The essential question for this unit was,“How do mathematicians think about place value?”

This essential question reflects the nature of the unit as a supplement to the main Pearson lessons. The Pearson textbook’s essential question for students is “How can you count, read, and show numbers to 1,000?” I chose to differentiate my essential question because this unit is in nature differentiated from Pearson. My students will be accomplishing the bulk of the counting, reading, and writing in the time spent on the Pearson textbook each day. In the extended math meetings, they will be working more on their mathematical thinking, number sense, and theoretical concepts associated with the unit. During the textbook lesson, they will learn more of the practical skills needed to build upon those theories. It is crucial that they build a strong sense of place value and identify those patterns linked to numbers and place value so that they can understand even more complex math and check to see if their answers and ideas make numerical sense. 

How does this unit develop content understanding of key concepts and ideas?

The following learning goals focus on connecting students with content standards through meaningful and intentional application of small group work directed at their understandings. These learning goals reflect Pearon’s EnVision Topic 9: Numbers to 1,000 and the additional work students will do in their revamped math meetings. 

• • Students will be able to identify the main place values (ones, tens, hundreds, thousands).
  • Students will be able to use relevant vocabulary (e.g. digit, greater than, less than, standard form, expanded form, increase, decrease) to describe numbers and talk about math.
  • Students will be able to count by 1s, 5s, 10s, and 100s to 1,000.
  • Students will be able to model 3 digit numbers with place value blocks.
  • Students will be able to draw 3 digit numbers pictorially.
  • Students will be able to tell the value of a digit based on its place in a number.
  • Students will be able to read and write 3 digit numbers in expanded, standard, and word forms.
  • Students will be able to compare and contrast different ways to represent the same number. 
  • Students will be able to compare the value of given numbers on hundreds charts, number lines, and by their place values.
  • Students will be able to use greater than and less than symbols to describe numbers’ relations. 
  • Students will be able to discover patterns and analyze them to solve problems.
  • Students will be able to practice basic computer skills including clicking, typing, scrolling, etc.

How does this unit enable students to experience the power of their minds and their capacities as learners and doers?

Students will be able to access a new vision of themselves throughout this unit. By seeing themselves be successful in concrete ways every day, they will gain confidence and see themselves as capable mathematicians. This is extremely important for our classroom as a whole. I have noticed that most of my students have become less and less interested and confident in math. In order to revive their inquiry and desires to discover in math, I knew they had to build their confidence. Almost all of my students dislike math and this makes it difficult to teach from the book in a predominantly whole-group setting. Those who enjoy math understand new concepts quickly and become bored with the slow-moving whole-group style lessons. 

By addressing my students as individuals instead of as a whole-group, they will see themselves as powerful learners and believe in their capabilities as mathematical learners. When my students take math assessments on paper and on the computers, they get anxious and place a lot of weight on their final scores. By allowing them to take check-in quizzes daily, they will see their scores improve, increasing confidence. This will convince them they are capable in math and can all achieve goals from lessons. Based on their results, I will group them and give them interventions based off of what they need to work on. This will directly correlate to an increase in attention to them as individual learners and allow them the exact attention and practice they need. This equation and whirlwind of activities and differentiation will help them strengthen their skills as they learn and move through the content. Not only will they see themselves as “good at math” and strong mathematicians, this will even out their prior knowledge and engagement so that whole-group instruction is more effective. They will get to work on their individual skills directly, use strong math vocabulary, and build a strong number sense which will all contribute to their confidence moving forward in math. 

How does this unit develop intellectual and academic habits of mind, work, and discourse within the discipline?

Students act like mathematicians when they embody the mathematical practice standards. By reinforcing math meetings, students get opportunities to practice all of the ways to “be a mathematician.” First, the fourth and fifth standards involve modelling and using appropriate tools. Throughout the unit, students will be practicing modelling 3 digit numbers with base ten blocks. They will also be using Chromebooks as learning tools and will be expected to practice their abilities to model and respect and use materials and tools to engage with math. Next, the first and sixth practice standards relate to persevering through problems and being precise. Students practice these standards by challenging themselves in the extension activities and trying their best on daily assessments to be accurately placed in groups. They will solve many problems within their zones of proximal development and they may need to persevere more and be more precise than they had to before. The seventh and eighth practice standards involve using structure and patterns to solve math problems. Students will complete activities built around recognizing the patterns within skip counting and hundreds charts regarding the place value changes in numbers. Lastly, the second and third practice standards address using reasoning and making arguments defending one’s own thinking. Students build their number sense and ability to reason with a strong idea about place value. Students practice making arguments by practicing their metacognition and explaining their work verbally, in writing, and with models. Throughout the entire unit, students act as mathematicians and improve upon all the mathematical practice standards and ways of thinking. This allows them to become stronger mathematicians and think in mathematical ways. 

How does this unit support literacy development?

Literacy is incorporated into this unit in a variety of ways.  Before the unit even began, I updated our Math Words wall. I kept all relevant vocabulary from previous lessons and added all the new vocabulary from this topic. This is important for students to begin to take ownership of the vocabulary and become stronger speakers and writers of math themselves. In addition to the vocabulary posted in the classroom, we will also go through the Topic Opener to define all the new vocabulary before the first lesson. One of the first online games available to the students will be a vocabulary hunt game provided on Pearson Realize. This extensive coverage of the vocabulary will ensure all students hear, see, read, write, and interact with the new vocabulary in this topic. 

Also, students’ constant exposure to word problems is another way they will be expected to interact with literacy in math. They will need to read the problems, solve, write, and model their answers. They will be expected to use vocabulary when appropriate. Their abilities to read will be scaffolded as necessary but all students will be able to identify math words to determine important information within a problem such as “in all” indicating a sum or whole. Students will practice speaking and listening in their small groups and partner-work. They will need to listen to each other and to problems online and they will need to speak to explain and clarify their ideas. Throughout the course of the entire Topic and unit, students will have had an immense amount of opportunities to talk to each other and the teachers about their thinking, read many word problems, and write in response to those problems, increasing their literacy skills and math skills. 

How does this unit develop trust and classroom community?

This unit is extremely impactful for building upon our classroom community. Math meeting is a moment within our school day routine for us to regroup after lunch and recess and come back together as a learning community. By recognizing its importance within our day, I know that this activity builds our classroom’s climate and community. In addition to the routine, this unit evens out the playing field for my students. By addressing their strengths and pinpointing their challenges in math, each student sees themselves as smart and capable of improvement. No one is “the smart math kid” and no one is “the one who’s bad at math.” Each student knows they can accomplish their tasks and each student faces their challenges with a strong support system. In this way, each day, everyone is challenged and pushed appropriately. This also allows each student to be humbled and encouraged to be great at math, creating a respect for our differences and similarities as a class. 

How does this unit position and empower students to “read the world” and act in it in support of equity and social justice?

Although not obvious on the surface, units in math like this one are important for my students in building their sense of problem solving abilities. By persevering and solving complex real-world problems, these types of activities are preparing my students for a world full of hard-to-solve problems. If they have the confidence in their problem-solving skills and can work through tough problems, they will be able to transfer those skills to solving social injustices and fight for equity in our world. Feeling capable of using the tools available to you to make sense of the world around you is the basis for activism. My students will begin to understand that problems are solvable and solutions can be found by collaborating with each other and using resources around. This will empower them to act in just ways as they move on from our classroom. 

How did I, as the instructor, take into account any differences in my socioeconomic, cultural, or racial background, gender, personality, approach to learning, or view of the world and what assumptions did I make about why my plan will connect to my Main South students?

I recognize that my students come from different backgrounds than my own. When approaching math, I recognize that people of color and women are groups that often struggle to see themselves as successful. In this type of unit, I took this into consideration. It is extremely important for these people, as young as second grade, to feel confident in their mathematical thinking and abilities. This type of intervention, while beneficial for their math scores and knowledge, is also designed to boost confidence and belief in oneself as a strong math learner. As a woman who loves math, this is apparent to me. I recall experiences trying to pretend to be bad at math as a young adult. I want to use that background and experience to provide my students with the idea that they should be good at math and not ashamed of it. It is my core belief that all students can be capable learners and achieve highly within a classroom regardless of their demographics and background. 

Important to this unit is the realization that many of my students come from a socioeconomic status which prevents them from accessing the online materials from home. That is why it is increasingly important for us to incorporate technological experiences within the lessons at school. The more students can use Chromebooks to play games, take quizzes, and just scroll and click around, the more likely they will not feel intimidated by the technology when they take larger tests such as the MCAS test in 3rd grade. I want to include online resources that are iPhone and Android friendly so that my students can access them on cell phones as that is their main access to the internet. Despite our differences, I have considered my students access to materials and backgrounds and demographics with this unit’s design and implementation.