Unit 1: Building a Math Community in 2nd Grade

With the introduction of the Florida Core 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 Florida Core 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 2014-2015, 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.

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 thinking2. Ask questions3. Challenge ideas, not students4. Say when I don’t understand or agree5. 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 3-5 math norms for your classroom.

Unit 1: Building a Math Community in 2nd Grade

Anecdotal notes about behaviors students’ exhibit during the problem solving process, familiarity with tools, perseverance and targeted content knowledge can be used to make instructional decisions throughout the year. Utilize the following chart throughout the Unit: Building a Math Community

Day # 1: Modeling Mathematics All Around Us (SMP 4)

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.

Task #1: Collecting Data: As you are developing your math community and learning about your students highlight the math in the first day of school tasks.Examples: Charting dismissal (graphing opportunity)School supplies collected (counting equal groups)Uniforms (graphing, combining, comparing <, >, =)First Day Packets Lunch Desk Arrangement

Task #2: Click here for examples of a real word math problem that could be used to model mathematics. 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”.

Day # 2: Accountable Talk (SMP 3)

Unit 1: Building a Math Community in 2nd Grade

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.

Task #1: Accountable talk is imperative in creating a productive math environment. To begin accountable talk, focus on the behaviors you want students to exhibit. Example:Pose the question, “How do we line up in the classroom?”Have Student 1 restate the question. Have Student 2 restate Student 1.Allow wait time for students to formulate their answer (about 15 seconds)Select student to answer the question. Allow students opportunities to agree/disagree or add on to the response.Remind students when they are being active listeners their eyes and ears are on the speaker.

Apply the previous accountable talk strategies to the following math problems. Have students use the same behaviors and techniques when discussing how they solved the problem.

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?

Sample Question: Marcellus looked at the clock and saw that the hour hand was between 2 and 3. What could be happening during this time?Teacher Note: As students are discussing activities, listen for JUSTIFICATION of responses.

Sample Question: Jontee has a quarter. Mikaya has two dimes. Mikaya thinks she has more money than Jontee because she has two coins. Do you agree with Mikaya. Justify your thinking.

These Kagan Strategies are helpful when pairing students to have accountable talk with a partner.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.

Unit 1: Building a Math Community in 2nd Grade

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 # 3: Journaling about Problem Solving (SMP 6 & 3)

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.

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 # 4: Choose an appropriate tool strategically (SMP 5 and 1)As part of Building Community, you will be previewing content that will be taught in subsequent units. Focus on exposure to these concepts versus mastery of the concept.

Task # 1: 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 2: Present students with the following problem:

Represent the number 38 three different ways.

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.

Task 3:

Lesley has these coins:

How can you show the same value using more coins?

Teacher Note: At times, it is appropriate for our students to select tools; however, our students need to understand that at times, certain tools are more appropriate

Day # 5: Direct Modeling (SMP 1)

Unit 1: Building a Math Community in 2nd Grade

Direct Modeling is when the student uses manipulatives and drawings along with counting to directly represent 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)

As students are directly modeling problem situations, prompt them to identify each object in their model represents from the problem.

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 the following problems in a word document.

Rebecca has 5 packs of gum with 3 pieces of gum in each pack. How many pieces of gum does Rebecca have altogether?

Patrick has 12 Smencils. How many more Smencils would Patrick have to make to have 19 Smencils altogether?

There were some seals playing. Three seals swam away. Now there are 5 seals playing. How many seals were playing before the three seals swam away?

Challenge students to write a problem for which they can show a direct model.

Teacher Note: Be sure to keep anecdotal records as students work with the concept of direct modeling on Day 5 and Day 6. The records that you keep will be what you use to sort your students into differentiated groups on Day 7.

Day # 6: Direct Modeling Using the K-W-P-R Chart (SMP 1)

Unit 1: Building a Math Community in 2nd Grade

A good strategy to use to help students make sense of the problem is a K-W-P-R chart (or any variation). 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:J’Kwon’s water cooler was filled with 89 ounces of water. J’Kwon drank some of the water from his cooler after playing tennis. After J’Kwon drank some of the water, the cooler contained 78 ounces of water. How many ounces of water did J’Kwon 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 the word problems below to practice using the K-W-P-R chart.

Task 1: 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?

Task 2: Samantha is taller than Kendra. Kendra is taller than Frank. Bobby is shorter than Samantha but taller than Kendra.

Who is taller than Bobby?

Day # 7: 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 than their peers. Using the anecdotal records that you have taken on days 5 and 6 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. Students who are struggling need to revisit Direct Modeling. Sample questions to use to remediate your students COULD include:Samantha baked 12 cookies. Her sister ate 4 of them, how many total cookies are left?Maria earned $11 doing chores on Saturday and $10 walking dogs on Sunday. How much money did she earn over the weekend?

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

1. Jala had 12 rocks in her collection. Then she added some more rocks to her collection. Now she has sixteen rocks. How many rocks did Jala add to her collection?

2. Sean has three more pencils than Stephanie. Sean has five pencils. How many pencils does Stephanie have?

3. The teacher wrote 13 - 6 = ? on the board and asked students to write a word problem to model the equation.

Keisha wrote:Keisha had 13 pennies. Then Keisha found 6 more pennies. How many pennies does she have now?

Albert wrote: Albert has 13 markers. Then Albert gave 6 markers to his friend. How many markers does Albert have now?Whose word problem correctly models 13 – 6 = ? How do you know?

4. Write a word problem that matches the following equation.6 + 11 = ?Show how you would solve the problem you wrote?

Enrich:Students who engage in the enrich activities should have already shown mastery of the ability to direct model problem solving strategies. 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 # 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?

Create additional problems to address the misconceptions identified in your classroom.

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)

Pose the following problems to your students:

Jimmy and Shanann each have 4 packs of Starbursts. Each pack has ten Starburst in it. If Jimmy gives

Shanann one whole pack and 4 pieces from another one of his packs, how many Starbursts would Jimmy and

Shanann each have?

Prior to giving the problem to your students, solve the problem to identify any misconceptions students may

encounter as they are solving the problem.

As students solve the problem, facilitate discussion regarding students’ solutions by having them share their

solutions starting with the most concrete representation (using manipulatives) to something representational

(drawing or pictures) and ending with something more abstract (addition and subtraction algorithms). Focus

on facilitating a discussion that connects the strategies. As you are selecting students to share, be purposeful in

selecting students that will lead you toward your learning goal. Keep an eye out for common misconceptions

you may need to address as you are monitoring students during the problem solving process.

Additional Problem to use:

Adam has 3 fewer dimes than Jana. Jana has some dimes. How much money do Adam and Jana have

altogether?

Accept any reasonable answer as long as it meets the criteria. This problem will promote discussion in the

classroom as it is open-ended.

2014-2015 School Year Page 12