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5E Kindergarten Math Lesson Plan
Eureka Module 4 Lesson 23

Teacher moves:
Ms. Owens reminded her students to use different strategies to count during the lesson, which stated that students should decompose numbers equal to 10, by using objects. She reminded her students how their fingers could be used as well counters, as well.

Ms. Owens, reiterated the same math problem for the first few demonstrations, but then she allowed her students to create their own number stories by using different values. So, through the use of reciprocal teaching strategies, she was able to change the mathematics in the problem to match the students’ level of understanding.

Ms. Owens was able to connect the child’s thinking to symbolic notation by asking her students to demonstrate the number story, in which another student had just recited. The students had to use their counters to symbolically illustrate it.

Objective: Decomposing numbers less than or equal to ten
Engage: Ms. Owens placed an addition (+) sign on the board and then asked the class whether or not it was a subtraction sign. The students replied, no. So, she placed the subtraction sign on the board and asked the class to tell her what the sign meant. Then the students were told that they were going to use the objects (cubes) on their desk to subtract with. But first, they had to count each cube on their desk to confirm that there were 10. Also, she reminded the students that they could use their fingers to subtract as well.
Explore: Ms. Owens selected ten students from the class to demonstrate her number story. The students performed, showing how 10 birds were flying (students were flapping their wings), then two birds flew away (Two students flapped their imaginary wings to the other side of the class), so there were eight birds left flapping their wings (the students really enjoyed that). The students were then asked to create the same number story using their counters.
Explain: Ms. Owens further explains subtraction by numerically entering it on the board 10  – 2 = 8. She asked the students, which number should be recited first and then demonstrated the problem again by using a number bond (it was a connection to their prior learning).  She explained and demonstrated, saying “we first start with a whole number and then take part of it away to end up with another part.”
Elaboration: Students names were picked from a cup of equity sticks. They had to make up their own number stories, and then the rest of the class modeled their stories by using counters. This was a great example of reciprocal teaching.
Evaluate: Students were told to turn to Module 4 Lesson 23 in their Eureka Math workbooks. They had to complete three problems on their own.

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I.                Introduction (The need for  Vertical Integration)

II.               Vertical Integration using Base 10 Blocks: Watch Video below

III.              Demonstrations of how to use Base 10 Blocks as a Vertical Integration     tool from Pre K 3 through Fifth Grade:

·         Pre-K 3: Making patterns with connecting blocks

·         Pre-K 4: Making patterns with base 10 blocks and connecting blocks

·         K-5: Adding and Subtracting. Counting with Base 10 blocks 1- 100

·         1st Grade: Adding and subtracting. Intro to Place Value. Showing students how the number system based on 10 works (ones and tens) (ten and some ones)

·         2nd Grade: Adding and subtracting two and three-digit numbers. Place Value Cont'd. regrouping and borrowing using base 10 blocks

·         3rd grade: Place Value Cont'd. Use base 10 blocks to understand how to round whole numbers

·         4th Grade: Representing decimals and fractions by using base 10 blocks (reteach regrouping/Base ten Blocks value changes)

·         5th Grade: Place value Contd' to understand how to round decimals to any place.

Works Cited
Ely, C. M. (2008). The effect of math manipulatives on first-grade student achievement (Order No. 10663076). Available from ProQuest Dissertations & Theses Global. (1984745612). Retrieved from https://search.proquest.com/docview/1984745612?accountid=28903

Fioriello, Patricia. (2017). The Return of Vertical Teaching. Retrieved from http://drpfconsults.com/return-of-vertical-teaching/

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On Friday, April 13th, I had the opportunity to perform my second lesson plan at Hendley Elementary school. The demo lesson plan was from Eureka, Grade 1 Module 2, Lesson 1, however, I put my own spin on it, using only the manipulatives that were provided with the lesson plan.

Engage: I immediately grabbed my students attention when I asked them whether or not they could count to 20. I had 20 packets of fruit snacks and we counted them all together. Then, I let them know that if they participated and behaved well during the lesson that they would get the fruit snacks after the lesson was over. After, I set the expectations, I went over the objective and vocabulary words.

Objective/s:
I can add 10 and some ones
I can recognize when numbers make a sum of 10
I can solve word problems with 3 addends, two of which make 10

Vocabulary words:
addends- a number that is added to another
grouping- put together (associative property)
re-arranging- changing the order (commutative property)
partners - with another
number bond- picture showing the relationship between a whole and its parts

Explore: Have students move from whole group to small group. Then give them cards 1-20 and have the students to arrange the cards in chronological order. Then give them the corresponding counters to go along with each number card.

Explain: After students have grouped the counters up with each number card (1-20) explain the directions to the game called, "Switch." Each student will try and solve each others number sentences, but when the teacher says switch the students will switch their cards with another person at their table. Each card should show 3 addends, two of which make 10. Each group will be paired up and given a set of cards. When the the teacher says go, each child will use either their fingers or counter cards to solve the number sentences.

Elaborate: Students will reconvene in a group, demonstrating how they had to recognize which numbers made a sum of 10, and how they needed to add ten and some ones to solve their equations in the game called, "switch." Then they will be split into groups to answer the number story prompts printed through out the classroom on chart paper. Each group will be at a different station, and the teacher should delegate a recorder for each group. Only one person will write on the chart paper. The teacher will monitor each group, clarifying misconceptions and providing hints to those who have challenges.

Evaluate: The class will be bought back together. Then the students will walk around the classroom in one single file line to evaluate each others work. Then we will conclude by having an oral quiz. If the students answer the questions correctly, then they will get one of the packs of fruit snacks that were used at the beginning of the lesson.

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Both videos were very short and informative. In the first video, I enjoyed how the teacher was able to make a connection with her students. Also, I enjoyed how she grabbed their attention very early on with the chocolates. In the second video, I enjoyed the way the presenter was able to explain fractions in a fun way, so that people could actually understand how and why fractions are used. In fact, I believe that the teacher in the first video should have helped students to see the big picture by including an activity like the one in the second video.

It is very important that students see the big picture, so this is why objectives are so important. I did not see the teacher revert back to it at all. If I were to teach fractions I would make sure that my students get a lot practice. I would provide many manipulative's. Also, I would look up games to play. In fact I would probably make a game out the cards the presenter developed in the second video. His cards helped students to see, feel and understand the difference between parts from a whole.

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Analyze the Common Core Math Standards and identify a possible standard for the lesson that you watched.What are your observations regarding instructional strategies, classroom management, and student engagement in the course? How can you apply the strategies (even if the content is higher or lower) for instruction, management, or engagement in your math class?

A possible standard for the lesson I watched demonstrates how students can reason abstractly and quantitatively, which is standard number 2. Students were responsible for grouping a large amount of items to show their fluency of counting within 1000. Also. I would like to add #6 Attending to precision to this post because it relates to the lesson, as well as, standard 2. With this lesson, students problem solving was done meticulously and precisely.

The teacher displayed great classroom management skills. Also, her students were very interested in the lesson. They were very engaged. It seemed as if the teacher grouped the students with their friends or someone that they worked well with. The lesson could be used at any k-5 grade level. In my kindergarten class, I would have students to group items with 30.

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I learned a lot of information that I can replicate from the article entitled, “Become Environmentally Aware” by Rob Allen and Kathryn Chval. I loved how the teacher used reflection to strategize how to communicate with those students who answered questions incorrectly. She exclaimed, “I began to praise students for sharing wrong answers and explained how much they helped others learn in class. The teacher then furthered her research and studies, which helped her to come to the conclusion that maybe she could explain how students may have answered another question rather than the one she was waiting on an answer for. This is a very cool technique. The authors of “Become Environmentally Aware” helps readers to understand the power of polls and surveys when examining student attitudes towards math. Although, the polls and surveys were done orally, written polls and surveys work, as well. This is what the article, “The mathematical survey: a tool for assessing attitudes and dispositions” was about. The author, Phyllis Whit-in (2007) gives examples of how strategically assessing students attitudes about math in the beginning and end of the school year can help students as well as instructors to create a learning environment we’re all students believe they can thrive. Whitin (2007) explains how results should be used to address students misconceptions. In the article, “Fluency without fear: research evidence on the best ways to learn math facts, I learned about students dispositions towards timed assessments and how they may not define fluency, accurately. In reading the article, it reminded me of how I had just given my students a timed activity as a sprint or timed warm-up assignment the other day. Many of the students were frustrated at the assignment. So, after reading the article and due to my experience, I may not use that strategy first next time. Instead of using a timer, I may use the strategy the teacher used in the Allen an Chval (2009) article. She allowed students to try and figure out another way to solve the problem until the other students received help or strategized through their problems. Students were able to use a gesture (they placed another pencil beside their paper) to indicate whether or not they were still working on the problem or figuring out another way to solve their problems. The three articles mentioned above were very helpful and I look forward to finding out how my students feel towards math.

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Atlas video: Response to a Geometry and Measurements lesson plan

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Atlas video: Response to a Geometry and Measurements lesson plan

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Transcript at the beginning of the video:

Teacher: “How do we want our building to sit? What’s going to be your front and your back? Would you like to talk about that.”

Student 1: so, we can have it like this (he eagerly positioned the cubes)

The teacher used constructing a building to make connections to real life in both groups. Group 2 was more advanced than group 1.

The teacher used univocal and dialogical discourse to facilitate the lesson on understanding volume. Her goal was for the students to come up with a strategy to find the volume of a rectangular prism. Within the first group after explaining to the young man that the perimeter wasn’t needed, dialogical discourse took place. In the second group, the teacher was able to use more dialogical discourse because they understood better than the first group.

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Math Autobiography

I have always liked math. I remember my father’s protractor set like it was yesterday. The protractor and compass were shiny and silver. The compass had a small blue pencil attached to one of its legs. It read, “DC Lottery.” Every time I attempted to touch it, I would get caught. It wasn’t until Middle School that I learned what a compass was used for. I purchased a compass for my seventh-grade geometry class. Ms. Holman was my seventh-grade geometry teacher at Roper Middle School. She weighed about 300 lbs and she always had a story to tell. Her favorite line was:

“Excuses are tools of the incompetent used to build monuments of nothingness. Those who specialize in them seldom amount to nothing but excuses.”

What I remember most about Ms. Holman is how she used real-life situations to help me understand math concepts. In fact, one day she told me to look out the window at the baseball field to envision a math problem. Although, I don’t remember the exact math problem. I do know, on that day, I realized that math was cool. I liked how everything could be described by using a math equation, everything from how long it takes a raindrop to land from the clouds to my body make-up. From seventh grade all the way through College, I never made below an A average in math.

At one point, in undergraduate school, I had minored in Math. In fact, I was a math tutor. I tutored math and made good money, as well.  I tutored several students with disabilities. Mostly students with cerebral palsy and autism. It was the most rewarding experience, and this is how I knew I would make a great teacher. I taught my tutees just the way I was taught, by using real-life situations and examples. Everyone that I tutored passed and graduated. Too bad, I dropped math as a minor. I dropped it because it was going to take me longer to graduate.

I graduated from Trinity College with a BA in Communications, but I have always had a passion for mathematics. I define mathematics as patterns in our everyday life that connect us to one another and other things that are stagnant or in which can be changed. Being able to make connections is one of my overall personal strengths. It is a skill that comes very easy to me.

When I was very young, my mom taught me how to connect the dots. It was through a game. The game was called, Connect the Dots. Connect the Dots required me to strategize how I could make the most boxes by connecting the dots, and then placing my initials within the box. I use to play this game with everyone I came in contact with. I loved it. Metaphorically, I have always known how to connect the dots, and it is a skill that is very important when learning and teaching mathematics.

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Reflection 1: Can you think of a task you used that was harder or easier for students than you had anticipated? What factors do you think contributed to the level of difficulty of the task for your students?

I remember giving my students a worksheet that required them to know how to write the numbers, 1-3. About ten minutes into the assignment, one of the students started to bust out crying. She cried out, "I don't know how to make a 3." At that very moment, I began to feel a little guilty because I did not model the lesson before asking my students to complete the worksheet. The child who was struggling was absent the day we had practiced writing the number 3. The I do, we do, you do is a great strategy, and it should be used in every lesson.

Reflection 2: Consider the eight tasks shown in figure1. How would your students go about solving these tasks? Using the four categories of cognitive demand, how would you categorize each of the tasks for your students.

Task A is High Level and it should be categorized as doing mathematics
My students would probably use number bonds to solve this equation

Task B is High Level and it should be categorized as procedures with connections
My students would convert the fractions into decimals and then they would have to figure out how to increase the percentage chance

Task C is High Level and it should be categorized as doing mathematics
My students would compare the relationships and then decide which is the better option

Task D is Low Level and it should be categorized as memorization
My students would use the formula for how to calculate the original price after a discounted item. this would require them to know how to convert percentages into decimals, multiplication and subtraction.

Task E is High Level and it should be categorized as procedures with connections
My students would use shapes and pattern blocks to figure out the answer

Task F is Low Level and it should be categorized procedures without connections
My students would measure each block

Task G is High Level and it should be categorized as procedures with connections
My students would figure out how to make all the blocks equal the same average/height

Task H is Low Level and it should be categorized as memorization
My students would convert decimals into fractions and percentage by using the formulas they were taught

Reflection 3: Can you think of other factors that might make a task appear to be high level on the surface but that actually only require recall of memorized information or procedures?

After reading Goldilocks and the 3 Bears and modeling the difference between small, medium, and large, I grouped students together so that they can try categorizing items into small, medium and large bins on their own. Although many students argued about the difference between medium and large, some worked very well together because there was not any ambiguity about what I was asking them to do-- I had labeled each been. This was a low-level task because I illustrated to my students exactly how they should complete the task, so it didn't require much thinking.

Reflection 4: How might you use this tool in professional-development sessions to stimulate rich and lively discussions about mathematical tasks and the levels of thinking required to solve them?

To provide math examples and then have my peer teachers to categorize them into the four categories of cognitive demand would be a great interactive activity during PD. I think the discussion would be relevant when determining best practices for the implementation of a concept that is to be taught in the classroom.

Reflection 5: What do the classifications "procedures with connections" and "doing mathematics" mean to you?  How are they alike? How are they different? In what ways can these classifications be helpful in selecting and creating worthwhile mathematics tasks for use in your own classroom?

"Doing mathematics and "procedure with connection" are similar classifications of cognitive demand because they both require students to think deeply. With "doing mathematics, “a student would have to think about and decide which concept to use for solving a problem. This is also required for "procedures with connections," but the thinking process requires more focus on actually how to use the concepts, which develops meaning. Therefore, the difference between the two is dependent on how the problem needs to be answered--What is the problem asking students to do?

Both cognitive demands should be taken into consideration when grouping students who require differentiation.

Reflection 6: What other issues might be important to raise in a discussion of tasks? What task would you add to the sort to stimulate additional discussion?

After reading the article, I would raise discussion about additional math examples to model for grades K-3.

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Click on the link below to see how I demonstrated the High Leverage teaching practices listed below:
- Identify and support productive mathematical dispositions
- Select tasks that are relevant to the specific students
- Identify big math ideas and common misconceptions

- Use different representations and connections among concepts
-  Select and implement tasks that are: cognitively demanding and accessible to all students (multiple entry points and varied solution strategies)
- Enact 5 practices to support discussions: anticipating, monitoring,

selecting, sequencing, and connecting responses. Use different talk moves and questioning strategies.
- Use collaborative strategies of participation. Attend to patterns of participation and use of equitable strategies
- Identify and use professional mathematics education resources to inform teaching practices. Develop a professional inquiry and share with others

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Teaching Kindergarten Math Eureka K-5 module 4 Lesson 10