Global Concept Guides: First Nine Days
Prior Learning: MAFS.K.CC.1.3, MAFS.K.OA.1.1, MAFS.K.OA.1.2
Sample Show What You Know Task: n/a
Common Core State Standards for Mathematical Content :
Represent and solve problems involving addition and subtraction.
MAFS.1.OA.1.1 Use addition and subtraction within 20 (10) to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. ([1]Students are not required to independently read the word problems.)
Tell and write time.
MAFS.1.MD.2.3 Tell and write time in hours and half-hours using analog and digital clocks. / Comments:
Strikethroughs indicate that only specific problem structures will be used within 10 in this unit of study.
Notes on Assessment:
There is NO Assessment or Performance Task for Building Community
Unpacking the Standards for this Unit:
Like other aspects of mathematics, communication and language need to be taught and learned in school classrooms. But they are also a primary means by which mathematics is taught and learned. (A Research Companion to Principles and Standards for School Mathematics, 2003, pg. 237).
“Direct Modeling is distinguished by the child’s explicit physical representation of each quantity in a problem and the action or the relationship involving those quantities before counting the resulting set” (Children’s Mathematics Cognitively Guided Instruction, Carpenter. T., et al., 1999 p. 22).
It is important for students to have experience Direct Modeling prior to counting strategies and number facts.
Common Performance Task with Rubric for this Unit:
There is NO Performance Task for Building Community
Future Learning:
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.
1st / Global Concept 1 of 1 for this Unit of Study (Click to view PowerPoint in slide show mode): First Nine Days
Day 1: Establishing Procedures and Choosing Manipulatives, Day2: Communicating Ideas, Day 3: Accountable Talk, Day 4: Justify through Journaling, Day 5: Class Norms, Day 6: Problem Solving Process, Day 7: Tackling Tough Problems, Day 8: Telling Time to the Hour, Day 9: Collaborative Groups / Projected Time
Allotment:
9 days
Sample Essential Questions:
Day 1: What are math tools and how should we use them?
Day 2: How does a math tool help me solve a problem?
Day 3: How can we communicate respectfully to learn from others?
Day 4: How does journaling help us share our thinking?
Day 5: How do math norms help our class?
Day 6: What should I consider when solving problems?
Day 7: What strategies can be used to help persevere in solving tough problems?
Day 8: How does knowing the pattern of telling time help us follow a schedule at school?
Day 9: How does working together help us learn?
Related Go Math Chapter Test Questions: N/A
Instructional Resources
Manipulatives:
· two-sided counters - use to model counting on to make ten as well as develop images of numbers up to 10
· snap cubes - use to model joining sets and separating sets in problem-solving
· centimeter cubes - use to model adding to and taking from problems
· geared clocks; teacher and student - use to model the hour hand
Lesson Ideas:
· See the Building Community within the Mathematics Classroom
For more information about integrating the content within this GCG click here to save the PowerPoint
Sample HOT Questions: Select or create appropriate questions to facilitate student discussion.
· How will this tool help you solve the problem?
· How can you determine the action in a problem situation?
· What strategies can you use help solve a problem?
· How is your representation similar or different from someone else’s?
· How can you describe the movement of the hour hand?
· What do I do when solving a problem is difficult?
Our students are better able to…
· Persevere in problem solving. (SMP1)
· Use Accountable Talk to communicate clearly and justify thinking through journaling. (SMP 3, 6)
· Direct model mathematical problems. (SMP 2, 4)
· Select appropriate tools. (SMP 5)
· Recognize structure as it occurs in the real world. (SMP 4, 7)
· Demonstrate the Mathematical Practices on a consistent basic. (all SMPs are included)
For more information on SMP’s click here. / Because as teachers we…
· Encourage students to attempt challenging problems and use many strategies to find success. (SMP 1)
· Explicitly model and hold students accountable for the ways we talk and write about math. (SMP 3)
· Model using a Think Aloud. (SMP 1)
· Provide an environment that encourages active inquiry, hands on engagement and discovery. (SMP 1, 4, 5)
· Provide real world problem situations. (SMP 4)
· Consistently refer to our Math Norms established by the class or school. (all SMPs are included)
·
Building a Math Community in First Grade
Day 1- Establishing Procedures and Choosing Manipulatives
EQ: What are math tools and how should we use them?
Manipulatives play an important role in problem solving, especially when students are first introduced to mathematics in early grades. It is important to know that manipulatives serve as a way for students to understand mathematics in a tactile way- to visibly model their thinking.
In this task, students will have the freedom to choose the manipulative of their liking. It is important that we as teachers do not limit the selection of tools because this will hinder their individual thinking.
SMP Connections: (SMP 5) Use appropriate tools strategically is emphasized
Teacher Preparation and Materials:
Gather math manipulatives/tools (these terms can be used interchangeably based on your needs) and place in a centrally located area of the room. The central location should be organized and visible to all students, as it will be accessed throughout the year. There should be enough of each tool so that every student will have a variety of manipulatives to choose from. Tools in this area may include, but not limited to: stackable counters, color tiles, 2 color counters, snap cubes, base 10 blocks, centimeter cubes, links, pattern blocks, color cubes, attribute blocks, clocks, tangrams, geometric solids, etc… The manipulatives should be labeled with precise language. Click here for sample manipulative labels.
In the manipulative area, place chart paper ready to record the “Manipulative Rules”.
Task:
Have students sit in a circle. Teacher will model how to:
· Walk to the manipulative area to choose a manipulative.
· Think about choosing a manipulative out loud. Teacher states, “I chose the red and yellow counters because I think they can help me with counting.”
· Think about how much of the manipulative is needed for the task. Teacher states, “I will take one baggie or one handful (depending on how the tools are organized) because I need to leave tools for my friends.”
· Come back to the carpet and sit appropriately with their manipulative.
Allow two students to walk to the manipulative area to choose a tool. Students should sit with their manipulative choice in front of them until all students have had the opportunity to choose.
After each student has chosen a manipulative, the teacher will share one rule that will apply to all manipulatives. Teacher states, “I think an important rule for my tool should be to keep tools in our work space because someone can get hurt if they get thrown across the room.”
Now, have students explore and share with their neighbor the tool they chose and discuss what rules they might need when using their manipulative. Explain the basic turn and talk procedures. Example: Turn your whole body to face your partner, while one partner is sharing, the other partner is looking at the speaker and their hands are empty and folded in their lap. Partners will then switch roles. Once each student in the group has shared with a partner, allow students to share their thinking with the whole group.
As students are sharing whole group, the teacher charts rules for manipulative use. As rules are being charted, teacher should allow students to model (act out) examples and non-examples of what each rule should look like to increase understanding, example: sharing & not sharing, taking too much of the manipulative & selecting enough needed for the task, etc….
Some Examples of Manipulative Rules:
· Tools should stay in the work space
· Share tools
· Keep tools out of our mouths
· Tools stay at school
· Be respectful of our tools (don’t write on them, don’t break them, etc.)
· Hands are off when someone (teacher or student) is sharing
· When we are finished with our tools, pick them up and put them where they belong
· Use only one manipulative at a time unless needed
· Take only what you need for the task
In an effort for students to self-reflect about their learning and strategies, students will complete a portion of the self-assessment rubric on each day 1-4. Students will color the smiley face that shows their reflection of today’s performance. Today, have students complete the first strip titled, “I chose an appropriate tool.”
Day 2- Choosing Manipulatives to Help Solve Problems and Communicating Ideas
EQ: How does a math tool help me solve a problem?
This day will continue the expectations for manipulatives and apply these expectations to a math task. Students will also engage in turn and talk procedures to communicate their thinking.
As students are working on the provided task with manipulatives, it is essential that the teacher monitors and probes students to make sure they are directly modeling the situation. Direct modeling is an approach to problem solving, where students model the action or structure in the story problem. Within a concept, students will use direct modeling before they develop counting strategies and derived facts. An example of direct modeling is Eliz had 8 cookies. She ate 3 of them. How many cookies doe Eliz have left? A student would represent this action with manipulatives by showing 8 counters and the action of removing 3 counters to display the remainder of 5. Students should be able to demonstrate understanding that one counter represents one cookie from the problem. Click here for a video example.
For more information on direct modeling, see professional resource, Children’s Mathematics: Cognitively Guided Instruction (1999).
SMP Connections: (SMP 5) Make decisions on whether a tool is helpful and needed for a situation; (SMP 3) Communicate thinking to others
Teacher Preparation and Materials:
A variety of tools should be placed in the middle of each table or available in the manipulative area. The teacher will display the beginning of the Accountable Talk anchor chart with the first example being: “What I heard you say was… ” Students will need access to the tasks, Kyle’s Seashells and Missing Crayons.
Task:
Provide and present students with the task, Kyle’s Seashells. Review the anchor chart, Manipulative Rules. Next, have students select a manipulative that will be helpful for completing the task and bring it to their workspace. Students will independently solve the problem using their math tool.
As students are working on the task, the teacher will monitor and probe to ensure students are direct modeling.
Sample probing questions:
· Why did you select this tool?
· How did you solve this problem?
· What does one ______(example- counter) represent?
· What does the group represent?
Once students have completed the task with tools, the teacher will model turn and talk procedures with a partner. The teacher models eyes on their partner and empty hands. The teacher’s partner states: “I used counters to show 7 and 2 more seashells in the bucket. Kyle now has 9 seashells in his bucket.” The teacher states: “What I heard you say is Kyle now has 9 seashells in his bucket because 7 and 2 more is 9.” The teacher’s partner states: “Yes, that is what I said.” Refer to the Accountable Talk anchor chart and add the first statement, “So what I heard you say is…”
Directions for Turn and Talk:
· Have students turn to the person seated next to them.
· Have the students high five to identify their partner.
· Students share their tool and strategy for the problem, following the example above.
· Partner A will share first (a resource has been provided to identify partners A and B).
· After partner A has shared, have partner B restate their partner’s thinking.
· If there is a debate, have the students discuss their reasoning.
Click here for partner A/B cards.
After students have shared with their partner, a few students will share responses to the whole group. Praise and give feedback on the turn and talk procedures.
Provide and present students with the task, Missing Crayons. Students will repeat the process of tool selection and direct modeling. Teachers will continue to monitor and probe students for direct modeling. Allow students time to turn and talk about their tool selection and solution. Discuss tools and strategies as a group.
Closure: Ask students, “How did the math tool help you solve the problem?” Discuss ways it helped the students.
In an effort for students to self-reflect about their learning and strategies, students will complete a portion of the self-assessment rubric on each day 1-4. Students will color the smiley face that shows their reflection of today’s performance. Today, have students complete the second strip titled, “I accurately modeled the problem.”
Click here for more problem-solving scenarios.