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 Common Core Standards for Mathematical Practice (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.
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 while focusing on the learning practices and structures to be used in your classroom 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 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 3-5 math norms for your classroom.
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 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:
Ø Charting dismissal (graphing opportunity)
Ø School supplies collected (counting equal groups)
Ø Uniforms (graphing, combining, comparing <, >, =)
Ø First Day Packets
Ø Lunch
Ø 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)
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 to create an anchor chart and/or glued in student math journals.
Below is a list of sample questions you could use to model and role play how the accountable talk question stems build productive classroom discussions. When using accountable talk question stems, the focus should be on the process of the mathematics not just the answer.
Task #1: Accountable talk is imperative in creating a productive math environment. To facilitate implementation of accountable talk, focus on the behaviors you want students to exhibit.
Example scenario to focus on student behaviors:
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 1:
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 2:
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 3:
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.
· 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 3 & 6)
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 concepts.
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.
Day # 4: Choose an appropriate tool strategically (SMP 1 & 5)
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)
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)
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?