LESSON PLAN OUTLINE JMU Elementary Education Program

Kacie Dixon Mrs. Shreckhise, 3rd Grade, Clymore Elementary December 3, 2013: 1:45p.m. Date written plan is submitted to teacher _____

A. TITLE OF LESSON – Math Monsters explore Equality and Inequality: I will begin the lesson by having coins in a cup and having them pull out coins in their right hand and left hand. I will have them lay the coins in two piles and decide which is greater. Once they decide which is greater, I will have them appropriately place the math monster between the quantities. I will then give the children thousands, hundreds, tens, and ones blocks to share with a partner to see which is bigger and using a math monster in between. Using math monsters, (popsicle stick creations of monsters shaped as <, >, = symbols) I will then have the children compare different numbers that I have written on each individual child’s whiteboard. The numbers will range from 0 to 9,999, meeting their SOL standard.

B. CONTEXT OF LESSON After observing my third grade class for a month now, I have uncovered their many interests. Their interests include hands on learning (which they are rewarded with after good behavior), working in small groups (because they love the interaction and being able to build off one another), and being able to express themselves creatively. My cooperating teacher has informed me that the class has already learned how to compare whole numbers using <, >, and =, but that the class will later learn how to compare fractions using the same symbols. Therefore, I will be doing a review lesson for the remedial math students in class so they are re-familiarized with the idea of equality and inequality. The students learned the symbols <, >, = in second grade, but only compared numbers as high as 999, now they are expected to compare numbers up to 9,999, as well as be able to compare fractions by the end of the year. In fourth grade the students will then be expected to compare numbers into the millions and to be able to compare decimals and fractions. Having the remedial math students review their knowledge on greater than, less than, and equal to and their correlating symbols will help the children be able to conquer harder related concepts like comparing fractions. My lesson will be developmentally appropriate because I am selecting students whose movement through the learning progression may be slower than their fellow classmates. The lesson will be appropriately challenging to support their development along the progression. The Math Monster activity will use numbers ranging from 0 to 9,999, which should be in this group of students zone of proximal development. Having the student first use chips to see how quantities differ is allowing the child to use a manipulative to compare, then having the student write out the statement on the whiteboard with the math monsters and then in their notebook using the appropriate

symbol allows them to use the abstract level of representation, the highest level. After the students successfully complete the various statements (ex. 7,891 > 7,198) I will have the children read it aloud to show their development of word by reading the symbol as greater than. Lastly, I will ask the student how they know they’re right in order to see their level of justification. C. UNWRAPPING THE VIRGINIA STANDARDS OF LEARNING

-Math SOL 3.1 The student will c.) compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, and equal to).

-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. (Reasoning and Proof- student will be able to explain to me why they know which is greater through Communication or Representation)

-English SOL 3.4 The student will expand vocabulary when reading f.) use vocabulary from other content areas

-Levels of Representation: Concrete-using manipulatives (chips, math monsters) Pictoral-children can draw pictures of quantities to help them solve problems Abstract-the children will reach this highest level of representation by fully understanding symbols (<,>,=)

D. LEARNING OBJECTIVES  

Understand Know Do Students will understand that numbers have values that can be compared to one another.

Students will know the symbols < means less than, > means greater than, and = means equal to when comparing two numbers.

Compare  two  whole  numbers  between  0  and  9,999  using  the  symbols  >,  <,  =.  

 E. ASSESS LEARNING

 Objective   Assessment  

What  documentation  will  you  have  for  each  student?  

Data  Collected  What  will  your  students  do  and  say,  

specifically,  that  indicate  every  student  has  achieved  your  objectives?      

U1:  Students  will  understand  that  numbers  have  values  that  can  be  compared  to  one  another.  

Through observation of a turn and talk with their partner, the students will explain how you can compare two numbers. I will record their answers on my assessment sheet. The students will answer questions like 5,470 is_greater_ 4,570 which can also be written as 5,470 _>_ 4,570 and then explain to me how they knew the answer.

Students will say “you can compare numbers by saying greater than, less than, and equal to” in their definition of comparing two numbers, as I record on my assessment sheet. Through me checking their answers on the worksheet and listening to how they knew the answer, it will show their individual understanding of less than and greater than. I will look for key words in their explanation such as, “5,470 has a greater value, 4,570 has a lesser value, I know that the bigger number is greater than the smaller number, and the greater than symbol looks like this >” I will record the

student’s response to how they knew the answer on my assessment sheet.

K1:  Students will know the symbols < means less than, > means greater than, and = means equal to when comparing two numbers.  

Through my observation of a group discussion the children will all answer what each symbol means and when to use it. Through the students answering my fill in the blanks of “< means____, > means____, and = means_____”

Each student will say “< means less than, > means greater than, and = means equal to” and will give me a number sentence example, as I record it on my own assessment sheet. Through checking their answers on the worksheet, will show their individual knowledge.

D1:  Compare  two  whole  numbers  between  0  and  9,999  using  the  symbols  >,  <,  =.  

Each student will fill out a worksheet created by me with number sentences to be completed using symbols and numbers.

The students individually completed and corrected the worksheet provided to them.

STRATEGIES USED BY STUDENTS:

One to one counting of manipulative

Drawing Math Monster

Number Line

Reading Aloud

Guessing

*Which did I notice as most effective strategies (Efficient, Accurate):  

F. MATERIALS NEEDED

o Worksheets (me) o Pencils (kids) o Whiteboards (teacher) o Markers (teacher) o Blocks (teacher) o Coins (teacher) o Math monsters (me) o I should have had Images of <,>,= (me)

G1. ANTICIPATION OF STUDENTS MATHEMATICAL RESPONSES TO THE TASK POSED IN THE PROCEDURE SECTION

• Student comparing two quantities through the use of manipulatives like chips/blocks and then placing a math monster (<,>,or=) to compare

o Strategies: count the manipulative chips by ones or twos

o Mistakes: the students may miscount the manipulative chips, the students may put the wrong math monster when comparing

• Student comparing two quantities through the use of a whiteboard and numbers written by me using math monsters (<,>,or=) to compare on a symbolic level

o Strategies: draw a number line to see which number is larger o Mistakes: the students may misread the numbers, the students may put

the wrong math monster when comparing • Student writing down mathematical comparative sentences in their notebooks

using the symbols (<,>,or=) and then reading it aloud to me o Strategies: figure out if the first number in the sentence is less or greater

so they know which is symbol will be read aloud o Mistakes: the students may misread the numbers, the students may read

the symbol wrong

G2. PROCEDURE Include 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:

o I will begin by asking the students to make fist lists of what they recall about comparing numbers. If the children are looking at me blankly I will give them the prompt of when you compare numbers they can either be greater than, less than, or equal to.

o I will check their lists for these symbols: <, >, = , as well as terms like greater than and less, I will then have them popcorn to share what they recall and build off one another.

o I should have had the students do quick images of the symbols o I will then explain to them that we will be working on sharpening our skills when it comes

to greater than and less than by first working with a partner where the partners take turns using the manipulative (blocks/ coins) to make numbers to compare using the math monsters. Using the coins, the students should experiment deciding if the greater pile has more coins or a higher value of coins. Then when I say so, the partners will then use whiteboard to write numbers for their partners to compare writing the comparative sign right on the whiteboard and reading the sentence to their partner. Lastly they will fill out a worksheet I give them on their own and of course they can feel free to ask questions as they move on, but to whisper with their partners because everyone in class is working. As I explain each step they will be taking in their lesson, I will model it by doing a practice problem with one of the students to keep them engaged, as well as have them fully understand what they will be doing.

DURING: o I will let the students work in their pairs and write down the strategies they use in a table I

have created beforehand as a form of monitoring. I will look for strategies such as using counting manipulatives one by one to get a number or by looking at which is bigger based purely on size. I will look for the strategy of drawing their own number line, or even use strategies I did not account for so I will leave space in my table to fill in new strategies.

o After giving some time to the students to work in their pairs, I will prompt them asking questions like, “can you tell me more about how you got your answer?” or “how do you know this sign should be >?” or “how did you get your answer” so I can figure out what strategy they are using and record it on my assessment sheet.

o As the students work in pairs by each grabbing a handful of coins and then comparing their piles to one another using a math monster. I would ask them to write their own number sentence using the coins and the math monster. Having the students record this on paper

shows their understanding between a number sentence and a real life problem using manipulatives. It is important for the students to see the relationship between the physical coins and their value and what that symbolically means on paper using the proper signs of <,>, and =.

o As the students work in pairs using the white boards I will have each partner write a number sentence, for example 346 ___ 436 and then their partner would solve this using the math monster and then writing it in with marker. After they feel they have solved the problem correctly I will have them read it aloud to make sure it makes sense to them, and then I will have them write out the entire sentence using only words. So the above example should be written as three hundred forty six is less than four hundred thirty six. This is good practice for the students to write their numbers into words, as well as allow me to see their understanding of what the number sentence really means.

o I will then give the students a worksheet I have created along with alternative means to solve the problem they are working on, by giving them scrap paper for drawing or writing, math monsters, manipulatives, number lines, or the whiteboard. I will suggest to them new ways to solve a problem that I may it their needs if I see a student struggling while working alone.

o For those who finish the worksheet early and have all answers correct, I will allow them to create their own problems to have their friends try to solve on the back of their worksheet.

AFTER: o After the students are done with their worksheets, I will promote a mathematical

community of learners by emphasizing how well they all did working together in pairs. I will then ask if we can have a small discussion about the lesson and if they wouldn’t mind sharing with one another the strategies they used, and be sure to listen because you all may have used different strategies. I will tell the students there is no wrong way of doing this, so we’re going to listen to each child in the group’s strategy(there’s only four kids). I will actively listen to the students and help them only if they’re struggling with the words to use in their describing of their strategy.

o Selecting: I will ask “how did you know if the sign should be greater than or less than?” Where I will look for answers such as, “ because I looked at the digits values to find the bigger number and then I knew the ‘alligator’s mouth’ opens to the larger number and then read the sentence aloud to make sure the sentence made sense.” I will ask this question first because this shows me the students understand the concept of comparing numbers, which is the big idea they were to understand.

o Sequencing:I will then ask each student to tell me one strategy they used. I will explain to them a strategy is something that helps you get an answer and give them examples of strategies as counting, using a number line, using the math monster, drawing, and reading the problem aloud. After each student has answered with their strategy, I will ask each of them “Why did you use (whatever strategy they used)?” This answer will vary depending on the strategy they ask, but I will look for key words like, “counting helps me find the bigger number, the math monsters helped me focus on which way the sign should be, drawing helps me see the size better, reading aloud allows me to make sure my sentence makes sense.” I will sequence the student’s turn sharing their strategy based on their answer. I will sequence the strategies based on where the strategies fall into the learning progression. The sequence would go as follows: using their hands, counting, number line, drawing, math monster, reading aloud, and lastly mental math. This sequence follows the levels of representation of manipulatives/concrete-pictoral-abstract. I will be prompting the children to see exactly why they used the strategy they chose because it shows where students are along the learning progression. The last question I’d ask would be “If I changed the numbers position, will the sign stay the same?” I believe this is an important question to ask to really gauge the student’s understanding because if they answer “No, it would not make sense because by changing the numbers you change the whole sentence the sign will actually completely switch” shows the children understands how the signs work and that order matters.

o I will ask the students again, “What greater than and less than means and how they

know” (where they can answer with their strategies they shared) and I will review the symbols <, >, = one more time. I will listen for their answers to include, “greater than means the first number is bigger than the second and less than means the first number is smaller than the second” and they know because of however they figured out the size of each number using their specific strategy. I will explain that in the future they will comparing fractions and they don’t have to worry about that now because they understand the concept of equality so well they will have no problem. Because just like with whole numbers you just have to decide which is bigger and smaller and I’ll even let them keep the math monster for when the time comes.

o Connection to real life experiences: I would ask “What skills did this lesson help you practice and learn? What strategies do you think are the most effective? Which strategy would use if you were to do this lesson again? When do you think comparing numbers would come in handy outside of the classroom?” (I am excited to see what the students will come up with for this answer.)

 H. DIFFERENTIATION  

  Content Process Product

Interest

Readiness

The students can decide how they wish to solve the sentences given to them. The

students may choose to use manipulatives, or draw a number line, or can solve it in

their head if they wish.

   

I. WHAT COULD GO WRONG WITH THIS LESSON AND WHAT WILL YOU DO ABOUT IT?

o Students may get rowdy working with their partner: I will rearrange partners telling them I want them to try working with someone else to compare their strategies

o Students may finish the worksheet way earlier than the other students I am working with: I will have a back with true false statements, and fractions to compare or tell them they may help their friends at the table

o Students may mistreat the manipulatives: I will tell them they won’t be allowed to use the manipulatives if they do not handle them with care.  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 lesson went very well. The lesson followed my plan of starting with partner activities of comparing piles of coins with their partner using the math monster. The children loved using the real life objects and especially loved the math monsters (I let the children keep the math monsters which made their entire day). I then had the same partners use whiteboards to give each other problems and solve them. The students enjoyed trying to stump their partner and got really into this activity. Once the kids got out of hand writing ridiculously long numbers, I had them then begin on the worksheet I provided. The students worked independently on their worksheet after some prompting from me. The students love to interact with me so kept asking me questions regarding the worksheet even when I knew they knew the answers, so I had to think fast. I wanted to see what they were capable of without me so told them if they finished the worksheet and tried their best I would give them each 1 cardinal cash. The children then worked very diligently on their worksheets and I helped them with corrections after they were complete. After all the work was done, I had small group discussion asking the questions listed in my “after” section above.

I expected my lesson to be taught to six students during math, but I ended up teaching it to only four students during “Power up.” The students who partook in the lesson struggled on writing what the symbols meant at first because it has been a long time since they compared numbers. The students were very cooperative as I asked them how they knew the answers. For example, when I asked how they knew which number was greater they said, “The 9’s were the same, so then I looked at the next number and 9 is greater than 4.” I received a similar answer from another child when I asked him to tell me more about how he got his answer. This child said, “I did that in my head-I knew that the first numbers are most important so 9,998 is greater than 9,989 because the 9 is in front.” It was great to see the children work through the problems in their own ways, and I encouraged them to use any strategy they wished offering them extra paper to draw on, coins as manipulatives, whiteboards, my math monsters, and number lines.

A change I actually made was using coins instead of chips for the children to compare two piles using the math monster. At first I had the children just go based on size of the piles, but then I had them compare the piles using the actual coin’s value. The children loved the challenge and it allowed them to activate their prior knowledge of coins and build off it. I made this change because I knew some of the students I was working with have trouble remembering the value of the coins, so I felt this would be a quick fun way to reinforce this knowledge for them. Other than that, the lesson went as planned with the children working in pairs using manipulatives to compare numbers then the students worked individually on the worksheets.

2. Analyze your assessment data.

My observation sheet

Student A

Student M

Student R

Student P

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.

After analyzing the assessment data it has given me a lot of insight into the students’ understanding, especially now that I have taken the time to review the students’ written work and combine that with the notes that I took. This helped me, as I was able to group the students based on this assessment data. As I sorted through my assessment data I could see where each student lied on the continuum to mastery of my learning objectives. Overall the students had a good grasp on comparing numbers. No student got more than five wrong

out of thirty questions. I could easily see patterns amongst the student’s answers and responses to my prompted questions. All of the students used mental math at some point during the lesson, whether it be from knowing what the symbols meant or comparing numbers in their heads. All the students understood that the bigger number means it has the greater value. The students understood for the most part that the ‘alligator mouth’ opens towards the greater number, but sometimes made minor calculation errors. Of the four students I taught, I feel two of them achieved mastery, while the other two students are approaching mastery but struggled figuring out which symbol (<,>) meant greater than and less than when the symbols were placed in isolation without the numbers. I feel each student had the proper skills to get the answers.

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

The analysis of my assessment data revealed quite a bit about the student’s understanding, knowledge, and skills after careful review. I looked at my notes I took as the students worked and compared it to their written answers and the verbal responses they gave me- and it all seemed to match up. The notes I made, as well as the student’s work indicated that the students were able to meet my ‘do objective’ of comparing two whole numbers between 0 and 9,999 using the symbols >, <, = with ease. Based off the question on the worksheet, < means _______ and > means _____ I could see which students were able to meet my ‘know objective’ of the students will know the symbols < means less than, > means greater than, and = means equal to when comparing two numbers. The assessment showed me that only two of the four students really know what the symbols mean, but all the students can properly use the symbols when writing it in a number sentence. I was assessing the students understanding that numbers have values that can be compared to one another through the entire lesson. I was first assessing when I asked the children what comparing numbers means and had each student make a fist list of what they believed it to be. The students answers included things like “numbers can be bigger or smaller than another number,” “you can compare numbers by subtracting the smaller number from the bigger number,” and “you can tell everyone which number is bigger or smaller by putting <,> in between them.” Their answers were a great starting point for the rest of the lesson where they further explained their understanding to me. When the students were working in partners using the coins, I asked the pairs how they knew which pile was greater. The children responded with, “well the pile with more coins in it-its bigger.” I then prompted them by asking well what if you had to count the pennies as one cent, the dimes as ten cents..etc then how do you know which pile is bigger? The students then answered, “the pile with more money in it!” So I made two piles; the first pile had 10 pennies and three nickels and the second pile had two quarters and asked them which pile is greater than. They told me the second pile was greater and when asked why is the second pile greater if the first pile has more coins; they responded, “because the second pile has the most money- it has a greater value.” We then had a

group discussion where the students and I discussed that value sometimes means more than size when comparing numbers. As the students went on to work individually on their worksheets, I could see how the students compared values of numbers and truly understood my objective.

c. Describe instructional groups that emerge from your analysis. For each group,

include the following information: • Pattern Groups – Avoid general names such as, “advanced,” “on-target”,

“few holes”, “struggling;” strive for content-specific names such as “Ready to Generalize”, “Conceptual Gaps”, or “____ Calculation Error”

• Distinguishing characteristics of each group (be more specific that you were in section 2b)

• Sample responses from each group • Number of students in each group

In my analysis I found that two students mastered the learning objectives, placing them in the ‘concept masters’ group. I knew Student R had mastered the learning objectives because not only did she know the answer to every question mastering my do objective, but she could explain how she got her answers. Both Student A and Student R were able to correctly fill in the blanks that < meant less than and > meant greater than mastering my know objective, as well. When I asked what strategy Student R used to find her answers, she replied, “my eyes! I just looked at them and knew.” Her answer proves that she does not need any manipulatives because she has already mastered the content, making her in the highest level of representation- symbolic. Student R was also able to properly answer the question-“If I changed the numbers position, will the sign change?” The student replied yes at first, but quickly changed her mind saying wait no order matters because the greater number is now moved.” The student understood how the signs work, how number order in the sentence matters, and the mere fact that numbers can be compared based on its value. Student A also fit into the ‘concept masters’ category because he too got nearly every question correct, making only minor errors and knew right away why he got the questions incorrect showing his mastery of both my do and understand objectives. Student A would used the strategy of reading the sentence aloud because he said, “When I read it out loud and say it- like 8,746 is blank 9,873, I know it’s less than because its smaller and it makes sense.” His understanding was clear based off how quickly he was able to not only correct his mistakes, but also tell my why they were wrong. I feel both of these students are masters of the concept of comparing numbers. The second group I created was the ‘isolated symbol conceptual gap’ group consisting of two students, Student P and Student M. These students did very well on the worksheet, but made one big error. These students both got the same question wrong. On the worksheet, I had written, < means _______ and > means _____ and both students got this answer wrong mixing up greater than and less than. This error proves these students did not

meet my know objective. The students knew when reading the number sentence whether greater than or less than would make sense, and knew that the ‘alligator mouth’ opened towards the larger number but in isolation did not know the signs. When I asked Student P how she knew that 11<111 she said because there’s more numbers-its bigger” and when I asked student M how she knew 744>477 she said, “because 7 is a bigger number than 4.” Both these student’s answers show their understanding of the concept and their otherwise perfect score on the sheet showed their mastery of the do objective, however it is also clear they do not know what the symbols mean just by looking at them.

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.

I feel my teaching strategies were quite literally half effective. Two of the students met the learning objectives and two did not. Overall I believe my strategies were well executed. By having the students begin with fist lists of what comparing numbers meant to them, I could hear the children’s prior knowledge and gauge where each child’s understanding was before beginning the lesson. Then having the student’s work with physical coins and allowing them to see that value is what is being compared tuned the student’s minds tuned into understanding that numbers have values that can be compared to one another. Next having the children work with white boards writing number sentences for their partner allowed a fun way for the students to start getting used to number sentences before I had them work individually on their worksheets. The students did really with my implemented teaching strategies, however I would change one thing in the future. I would discuss the symbols <,>,= in depth and about which one means and how they can tell just by looking at the symbol due to the fact that two students had trouble identifying the symbols.

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.

As I just mentioned, I would incorporate more practice about the symbols meanings (<,>,=) . I only briefly talked about the symbols and showed the symbol with the term greater than or less than. In hindsight I would have included a quick images game. I would hold up a symbol and have them quickly decide what the symbol meant. I think this game would have been fun for the children, but helpful for them to experience the repetition of seeing the symbol and saying if it meant greater than or less than or equal to. I feel this activity would be developmentally appropriate

and quite effective for the children who do not the symbols meanings and good practice for those that already know.

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.

-Look above in green.

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 include s 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.

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? This lesson reinforced my belief that children need manipulatives. Manipulatives

help students grasp a concept. When the students used coins and physically counted them out and then decided which pile had more helped them see which pile had the greater value. This activity helped students see the bigger amount was greater, which helped them when they only had numbers to look at to decide which value was greater. Students could activate their prior knowledge and know whichever number is worth more is greater and the ‘alligators mouth’ must be open to the bigger amount. Giving the children a math monster, which is essentially </> symbol allowed the children to feel comfortable with symbol and made the lesson more engaging for them. Even allowing the students to use whiteboard instead of paper, kept the students engaged in creating their own comparison of numbers problem. Having and allowing for a variety of manipulatives helps children fully grasp concepts by building fundamental knowledge for them to relate back to, but also helps to keep students engaged. Children learn best with the use of manipulatives, so I will certainly have my classroom stocked full of a wide range of manipulatives.

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

reinforced about teaching? I have learned that teaching math is not an easy task. I had always

assumed math would be one of the easier subjects to teach because with math there is always a right answer and a uniformed way of solving each problem. After taking this class and planning/teaching this lesson I have found out that I was very wrong. Math is not easy to teach because yes there is almost always a right answer, but there are tons of ways to finding that one answer. It is the teacher’s job to make sure the children know there are multiple ways of solving the same problem because each child thinks differently. The teacher must

facilitate discussions about all the different strategies and encourage each child on their individual learning progression. Teaching math is not easy, but it can be made easier through the use of manipulatives. I have been in many classrooms that do not value manipulatives, but I have learned that manipulatives are a great tool to use when children are just learning concept and I will certainly have manipulatives in my classroom. I also have learned that assessment must be used during every lesson so the teacher can see what each child understands. Planning for assessment is quite time consuming and also difficult to do during the lesson, but with experience I am sure it will become second nature and I am excited for that day. I feel planning, teaching, and analyzing this lesson has prepared me for the real life of math teacher. Teaching math is not easy, but it is enjoyable and it is great to see the child’s understanding grow right in front of you.

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

reinforced about yourself?

I learned that I do not hate math. Since I started school, I always preferred letters over numbers. I really never gave math a chance and my teachers never showed me any reason to enjoy math. I always made silly mistakes on my math work and that was very discouraging to me, especially since every other subject came so naturally to me. From preparing this lesson I learned that I should have given math chance. Math can be enjoyable, especially if teachers make it that way. By being able to make this lesson fun for the children, this taught me that I could instill a love for math into my students in a way that I was never given to me as a child. By providing manipulatives, games, and turn and talks will allow the children to enjoy math. I also plan on using lessons like the Yellowstone map activity in my class to keep my students engaged and feel personally attached to math and see how math can be applicative to real life situations. By connecting math to real life scenarios will help students feel they need math and keep them interested. Doing this lesson reinforced the fact that I am still learning, just as my students will be and we can have fun learning together.

8. How did your experience planning, teaching, and reflecting on this lesson impact your

progress toward your goal as a mathematics teacher?

My goal for the semester was to learn how to differentiate math instruction to become an effective math teacher in the future. Planning this lesson allowed me to put my knowledge of differentiate to the test. I would correct the student’s morning math review every practicum day, which gave me a chance to analyze the student’s knowledge of comparing numbers based off their answers. I chose to differentiate by choosing the six students who did not grasp the concept. By creating a mini lesson for a specific group of children to help them expand their knowledge of comparing numbers is differentiating for these specific children. Within the lesson I differentiated by allowing the students to find the solution by whichever means they chose. I offered the students coins, number lines, scrap paper for drawing, a math monster, and mental math as all possible means of

solving the problems proposed to them. This allowed differentiation of readiness through the process. I understand that differentiation is the key to being an effective math teacher because every student is on his or her own individual learning progression and you will need different lessons for kids sometimes. You can have different worksheets, or the same worksheets with different manipulatives and allow for early finishers to work on math games. Differentiation is essential to keep all the students engaged and appropriately challenged and I know that after my lesson planning.