Introductory Lesson for Multiplication and Division
Name: Kristin Michelena
Lesson Title: Base 10 Manipulatives
Grade Level: 1st grade
Big Idea:
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|How do we represent two-digit numerals using base 10 blocks and how do we represent base 10 blocks as two-digit numerals? |
Instructional Objectives:
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|Students will be able to decompose numbers from base 10 manipulatives |
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|Students will be able to recognize whether an amount shown in base 10 manipulatives is equal to an amount represented in numerals. |
Arizona and Common Core Math Standards Addressed:
|Common Core Standards: ) |
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|1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. |
The TASK: Choosing Tasks
Think about what makes a good problem or task, and how well the problem or task will engage students in the important mathematical ideas you want to address in the lesson. For example, for each task, think about numbers, context, and problem structures, and say why you are choosing the numbers, contexts, and problem structures you decide upon.
TASK(S):
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|The format I will follow is the “I do, we do, you do.” This means that while going through the slides and presenting the material I will |
|demonstrate how I solve the problems after that the whole class will work on solving it and then finally individual students will come up to the |
|board and show their work. After a few students show their work explain why and the students ask questions we will move to bookwork where all |
|students can try individually. The questions are set up on the smartboard with a visual representation of blocks on one side and a two-digit |
|numeral on the other. The students must count the blocks and then put either a = or ≠ to make the statement true. The students then must |
|manipulate the blocks on the board to match the numeral and the maniuplatives. In their work books they are starting with drawing the numeral |
|given in base 10 manipulatives and also are building with real base 10 manipulatives. If the students are finished working on that they move onto |
|looking at base 10 block and writing out the two-digit numeral |
WHY:
|Why these numbers: |
|I wanted to stretch the student’s ability to work with numbers outside of 10. I thought this visual way would facilitate support to introduce |
|higher numbers. |
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|Why this problem context (setting or objects in problem): |
|My problems do not have setting and the base 10 manipulatives are used because they are useful tools to visualize and they are a part of the |
|curriculum |
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|Why this problem structure (what mathematical information is given and what is unknown): Students know how to count up to 50 but it is unsure how |
|if they have ever represented it. This structure allows them to come up with numbers higher than 10 will only recording how many rods in a 1-9 |
|numeral. For instance, when asked about the visual representation of 32 they are asked how many 10’s and they would record the number 3 and how |
|many 1’s and they would record 2. |
ANTICIPATED STUDENT RESPONSES: Students’ Thinking
List many different ideas for how students might respond to your task. For each idea explain why students might think that and how you might respond to challenge or extend their thinking.
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|Students may count all base 10 blocks as one instead of counting the rods as ten’s and the units as one’s. – Students may not have been exposed |
|to counting in chunks and may fall back to their strategy of counting one-to-one correspondence, which they typically do when using linking cubes.|
|In anticipating this struggle before we count using our rods and units I set up a slide where we can fit 10 units into 1 rod. If they still |
|struggle I will have them prove that each rod is a 10 and we can think of an easier way to count when we already know the number. |
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|When describing two-digit numbers students may not understand the difference between a digit and a number. – This may not be a concept that |
|students have talked about yet so instead of going into a huge explanation that would be a part of a lesson in and of itself I will help them |
|build patterns. Anticipating their confusion I will have them give examples of two-digit numbers, playing the ‘yes/no’ game to help them figure it|
|out. Once we have a good amount of examples of two-digit numbers we can look and see what they have in common and I will tell them what I see in |
|common and show that they all have a tens and ones column to help lead into the lesson. A more in depth explanation will have to be given at a |
|different time. |
Vocabulary and Language Objectives
State the key mathematical vocabulary to be used in the lesson, including vocabulary in students’ native language, if appropriate. If an ELD classroom, state the language objective for the lesson.
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|Tens, ones, base 10 manipulatives, two-digit numbers |
Materials & Tools
Consider the following questions about tools (e.g., manipulatives, oganizers):
How do the tools I use in the lesson act as learning supports?
Do the tools make the topic easier for the students to understand?
Do I offer a variety of tools for students to use?
Description of the Mathematics Tools you will have available for students:
|The base 10 manipulatives will become a great tool and visual support for the students to utilize throughout their entire math career. The tools |
|are directly linked to the lessons success. The students have not yet used these tools before but have been exposed to linking cubes. |
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|For the lesson I will be presenting on the smartboard which I typical of this classroom. The students have all interacted with the smartboard |
|before and they are excited when they get to use it in front of the class. The smartboard makes the lesson easier for the students to understand |
|because even though the information is virtual they are able to manipulate the material on the slides an can solve the problems and refine their |
|solutions as easily as they could when using 3D objects and pencil and paper. |
Public Criteria
Consider and state the key rules and expectations you need to make clear to students before you start the lesson. For example, rules for using materials, for working in groups, etc.
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|While students wish to share their ideas they must raise their hands. When the students are done using the materials they need to pack all of them|
|back up and make sure they have the correct amount. |
3 PART LESSON PLAN
1) BEFORE: Introduction
Consider and State how you will:
Transition students into the lesson (Before Before).
Introduce the task. You might introduce the problem through a story book, a picture, a question, simply by discussing the context and getting students to talk about it, or something else.
Get the students ready. Here you need to find out what students already know about the topic / task, and help get them ‘ready’ to work on the task. You might begin with an easier version of the same task. You might have them brainstorm ways of solving the task. Or something else.
Pose the task. Make sure all students understand what the task is asking.
Include SPECIFIC QUESTIONS that you will ask students during this part of the lesson.
YOUR PLAN for what teacher and students will do and WHY:
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|Transition: Math time for the students comes right after lunch/recess for the 1st graders. This means as students come in from lunch they will, as|
|they do everyday, put their lunchboxes away and come to sit on the rug. |
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|Introduce Task: Prior to starting the lesson I will take out the base 10 blocks and tell them the name and ask them if they are familiar with |
|them. I will also ask the class to share what they think they might be useful for and let them share any experiences they may have had with the |
|blocks. |
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|Get Students Ready: Now I will go over the content objectives and deconstruct any vocabulary. At this point it will be important to go over |
|two-digit numbers and assess their knowledge and correct any misconceptions/build their knowledge. |
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|Pose the task: I will ask for students to think about what our objective is and have them pair up to share with an elbow partner and then have a |
|few students share aloud. |
2) DURING: Exploring
Consider and State how you will:
Find out about students’ thinking. What will you be listening and looking for, what strategies do you expect to see?
Support students’ thinking when needed – hints, suggestions, questions to get students moving on the task, or to help students who are struggling.
Encourage students to test out their own ideas.
Support diverse groups of learners.
Pose questions that help students extend their thinking by looking for patterns, considering multiple solutions, explaining their reasoning and thinking, etc.
Include SPECIFIC QUESTIONS that you will ask students during this part of the lesson.
YOUR PLAN for what teacher and students will do and WHY:
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|Find out about students’ thinking: As we are going through our progression of problems I will be looking to make sure students are counting the |
|rods by 10’s and the units by 1. It will be important to look for the students understanding of the equals sign and not equals sign. This can be |
|evaluated as they working through the problems. |
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|Support students’ thinking: How many tens? How many ones? What is the ones column? What is the tens column? Is the base 10 blocks showing the same|
|thing as the two-digit number? |
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|Encourage students to test out their own ideas: During the ‘we do and they do’ sections students will be able to agree or disagree with others |
|work and will be able to try out their own ways during this process. Students will be encouraged to refine their ideas throughout the entire |
|process. Students will not be penalized for getting a wrong answer. |
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|Pose questions: If this is a two-digit number what would do think a three-digit number might be? What numbers would you like to try out? Do you |
|think there is a two-digit number that we cannot show with our base 10 blocks? Is the number equal to the amount of the blocks shown? |
3) AFTER: Summarizing
Consider how you will:
Facilitate a class discussion and a sharing of students’ strategies. Think about how and where students will share, how many will share, and how you will choose those students.
Encourage dialogue and debate among students. Think about how the class will determine whether a solution is correct or incorrect. Think about how to extend the children’s thinking.
Summarize the important mathematical ideas. Consider how you will draw students’ attention to the big mathematical concepts. Make sure you define here what those important mathematical ideas are.
Include SPECIFIC QUESTIONS that you will ask students during this part of the lesson.
Transition students from the lesson to the next activity (After After).
YOUR PLAN for what teacher and students will do and WHY:
|Facilitate a class discussion: Students will be sharing with one another in pairs as well as to the whole class during appropriate times. |
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|Encourage dialogue and debate: Students will be able to share whether they believe each solution is correct or incorrect by giving thumbs up or |
|thumbs down. A few students will then be asked to share why they think the solution is correct or incorrect. The student presenting can either |
|defend their solution or can refine their solution. |
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|Summarize the important mathematical ideas: |
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|Transition: Instructions and an image of the pages in the book for students to work on in their workbook will be shown on the smartboard. |
|Students will be able to ask questions before they are dismissed to their seats by table. |
ASSESSMENT
How will you assess what students learned?
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|An informal assessment will be done throughout the lesson. Each time a student presents their answer of the visual representation of the base ten |
|manipulatives and a numerical representation is given the students will give a thumbs up or thumbs down to agree or disagree with the answer. The |
|students who present agree incorrectly with a solution will be noted and further individual work will be given with them during their workbook |
|time. |
ACCOMODATIONS
Select TWO groups of students (e.g., English Language Learners, inclusion students) and describe how you will adapt the lesson, as appropriate, to meet their needs.
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|My students are not in need of these modifications but if I were to make some these are what they would be: |
|IEP students- IEP students will be given additional time and additional support to complete their bookwork prior to the lesson given in their |
|resource classroom, per typical practice at Laguna Elementary. IEP students will also be given seating assignments when on the carpet that |
|encourages their academic learning. |
|ELL students-Because of the strong visual representations throughout the lesson the main ELL support will be given throughout bookwork time. |
|During the smartboard discussion gestures, asking of clarify questions and slow to moderate speech will be done to support the learning of our ELL|
|students. Prior to letting the class go on their own students will partner up and explain to each other the instructions for the pages of the |
|workbook. Then the groups of students will be encouraged to work with one another at their tables, therefore hopefully employing BICS to promote |
|an initial academic response to the work given. |
EXTENSIONS UP AND DOWN
Describe how you could adapt the task (i.e., task structure, context, and/or numbers) for students who struggle with the mathematics (extensions down) and for students who are ready for an additional challenge (extensions up).
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|Extensions are given to the students who are above the task to use the first set of workbook pages as review and then they move onto the second |
|set of workbook pages, which have high two-digit numbers. For students who need extensions below they will not be pushed to the second set of |
|pages but will instead stay on the first set of workbook pages. Students who need extensions down will be given more one-on-one attention and may |
|do work more on exploring the base 10 blocks. For instance, they may make their own two-digit numbers and record those on a slate, if they |
|workbook is not an option for them. |
Summary of Lesson
The lesson I prepared for the class was mainly picked to introduce base 10 blocks. My mentor teacher did not give me much of a lesson to modify so I jumped right in and created a lesson from scratch using her previous lessons as a model. The lesson took form with the big idea of representing base 10 blocks as numerals and setting them equal or unequal to each other. I began by going over the objectives and talking about two-digit numbers. This is a modification I made to my teachers typical lessons because she does not present the content objective of the lesson. Next we discussed their understanding of two-digit numbers (key vocabulary) and the students gave a few examples, at this point I realized the students needed a more in-depth lesson on two-digit numbers, but because of the time it would have to be revisited at a later date. We then move onto working on a few problems together that show a set of rod and unit manipulatives with an equal sign and a blank. Underneath the manipulatives is a spot to record the number of tens and the number of ones. We use this to record our information and to write in the blank section next to the equals sign. After that we go over what the equals sign and not equals sign means by relating it to different signs we may see in real life. This was a modification I used because I took the information that my teacher had, she conveyed the students were having difficulty understanding the equal sign, so I tried to use their funds of knowledge to help scaffold their learning. Next we move onto the “I do, we do, they do” strategy to fill in a = or ≠ to make a statement true. The statement shows a set of base 10 blocks (with the scaffolded tens and ones recording space) and on the opposite side a two-digit number. The students needed to find out the number of base 10 blocks and see if they matched the two-digit number also represented. Throughout this portion students seemed fully engaged, they were participating by giving thumbs up and thumbs down agreeing and disagreeing indicators. The students also did a good job being vocal and describing why they agreed or disagreed. Once we went through this a few times the students were given instructions to complete a few pages in their workbooks. Clarifying questions were asked and they were sent to their seats. After the students worked on their lesson for a few minutes it became clear that the first set of pages did not align well enough with the lesson therefore I had to pull the classes attention back to the smartboard. I took one of the students numbers that they were having trouble with and I went through it on the board with them briefly showing them where the tens place was and where the ones place was. This was an unintended portion of my lesson and was made up on the spot to help scaffold the students learning. After the brief mini lesson the students seemed to have less frantic questions. Some students were still struggling which means there were modifications that I missed out on but a few of the majority of the class was able to fill out the worksheets.
Reflection of Implementation
Overall I was pleased with the implementation of the lesson. I found the modification of adding the content objective to the lesson really helped me guide the students in the right direction and helped set up the lesson in a way that had purpose. I felt during the whole group lesson the students were engaged. There were a few key goals I was trying to accomplish while presenting the lesson: classroom management, student modeling and active learning. As I had anticipated the students were more talkative and rambunctious during my lesson then when they are with their typical teacher. Because of this I had to employ the classrooms typical behavior management strategy, using the clip system. As I began I let them know my expectation that they needed to raise their hand to answer a question. When they called out I gave them verbal warnings. When it happened one more time I gave them an additional warning but then had to have a few students move their clip down from the neutral green color to the lower color yellow. This method worked to keep my expectations for the class even though I was not fond of having to make them move the clip. To address my goal of student modeling I took the method employed in the classroom (I do, we do, they do) and broke the slides up so the students were able to participate in most. I’m mostly pleased with the student participation but I feel I could have done better to promote critical thinking. I think the reason I could have done better with student participation id because I was so intent on getting everything I needed out about the lesson to complete my portion of the assignment. My nerves also played a part in my inability to take the lead from the students. That being said I do not feel that the students were left hanging but when looking back at the video there were definitely a few opportunities I missed out on because I misheard or pushed through after a students comment. I think this is the most important modification I missed out on because I believe it affected their overall understanding of the lesson and therein their ability to complete the worksheet.
After the students had been dismissed to the work at their desks I initially went around to three students and found they were all having difficulty identifying the tens and ones, even though as a whole group we were able to identify them. Because of all the questions and confusion about this part I felt I needed to speak to the whole class. At this time I kept the students in their seats, got their attention, and asked for a student to supply one of the questions they were having difficulty on. I modeled how I would solve this problem and I showed them explicitly where the tens column is and the ones column is in a two-digit number. After the regroup session I found that students were able to better solve the problems although some students were still struggling.
Children’s Mathematical Understanding
Throughout the lesson students learned a few things. Students learned what a two-digit number is but did not explicitly learn the components of a two-digit number. I know this because students were able to produce examples of two-digits numbers during whole group, I do not believe they would be able to explain a rule and apply their understanding of a two-digit number to create a three-digit number. This was also not the objective of the lesson therefore I did not pursue the topic in great detail. I think the students learned a bit about counting tens and ones and how a two-digit number can be broken up. I do not think every student met the content objective and I think some met the content objective without grasping a deeper understanding. I believe this lesson would have fit well if their were a few lessons prior to it that allowed for more explanation and scaffolding of the tens and ones place and use of manipulatives. When looking at the students work I found it important to remember this was their first formal exposure to tens and ones place and the manipuatives.
When looking at where the students were with pre-place value understanding I can see students distinctly in each of the 3 levels:
“ Level 1: Initial Concept of Ten. Children understand ten not as a unit that consists of ten ones, but only as ten ones.
Level 2: Intermediate Concept of Ten. Children see ten as a unit that consists of ten ones, but they must rely on physical or mental reconstructions of models to help them work with units of ten.
Level 3: Facile Concept of Ten. Children are able to easily work with units of ten without the use of physical or mental reconstructions of base- ten models.” (Van de Walle, pg. 176)
While observing the students as they worked independently I was able to see how they would apply the information they learned to their own situation. I noticed that some students still struggled with the concept of ten and I would place them at a Level 1 in their pre-place-value concept knowledge. I observed the children still counting the rod of 10 by 1’s and they were not able to apply the schema that the rod represented ten and that they were supposed to count the number of rods or at least count the rods by 10’s. There were other students who demonstrated their pre-pace-value at Level 2. These students were able to successfully complete the bookwork by counting the rods by 10’s and the units by 1’s. These students approached the problem differently and did not look at the number as a whole but instead broke the problem down into the tens and ones. They were able to demonstrate how many tens and then separately demonstrate how many ones and then were able to create a two-digit number out of the numbers they found. Lastly there were students who grasped this very quickly and when solving the first page of worksheets utilized no manipulatives, and drew no representation of manipulatives. These students were able to look at the numbers and break it down into tens and ones with no supports. They also did not refer to the drawings when working on the second set of worksheets. With this evidence I believe those students were at a Level 3 understanding of pre-place-value concept.
Supporting All Children
I think in any whole group activity there will be students who are more engaged then others. At times however when scanning the room I had 90%-100% participation and then as the material got a bit more difficult it seemed to drop down to 75% of the students being actively engaged. Even though the material and presentation of the lesson required active participation I think that some kids will naturally shy away and avoid bringing attention to themselves. This is one of the reasons I attribute to some of the students lack of engagement. It can also go the other way the students can become bored with the material and lack motivation to participate. I think this was less of a reason but was still the case for at least one of the students who seemed disengaged. It also seemed more students participated with giving the thumbs up and down activity but were not as willing to speak in front of the whole class or explain their reasoning. And finally the last reason I suspect played a factor in the student’s reluctance to participate or give answers was because they were not used to the types of questions I was asking.
Extend Your Thinking
If I were to start all over I would not necessarily scrap my lesson but I would create a lesson that is a precursor to the one I actually did. I found out the hard way, as the lesson went on, that the students needed more background knowledge for the lesson to be successful. Although, the lesson was successful for probably a half of the class I now realize it is better to start out building basic knowledge and creating upward extensions for the students who need it rather than creating a lesson and losing half of the class because their was not a way to create a downward extension that would be helpful without changing the objective of the lesson. If I were to do this again my initial thoughts are I would try and build their understanding of the manipulatives. First I would have them create numbers with the units. Then have them create numbers with the rods. And then finally have them create numbers with the units and rods together. I would not have them use a worksheet but instead have them work in partners on slates and after working with each manipulative (units, rods, units & rods) I would have a few students share with the group and we would look at patterns we saw when working with the base 10 blocks. I would anticipate, in the final step, we would run into a scenario where a student created a number with x amount of rods and 10 or more units. I would ask then ask the class if they thought they could show a way represent the same number in a different way, I also may introduce the word ‘simplify’ and ask them to simply this groups answer and have them work back with their pairs again to see what they could come up with on their own. Now that I have thought of an alternative way to teach a similar lesson with the students I am very disappointed I did not come up with it initially. I think that this lesson prior to lesson I taught would give them the background knowledge they need to be successful when completing further extensions. I recognize that the lesson does not give a concrete description of place value but I think they need to have some experience working with it (even though they may be unaware they are) before I explain it in more detail to the students; this way they have an experience to attach their new concept too.
Works Cited:
Van de Walle, J. A., Lovin, L. H., Karp, K. S., Bay-Williams, J. M. (2014) Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades Pre-K-2.. Boston: Pearson.
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