GlobalConceptGuides:First Nine Days
Prior Learning:MAFS.K.CC.1.3,MAFS.K.OA.1.1, MAFS.K.OA.1.2
SampleShowWhatYouKnowTask: n/a
CommonCoreStateStandardsfor MathematicalContent:
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.2.3Tell and write time in hours and half-hours using analog and digital clocks. / Comments:
Strikethroughsindicate that only specific problem structures will be used within 10 in thisunit ofstudy.
NotesonAssessment:
There is NO Assessment or Performance Task for Building Community
UnpackingtheStandardsfor thisUnit:
Likeotheraspectsofmathematics,communicationandlanguageneedto betaughtandlearnedinschool classrooms.Buttheyarealsoaprimarymeansbywhichmathematicsis taughtandlearned.(AResearch CompaniontoPrinciplesandStandards forSchool 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.
CommonPerformanceTaskwithRubricfor thisUnit:
There is NO Performance Task for Building Community
FutureLearning:
The first9 days ofthe schoolyearhave been devotedto buildingcommunityin themathematicsclassroom. Buildingcommunitywillnotbe donein 9days, but the foundation can bedeveloped. Communitywillcontinueto develop and build throughouttheremainderoftheschoolyear, however, withoutasolidfoundationin the beginningof the year,communitywillnotblossom. Thesefirst9 days ofcommunity buildingshould place an emphasis on collaboration and problemsolvingthrough the useof the practice standardsand prioryears’contentstandards.
1st / GlobalConcept1of1forthis UnitofStudy(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:
9days
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 ChapterTest Questions: N/A
InstructionalResources
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
- See the BuildingCommunitywithinthe MathematicsClassroom
SampleHOTQuestions: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?
Ourstudents arebetter ableto…
- 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)
- 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)
BuildingaMath CommunityinFirst Grade
Day1-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: (SMP5)Use appropriate tools strategically is emphasized
TeacherPreparationandMaterials:
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.
Allowtwo 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.”
Day2-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: (SMP5)Make decisions on whether a tool is helpful and needed for a situation; (SMP 3) Communicate thinking to others
TeacherPreparationandMaterials:
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.
Day3- Accountable Talk with Math Language
EQ: How can we communicate respectfully to learn from others?
Thegoal forthis lesson is to get students comfortable with sharingand justifyingtheirthinking forother students.
SMP Connections: (SMP 3) Use accountable talk to share and justify reasoning and understand the reasoning of others;(SMP 6) Use specific vocabulary when describing number representations
TeacherPreparationandMaterials:
Different Ways Number Cards cut apart, Numbers (0-9) posted around room, Accountable Talk anchor chart from Day 2
Task:Representing Numbers in Different Ways
- Cut out the pre-made number representation cards. You may want to select only enough number representations for each of your students to have one, but make sure that there are at least two representations of each number that you choose.
- Have the numbers selected for the task posted in locations throughout the room for students to meet at later in the lesson.
- Introduce two new accountable talk stems and add them to the anchor chart started yesterday: “I agree because…”, “I disagree because…” and facilitate a discussion about why using this language is important in mathematics.
- Students will randomly choose a number representation card and determine what number that they have. Students can record this information on an index card. Tell students not to share their number with anyone else.
- Kagan Structure: Stand Up, Hand Up, Pair Up-
- Have students stand up with one hand up in the air.
- Students continue moving throughout the room until a signal is given (i.e. turning off music).
- Students high fives the student nearest to them once signal is given, this will be their partner.
- Students put hand down once partner is found.
- Teacher poses the following statement for students to consider “You and your partner have the same number.”
- Instruct students to use the accountable talk stems discussed at the beginning of class to agree or disagree with the statement, students must justify their thinking.
- Repeat this process two more times.
- Once the activity is concluded, bring the students back together to discuss the task. Ask questions such as: “What did you notice?”, “Did everyone have the same representation of their number?”(Specifically discuss key math terms such as dot cards, ten frames and word form) “Did anyone find a matching partner?”
- Introduce two new accountable talk stems and add them to the anchor chart started yesterday: “My representation is like yours because…” “My representation is different than yours because…”
- Once activity has been debriefed, instruct students that they have 30 seconds to move to the location in the room where their number is posted.
- Give students time to use the new accountable talk stems in their group.
- Circulate through the room and listen for students that are doing a good job explaining the similarities and differences of their representations to share with the whole group.
- Bring students back together and allow selected students to share their thinking. It is a good idea to let students show their representations under the Elmo while they are explaining their thinking.
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 fourth strip titled, “I used accountable talk to share my thinking.”