Ffformal Review 3224 Clinical Assignment Template 2

Clinical Assignment You will • Plan a lesson that addresses the development of students’ conceptual understanding of some mathematical topic. • Teach the lesson, collect, and analyze the student work samples. • Use the rubric to score the student work samples. Look for patterns of similar issues that a small group of 3 students display. Identify a targeted learning objective/goal for these 3 students. • Plan and teach a re-engagement lesson to those 3 students. At least one student should have specific learning needs, for example, a student with an IEP or a gifted student. • Analyze the student work collected from the re-engagement lesson and describe the effectiveness of the instruction.

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Identify the standard that your teacher will be addressing and paste it below. If you’re not yet sure of the standard, identify the topic. 2.NBT.7 How to add 3-digit numbers using a strategy NC2.NBT.7 Add and subtract, within 1000, relating the strategy to a written method, using: • Concrete models or drawings • Strategies based on place value • Properties of operations • Relationship between addition and subtraction Pick a task and include it here.

Students will work with a partner to solve a three-digit addition problem on the board using a strategy learned in class.

Anticipate the variety of ways students might go about solving the task. Use the Unpacked Standards to help you, if necessary. Students may use the break down method, number line, manipulatives, a hundred chart, drawing images, use expanded form, and solving the equation as it was. They could use concrete models or drawings, strategies based upon place value, properties of operations, and relationship between addition and subtraction.

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What are the concepts that are being addressed by this task? Some possible examples: • The equal groups meaning of multiplication • The “times as many” meaning of multiplication • The relationship between multiplication and addition • The relationship between multiplication and division • The partitive meaning of division; the measurement meaning of division • Place value (particularly with multi-digit calculations or decimal calculations) • The distributive property (decomposing factors in order to multiply) • The associative property (adding numbers in whatever order is easiest) There are many other possibilities. What concepts are being addressed in your task? Adding 3-digit numbers together and knowing the place value for each number. Student’s will be able to make sense of problems and

persevere in solving them. They will be able to reason abstractly and quantitatively while looking for and making use of structure. They will also be able to demonstrate mathematical knowledge through using different strategies to solve the equation and modeling the problem. 3. Construct viable arguments and critique the reasoning of others

What are the procedures students might use to solve your task? Some possible examples: • Multiplying by direct modeling, skip counting, repeated addition, derived facts, recall • Dividing by direct modeling repeated subtraction, using multiplication, recall • Multiplying multidigit numbers using array models, partial products, standard algorithm • Finding area or volume by counting, using repeated addition, using multiplication There are many other possibilities. What procedures are being addressed in your task? •

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Adding multidigit numbers using expanded form, a number line, concrete drawings, hundred’s chart, properties of operations, and other

strategies based upon place value.

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Develop a rubric to analyze the work sample (either use the Explore task work or a similar exit ticket). Your rubric must have conceptual understanding, procedural fluency and either problem solving or reasoning.

Conceptual understanding (showing that they understand what the operation means, the place values involved, being able to draw the picture to represent what is happening) Procedural Fluency (doing the calculations correctly) Problem solving (identifying the correct operations to match the problem) Reasoning (making a claim and providing evidence to support the claim).

Proficient _3_ pts Students show that they completely understand the place values involved using a strategy

Developing _2_ pts Students show that they somewhat understand the place values involved using a strategy

Beginning _1_ pts Students show that they barely or do not understand the place values involved using a strategy

Students correctly demonstrate procedural fluency Students correctly identify a strategy that correlates and solves the problem

Students demonstrate some understanding of procedural fluency Students somewhat identify a strategy that correlates and solves the problem

Students barely or do not demonstrate procedural fluency Students barely or do not identify a strategy that correlates and solves the problem

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Lesson plan 1 Subject: mathematics

Central Focus: Adding three-digit numbers

Common Core/Essential Standard Objective: NC2.NBT.7 Add

and subtract, within 1000, relating the strategy to a written method, using: • Concrete models or drawings • Strategies based on place value • Properties of operations • Relationship between addition and subtraction

Date submitted:

Date taught:

Daily Lesson Objective: Here, you want to look at the Standard and figure out which part of the Standard you are addressing. Write your objective making sure the verb is something observable. For example, students will solve… students will explain… Students will be able to add three-digit numbers by working with a partner to solve problems on the board using different strategies. Prior Knowledge: They must know how to add two-digit numbers and they need to know place value. They also need to have a basic knowledge of different strategies they can use to solve a problem.

Activity

Description of Activities and Setting Describe the Launch of the task here. In your plan, make sure that you • •

1. Engage

• •

activate prior knowledge make sure the context (or the story) and the question in the task are understood (paying attention to ELLs or students with special needs) establish clear expectations for what the students are to produce Address norms, roles and multiple strengths

Time

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Remember, that in this type of lesson, you are not modeling for students how to do the problem. You are giving them a problem and having them solve it. Then in the discussion, they will learn from each other because they will solve it in different ways...

Present this problem to the students: Ed and Tom were showing 345 with their materials. Ed showed 345 with 3 hundreds, 4 tens and 5 ones. Tom showed 345 with 3 hundreds, 3 tens and 15 ones. Allow students time to figure out the problem and justify their thinking about who was right. Give them the opportunity to discuss what they believe is the correct answer with a partner. Then allow students to share what they think is the correct answer and their reasoning behind it. Then have a student who had the correct answer explain why their answer is correct and show it on the white board. Possible questions to ask: ● Is there another way to show 345? ● Could you use an open number line to show 345? Teacher Note: ● If a group determines either Tom or Ed were correct, ask them to prove it to the class. ● When a group says, “They are both right,” allow them to justify their answer to the class. Describe the Explore Phase of the lesson here where students are working on the task and you are walking around asking questions and seeing what strategies they use. 2. Explore

First, identify what strategies you will be looking for. (Think about the four types of strategies: direct modeling, some by more advanced strategies like counting on (depending on the task), some will use their number sense by developing a "derived fact", and some will use known facts.) Show a detailed, completed strategy for each method. Also think about misconceptions students might have and incorrect strategies they might demonstrate.

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Then, make sure you answer each of the following questions: • How long will students work or what point will you want all students to get to? • What will you ask to find out what students are thinking? (In addition to general questions, look through the strategies you anticipated and think about whether there are questions specific to those strategies that you might want to ask) •

•

What will you do if some students are stuck? How will you help them without giving them the answer? (I usually ask them “What is the problem asking” or what are you understanding about the problem so far? Consider asking them to model the situation using manipulatives or posing a simpler problem. What will the groups that finish early do? How will you make the task a “high ceiling?”

Allow students to work with partners to solve the following problem: There are 251 girls and 328 boys in an elementary school. How could you show the total number of students in this school? ● Teacher will monitor the students’ work; asking appropriate questions. ○ How did you begin to think about this problem? ○ What will be your next step? ○ Tell me about the strategy you chose to solve the problem? ○ What is another way you could solve the problem? ○ What would happen if___? ● When partners have one strategy, ask them to decide on a second strategy to check their work. ● Allow students to join another group to check their answers. ● Create a list of the different strategies your group used to solve the problem. Students will get into partners to solve a problem that will be written on the whiteboard. They will be given 15-20 minutes to work on solving the problem using more than one strategy. If they have problems solving the problem with their partner, they can join another group to have them explain how to use a certain strategy to solve the problem.

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Plan the Discussion of the task here. Make sure to address the following: • How will you remind students of the norms of how to participate in a whole class discussion, both how to share and what to do when they are not sharing? • What solution paths do you want to have shared during the class discussion? In what order do you want the solutions presented? Why? • How will you notate the students' strategies to help make the thinking clear to other students? (or what would you look for in a students' written work or work with manipulatives to decide that you want that shared?) • What questions will you ask as students share to emphasize the key mathematical ideas that you want to come out of the discussion? • What connections or differences might students notice and how might you respond to their thinking? What connections do you want them to see? • What is the key idea you want to highlight at the end of the discussion?

3. Explain

Allow students to show different strategies on how they solved the problems and discuss using talk moves. Possible Strategies Possible Discussion Prompts Expanded form How is ____ strategy similar to ____ Base ten blocks strategy? Open Number line How is ____ strategy different from ____ Landmark numbers strategy? Create easier or known sums Why did you decompose your number in that way? Which strategy is most efficient? Explain why you think that. Allow students to ask questions for clarification. Students will be selected based upon the different strategies they used to solve the problem to come up to the white board and demonstrate the strategy they used and explain how they used it to solve the problem. They will act like the teacher and answer any questions the students may have about using that specific strategy. The student may reference the teacher for help if they cannot

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answer another student’s question. I want for the students to be able to see how all of these different strategies were able to get them to the right answer and they can use them if they need them to solve a problem.

4. Elaborate

5. Evaluate Assessment Methods of all objectives/skills

(optional) Develop some sort of follow up activity where students apply what they learned from the discussion. This can be done as a whole class, in groups, or individually. Students can create their own three-digit addition math problem where they have to use two different strategies to solve the problem. Then they have to show the correct answer by using those strategies. (we did not have time to do this.) Explain how you will assess students’ understandings of the key concepts addressed by the lesson. Informal assessments (also called formative assessments during the lesson) could be description of some of the questions you would ask while they work or during the discussion. (Just copy/paste them here even if you included them above) The teacher will walk around and listen to the student’s discussions with their partners. The teacher will ask these questions during their discussions and explanations:

○ ○ ○ ○ ○

How did you begin to think about this problem? What will be your next step? Tell me about the strategy you chose to solve the problem? What is another way you could solve the problem? What would happen if___?

Formal assessments (also called a formative assessment of the lesson) would be collecting students’ work on the Explore task, an exit ticket or an independent assignment Students will be evaluated on how they solve the equation, the work shown in their math journals, and how they explain their answer.

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Next, you will score all of the work samples with the rubric. Create a table that helps you find patterns. SAVE ALL YOUR WORK SAMPLES. Eventually you will turn in the work samples from the 3 focal students. Write a grade for conceptual understanding (CU), procedural fluency (PF), and either reasoning (R) or problem solving (PS) Student Student 1 Student 2 Student 3 Student 4 Student 5 Student 6 Student 7 Student 8 Student 9 Student 10 Student 11 Student 12 Student 13 Student 14 Student 15 Student 16 Student 17 Student 18 Student 19 Student 20 Student 21

Conceptual understanding score 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Procedural Fluency Score 3 3 2 3 3 3 3 3 2 2 3 3 3 3

Problem Solving or Reasoning Score 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Summary Table Rubric Score 1

Rubric Score 2

Rubric Score 3

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Conceptual understanding Procedural Fluency Reasoning

42/42

42/42

42/42

39/42 42/42

39/42 42/42

42/42 42/42

From your analysis of whole class student learning, identify one area where students tended to struggle mathematically. Select 3 student work samples that represent the struggles in this area. These students will be your focus students for this task. At least one of the students must have specific learning needs, for example, a student with an IEP (Individualized Education Program) or 504 plans, an English language learner, a struggling reader, an underperforming student or a student with gaps in academic knowledge, and/or a gifted student needing greater support or challenge. [The students all understood how to solve the problem without any issues, so I asked the students to solve the problem using more than one strategy. There were three students who had a little difficulty solving the problem using a different strategy from the one they used the first time. One of the students is on the autism spectrum and two of the students have ADHD.]

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]

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What do these 3 students’ errors tell you about their mathematical understanding? If they are having trouble showing conceptual understanding, what concept are they not understanding? If it is subtraction, for instance, are they not demonstrating that they understand what subtraction means, or are they having difficulty showing what occurs during regrouping? [These three students have a strong conceptual understanding and have a fairly strong procedural understanding, but the procedural understanding could improve. They know how to use a strategy to effectively solve the problem, but they need to develop a stronger understanding of different strategies to use incase another strategy is more effective than the one they are using. They hesitate when using a different strategy and they do not seem as confident when using another strategy.]

Based on your analysis of the focus students’ work samples, write a targeted learning objective/goal for the students related to the area of struggle. This should be different than your original objective from your lesson because it should target the issue the three students were demonstrating. [Students will be able to add three-digit numbers using more than one strategy that is different from their original strategy.]

Then you will plan a re-engagement lesson. You do not need a formal lesson plan for this lesson. Just describe the following: • • • • •

Targeted learning objective/goal NC Standard strategies and learning tasks to re-engage students (including what you and the students will be doing) representations and other instructional resources/materials used to re-engage students in learning assessments for monitoring student learning during the lesson (e.g., pair share, use of individual whiteboards, quick quiz)

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[Students will be able to add three-digit numbers using more than one strategy that is different from their original strategy Standard: NC2.NBT.7 Add and subtract, within 1000, relating the strategy to a written method, using: • Concrete models or drawings • Strategies based on place value • Properties of operations • Relationship between addition and subtraction The students and I will be talking about the problem we worked with the day before and discussing the all the strategies they could have used. Also discussing what is their favorite strategy and their least favorite strategy and why. Then we talked about them using a different strategy than their favorite one and highlighting what to do in each strategy. The students then solved a math problem using a different strategy than their original one and their favorite one. They used their math journals to write in their strategies and solve the problem. Once they solved the problem using more than one strategy then they explained how they used the strategies to solve the problem. They answered any of the questions the other students had about solving with that strategy. I assessed the students based upon their explanations of the strategies they used, and the work shown in their math journal.] Use a similar rubric to the first one in order to describe whether the focus students showed growth after your re-engagement lesson, in terms of your targeted objective.

Conceptual understanding (showing that they understand what the operation means, the place values involved, being able to draw the picture to represent what is happening)

Proficient _3_ pts Students show that they completely understand the place values involved using a strategy

Developing _2_ pts Students show that they somewhat understand the place values involved using a strategy

Beginning _1_ pts Students show that they barely or do not understand the place values involved using a strategy

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Procedural Fluency (doing the calculations correctly) Problem solving (identifying the correct operations to match the problem) Reasoning (making a claim and providing evidence to support the claim).

Students correctly demonstrate procedural fluency Students correctly identify a strategy that correlates and solves the problem

Students demonstrate some understanding of procedural fluency Students somewhat identify a strategy that correlates and solves the problem

Students barely or do not demonstrate procedural fluency Students barely or do not identify a strategy that correlates and solves the problem

[The three students all understood the information well and two of the students were able to demonstrate growth in their understanding of different strategies. The student on the autism spectrum was refusing to use any other strategy than his favorite one that he was used to. He would become extremely upset if I tried to get him to use a different strategy, so I let him use his original strategy and explain it to the other two students. The two other students were able to use the different strategies effectively and explain how to use them extremely well.]

SAVE WORK SAMPLES FROM YOUR RE-ENGAGEMENT LESSON. You will need to turn in samples from each of your focal students.

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Once you have completed your work at your school site, I will give you a chance to practice writing your commentary for your portfolio in the official templates. It will be a lot of cut and paste from this document, with some additional details.