Understanding Tens and Ones A- Summary of Lesson: 1. Content Standard: o 1.NBT.B.2 : Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 1. 10 can be thought of a bundle of ten ones- called a “ten” 2. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). (Georgia Department of Education, 2021) 2. Grade Level: o First Grade 3. Objectives: o Represent two-digit numbers as tens and ones o Decompose a two-digit number as some tens and some ones in multiple ways o Model a two-digit number in multiple ways 4. The strategy I will use is a spin-off of the gradual release of control. o First, I’ll pull students whole group to the front of the room all together on the meeting carpet. Here, I will present a starter where students will all explain or show how to show the number 14 as one ten and some ones to review a previous lesson they have collectively mastered. This will get their brains working in the direction of tens and ones for the lesson beginning this day. o Next, I’ll present the class with a new problem by telling them to guess how many cubes (32) I have in a bag I will hold up for them to stare at for about ten or fifteen seconds. During this time, I will cover the new academic vocabulary and translate it into Spanish for the ELL students. (Vocabulary- digit, place value, ones, tens) o Then, I’ll send the students back to their seats and tell them to record how many cubes they guess are in the bag. o Next, I will hand each student a bag of the same number (32) of cubes and tell them to count the number of cubes to see if their guess was correct. After counting, they should record the number of cubes they have in tens and some ones as we have learned in the previous lesson. This portion of the solving will be independent. o Then, they can turn and chat about their strategy for solving it the way they did. During this time, students are able to change their strategies if they are introduced to one that seems more convenient or they better understand. Some students may have 32 ones. Some may have 3 tens and 2 ones. Some may have 2 tens and 12 ones. Others may have 1 ten and 22 ones. Answer should vary. o Next, as I walk around the room observing the students’ engagement about their strategies, I will (discreetly) choose two or three students’ strategies to be shared (by the students themselves) with the class. The whole class will come together at the front of the room again just near the white board and T.V. where the presenters will explain their strategies. o The next day, I will review the initial strategies presented by the students. o Then, if any of the strategies they used do not match a sensible or common strategy, I will model a strategy that I would use to solve the problem. My way of modeling it would be the 3 tens and 2 ones way. o If a student DID use a sensible or convenient strategy to present to the class, I will NOT model a new way. I would use this strategy to build upon with explicit instruction as to how to practice the best strategy. o The following day(s), students will review the practiced strategy from the prior lesson and then also be encouraged to use any strategy that makes the most sense to how they think, personally. 5. Assessment: o The front side of the assessment will be 8 problems. Each problem will be a twodigit number in numerals with the directions, “Show the number __ using tens and ones two different ways.” o The back side will be 8 more problems. The first four problems will be illustrations with tens and ones (making a number consisting of two digits - 56) with the directions, “Write the number these tens and ones represent.” (The illustrations of tens and ones will be various possibilities of 56 using tens and ones. For example, 5 tens and 6 ones, 3 tens and 26 ones, 1 ten and 46 ones.) The last four problems will be the same type of problem but using a different two-digit number (73). B- Reflection Log: 1. Prerequisites: o Count to 100 by ones o Count to 100 by tens o Understand teen numbers o Represent 10 ones as one ten 2. Two Characteristics of Students o Multiple students in this class have problems controlling their bodies’ high levels of energy. They are constantly getting out of seats, fidgeting with something, or distracting others. It is important to consider students who have a hard time controlling their bodies’ high levels of energy because it makes them lose focus. This also makes it difficult to teach a full lesson without interruptions to instruction or distractions for other students in the class, so by considering this set of student needs, I am ensuring all students are able to receive the necessary instruction and understanding of the standard. o Multiple students in this class are ELL. This is important to consider because these students often need Spanish versions of new vocabulary related to the content being taught. 3. Two Learning Needs o The students who need help controlling their bodies’ energy need ways to direct their extra energy without missing instruction and practice while not distracting the other students during instruction and practice. This is important to consider because these students are likely to distract other students in the class. o The ELL students (all Spanish speaking) need a concrete way to understand the concept in their native language, and then a way to transfer (translate) that understanding into the English language. This is important because ELL students need the same opportunity to hear and understand the concept in their own language as non-ELL students. 4. Why I chose these instructional strategies o For this class specifically, I chose to use manipulatives and talking with friends to compare strategies to keep their focus as narrowed as possible to the content being covered. This will help the student needs of the ones who have a hard time controlling their physical energy. If they are able to talk it out with one another and show their strategies with the manipulatives, their minds are able to switch back and forth from listening to my guidance in short bursts, then self-propelled learning in short bursts. Also, having students move to and from different places in the room so often will keep aid in the same thing. o For the ELL students, I have to know, understand, and use Spanish a few times for them to understand what is expected, then I am usually able to transfer their understanding to the English language of what is expected. This will help students who are ELL better understand the content being taught opposed to leaving them guessing what I am saying, asking, or expecting them to do. It is also CRUCIAL in my class’ experience for vocabulary acquisition for many of the ELL students. 5. Why I chose the assessment o I chose this form of assessment because I do not like to make all students use the same strategy, I feel it is the best way. I want them to be able to choose a strategy that works best for them. If they see the illustrations presented in various ways but showing the same two-digit number, they are likely to better understand the learning objective “decompose a two-digit number as some tens and some ones in multiple ways” and likewise for the first part of the assessment where they should show two-digit number two different ways using tens and ones correlated with the learning objective “model a two-digit number in multiple ways”. C- Reflection Log focused on the outcome of the lesson and assessment 1. I observed all students engaged with the manipulatives at the beginning of the lesson, especially. They were also engaged with each other when explaining their strategies to classmates. They progressively were able to use the highest number of ten sticks needed for each two-digit number and then count the remaining number of ones. 2. The assessment showed 16 out of the 19 students were able to answer all questions correctly. This indicates that those 16 students were able to: 1. Represent two-digit numbers as tens and ones 2. Decompose a two-digit number as some tens and some ones in multiple ways 3. Model a two-digit number in multiple ways It also showed 2 students were able to answer all questions except two correctly. Lastly, it showed one student who was able to answer all questions on the back correctly, but all questions on the front incorrectly, indicating that he understands the learning objective “model a two-digit number in multiple ways” but does not understand “decompose a twodigit number as some tens and some ones in multiple ways.” 3) I believe a successful element of this lesson was having them physically engaged because it helped control their focus and attention. I also believe a successful element of the lesson was having the students see, understand, and demonstrate showing the two-digit numbers in multiple ways with the manipulatives because it solidified their understanding that ten ones can be traded for a group of ten (or a “ten stick”). 4) I believe not asking students to practice decomposing two-digit numbers as tens and ones by having them draw tens and ones for a two-digit number I provided them hurt the students who didn’t master the learning objective “decompose two-digit numbers as some tens and some ones in multiple ways.” I also believe by not implementing additional avenues for students to release extra energy somewhat hurt the class because I still found myself pausing instruction to redirect the ones who still couldn’t sit still while I was instructing. I could provide “preferred seating” in the form of a yoga ball or “feet bands” attached to the bottom, front legs of their seats. 5) The next instructional steps for this lesson are to ask students to practice decomposing twodigit numbers as tens and ones by having them draw tens and ones for a two-digit number which I provide. Also, I will provide preferred seating in the form of a yoga ball and “feet bands” for students who have a hard time controlling their bodies’ energy. A. By asking students to practice decomposing two-digit numbers as tens and ones by having them draw tens and ones for a two-digit number which I provide, students will better grasp and visualize the part of the standard that says, “decompose a two-digit number as some tens and some ones in multiple ways.” Also, by providing preferred seating in the form of a yoga ball, it allowed them to manipulate and bounce within set boundaries (by me). Also, by providing preferred seating in the form of “feet bands”, it allows them to quietly manipulate something with their feet while remaining seated. These preferred seating methods will help those students needing it to get rid of extra energy without disrupting or distracting the rest of the class. D - Two Insights Relevant to Student Learning That Will Influence Future Teaching Practices 1. I have learned that some students may understand being able to decompose two-digit numbers as some tens and some ones, but that does not mean they automatically understand how to model two-digit numbers with tens and ones. 2. I have also learned that some students may not always understand that when you count ten ones, you can then trade it for a ten stick. I will use this insight to model more and issue more student practice of this understanding. E - Two methods of reflection that will be the most effective for future teaching practices. E.1 - One method of reflection I would use is to actively observe students practicing these math concepts during independent practice by using a checklist of objectives as I walk around the room and take note of students who seem to understand the concepts being taught. E.1a. - This will be effective because it will help me remain cognizant of which students are in need of remediation or being retaught these concepts versus which students need more practice of presented concepts. E.2 - Another reflection for future practices will be to use a peer observation from a veteran first grade teacher. The teacher will observe and provide feedback of my instruction of content presented. E.2a. - By doing this, it will give me insight as to what an experienced teacher observed during the lesson and be able to provide feedback as to why things were or were not understood by the students. F- Acknowledge sources, using APA formatted in-text citations and references (Georgia Department of Education, 2021) Works Cited Georgia Department of Education. (2021, July). Georgia Standards of Excellence Grade Level Curriculum Overview. Retrieved from GaDOE: https://www.georgiastandards.org/georgia-standards/frameworks/1st-math-gradelevel-overview.pdf