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Building a Math Community in the Third Grade Classroom

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. Though third grade classrooms in Hillsborough County will not be using the Common Core content standards for instruction this year, the C o m m on C o r e S t and a r ds f or M at h e m a ti c a l P r a c t i ce should be implemented in all math classrooms. The practice standards describe ways that students will engage in subject matter and also ways 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 third grade instructional guidelines, 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 practice standards and prior years’ content standards.

First, most students should already have mastered these standards prior to the current grade level, but may benefit from exploring with these standards coming back to school in a new grade level, as well as connecting prior content and strategies to grade level content. Secondly, some students may not have mastered prior content standards. For these students, teachers will have the opportunity to informally assess and provide reteaching structures. Finally, students will be able to use content they are familiar with to focus upon building community and using the practice standards.

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As you work through the First 9 Days of Mathematics, be sure to practice classroom norms and classroom routines. These learning tasks are designed to help students practice mathematical classroom norms and routines. Incorporate number sense content from the previous grade level to use familiar concepts while learning structures to be used year round. The suggestions below include a focus on two-digit addition and subtraction in problem solving.

Day 1- Choose and Solve Problems Using Manipulatives:

During Day 1, teachers should establish 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 classmates (peers)4. 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.

Task 1: Students choose a manipulative from a wide selection of tools. Have manipulatives easily accessible, so students don’t have to ask you for them. Once students select their manipulative, have them draw a representation of it in their journals and brainstorm at least 5 math concepts that they could learn more about by using them. (SMP 5)

Task 2: Present students with the following problem: There are 32 animals at the zoo. 14 of the animals were monkeys. How many animals were not monkeys? Students will work individually or in pairs at this time and choose an appropriate manipulative to help them solve the problem. Students will record their solution in their math journal. Remind students that they will be expected to share their thinking. Students should directly model the problem situation referenced in bold using manipulatives and or pictures (SMP 1, 2, 4). Direct modeling is a strategy that helps to build students’ understanding of what is happening in a problem solving scenario and what operations might be useful in finding a solution. The more opportunities students have to directly model situations, the better they will conceptually understand the operations.

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Day 2 - Journaling about Problem Solving and Creating Rubrics:

Task 1: Students review their solution and manipulative choice from Day 1. Students will write in their journals about their manipulative choice and explain how it helped them to solve the problem. (SMP 3)

Task 2: 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 for evaluating journal responses. (SMP 3, 6)

Example Rubric:4 The student demonstrates an in-depth understanding of the mathematics.

Information is correct and complete.Explanation, description, or justification is clear.Writing may include details and/or examples.

3- The student demonstrates considerable understanding of the mathematics.Information/explanation is correct.Minor computational errors may be present.Explanation, description, or justification may lack clarity and details.

2 -The student demonstrates limited understanding of the mathematics.Information and/or explanation are incomplete. Significant computational errors may occur.

1- The student demonstrates little understanding of the mathematics.Information is incorrect.Explanation, description, or justification is unclear or incorrect.

0- No attempt was made.

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Day 3- Be responsible for your learning and what to do when you are done journaling.

Task 1: Using the journal response and the rubric that you created on Day 2, have students self assess their work using the rubric. Then, have students swap their journal with a peer for evaluation. Use SMP 3 (construct viable arguments and critique the reasoning of others) to promote discourse in the classroom. Model how to have appropriate conversations when critiquing others’ work.

Additional activities for being responsible for their learning might include: Concept Cards - students generate a definition of the concept, pictorially

represent the concept and create examples and non-examples of the concept to create a deeper understanding of it.

Task 2: Students create word problems based on the following expressions:

143 + 29 and 100 – 63

Record the word problems in their journal to be used on Day 4.

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Day 4- Share and Compare your Solution and Accountable Talk

Task 1: Using the word problems created on Day 3, students will pair up with a partner, swap questions and solve them. (SMP 1, 2, 3, 4)

Strategies to pair students: Parallel Lines-

Students number off 1-22 or however many are in your class Even numbers form one line Odd numbers form another line, so that they are facing the even line

and each student has a face partner High five your face partner Have pairs find a space in the classroom to solve each other’s problem. After students have solved the problem, switch back papers and have

students evaluate how the problem was solved. Was it solved correctly or incorrectly?

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 partner High five your partner Have pairs find a space in the classroom to solve each other’s problem After students have solved the problem, switch back papers and have

students evaluate how the problem was solved. Was it solved correctly or incorrectly.

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Use these question stems to promote accountable talk solving each other’s problems.

So what I heard you say

is….

I agree with youbecause…

I disagree with youbecause…

My strategy is like yoursbecause…

Could you explain that to me another way?

What is another strategy we could use to check?

How do you know your answer is right?

I don’t understand …

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Day 5- Small Group Instruction:

Explain to students that sometimes in the mathematics classroom they may have different tasks to complete than their peers. Engage the class with the following problem to determine your small groups. Mrs. Short baked some yummy chocolate brownies. She placed 7 plates on the kitchen table and put 2 brownies on each plate. How many brownies did she put on plates? Be prepared to justify your answer. As students solve this problem, sort students into 3 different groups; Reteach, Core, Enrich (You may not always have 3 groups during small group instruction). Use the following questions with your 3 groups. (SMP 2, 3, 4)

Journal Prompts: (SMP 1, 3, 4)

Reteach: Colin had 2 baskets with 3 apples in each basket. Colin said he had about 20 apples altogether. Is this a reasonable estimate? Explain why or why not?

How many apples did he have?

Core: Meg’s mom puts 5 cupcakes on each plate. She has 8 plates for a party. Meg said she had about 50 cupcakes altogether. Is this a reasonable estimate? Explain why or why not?

How many cupcakes does she have for the party?

Enrich: Ladybugs in Kim’s yard have 10 spots. She catches 4 ladybugs on Tuesday, 5 ladybugs on Wednesday, and 6 ladybugs on Thursday. Kim said she there were about 1,000 spots on the ladybugs. Is this a reasonable estimate? Explain why or why not?

How many total spots did she catch? Explain how you know.

Allow students to work with their groups or in partners to solve their assigned problem. Encourage the use of direct modeling. Have the question stems available from Day 4, so that students can have productive mathematical conversations to help them make sense of the problem. Circulate and monitor as needed and pull a small group as needed to provide additional support. As students are solving their problem remind them to explain their thinking in their journals. Once students solved the problems through direct modeling have them complete the following journaling prompts. Have students provide evidence for their response.

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Day 6- HOT Questions:

One goal of rigorous education is to increase student’s higher order thinking skills. This can be accomplished through the use of Higher Order Thinking (HOT) questions to extend students thinking. HOT questions should be more than just reproducing a skill or fact. They are NOT yes or no questions, they are open ended. For this mini-lesson, students need to have access to their math journals, the rubric, and a variety of manipulatives to help in the problem solving process. Students will receive their HOT question and will work with a partner to solve the problem and provide justification for their solution method. The most important part of this process is for students to provide justification with precision (vocabulary, explanation etc.) (SMP 3, 6) Students deepen their understanding because in order to explain an idea, a student must conceptually understand it. If students are mathematically proficient, they will be able to explain their thinking.

Task 1: Use the following question with your students:

The third and fourth grade classes were on the playground for recess. 18 of them went back to their classrooms to work on a special project. Now there are 37 on the playground. How many students were on the playground to begin with?

Have the question stems available to help with productive mathematical conversations. Purposefully select and sequence students to share their solutions. Start with the student who used a concrete representation, then move to a student who use pictorial representation and finally have a student who used an abstract representation to share. Use the question stems to connect the student strategies.

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Day 7: Problem Solving Process

During Day 7, students will engage in the problem solving process, understand what the question is asking in a problem situation and formulate a plan for solving the problem. A good strategy to use to help students make sense of the problem is a K-W-P-L chart. K- What do I know about the problem, W- What do I Want to Know about the problem, P- What is my plan for solving the problem, L- What have I learned by solving this problem. (SMP 2)

Task 1- Present the following problem to the students in your class:

The Boy Scouts were planning a breakfast in the school gym. There were 5 round tables and 4 square tables. 6 people can sit at each round table and 4 people can sit at each square table. How many people can sit at all of the tables? (SMP 1, 4)

In pairs, have students restate the problem in their own words to ensure comprehension of the question. Students then complete the K-W-P portions of the KWPL chart in their journal. After students have completed the KWP sections of their chart, have students turn and talk to a neighbor about their work. Remind students that during a turn/talk you are sharing your mathematical thinking and actively listening to your partner’s thinking to help make sense of the problem (SMP 3). The teacher’s role is to circulate and monitor these discussions throughout the classroom. Once students have shared their KWP, students will try their plan. Have students directly model the action in the problem to find a solution. (SMP 1, 2, 4) Students will individually solve the problem first, then with a partner and finally with their group. Students complete the L portion of the KWPL Chart at this time. A good strategy to use is 3-3-3. Students spend 3 minutes working individually, 3 minutes working with a partner, and 3 minutes working with their group. This allows individual think time as well as support of their team to help students work through the problem solving process.

After 3-3-3, bring the class back together whole group. Facilitate whole group discussion that should focus around how students may have used different plans to solve the problem, how did the small group discussion help justify correct solutions and make connections to other concepts. In addition, look for misconceptions students may have while solving this problem. You will use this information on Day 9.

Prior to students actually solving the problem, have students respond to the following prompts:

The troop leader had 50 seats. He says that is enough for the breakfast. Do you agree with his thinking? Why or why not?

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Day 8: Problem Solving Process

During Day 8, students will engage in the problem solving process, understand what the question is asking in a problem situation and formulate a plan for solving the problem. A good strategy to use to help students make sense of the problem is a K-W-P-L chart. K- What do I know about the problem, W- What do I Want to Know about the problem, P- What is my plan for solving the problem, L- What have I learned by solving this problem. (SMP 2)

Task 1- Present the following problems to the students in your class:

In pairs, have students restate the problem in their own words to ensure comprehension of the question. Students then complete the K-W-P portions of the KWPL chart in their journal. After students have completed the KWP sections of their chart, have students turn and talk to a neighbor about their work. Remind students that during a turn/talk you are sharing your mathematical thinking and actively listening to your partner’s thinking to help make sense of the problem. (SMP 3) The teacher’s role is to circulate and monitor these discussions throughout the classroom. Once students have shared their KWP, students will try their plan. Have students directly model the action in the problem to find a solution. (SMP 1, 2, 4)

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Students will individually solve the problem first, then with a partner and finally with their group. Students complete the L portion of the KWPL chart at this time. A good strategy to use is 3-3-3. Students spend 3 minutes working individually, 3 minutes working with a partner, and 3 minutes working with their group. This allows individual think time as well as support of their team to help students work through the problem solving process.

After 3-3-3, bring the class back together whole group. Facilitate whole group discussion that should focus around how students may have used different plans to solve the problem, how did the small group discussion help justify correct solutions and make connections to other concepts. In addition, look for misconceptions students may have while solving this problem. You will use this information on Day 9.

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Day 9- Reflect and Analyze Misconceptions

Based on the observations from Day 7 and 8, highlight common misconceptions that you saw while monitoring the classroom. Rewrite the misconception that 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 journal. Bring pairs back to their respective small groups and have students share their reflections by using the Kagan Structure Round Robin.

Randomly choose a teammate to go first (example: student with the longest hair goes first).In teams, participants respond orally identifying possible misconceptions.Each student takes about 1 minute to share.

Once all small groups have shared, allow one representative from each group to share the misconceptions their group noticed to the class. Facilitate discussion by using Accountable Talk structures. “Do you agree with that misconception and why?” “What other misconceptions might the students have?”

After students have identified possible misconceptions, work as a class to generate an anchor chart on “Ways to prevent misconceptions.”

Ways to Avoid Misconceptions

Reread the problem Use tools to model the action Ask myself, “Does this make sense?” Make a KWPL

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Days 10, 11…

Conti nuing to bui ld math comm unit y

9 days will not be enough to fully establish the math community in a classroom, it will take much longer. Continue to use the skills presented here and the standards for mathematical practice to build a community of problem solving, collaborative, mathematically inclined thinkers. Also continue to add new tasks for students such as creating goals, charting scores, flexible thinking, Share and Compare, Kagan strategies and other ideas for building community. As new students join the class, they will also have to be introduced into what is expected in this particular math class’ community. Continue to refer to the Global Concept Guides in the instructional guideline for ideas.

****As you work through the First 9 Days of Mathematics, be sure to practice classroom norms and classroom routines. These learning tasks are designed to help students practice mathematical classroom norms and routines.****

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