ELED 433 LESSON PLAN FORMATJMU Elementary Education Program

A. Addition and Subtraction practice with ten-frames and dice

B. CONTEXT OF LESSON What pre-assessment did you do that tells you the students’ readiness and/or interests?

I actively pay attention to the students as they complete math assignments given out by their current teacher. I have noticed that certain students appear to be struggling in certain areas, and the current number sense activities are easy for the other students. Every morning, they have a “math idea,” which is a slip of paper with a math problem (often a story problem) that they need to figure out and illustrate. I watch them as they work and check their work when they are finished to see if they answered correctly, and whether it was done mentally or drawn our physically.

They have worked with ten-frames before, and a lot of them struggle with filling out the dots in the right order (starting at the top left and ending at the bottom right). I’m not sure if we need to be strict about that, but Mrs. Edwards is. Doing addition is easy for most of the class, so this is a review activity. Some students still struggle with telling which numbers are represented in the ten-frames. Subtraction is also a struggle for most of the class. This tells me that they need more practice in subtraction, and they are ready for more difficult addition problems.

Why is this an appropriate activity for these students at this time? How does this lesson fit in the curriculum sequence (consider vertical and horizontal planning)?

Vertical Planning: Explain where this lesson fits within the related prior and subsequent grade level standards.

o My lesson about strategies fits right in with related prior grade level standards because ever since kindergarten, these students should have been learning all about numbers and the patterns they make. They built on that knowledge when they learned to add and subtract, and in subsequent grade levels, they will use this practice to learn more multiplication and division and more complicated things.

o In 1st grade, they already had to learn basic addition facts, up through sums of 18 (SOL 1.6).

o In 3rd grade, they will need to move on to multiplication and division (SOL 3.5), so this lesson will give them a firm grasp of addition and subtraction as a foundation. The ten-frames also introduce some division concepts by the way numbers are divided into different sections of the ten-frame.

Horizontal Planning: Explain where this lesson fits within the ongoing unit and within the school year.o My lesson in using ten-frames to develop addition and subtraction strategies will fit

right in with the flow of the school year. They have done a 5-week unit on number sense (place value, rounding, comparing, ordinal numbers, and skip counting), and another unit on addition and subtraction facts, inverse relationships, and equality. My lesson is a review of that, helping them practice addition and subtraction facts and develop strategies. They are currently starting a unit on geometry and patterns, and the ten-frames is another way to practice patterns. Next they will have a unit on money, and addition and subtraction skills are very necessary for that.

How does this lesson fit with what you know about child development (developmentally appropriate practice and learning progressions)?

o Children at this age still may need direct modeling. They need to see it before they can do it. By this stage they should have good number sense and decent cardinality. Some may still need to count the numbers out loud or on their fingers in order to add or subtract.

o Learning Progressions: in levels of justification, my students most often use “Restating the Conjecture” to justify something. They are best at pictorial representation.

o Throughout this semester, they have been doing a lot of work with the 100’s chart, and place value. So they should have a good grasp of numbers up through ten. But showing those numbers as dots on a ten-frame may be new to them, so it will be a good way to challenge them.

C. RELATED VA SOLs and/or CCSS (include both mathematical content and processes/practices) Also include cross-curricular connections – look at the standards for other content areas for ways to make connections across the curriculum.

CCSS:CCSS.Math.Content.2.OA.A.1 Use addition and subtraction within 100 to solve one- and two-

step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (This process progression deals with direct modeling.)

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

CCSS.Math.Content.2.OA.C.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

CCSS.Math.Content.2.OA.C.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

SOL: “Computation and Estimation” 2.5 The student will recall addition facts with sums to 20 or less and the corresponding

subtraction facts. 2.6 The student, given two whole numbers whose sum is 99 or less, will

a) estimate the sum; andb) find the sum, using various methods of calculation.

2.7 The student, given two whole numbers, each of which is 99 or less, willa) estimate the difference; andb) find the difference, using various methods of calculation.

2.8 The student will create and solve one- and two-step addition and subtraction problems, using data from simple tables, picture graphs, and bar graphs.

2.9 The student will recognize and describe the related facts that represent and describe the inverse relationship between addition and subtraction.

This lesson also relates to Science SOL 2.1. But not all of the following will be included in the lesson. Only the bold sections will be addressed.SOL 2.1 The student will demonstrate an understanding of scientific reasoning, logic, and the nature of science by planning and conducting investigations in which

a) observations and predictions are made and questions are formed; (when students roll the dice and form their own number sentences)

b) observations are differentiated from personal interpretation; c) observations are repeated to ensure accuracy; (double-checking problems)d) two or more characteristics or properties are used to classify items; e) length, volume, mass, and temperature are measured in metric units and standard English

units using the proper tools; f) time is measured using the proper tools; g) conditions that influence a change are identified and inferences are made;

h) data are collected and recorded, and bar graphs are constructed using numbered axes; i) data are analyzed, and unexpected or unusual quantitative data are recognized; j) conclusions are drawn; (writing answers)k) observations and data are communicated; (filling out worksheet)l) simple physical models are designed and constructed to clarify explanations and show

relationships; and (ten-frames, dice)m) current applications are used to reinforce science concepts.

D. LEARNING OBJECTIVESUnderstand – what are the broad generalizations/concepts the students should begin to develop? (These are typically difficult to assess in one lesson.)

Know – what are the tools, vocabulary, symbols, etc. the students will gain through this lesson? (These “knows” must be assessed in your lesson.)

Do – what are the specific thinking behaviors/procedures students will be able to do through this lesson? (These will also be assessed in your lesson.)

The student will understand: Mental and representational

strategies for addition and subtraction.

Regrouping is a process of renaming a number to make subtraction easier.

The student should know: Certain terms imply joining,

and certain terms imply separating, but there are always exceptions. I will not be teaching key words, but I will use their chart on the wall that shows general patterns in story problems.

The student should be able to: Recall and write the basic

addition facts for sums to 20 or less and the corresponding subtraction facts, when addition or subtraction problems are presented horizontally or vertically.

Use various strategies to compute mentally.

Develop fluency in recalling addition and subtraction facts.

Combine numbers in various ways in order to develop flexible methods of adding/subtracting.

E. ASSESSING LEARNING How will you assess student learning of the objectives? What type of assessment will you use

and why? Remember – every objective must be assessed for every student!

Objective AssessmentWhat documentation will you have for

each student?

Data CollectedWhat will your students do and say,

specifically, that indicate every student has achieved your objectives?

Develop fluency in recalling addition and subtraction facts

Worksheet Answer the ten-frame flash game faster at the end of the lesson than at the beginning

Combine numbers in various ways in order to develop flexible methods of adding/subtracting

Worksheet Use dice to find different combinations of numbers

Recall and write the basic addition facts for sums to 20 or less and the

Worksheet Perform addition and

corresponding subtraction facts, when addition or subtraction problems are presented horizontally or vertically

subtraction problems vertically on paper

Use various strategies to compute mentally

Worksheet Answer the ten-frame flash questions without writing on paper

F. MATERIALS NEEDED

Worksheets (supplied by myself, see last page of lesson)10-frames, dice, mini white boards, and expo markers (supplied by Mrs. Edwards)

G1 ANTICIPATION OF STUDENTS’ MATHEMATICAL RESPONSES TO THE TASK(S) POSED IN THE PROCEDURE PORTION OF THE LESSONSelect the mathematical task(s) for this lesson.o I will flash the ten-frames to the students and they will have to quickly say the number represented.o Then I will ask them addition and subtraction questions, such as, “take away 3 from this number.”o Then they will illustrate some given subtraction and addition problems by filling in ten-frames.Anticipate students’ strategies and mistakes as they work on the task(s) in the lesson. What valid strategies might students use? What mistakes would make sense and indicate a misconception? This section is one of the practices for orchestrating productive mathematics discussions: Anticipating. o Some students may get confused by the different combinations on the ten-frames. They may try to

count the dots one-by-one, rather than looking for patterns.o Sometimes students think the top row has 6 dots, instead of 5.

G2 PROCEDUREInclude a DETAILED description of each step, including how you will get the students’ attention, your introduction of the activity, the directions you will give students, the questions you will ask, and appropriate closure. Write exactly what you will SAY and DO. Think of this as a script.

BEFORE: Engagement - How will you prepare students to be ready to engage with the main task/activity? (see pp. 26 of your 3-5 text).In your procedure, be sure to address the 3 Before Phase Teacher’s Agendas:

Get students mentally prepared for the task. Be sure the task is understood. Establish clear expectations for products.1. State my behavioral expectations: I expect you all to listen to instructions, and only speak when you raise

your hand AND I call on you.2. Introduce Quick Images game with the ten-frames: You all have seen these before! Let me see how well you

remember them. I am going to show you some cards really quick, and you get to tell me the number. (Sometimes these students think the top row has 6 dots, instead of 5, so I will clarify that through questioning before starting.)

3. Now let’s add a rule to this game. Now the rule is ADD 3. (Write it on the board.) You get to tell me what the number is, plus 3. (Show 5-8 cards with rule #1.)

4. The next rule is SUBTRACT 2. You get to tell me what the number is, minus 2. (Show 5-8 cards with rule #2.)5. (If I find that the ten-frames are too easy during whole group or small groups, I can have them come up with

a related fact or even a story problem for two of the ten frame cards...if they see a 5 and a 7, they can come up with the missing number, either a 2 or a 12, and create a story problem using the 5, 7, 12 (addition problem) or the 5, 7, 2 (subtraction problem.) This may also reinforce the objective of joining and separating concepts.)

6. Introduce the worksheet (explain terms “addend” and “sum”).

7. Introduce the dice game by modeling it on the board (students can work in partners or individually. Each student gets a mini white board, expo marker, and two dice. They roll the dice, and write an equation that adds the dice up. When they have gotten 11 different sums (numbers 2-12), they can move up to 3 dice.)

8. (They usually split into 3 groups for math and rotate through stations, so today they will do two stations for my lesson [dice game and worksheet], and another with Mrs. Edwards on the new lesson. I will give them 15-20 minutes per station. When a student has finished his worksheet or white board, he/she may come to me and I’ll show them some related math games on IXL on the computers, or I’ll show them the Ten-Frame Go Fish.)

DURING: Implementation – this is the time when students are either working independently or in small groups and you are conferring with students. (see pp. 26 of your 3-5 text)In your procedure, be sure to address the 4 During Phase Teacher’s Agendas:

Let go! Listen actively. Provide appropriate hints but not solutions. Provide worthwhile extensions. (Encourage testing of ideas.)1. My groups will take turns doing the worksheet and playing the dice game, and moving on to the math games

on the computer or Ten-Frame Go Fish if they finish early.Part of listening actively is one of the practices for orchestrating productive mathematics discussions: Monitoring. In your procedure, explain how you will monitor student strategies to prepare for the After phase.

AFTER: Engage the full class in discussion; encourage students to evaluate the ideas; look for opportunities to highlight significant ideas in students’ work to make these mathematical ideas more explicit to all students. (see pp. 26 of your 3-5 text).In your procedure, be sure to address the 3 After Phase Teacher’s Agendas:

Promote a mathematical community of learners. Listen actively without evaluation. Summarize main ideas and identify future problems.

Part of creating a mathematical community of learners in the after phase involves 3 practices of orchestrating productive mathematics discussions: Selecting & Sequencing & Connecting. In your procedure, explain how you will use your anticipating and monitoring of student strategies to select, sequence, and connect student strategies.

1. Recap on the floor by the rocking chair: What did you learn from using the ten-frames? What was the hardest part? What was the easiest part? Do one more rule with the ten-frames: add 4.

H. DIFFERENTIATIONDescribe how you have planned to meet the needs of all students in your classroom with varied interests and readiness levels. How will you differentiate your lesson – by content, process, or product? Include a specific differentiation plan. Use the learning progressions to support your decisions.This connects to your During Phase Agendas: providing appropriate hints and extensions.

Content Process Product

InterestThe students are

interested in figuring out how numbers work.

They are interested in the process of drawing shapes and patterns.

The students will appreciate having a written product, their own filled-in

ten-frames.

They have worked several times with ten-

They have been using the hundreds chart to

solve addition and

They are ready to have more

independent work,

Readinessframes this

semester, so most students

should fly through the activities.

subtraction problems, so they are familiar with the

process of adding and subtraction.

so perhaps we won’t spend as

much time orally as doing seatwork.

I. WHAT COULD GO WRONG WITH THIS LESSON AND WHAT WILL YOU DO ABOUT IT?Think about this specifically for THIS lesson plan. This CANNOT include fire drills, interruptions due to announcements, weather, or other emergencies. 1. The students could finish their worksheets and/or dice games in less than 15 minutes, so I will have

other activities they can work on in that case. Suggestions:- They can play a 10-frame card game (a version of Go Fish that they have played before in class)- Do a seatwork review (Ms. Edwards suggested fact families: they are given the 3 numbers on top, and fill in the rectangle)- Do a bunch of different games that practice addition and subtraction and finding the pattern

2. Some students may get confused by the different combinations on the ten-frames. They may try to count the dots one-by-one, rather than looking for patterns. To prevent this, I will point out some patterns in the beginning. And after flashing the cards (before moving on to addition and subtraction), I could ask them to tell me how they were able to tell what number was there.

3. Sometimes students think the top row has 6 dots, instead of 5, so I will clarify that in the beginning as well.

4. Some students may find the ten-frames to be too easy. In that case, I can have them come up with a related fact or even a story problem for two of the ten frame cards...if they see a 5 and a 7, they can come up with the missing number, either a 2 or a 12, and create a story problem using the 5, 7, 12 (addition problem) or the 5, 7, 2 (subtraction problem.) This may also reinforce the objective of joining and separating concepts.

Addend + Addend = Sum Name: _________________

Find any two addends that complete the equation.

_______ + _______ = 1_______ + _______ = 2_______ + _______ = 3_______ + _______ = 4_______ + _______ = 5_______ + _______ = 6_______ + _______ = 7_______ + _______ = 8_______ + _______ = 9_______ + _______ = 10

_______ + _______ = 11_______ + _______ = 12_______ + _______ = 13_______ + _______ = 14_______ + _______ = 15_______ + _______ = 16_______ + _______ = 17_______ + _______ = 18_______ + _______ = 19_______ + _______ = 20

Illustrate these problems by filling in the empty ten-frames.

+

= 18

+

= 13

+

= 9

Lesson Implementation Reflection & Assessment Analysis

As soon as possible after teaching your lesson, think about the experience. Use the questions/prompts below to guide your thinking. Be thorough in your reflection and use specific examples to support your insights.

1. What actually happened in your lesson? Cite examples of dialogue or student work. How did your actual teaching of the lesson differ from your plans? Describe the changes and explain why you made them.

The ten-frame problems were much easier for the class than I expected. So I went more quickly through those than I had planned. At first, I had them raise their hand to answer each question. But this wasn’t involving everyone, so I decided to have them think of the answer in their heads, raise their hand, and wait until I say “go” to whisper it as a class. This way they weren’t all shouting at once.

The rule for the dice game about getting 11 different sums was confusing, so instead I told them to make 5 equation with 2 dice, then make 5 equations with 3 dice, and then if they still had time, make 5 equations with 4 dice.

On the worksheet, one student figured out that he could just add 0 for each number, so I told them they could only use 0 in the first equation ( ___ + ___ = 1 ), and not in the rest of them.

2. Analyze your assessment data.

a. Sort your assessment data based on where students lie in the continuum to mastery of the learning objectives. Which students have mastered the learning objectives? Which students are approaching mastery? Which students have similar misconceptions? Look for patterns among student responses that demonstrate particular areas of need.

Mastery: About 8 of the students seem to have really mastered the learning objectives intended for this lesson. They sped through the worksheet and got all the answers correct. In section 1 of the worksheet, 3 of these students used the “1 plus” strategy (simply adding one to the previous sum), 3 of them used the “10 plus” strategy (writing “10 + __” for sums 11-19), and 4 of them used the “doubles” strategy (adding the two halves for every even sum). These strategies demonstrate that they have really mastered the concepts and are able to find patterns in the problems. For section 2 of the worksheet, 3 of them filled in extra spaces on the top ten-frame (see the left side of the picture below) rather than starting on the second ten-frame (see the right side of the picture below). This is not what I intended for the students to do, but my instructions were not clear enough to avoid this, and it still helped them reach the right answer. The fact that these students realized they could do this demonstrates an advanced understanding of ten-frames and addition.

Approaching Mastery: About 7 students are approaching mastery of the learning objectives. They took a little longer with the worksheet and dice game, but got most problems correct. I noticed some of the same patterns as with the “mastery” group, but just not as prevalent. Several students made mistakes on the second half of section 1. 2 of them used the “1 plus” strategy, 2 of them used the “10 plus” strategy, and 2 of them used the “doubles” strategy. Many of them struggled with section 2, filling in too many or not enough dots. 2 of them filled in extra dots as explained above.

Don’t Quite Understand: About 5 students still don’t quite understand the learning objectives. 3 of them didn’t finish most of the worksheet. I suspect it was due to language issues for one student, and due to attitude/lack of motivation for the other two students. There were not many patterns in this group, but 2 students did use the “1 plus” strategy.

b. Describe overall what the analysis of assessment data reveals to you about students’ understanding, knowledge, and skills relative to the learning objectives.

As this was a review activity, I expected more of the students to master this content, but the assessments show that many of them were still struggling.

c. Describe instructional groups that emerge from your analysis.

Pattern Group 1: “Ready to Generalize”Number of students: 8Distinguishing characteristics: They understand the basic concepts and found patterns. Completed worksheet quickly and correctly. Many students used the strategies 1 plus, 10 plus, doubles, and filling out the extra spaces in the ten-frames. In the dice game, they were very excited to use more than 2 die.Sample responses:

Pattern Group 2: “Conceptual Gaps”Number of students: 7Distinguishing characteristics: Some noticed patterns. Took longer to complete worksheet. Got most problems correct, but some mistakes, especially on the second half of section 1. Some students used the strategies 1 plus, 10 plus, doubles, and filling out the extra spaces in the ten-frames. Many of them struggled with section 2, filling in too many or not enough dots.Sample responses:

Pattern Group 2: “Calculation Error”Number of students: 5Distinguishing characteristics: Did not quite understand the directions. 3 students didn’t even get halfway through the worksheet. 2 students used the plus 1 strategy. 1 student wrote the numbers next to the ten-frames in section 2 to help her concentrate.Sample responses:

3. Analyze your teaching strategies.

a. Based on your assessment data, how effective were your teaching strategies for helping students meet the learning objectives? Justify your analysis using the assessment data.

My teaching strategy of using visuals (ten-frame card) was effective because it got all the students engaged during whole group. It helped the students who may have been confused to understand my expectations based on what other students answered. Using hands-on games (the dice game) was effective because it got the students excited to make equations and therefore really think about what the correct sum would be. Most of them were really excited to use as many dice as they could. Leaving the option for myself to walk around the classroom helping whichever students need help was very effective because some students knew what they were doing and others needed me to explain the instructions 3 or 4 times. When too many students needed help, I paired them up and told them to help each other. This was great because some students really understand better when they explain it out loud to someone else.

b. Describe at least one way you could incorporate developmentally appropriate practice in a better or more thorough way if you were to teach this lesson again.

I know that these students have done lots of work with addition and subtraction, so if I taught this lesson again, I could have them work more on subtraction, since they seem to need practice in that area.

c. Use these reflections and your teaching experience to revise your lesson plan. Highlight the revisions and include this revised lesson plan in your Phase 5.

(See the rest of this document.)

4. Based on your analysis of assessment data and teaching strategies, write a lesson plan for “the next day” using the ELED 433 lesson plan format. You may have the same, similar, or different learning objectives. Be sure that your During Phase includes a small-group activity for each group described in section 2c. This will also be your differentiation plan based on readiness. These small group activities should be structured to help diverse groups of students…

…achieve the same UKDs with appropriate degrees of support and challenge, …correct the misconceptions revealed by the assessment, and …feel involved in equally respectful tasks.

(See document NEXT DAY Lesson Plan)

5. As a result of planning, teaching, and analyzing this lesson, what have you learned or had reinforced about young children as learners of mathematics?

The idea that young children love hands-on activities and games with the whole class was reinforced.

6. As a result of planning, teaching, and analyzing this lesson, what have you learned or had reinforced about teaching?

This lesson reinforced my realization that lessons do not always go as planned, and students often think of correct or incorrect ideas that I never would have predicted.

7. As a result of planning, teaching, and analyzing this lesson, what have you learned or had reinforced about yourself?

I learned that I use the phrase “ok, so” a little too much when I am in front of the class.

8. How did your experience planning, teaching, and reflecting on this lesson impact your progress toward your goal as a mathematics teacher?

I feel like a lot more planning went into this lesson than was necessary. It is difficult to be motivated to write an entire new lesson plan for that next day that I will never even implement. But the first part of the reflection did help me learn how to analyze and categorize student assessments.