Unit 1: Building a Math Community in 2Nd Grade

Unit 1: Building a Math Community in 2nd Grade With the introduction of the Common Core State Standards for Mathematics, teachers and students will have the opportunity to engage in mathematics with focus, coherence, and understanding. Second grade will be fully immersed in the Common Core State Standards Content Standards and the C o mm on C o r e S t and a r ds f o r M a t he m a t i c a l Pr a c t i ce (SMPs). The practice standards describe ways that students will engage in subject matter, and also ways in which teachers should facilitate instructional opportunities for students’ development of understanding. A community can be thought of as a group of people, interacting with each other, sharing common interests or goals, and who can work together to help each other achieve. Applying this to a mathematics classroom, this would produce a group of students, with common learning goals (math content standards), cooperating with each other to learn these goals with understanding (standards for math practice). In other words, a math classroom community will be built and defined by the opportunities, structures, and support the teacher facilitates to help students work and learn together. In the 2013-2014, 2nd grade instructional guideline, the first 9 days of the school year have been devoted to building community in the mathematics classroom. Building community will not be done in 9 days, but the foundation can be developed. Community will continue to develop and build throughout the remainder of the school year. However, without a solid foundation in the beginning of the year, community will not blossom. These first 9 days of community building should place an emphasis on collaboration and problem solving through the use of the Standard for Mathematical Practice (SMPs) and the prior year’s content standards. Prior year’s content is being used for the first 9 days because most students have mastered these standards the previous year. Students will benefit from reviewing these standards at the beginning of the year. Some students may not have mastered prior year’s content standards. For these students, teachers will have the opportunity to informally assess and provide re-teaching structures. In addition, students will be able to use content they are familiar with to focus upon building community and using the practice standards. This document is not intended to be a lesson plan. This document should act as a guide for your instruction for the first 9 days to help build a rich math community. As the classroom teacher you may use these ideas to create your lesson plans that will meet your unique teaching style and the specific needs of your student population. Unit 1: Building a Math Community in 2nd Grade

As you work through the First 9 days of Mathematics, the emphasis is to build classroom norms, classroom routines and an introduction to the Standards for Mathematical Practice (SMP). Incorporate number sense content from the previous grade level to use familiar concepts while learning practices to be used year round. The suggestions below include a focus on addition and subtraction problem structures.

Throughout the first 9 days you may want to introduce the kid friendly SMP (that were given at the CCSSM Applying Training) posters as applicable to the lesson.

It is imperative to establish math classroom norms to create an environment where children feel comfortable to share strategies, take risks, and critique others’ reasoning. Students need to build their capacity for disequilibrium. Building math classroom norms and practices will assist students in doing this. Click here for more information on disequilibrium. There are 2 options below you may choose from to implement these math norms.

Option # 1: Teachers should establish math classroom norms to promote a positive classroom environment. The following are some examples of norms that you can utilize to promote productive communication in the classroom:

1. Explain your thinking 2. Ask questions 3. Challenge ideas, not students 4. Say when I don’t understand or agree 5. Actively participate in all learning tasks

These are just examples, work with your students and/or school to establish these norms.

Option # 2: Debrief at the end of each day about student and teacher behaviors that enhance math learning. As a teacher you may want to guide the conversation to the norms listed above. The debriefing time throughout the first 9 days will culminate to create an anchor chart of approximately 5 math norms for your classroom.

While the first 9 days teach these math practices in isolation to help build student understanding you will want to integrate the practices as students develop mastery. Unit 1: Building a Math Community in 2nd Grade Day # 1: Choose Appropriate Tools and Solve problems (SMP 1 & 5)

Task # 1: Students choose a manipulative from a wide selection of tools. Have manipulatives easily accessible so that students don’t have to ask you for them. Once students select their manipulatives, have them draw a representation and brainstorm ways they could use the tool in mathematics. Differentiation Note: This activity may be extended by challenging students to write a word problem that they could solve using their selected tool.

Task # 2: Present students with the following problem: Connie had 5 marbles. Juan gave her 8 more marbles. How many marbles does Connie have all together? Students will work individually (or in pairs) at this time and choose an appropriate manipulative to help them solve the problem. Students will record the solution and justify with words and/or pictures. Remind students that they will be expected to share their thinking. Teacher Note: Be sure to highlight different ways that students solved the problem using different tools.

Task 3: Present students with the following problem:

Show the different ways to represent the number 38.

Teacher Note: When selecting students to share start with a less efficient tool and end with base ten blocks. The goal of the conversation is for students to determine the most efficient tool to use.

Day # 2: Journaling about Problem Solving (SMP 6 & 3) Unit 1: Building a Math Community in 2nd Grade

Task # 1: Journaling is an important part of the learning process in mathematics. Students should know and be comfortable with the expectations for journaling. In order to facilitate this, work with your students to create a class rubric on evaluating journal responses. (Refer to yesterday’s problem solving for journal examples.)

Sample Rubric: 3-The student work demonstrates a clear understanding of the mathematics. The answer is correct. Minor errors may be evident. The words, pictures, and/or numbers indicate an understanding of the math concepts. 2 -The student work demonstrates a partial understanding of the mathematics. The answer is partially correct. The words, pictures, and/or numbers indicate a partial understanding of the math concepts. 1- The student work demonstrates an insufficient understanding of the mathematics. The answer is incorrect. The words, pictures, and/or numbers indicate a lack of understanding of the math 0-There is no response.

Task # 2: Use the problem below to practice a journal response. Students can self evaluate using the class made rubric. The teacher may need to model this behavior and monitor the student’s self evaluation.

Fly the Sky Airlines charges extra money for bags over 50 pounds. Joe puts his bag on the scale and it weighs 58 pounds. After taking out his math books his bag was 46 pounds. How much did the math books weigh?

Teacher Note: SMP 6 Attend to precision is evident in this day because students need to use precise language when explaining their strategy (SMP 3) and should label all parts of their mathematical work. Highlight SMP poster and refer to the poster with your students. You can highlight the SMP posters that apply to each lesson throughout these 9 days and during the school year. Unit 1: Building a Math Community in 2nd Grade Day # 3: Accountable Talk (SMP 3) Accountable talk practices are essential for the math norms you are establishing in your classroom. Click here to access the accountable talk question stems. These can be used to help guide your lesson plans. The question stems may be used as an anchor chart and/or glued in student math journals. Below is a sample of a question you could use to model and role play how the accountable talk question stems build productive classroom discussions. When using accountable talk the focus on the process of the mathematics not just the answer. Sample Question: Kaiya and her friends were sharing Silly Bandz. Kaiya started with 25 Silly Bandz. She gave 5 Silly Bandz to Jill and 3 to Alec. Lucy gave Kaiya 8 Silly Bandz. How many Silly Bandz does Kaiya have now? Task # 1: Use the Fish Bowl Strategy as a tool for modeling discussion. The teacher provides a problem solving task. Once students have completed solving the problem the teacher selects 3 to 5 students for the “fish bowl” group. The “fish bowl” group will discuss their strategies using accountable talk. “The other students must remain quiet but write down their observations about the discussion. After a few minutes the “fish bowl” group stops discussing and the other students critique the discussion or offer suggestions to the “fish bowl” group. The teacher can point out strengths of the discussion, offer helpful comments and discussion, and make suggestions on how to strengthen the discussion. This is a great way to model a discussion and talk about what makes for an effective small group discussion.” (Taylor, 2007)

Below are some Kagan strategies to pair children: o Parallel Lines-  Students number off 1-18 (or however many are in your class).  Even numbers form one line.  Odd numbers form another line and face an even number so that each student has a face partner.  High five your face partner.  Have pairs find a space in the classroom to solve each other’s problems.  After students have solved the problem, switch back papers and have students evaluate how the problem was solved. Was it solved correctly or incorrectly? o Stand Up, Hand Up, Pair Up-  Instruct students to stand up and push in their chairs.  Have them place their hand in the air.  Students walk around the room with their hand up.  When the teacher says, “Pair Up”, students find the closest person to them.  High five the person closest to you, high five that person, that is now your partner.  Have pairs find a space in the classroom to solve each other’s problems. After, students have solved the problem, switch back papers and have students evaluate how the problem was solved. Was it solved correctly or incorrectly? Unit 1: Building a Math Community in 2nd Grade Day # 4: Direct Modeling (SMP 1)

Direct Modeling is when the student uses manipulatives and drawings along with counting to represent directly the actions in a story or problem. If a child cannot model a problem he or she cannot solve a problem. If students are struggling, avoid referring to the operation. Students should be reminded to think about what is happening in the story and find a way to show it. (Levi, 2006)

Sample Question: (Direct modeling can be done using manipulatives or a quick picture.) Chuck had 3 candy bars. Clara gave him some more candy bars. Now Chuck has 8 candy bars. How many candy bars did Clara give him?

Sample student model: A set of 3 objects is constructed. Objects are added to this set until there is a total of 8 objects. The answer is found by counting the number of objects added.

Click here to access additional word problems that implore the use of direct modeling

Teacher Note: Be sure to keep anecdotal records as students work with the concept of direct modeling on Day 4 and Day 5. The records that you keep will be what you use to sort your students into differentiated groups on Day 6. Unit 1: Building a Math Community in 2nd Grade Day # 5: Direct Modeling Using the K-W-P-R Chart (SMP 1)

A good strategy to use to help students make sense of the problem is a K-W-P-R chart. K-What do I Know about the problem? W- What do I need to find out? P- What is my Plan for solving the problem? R-Why is my answer Reasonable? Click here to see a sample of a K-W-P-R chart. This is a suggested organizational strategy for problem solving.

Sample question to fill out the K-W-P-R chart: Jkwon’s water cooler was filled with 89 ounces of water. Jkwon drank some of the water from his cooler after playing tennis. After Jkwon drank some of the water, the cooler contained 78 ounces of water. How many ounces of water did Jkwon drink?

Students then complete the K-W-P-R chart in their journal. After students have completed their K-W-P-R chart have students turn and talk to a neighbor about their work. Remind students that during a turn and talk, you are sharing your mathematical thinking and actively listening to your partners thinking to help make sense of the problem. The teacher’s role is to circulate and monitor these discussions throughout the classroom.

Click here to access additional word problems to practice using the K-W-P-R chart.

Day # 6: Differentiation in the Math Classroom (SMP 2 & 1) Unit 1: Building a Math Community in 2nd Grade

Explain how students in the mathematics classroom may have different tasks to complete then their peers. Using the anecdotal records that you have taken on days 4 and 5 to sort your students into groups-> re-teach, core and enrich. Below are lesson ideas for the groups:

Re-teach: Use your teacher observations to determine a skill that your students would benefit from you re-teaching.

Core: Click here for problem ideas for your core students to complete.

Enrich: Task # 1: Use the equation cards to give each student their own equation so they can write a word problem to go with it. Task # 2: Students will pair up with a partner, swap questions, and solve each other’s problems in their math journals.

Day # 7: Modeling Mathematics All Around Us (SMP 4) Unit 1: Building a Math Community in 2nd Grade SMP 4 is focused on using the real world to model mathematical situations. Using real world math problems engages students and lets them see how math is used all the time. Finding the real world math in their physical environment happening all around them is essential to build students mathematical proficiency.

Click here for examples of a real word math problem that could be used to model mathematics.

However, since all schools are unique these questions are just general guidelines. You may need to modify these questions to appeal to your students “real world”.

Teacher Note: To build classroom community, this would be an appropriate time to add in the practices that have been reviewed over the past 6 days. For example: KWPR chart, accountable talk, direct modeling, journaling, and selecting appropriate tools.

Day # 8: Learning From Our Mistakes

Based on observations from Day 7, as students solved their problems, highlight a common misconception Unit 1: Building a Math Community in 2nd Grade that you saw while you were monitoring student work. Rewrite the misconception you saw multiple students making either on a piece of chart paper or displayed under the Elmo. Have students work in pairs to analyze what the misconception was and reflect and record the errors in their journals.

Once students have shared in their group, have one representative share what misconception their group noticed to the WHOLE GROUP. Facilitate discussion using accountable talk structures and questions such as, “Do you agree with that misconception and why?”, “What other misconceptions might this student have?”, and “How could we clear up this student’s misconceptions?”

Below is a sample student misconception that could be used to learn from our mistakes.

When Kallie got home from school she had 12 baseball cards. At school that day her friend gave her 5 baseball cards. How many cards did Kallie go to school with?

Discussion points: Do you see where the student who solved this made a mistake? Where did this student go wrong? Do you see anything good that this student did when solving this problem?

Teacher Note: Emphasize to students the importance of learning from our mistakes and being willing to share our mistakes. This will build your classroom community by creating a risk free environment where students are willing to take chances because it is okay to be wrong and learn from it. It is suggested that developing a management system that rewards students who support their classmates and provides consequences for those who do not. As the teacher you must insist that classmates demonstrate an encouraging attitude towards their peers. Unit 1: Building a Math Community in 2nd Grade Day # 9: Our Working Math Classroom

This is a day to reinforce all of the math behaviors and norms that have been established in prior days. Depending on how you choose to develop math classroom norms (option 1 or 2), use this day to either reinforce or draft the norms. In addition content and activities should be designed based on student needs observed in previous days. Consider utilizing the attached checklist to guide your planning. (Click here)

This year students will be assessed using performance tasks. These are comprehensive assessments that require students to justify their thinking. Click here for an example of what a 1st grade performance task looks like. This is an opportunity for students to get acclimated to these types of tasks and to practice all of the math norms and behaviors you have been building upon all week.

2013-2014 School Year Page 11