=c is the same as c=a+b. The students may say that it is not correct because it if “backwards”. This misconception will be addressed by discussing what a+b equals. After solving this, I will ask the students if c=c.

Another common misconception will have to be addressed is when solving 8+4=[ ]+5. The Thinking Mathematically textbook states, “fewer than 10 percent of students in any grade gave the correct response of 7.” (Carpenter, 2003, p.9) Many of the student swill answer the question with either 12 or 17. This misconception will be addressed when discussing the equal sign, and how each side must equal the same number. The students will be asked questions like “If 8+4=12, does 12+5 also equal 12?” Asking questions, and having a classroom wide discussion on these topics will “provide a basis for considering alternative perspectives of the meaning of the equal sign.” (Carpenter, 2003, p.15)

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Instructional Strategies and Learning Tasks

Launch

How will you start the lesson to engage and motivate students in learning?

3 minutes

I will start the lesson by asking the students what they believe it means when two things are equal. I will have a few students share their responses with the class.

Example student responses:

“when two things are equal they are the same”

“they are the same size”

Instruction

What will you do to engage students in developing understanding of the lesson objective(s)?

How will you link the new content (skills and concepts) to students’ prior academic learning and their

15 minutes

The lesson will include a series of 6 true/false and calculations number sentences. The students will be asked these questions as a means to develop their understanding of equality. The students will be given white boards, and will be asked to work together as tables to come up with the correct responses. Throughout the lesson, I will call on specific students who struggle with mathematics to determine if they understand the concepts.

The lesson will begin by writing the number sentence 7=4+3 on the board. The students will be asked if this statement is true or false. A typical student response may be that it is backwards. Some students may say that it is false, because it is backwards.

I will then write the question 3+4=3+4 on the board. I will then ask the students if this is true of false. A typical student response may be that it is true because the numbers are the same. For example, a student may say that the 3 is in the front of both sides, therefore it is true.

I will then ask if this equation is true or false: 3+4=4+3. I will ask this question to gauge if they are grasping an understanding of the commutative property of addition. Some students may respond that it is false, because the numbers are switched around. We will then as a class solve the equation on both sides to get 7=7. I will ask the

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personal/cultural and community assets?

What will you say and do? What questions will you ask?

How will you engage students to help them understand the concepts?

What will students do?

How will you determine if students are meeting the intended learning objectives?(must reference research supporting EBPs)

students if 7=7 is true or false. At this stage of the lesson, I will have the students give reasons why 7=7 is true. I will then tell the students that when they see an equal sign then they have to make the two sides have the same value or number.

Once we have briefly discussed equality, I will write the equation 8+4=[ ]+5 on the board. I will give each student a white board and marker. I will ask each student to come up with the number that needs to go in the box. The most typical student responses will be 12 or 17. We will then have a class discussion about how to get the correct answer. We will solve the question 8+4 to get the answer 12. I will then ask the students if we need to make [ ]+5 also equal 12, then what do we need to do to solve the problem. The students will talk as table groups to discuss possible strategies. We will then, as a class, determine that 7 is the answer that needs to go in the box.

During this lesson, the students are trying to reach equality benchmarks. The benchmark that the students are working toward in this lesson is Equality Benchmark 3. This benchmark is found in “Thinking Mathematically: Integrating Arithmetic &Algebra in Elementary School”. “The third benchmark is achieved when children recognize that the equal sign represents a relation between two equal numbers. At this point they compare the two sides of the equal sign by carrying out the calculations on each side of the equal sign.” (Carpenter, 2003, p.19) I will determine if the student is meeting the learning objective by using informal observation. Throughout the lesson, I will walk around the classroom to check student work. For students who are struggling with the concepts, the teacher will provide extra support during the structured practice and application portion of the lesson. During the classroom instruction and discussion, I will also be asking divergent thinking questions as a form of informal assessment. Using divergent thinking questions as a form of assessment “provides information about the child’s ability to formulate new ideas and produce a variety of responses.” (Sattler, 1988, p.354) The types of divergent thinking questions I will be asking are planning elaboration questions. These questions occur when a “child is asked to detail the steps needed to make a briefly out-lined plan work.” (Sattler, 1988, p.356) For this lesson in particular, after providing a correct or incorrect response, then the students will be asked to explain their step on how they were able to come up with that answer.

Structured Practice and Application

7 minutes

This section of the lesson will include asking two follow up questions. We will review these questions as a class

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How will you give students the opportunity to practice so you can provide feedback?

How will students apply what they have learned?

How will you determine if students are meeting the intended learning objectives?

to provide extra support to the students who may still need reinforcement. The two questions I will ask are: 9+1=[ ]+2 and 6+3=[ ]+2. The students will be asked to solve these questions independently first. As the students are working on each question, the teacher will walk around to monitor the students’ work. Once each student has put up a thumb to tell me they have completed the work then we will review and discuss the answer as a class. Having these two problems that are the same type of problems as the ones provided in the instruction phase of the lesson will show if the students are able to apply their learning.

I will determine that the students are meeting the learning objectives if they are able to make and use calculations to come up with the correct number for the empty boxes. The students should be able to make the two sides of the equation equal the same number.

Closure

How will you end the lesson?

5 minutes

The lesson will end with independent practice. The students will be given three more questions to answer independently with little to no teacher support to determine if the students have mastered the skill. The three questions that will be administered are:

1. 10+5=[ ] +62. 4+8=[ ]+93. 3+7=[ ]+8

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Differentiation/ Planned Support

How will you provide students access to learning based on individual and group needs?

How will you support students with gaps in the prior knowledge that is necessary to be successful in this lesson?

(must reference research supporting EBPs)

Whole Class:This lesson is a whole group lesson. “Whole-group instruction establishes common understanding and a sense of community for students by sharing discussion and review.” (Tomlinson, 2001, p.5) The lesson is rooted in classroom discussion, and allowing student’s to work together and share ideas in order to increase their knowledge of equality.

Groups of students with similar needs:During the lesson, I will informally assess the students’ abilities. From this assessment, I will be better able to “design learning experiences based on their best understanding.” (Tomlinson, 2001, p.4) I will groups together students who have mastered the benchmark, have demonstrated and emergent understanding of the benchmark, and the students who make little to no understanding of the benchmark. After forming these groups, I will work with each group at a later point in the week to continue working on the skills or to use their knowledge of the skill and apply it to larger numbers.

For the students who master the skill with the smaller numbers, we will work on accomplishing the equality benchmark 4, and then go on to working with larger numbers. The 4th benchmark requires that the student be able to “compare the mathematical expressions without actually carrying out the calculations.” (Carpenter, 2003, p.20) Sample questions for this group may include:

1. True/False 25+25=26+242. 36+24=373. True/False 37+86=39+844. 67+49=70+465. True/False 583-529=83-29

For students who are emergent on the skills, we will work on similar problems until the students are able to master benchmark 3. Sample questions for this group may include:

1. 10+2=[ ]+32. True/False 8+8=7+93. 3+9=[ ]+84. 6+7=7+65. 5+3=[ ]+4

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For students who show little to no understanding of the objective, we will work further on benchmarks 1 and 2. Benchmark 1 requires that students to “be specific about what they think the equal sign means or represents.” (Carpenter, 2003, p.19) Benchmark 2 requires that the student gain an understanding that a number sentence may not be in the form of a+b=c.

Individual students:I know of at least two individual students in my classroom that will need support with the prior knowledge that is needed to be successful in this lesson. These two students struggle with the concept of addition. They are able to add using manipulatives, but I have been focusing on teaching the students to use the strategy of counting on to add. For these two students, I will make sure that they have enough manipulatives and counting blocks on their table so they are able to be successful with the lesson.

Students with IEP’s or 504 plans:All of the students in my classroom have an IEP, but because we are in a private school, we are not required to follow IEP goals. Although we are not required by the state to follow IEP goals, my classroom is set up to provide small group and individual support to any and all students who may be unsuccessful with certain lesson or skills.

Strategies for responding to common errors and misunderstandings, developmental approximations, misconceptions, partial understandings, and/or misunderstandings:For this lesson, most students will demonstrate misunderstandings and misconceptions in the beginning stages of the lesson. It is important, that through classroom discussion, students are able to develop a better understanding of equality. For students who still demonstrate misunderstanding and misconceptions at the end of the lesson, then I will work at individual and small group levels to get the student to reach specific equality benchmarks.

Student Interactions

How will you structure opportunities for students to work with partners or

The students are currently in mixed ability groups at their tables. There are three tables in the room. Each table had 3 or 4 students. The tables are structured so that there are at least one high level student, one mid level student, and one lower level student at each. During the instruction section of the lesson, students will work together at their table groups. The students will be given opportunities to discuss their opinions and ideas with the peers at their table, before sharing them with the whole class.

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in groups? What criteria will you use when forming groups?

What Ifs

What might not go as planned and how can you be ready to make adjustment?

In a class with 11 students with special needs, there is always a possibility of the lesson not going as planned. There is always a possibility of a meltdown or anything. I will handle these behaviors as I do on a regular basis. The student will be asked to stop the inappropriate behavior, and then the other students and I will practice extinction. We will ignore the behavior until it stops or until it becomes such a distraction, that the student will be removed from class.

Theoretical Principles and/or Research–Based Best Practices

Why are the learning tasks for this lesson appropriate for your students?

(must reference research supporting EBPs)

The learning tasks for this lesson are appropriate because the standard is grade level appropriate for the mathematics level that the students in my class work at. The math content standards “define what students should

understand and be able to do in their study of mathematics.” (Mathematics Standards) Along with the common core content standard, this lesson also covers equality benchmarks. These benchmarks are important for students to understanding, because “inappropriate generalizations about the equal sign that children make and often persist in defending are symptomatic of some fundamental limits in their understanding of how mathematics ideas are generated and justified.” (Carpenter, 2003, p.23) The equality benchmarks, although students may not proceed through them in the same order, are in developing students understanding of the equal sign, and in turn will increase the likelihood that these students can be successful in algebra. “A limited conception of what the equal sign means is one of the major stumbling blocks in learning algebra.” (Carpenter, 2003, p.22) I want the students in my classroom to one day carry their understanding of the equal sign with them to middle and high school, so they can be successful in higher level math classes.

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Materials

What materials does the teacher need for this lesson?

What materials do the students need for this lesson?

Teacher Materials: Board Marker Question list

Student Materials: White Board Expo Marker Paper Pencil Assessment Worksheet Counting/Adding Manipulatives

Description of what the teacher (you) will be doing and/or what the students will be doing.

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Academic Language Demand(s):What language function do you want students to develop in this lesson? What must students understand in order to be intellectually engaged in the lesson?

I want the students to further develop their listening and speaking skills in large and small group settings. In order to be successful with this lesson, the students will need to be able to understand that they cannot all speak at once. In a discussion, only one person can speak at once. They also must remember to give everyone in their groups a turn to speak and share their opinions. It will also be a very great lesson to improve the students listening skills. When the other members of their group or class are speaking, then they will have to listen closely. Paying very close attention to what is being said is very important for this lesson, because so they need to understand what their peers are trying to add to the discussion.

What content specific terms (vocabulary) do students need to support learning of the learning objective for this lesson?

The content specific vocabulary word for this learning objective is equality. The term equality refers to and understanding that two sides of an equal sign have the same numerical value.

What specific way(s) will students need to use language (reading, writing, listening and/or speaking) to participate in learning tasks and demonstrate their learning for this lesson?

The specific way that the students will be using language is through their speaking and listening skills in the classroom discussion. The students will use their listening skills with the other members of their group or class is sharing their ideas. Each student will have to remember that they cannot all speak at the same time. They will have to practice taking turns to share their thoughts and ideas. Another listening skill that will be important for this lesson is making sure not to share the same idea that another student has already shared. Paying attention and making sure not to repeat the same ideas over and over again. The students will be using their speaking skills when sharing their ideas with their group or class. They will have to ensure that they have a complete thought to share with the class.

What are your students’ abilities with regard to the oral and written language associated with this lesson?

A majority of the students in my class are proficient enough in oral language to be successful in this lesson. There are three of my students with autism that may struggle with the oral language capabilities to be successful with this lesson. Two of the students use television quotes to speak. If a television quote, or phrase that they have heard before does not apply to the conversation, then they do not speak. The other student with autism struggles with his listening skills. He often repeats ideas that were discussed in the conversation earlier.

How will you support students so they can

I will support the students by walking around and probing questions during small group discussions. I will also remind the students before they begin small group discussion time to make sure that they remember

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understand and use the language associated with the language function and other demands in meeting the learning objectives of the lesson?

to let each person get a turn, to listen closely when another person is talking, and not to talk while another person is talking.

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Assessments:Type of assessment(Informal or Formal)

Description of assessment Accommodations to the assessment so that all students could demonstrate their learning.

Evaluation Criteria - What evidence of student learning (related to the learning objectives and central focus) does the assessment provide?

Informal This assessment will be done through observation and probing questions during large and small group discussions. For this assessment, the students should be able to tell me about their understanding of the equal sign. Questions the students will be asked are:

“What is an equal sign? What is on either side of an equal sign? Can the two numbers on each side of the equal sign be different?”

Students who are not able to formulate a response in a whole group or small group setting will be aloud to answer privately. I will also provide students with extra time, if it is required for them to be able to formulate a correct response to the questions.

Being about the answer these informal assessment questions correctly demonstrates a knowledge and understanding of the following learning objective:

The students will be able to recognize that the equal sign represent a relationship between two equal numbers.

Informal This assessment will be done through observation and probing. The teacher will ask students questions both in large and small group settings to determine if the students can demonstrate understanding of the commutative property of addition. Examples of

Students who are not able to formulate a response in a whole group or small group setting will be aloud to answer privately. I will also provide students with extra time, if it is required for them to be able to formulate a correct response to the questions.

Being able to answer these informal assessment questions correct demonstrates a knowledge and understanding of the following learning objective:

The students will be able to understand the Commutative property of Addition.

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questions that will be asked are:

7=4+34+3=7

When given these equations, the student should be able to answer the question “Are these two equations the same? Do they equal one another? How? Why?”

Formal This assessment will be a summative worksheet to be administered at the end of the lesson. The assessment will include three equality questions that require the students to find a number that will fit in the box to make the two sides of the equation equal the same number. The three questions that will be on the assessment are:

1. 10+5=[ ] +62. 4+8=[ ]+93. 3+7=[ ]+8

Each student will be provided with manipulatives to help them with adding the numbers.

This assessment provides evidence that the student understands the concept of equality. To complete this assignment correctly, then the student would have to take what they learned during the discussion, and apply it to these three questions. In order to successfully complete this assessment, the student will have to demonstrate an understanding of the following learning objective:

The students will be able to compare two sides of the equal sign by carrying out the calculations on each side of the equal sign.

Describe the tools/procedures that will be used in this lesson to monitor students’ learning of the lesson objective(s). Attach a copy of the assessment and the evaluation criteria/rubric in the resources section at the end of the lesson plan.

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Analyzing Teaching

To be completed after the lesson has be taughtWhat worked?What didn’t?For whom?

I thought overall, that the lesson went very well. The students were very responsive and active in the classroom discussion. Even some of the more shy students spoke up and were attentive during the discussion.

One student spent the entire lesson playing with the blocks on the table instead of participating, but she is known to do this. I think it would have been best to not put blocks at her table as all of the students at her table can add without using the blocks. I think without the extra distraction, she would have focused more and participated better in the lesson and activity.

Adjustments

What instructional changes do you need to make as you prepare for the lesson tomorrow?

I think the only instructional changes I would make to this lesson would be to remove the blocks from the table that the distracted student was sitting at. She did not use the blocks for their intended use, instead she used them as a way to avoid her tasks.

Proposed Changes.

If you could teach this lesson again to this group of students what changes would you make to your

Whole class:The only change I would make to the whole group instruction with this lesson is to spend a little more time with the one student that was distracted.

Groups of students:I found that during the lesson I spent more time with one group than I did the other two. I did this because the other two groups were completing the questions successfully with no teacher intervention. The table that I had to probe and question a little more needed my assistance more than the other two tables. If I could do this lesson again, I would try to spend an equal amount of time trying to gage the students’ understanding at the other tables as well.

Individual students: The two students that I was concerned about not have the adequate prior knowledge of addition

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instruction? were actually very successful with this lesson. Allowing those students extra time and the ability to use their counting blocks allowed them to participate and be successful with the classroom discussion.

Justification

Why will these changes improve student learning?

What research/ theory supports these changes?

The biggest and only real change I would make to this lesson is to use extinction with the student that became distracted with the blocks. “Extinction involves the removal or withdrawal of the reinforcer responsible for maintaining behavior. In the classroom setting, the target behavior will be extinguished once the reinforcer has been withdrawn for a sufficient period of time.” (Shea & Bauer 2012, p. 53) I would use extinction through removing the distraction, and in turn increasing the student’s ability to stay focused on the task.

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References:

Carpenter, T., Franke, M., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school.

Portsmouth, NH: Heinemann.

Mathematics Standards. (n.d.). Retrieved March 31, 2015, from http://www.corestandards.org/Math/

Sattler, J. (1988). Assessment of children (3rd ed.). San Diego: J.M. Sattler.

Shea, T., & Bauer, A. (2012). Behavior management: a practicap approach for educators (10th ed.). Boston: Pearson.

Tomlinson, C. (2001). How to differentiate instruction in mixed-ability classrooms (2nd ed.). Alexandria, Va.: Association for

Supervision and Curriculum Development.

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Assessment:

Name:___________________ Date:___________

Equality Assessment

1. 10+5=[ ] +6

2. 4+8=[ ]+9

3. 3+7=[ ]+8

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