8/4/15 CLAIMS 1-Concept and Procedures 2-Problem Solving 3-Communicating 4-Modeling and Data Analysis MATHEMATICAL PRACTICES 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning CLUSTERS (SBAC Target) TARGET A: Major Know number names and count the sequence. TARGET B: Major Count to tell the number of objects. TARGET C: Major Compare numbers. STANDARDS K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0 20 (with 0 representing a count of no objects). K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality. K.CC.4a When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. K.CC.4c Understand that each successive number name refers to a quantity that is one larger. K.CC.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. Benchmark Blueprint 3 CR 3 CR PT PART A and B 3 CR PT PART C and D NOTES Major (Priority)- Areas of intensive focus where students need fluent understanding and application of the core concepts. These clusters require greater emphasis than the others based on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness Supporting- Rethinking and linking; areas where some material is being covered, but in a way that applies core understanding; designed to support and strengthen Additional- Expose students to other subjects; may not connect tightly or explicitly to the major work of the grade Benchmark Item Types and Points 9 Constructed Responses (1 point each) 1 Performance Task with 4 parts (total of 6 points) 1
Mathematical Task Development Purpose: At the end of the unit, students should be able to make connections with the learning of concepts and skills, problem solving, modeling, analysis, communication and reasoning. Students should be able to perform at higher levels of complexity in their thinking and application of the math content. Task Development Mathematical tasks should Integrate knowledge and skills across multiple claims and targets Engage students in relevant and interesting topics Measure depth of understanding, research skills, complex analysis Have an authentic purpose and connected components Take age appropriate development into consideration Accessible to all learners Professional Learning Communities will Step 1: Consider the learning targets needed to be mastered throughout the unit. Step 2: Consider the Depth of Knowledge or level of complexity that students will need to perform. (DOK 1) Recall and Reproduction (DOK 2) Skills and Concepts/ Basic Reasoning (DOK 3) Strategic Thinking/ Complex Reasoning Performance Task Expectations (DOK 4) Extended Thinking/ Reasoning Recall of a fact, information or procedure Recall or recognize fact Recall or recognize definition Recall or recognize term Recall and use a simple procedure Perform a simple algorithm. Follow a set procedure Apply a formula A one-step, well-defined, and straight algorithm procedure. Perform a clearly defined series of steps Identify Recognize Use appropriate tools Measure Students make some decisions as to how to approach the problem Skill/Concept Basic Application of a skill or concept Classify Organize Estimate Make observations Collect and display data Compare data Imply more than one step Visualization Skills Probability Skills Explain purpose and use of experimental procedures. Carry out experimental procedures Requires reasoning, planning using evidence and a higher level of thinking Strategic Thinking Freedom to make choices Explain your thinking Make conjectures Cognitive demands are complex and abstract Conjecture, plan, abstract, explain Justify Draw conclusions from observations Cite evidence and develop logical arguments for concepts Explain phenomena in terms of concepts Performance tasks Authentic writing Project-based assessment Complex, reasoning, planning, developing and thinking Cognitive demands of the tasks are high Work is very complex Students make connections within the content area or among content areas Select one approach among alternatives Design and conduct experiments Relate findings to concepts and phenomena DEFINITIONS To view full list of DOK descriptors, visit http://education.ky.gov/curriculum/docs/documents/cca_dok_support_808_mathematics.pdf 2
Mathematics Depth of Knowledge Levels by Norman L. Webb Level 1 (Recall) includes the recall of information such as a fact, definition, term, or a simple procedure, as well as performing a simple algorithm or applying a formula. That is, in mathematics a one-step, well-defined, and straight algorithmic procedure should be included at this lowest level. Other key words that signify a Level 1 include identify, recall, recognize, use, and measure. Verbs such as describe and explain could be classified at different levels depending on what is to be described and explained. Level 2 (Skill/Concept) includes the engagement of some mental processing beyond a habitual response. A Level 2 assessment item requires students to make some decisions as to how to approach the problem or activity, whereas Level 1 requires students to demonstrate a rote response, perform a well-known algorithm, follow a set procedure (like a recipe), or perform a clearly defined series of steps. Keywords that generally distinguish a Level 2 item include classify, organize, estimate, make observations, collect and display data, and compare data. These actions imply more than one step. For example, to compare data requires first identifying characteristics of the objects or phenomenon and then grouping or ordering the objects. Some action verbs, such as explain, describe, or interpret could be classified at different levels depending on the object of the action. For example, if an item required students to explain how light affects mass by indicating there is a relationship between light and heat, this is considered a Level 2. Interpreting information from a simple graph, requiring reading information from the graph, also is a Level 2. Interpreting information from a complex graph that requires some decisions on what features of the graph need to be considered and how information from the graph can be aggregated is a Level 3. Caution is warranted in interpreting Level 2 as only skills because some reviewers will interpret skills very narrowly, as primarily numerical skills, and such interpretation excludes from this level other skills such as visualization skills and probability skills, which may be more complex simply because they are less common. Other Level 2 activities include explaining the purpose and use of experimental procedures; carrying out experimental procedures; making observations and collecting data; classifying, organizing, and comparing data; and organizing and displaying data in tables, graphs, and charts. Level 3 (Strategic Thinking) requires reasoning, planning, using evidence, and a higher level of thinking than the previous two levels. In most instances, requiring students to explain their thinking is a Level 3. Activities that require students to make conjectures are also at this level. The cognitive demands at Level 3 are complex and abstract. The complexity does not result from the fact that there are multiple answers, a possibility for both Levels 1 and 2, but because the task requires more demanding reasoning. An activity, however, that has more than one possible answer and requires students to justify the response they give would most likely be a Level 3. Other Level 3 activities include drawing conclusions from observations; citing evidence and developing a logical argument for concepts; explaining phenomena in terms of concepts; and using concepts to solve problems. Level 4 (Extended Thinking) requires complex reasoning, planning, developing, and thinking most likely over an extended period of time. The extended time period is not a distinguishing factor if the required work is only repetitive and does not require applying significant conceptual understanding and higher-order thinking. For example, if a student has to take the water temperature from a river each day for a month and then construct a graph, this would be classified as a Level 2. However, if the student is to conduct a river study that requires taking into consideration a number of variables, this would be a Level 4. At Level 4, the cognitive demands of the task should be high and the work should be very complex. Students should be required to make several connections relate ideas within the content area or among content areas and have to select one approach among many alternatives on how the situation should be solved, in order to be at this highest level. Level 4 activities include designing and conducting experiments; making connections between a finding and related concepts and phenomena; combining and synthesizing ideas into new concepts; and critiquing experimental designs. 3
Collaborative Team Planning Guide SEGMENT 1: Read, Write, and Count Numbers 0 to 5 What do I want my students to know and be able to do? Questions to Consider How can framework examples help make sense of mathematical tasks? How will we use number talks along with conceptual strategies to check for reasonable responses and build fluency? What tools/models are appropriate in demonstrating mastery towards the skills addressed by the standard/cluster? What misconceptions/errors do the frameworks anticipate with this particular skill set? Which correlating lessons are appropriate in rigor in alignment to clusters and standards as presented in the frameworks? What does the framework say about grade-level specific mathematical practices and implementation? What previous skills/concepts were addressed in previous grade(s) in order to make connections to current learning? Application of Mathematical Practices (Behaviors/Actions) K.CC.3 K.CC.4a Standard Content Objective Language Objective Social Objective What will my students learn? What language will my students use? What will my students do as they learn? K.CC.3 K.CC.4a Language Functions and Considerations Vocabulary (specialized, technical): I can use the following math words: count, number, one, two, three, four, five, zero ( 0, 1, 2, 3, 4, 5) Structure/Syntax (The way words and vocabulary are used to express ideas): I will use the following sentence frame: Function (The intended use of language): I can explain my thinking for solving problems 4
Skills/Concepts Counting/Explaining Language Function: Representation. Numerals to represent meaning within a conventional context. (nouns, subject-verb agreement) i.e. This is the number. There are in my picture. This is the number 5. There are 5 cats in my picture. Behaviors/Actions Making Use of Structure Language Function: Describe. Word, phrase, or sentences to express or observe the attributes of an object. (nouns, subject-verb agreement) i.e. After comes the number. I show the number with. After the number 4 comes the number 5. I show the number 5 with 5 cubes. Curricular Connections: Chapter 1 Lesson 1 Count 1,2, and 3 Lesson 2 Read and Write 1,2, and 3 Lesson 3 Count 4 and 5 Lesson 4 Read and Write 4 and 5 Lesson 5 Read and Write Zero Unit Connections: Ready Common Core Unit Connections: iready Content Specific Vocabulary: count, number, one, two, three, four, five, zero (0, 1, 2, 3, 4, 5) How will we know if they have learned it? Teachers will plan and implement daily formative assessments in order to provide specific immediate feedback in the classroom. Grade level teams will develop and implement common formative assessment. Claim Claim Descriptor MPs SBAC TARGET DOK Claim 1 Concepts and Procedures Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency. *5, 6, 7, 8 Major: Know Number Names and the count sequence (K.CC.3) Target B Major: Count to tell the number of objects (K.CC.4a) Claim 2 Problem Solving Claim 3 Communicating Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. Relevant Verbs: Understand, Solve, Apply, Describe, Illustrate, Interpret, Analyze Students can clearly and precisely construct viable arguments to support their own reasoning and to critique *1, 5, 7, 8 *3, 6 Apply Mathematics to solve well-posed problems in pure mathematics and those arising in everyday life, society, and the workplace. Target F Base Arguments on concrete referents such as objects, drawings, 2, 3 2 5
Claim 4 Modeling and Data Analysis the reasoning of others. Relevant Verbs: Model, Construct, Compare, Investigate, Build, Interpret, Estimate, Analyze, Summarize, Represent, Solve, Evaluate, Extend, Apply Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems. Relevant Verbs: Understand, Explain, Justify, Prove, Derive, Assess, Illustrate, Analyze *2, 4, 5 diagrams, and actions. Apply mathematics to solve problems arising in everyday life, society, and the workplace. *All practices may be integrated in each claim, however certain practices are emphasized above http://www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.asp http://bcsd.com/cipd/sbac-item-specification-tools-2/ How will we respond when learning has not occurred? Professional Learning Communities will develop and implement Response to Intervention. How will we respond when learning has already occurred? Professional Learning Communities will develop and implement Enrichment. 6
Collaborative Team Planning Guide SEGMENT 2: Compare Numbers 0 to 5 What do I want my students to know and be able to do? Questions to Consider How can framework examples help make sense of mathematical tasks? How will we use number talks along with conceptual strategies to check for reasonable responses and build fluency? What tools/models are appropriate in demonstrating mastery towards the skills addressed by the standard/cluster? What misconceptions/errors do the frameworks anticipate with this particular skill set? Which correlating lessons are appropriate in rigor in alignment to clusters and standards as presented in the frameworks? What does the framework say about grade-level specific mathematical practices and implementation? What previous skills/concepts were addressed in previous grade(s) in order to make connections to current learning? Application of Mathematical Practices (Behaviors/Actions) K.CC.4a K.CC.4c Standard Content Objective Language Objective Social Objective What will my students learn? What language will my students use? What will my students do as they learn? K.CC.4a K.CC.6 K.CC.4c K.CC.6 Language Functions and Considerations Vocabulary (specialized, technical): I can use the following math words: equal to, greater than, less than Structure/Syntax (The way words and vocabulary are used to express ideas): I will use the following sentence frame: The number is (greater than, less than, equal to) the number. 7
Function (The intended use of language): I can explain my thinking for solving problems Skills/Concepts Comparing Behaviors/Actions Reasoning/Explaining Language Function: Compare/Contrast. Use words, phrases, or Language Function: Explain. Use phrases or sentences to express the relationship or sentences to express similarities/differences or to distinguish between rationale related to one or more actions, events, ideas or processes. (adverbials two objects. (adverbials because, so) because, so) i.e. is (greater/less/equal to). 0 is less than 5. i.e. has and I have. So, has greater/less. Michael has 3 bears and I have 1 bear. So, Michael has a greater number of bears. My partner has more because is. My partner has more because 4 is greater than 2. Curricular Connections: Chapter 1 Lesson 6 Equal to Lesson 7 Greater Than Lesson 8 Less Than Lesson 9 Compare Numbers 0 to 5 Lesson 10 One More Lesson 11 Problem Solving Strategy: Draw a Diagram Unit Connections: Ready Common Core Unit Connections: iready Content Specific Vocabulary: equal to, greater than, less than, number, how many, more, lesserone, two, three, four, five, zero (0, 1, 2, 3, 4, 5) How will we know if they have learned it? Teachers will plan and implement daily formative assessments in order to provide specific immediate feedback in the classroom. Grade level teams will develop and implement common formative assessment. Claim Claim Descriptor MPs SBAC TARGET DOK Claim 1 Concepts and Procedures Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency. *5, 6, 7, 8 Target B Major: Count to tell the number of objects (K.CC.4a, 4c) Target C Major: Compare numbers (K.CC.6) Claim 2 Problem Solving Claim 3 Communicating Claim 4 Modeling and Data Analysis Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. Relevant Verbs: Understand, Solve, Apply, Describe, Illustrate, Interpret, Analyze Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. Relevant Verbs: Model, Construct, Compare, Investigate, Build, Interpret, Estimate, Analyze, Summarize, Represent, Solve, Evaluate, Extend, Apply Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems. Relevant Verbs: Understand, Explain, *1, 5, 7, 8 *3, 6 *2, 4, 5 Apply Mathematics to solve well-posed problems in pure mathematics and those arising in everyday life, society, and the workplace. Target F Base Arguments on concrete referents such as objects, drawings, diagrams, and actions. Apply mathematics to solve problems arising in everyday life, society, and the workplace. 2, 3 2 8
Justify, Prove, Derive, Assess, Illustrate, Analyze *All practices may be integrated in each claim, however certain practices are emphasized above http://www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.asp http://bcsd.com/cipd/sbac-item-specification-tools-2/ How will we respond when learning has not occurred? Professional Learning Communities will develop and implement Response to Intervention. How will we respond when learning has already occurred? Professional Learning Communities will develop and implement Enrichment. 9
Collaborative Team Planning Guide SEGMENT 3: Read, Write, and Count Numbers 6 to 8 What do I want my students to know and be able to do? Questions to Consider How can framework examples help make sense of mathematical tasks? How will we use number talks along with conceptual strategies to check for reasonable responses and build fluency? What tools/models are appropriate in demonstrating mastery towards the skills addressed by the standard/cluster? What misconceptions/errors do the frameworks anticipate with this particular skill set? Which correlating lessons are appropriate in rigor in alignment to clusters and standards as presented in the frameworks? What does the framework say about grade-level specific mathematical practices and implementation? What previous skills/concepts were addressed in previous grade(s) in order to make connections to current learning? Application of Mathematical Practices (Behaviors/Actions) K.CC.3 Standard Content Objective Language Objective Social Objective What will my students What language will my students What will my students do as they learn? learn? use? K.CC.3 K.CC.4 K.CC.4 Language Functions and Considerations Vocabulary (specialized, technical): I can use the following math words: number, six, seven, eight (6, 7, 8) Structure/Syntax (The way words and vocabulary are used to express ideas): I will use the following sentence frame: I counted cubes (or any object). Function (The intended use of language): I can explain my thinking for solving problems 10
Skills/Concepts Recognizing. Language Function: Representation. Numerals to represent meaning within a conventional context. (nouns, subject-verb agreement) i.e. We have cubes (or any object). There are (trees, bats, kids). We have 7 cubes. There are 6 kids in our class. Curricular Connections: Chapter 2 Lesson 1 Numbers 6 and 7 Lesson Number 8 Lesson 3 Read and Write 6, 7, and 8 Unit Connections: Ready Common Core Behaviors/Actions Make Sense of Numbers. Language Function: Describe. Use words, phrases, or sentences to express or observe the attributes or properties of an object. (nouns, subject-verb agreement) i.e. A spider has legs. There are kids at my table. A spider has 8 legs. There are 6 kids at my table. Unit Connections: iready Content Specific Vocabulary: number, six, seven, eight (6. 7. 8) How will we know if they have learned it? Teachers will plan and implement daily formative assessments in order to provide specific immediate feedback in the classroom. Grade level teams will develop and implement common formative assessment. Claim Claim Descriptor MPs SBAC TARGET DOK Claim 1 Concepts and Procedures Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency. *5, 6, 7, 8 Major: Know Number Names and the count sequence (K.CC.3) Target B Major: Count to tell the number of objects (K.CC.4) Claim 2 Problem Solving Claim 3 Communicating Claim 4 Modeling and Data Analysis Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. Relevant Verbs: Understand, Solve, Apply, Describe, Illustrate, Interpret, Analyze Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. Relevant Verbs: Model, Construct, Compare, Investigate, Build, Interpret, Estimate, Analyze, Summarize, Represent, Solve, Evaluate, Extend, Apply Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems. Relevant Verbs: Understand, Explain, Justify, Prove, Derive, Assess, Illustrate, Analyze *1, 5, 7, 8 *3, 6 *2, 4, 5 *All practices may be integrated in each claim, however certain practices are emphasized above Apply Mathematics to solve well-posed problems in pure mathematics and those arising in everyday life, society, and the workplace. Target F Base Arguments on concrete referents such as objects, drawings, diagrams, and actions. Apply mathematics to solve problems arising in everyday life, society, and the workplace. 2, 3 2 11
http://www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.asp http://bcsd.com/cipd/sbac-item-specification-tools-2/ How will we respond when learning has not occurred? Professional Learning Communities will develop and implement Response to Intervention. How will we respond when learning has already occurred? Professional Learning Communities will develop and implement Enrichment. 12
Collaborative Team Planning Guide SEGMENT 4: Read, Write, and Count Numbers 9 to 10 What do I want my students to know and be able to do? Questions to Consider How can framework examples help make sense of mathematical tasks? How will we use number talks along with conceptual strategies to check for reasonable responses and build fluency? What tools/models are appropriate in demonstrating mastery towards the skills addressed by the standard/cluster? What misconceptions/errors do the frameworks anticipate with this particular skill set? Which correlating lessons are appropriate in rigor in alignment to clusters and standards as presented in the frameworks? What does the framework say about grade-level specific mathematical practices and implementation? What previous skills/concepts were addressed in previous grade(s) in order to make connections to current learning? Application of Mathematical Practices (Behaviors/Actions) Standard Content Objective Language Objective Social Objective What will my students learn? What language will my students use? What will my students do as they learn? K.CC.3 K.CC.3 K.CC.4 K.CC.4 Language Functions and Considerations Vocabulary (specialized, technical): I can use the following math words: number, nine, ten (9, 10) Structure/Syntax (The way words and vocabulary are used to express ideas): I will use the following sentence frame: There are birds in all. Function (The intended use of language): I can explain my thinking for solving problems Skills/Concepts Representing Numbers. Language Function: Describe. Words, phrases, or sentences to express the meaning or the given expression. (nouns, subject-verb agreement) Behaviors/Actions Modeling/Explaining. Language Function: Describe. Words, phrases, or sentences to express the meaning or the given expression. (nouns, subject-verb agreement) i.e. There are. i.e. I drew.,,,... 13
,,,.... There are in all. There are 9 oranges. 1, 2, 3, 4, 5, 6, 7, 8, 9. There are 9 oranges in all. There are in the. I drew 10 apples. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. There are 9 fish in the river. Curricular Connections: Chapter 2 Lesson 4 Number 9 Lesson 5 Number 10 Lesson 6 Read and Write 9 and 10 Lesson 7 Problem Solving Strategy: Act it Out Unit Connections: Ready Common Core Unit Connections: iready number, nine, ten (9, 10) How will we know if they have learned it? Teachers will plan and implement daily formative assessments in order to provide specific immediate feedback in the classroom. Grade level teams will develop and implement common formative assessment. Claim Claim Descriptor MPs SBAC TARGET DOK Claim 1 Concepts and Procedures Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency. *5, 6, 7, 8 Major: Know Number Names and the count sequence (K.CC.3) Target B Major: Count to tell the number of objects (K.CC.4a) Claim 2 Problem Solving Claim 3 Communicating Claim 4 Modeling and Data Analysis Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. Relevant Verbs: Understand, Solve, Apply, Describe, Illustrate, Interpret, Analyze Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. Relevant Verbs: Model, Construct, Compare, Investigate, Build, Interpret, Estimate, Analyze, Summarize, Represent, Solve, Evaluate, Extend, Apply Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems. Relevant Verbs: Understand, Explain, Justify, Prove, Derive, Assess, Illustrate, Analyze *1, 5, 7, 8 *3, 6 *2, 4, 5 *All practices may be integrated in each claim, however certain practices are emphasized above Apply Mathematics to solve well-posed problems in pure mathematics and those arising in everyday life, society, and the workplace. Target F Base Arguments on concrete referents such as objects, drawings, diagrams, and actions. Apply mathematics to solve problems arising in everyday life, society, and the workplace. 2, 3 2 14
http://www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.asp http://bcsd.com/cipd/sbac-item-specification-tools-2/ How will we respond when learning has not occurred? Professional Learning Communities will develop and implement Response to Intervention. How will we respond when learning has already occurred? Professional Learning Communities will develop and implement Enrichment. 15
Collaborative Team Planning Guide SEGMENT 5: Compare Numbers 0 to 10 / Ordinal Numbers What do I want my students to know and be able to do? Questions to Consider How can framework examples help make sense of mathematical tasks? How will we use number talks along with conceptual strategies to check for reasonable responses and build fluency? What tools/models are appropriate in demonstrating mastery towards the skills addressed by the standard/cluster? What misconceptions/errors do the frameworks anticipate with this particular skill set? Which correlating lessons are appropriate in rigor in alignment to clusters and standards as presented in the frameworks? What does the framework say about grade-level specific mathematical practices and implementation? What previous skills/concepts were addressed in previous grade(s) in order to make connections to current learning? Application of Mathematical Practices (Behaviors/Actions) K.CC.4a K.CC.4c K.CC.6 Standard Content Objective Language Objective Social Objective What will my students learn? What language will my students use? What will my students do as they learn? K.CC.4a K.CC.4c K.CC.6 Language Functions and Considerations Vocabulary (specialized, technical): I can use the following math words: number, compare, greater, and less Structure/Syntax (The way words and vocabulary are used to express ideas): I will use the following sentence frame: When I compare and, is (greater/less). Function (The intended use of language): I can explain my thinking for solving problems 16
Skills/Concepts Counting with Ordinal Numbers. Language Function: Describe. Words, phrases, or sentences used to express the meaning of a given word, phrase, or expression. (nouns, subject-verb agreement) Behaviors/Actions Attending to precision/stating Language Function: Describe. Words, phrases, or sentences used to express the meaning of a given word, phrase, or expression. (nouns, subject-verb agreement) Curricular Connections: Chapter 2 Lesson 8 Compare Number 0 to 10 Lesson 9 One More with Numbers to 10 Lesson 10 Ordinal Numbers to Fifth Lesson 11 Ordinal Numbers to Tenth Unit Connections: Ready Common Core Unit Connections: iready Content Specific Vocabulary: number, compare, greater, less, ordinal number, before, after, between How will we know if they have learned it? Teachers will plan and implement daily formative assessments in order to provide specific immediate feedback in the classroom. Grade level teams will develop and implement common formative assessment. Claim Claim Descriptor MPs SBAC TARGET DOK Claim 1 Concepts and Procedures Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency. *5, 6, 7, 8 Target B: Count to tell the number of objects (K.CC.4a, 4c) Target C: Compare numbers (K.CC.6) Claim 2 Problem Solving Claim 3 Communicating Claim 4 Modeling and Data Analysis Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. Relevant Verbs: Understand, Solve, Apply, Describe, Illustrate, Interpret, Analyze Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. Relevant Verbs: Model, Construct, Compare, Investigate, Build, Interpret, Estimate, Analyze, Summarize, Represent, Solve, Evaluate, Extend, Apply Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems. Relevant Verbs: Understand, Explain, Justify, Prove, Derive, Assess, Illustrate, Analyze *1, 5, 7, 8 *3, 6 *2, 4, 5 *All practices may be integrated in each claim, however certain practices are emphasized above Apply Mathematics to solve well-posed problems in pure mathematics and those arising in everyday life, society, and the workplace. Target F Base Arguments on concrete referents such as objects, drawings, diagrams, and actions. Apply mathematics to solve problems arising in everyday life, society, and the workplace. 2, 3 2 17
http://www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.asp http://bcsd.com/cipd/sbac-item-specification-tools-2/ How will we respond when learning has not occurred? Professional Learning Communities will develop and implement Response to Intervention. How will we respond when learning has already occurred? Professional Learning Communities will develop and implement Enrichment. 18
G.R.R. (Gradual Release of Responsibility) Lesson Delivery Model You do it together collaborative component is infused throughout the Focus Lesson, Guided Instruction and Independent delivery stages. GRR Claims & Targets MP s Instructional Lesson Sequence: Focus- Coherence- Rigor Step 1: Introduce Content, Language and Social Objective: as determined by PLC Modeling Focused Lesson Infuse Claims and Targets throughout lesson delivery/ learning Infuse Mathematical Practices throughout lesson delivery/ learning Step 2: Connect to real world problems and/or prior learning (i.e. concepts that link across grade spans, future learning, or construction justification of a concept) : Teacher presents the problem Teacher overtly explains purpose of strategies, tools/models, etc. for the day s learning Engage in Collaborative Conversations and use Language Functions (Develop within PLC and embed within steps) : The learning objective for today is. I think that we will learn about. reminds me of. One strategy for is. Step 1: Introduce and Contextualize Vocabulary (Throughout the learning): Step 2: Model how and why the math works using Skills and Concepts along with Think A Louds: Step 3: Deconstruct the math problem and state the operations needed to solve the problem(s): Teacher and students share thinking Teacher asks students what is their understanding of the problem Teacher asks students the skills needed to get to the solution A way of thinking about solving this problem is. The most important thing to remember in this problem is. I believe the question is asking us to. Engage in Collaborative Conversations and use Language Functions ( Develop within PLC and embed within steps): In order to add two numbers you need to. and are accomplished by. This first step in is to, followed by. 19
Step 1: Revisit or introduce a new real world math problems that are connected to Content, Language and Social Objective: Step 2: Provide students with opportunities to engage in the learning process: Solving real-world problems Describing and illustrating their understanding (speaking and writing) Justifying and explaining their reasoning in solving problems (speaking and writing) Asking questions to generate mathematical thinking We Do You Do Together Infuse Claims and Targets throughout lesson delivery/ learning Infuse Mathematical Practices throughout lesson delivery/ learning Step 3: Differentiation and Feedback Provide differentiated problems and Think A Louds Specific feedback and scaffolding Multiple explanations for solving particular problems Aide in the processing of the content for students (Questions, Prompts and Cues) Assessing students progress and adjusting teaching Determine student grouping or pairing Intervene as needed (responsibility begins to shift) Engage in Collaborative Conversations and use Language Functions ( Develop within PLC and embed within steps): Based on, I determined that. Given that we can deduce that. I agree/disagree with that. Given that we can deduce that. I agree/disagree with that. Step 1: Revisit Objectives. Clearly define expectations and structures for collaborative conversations. Provide appropriate Mathematical Tasks. Step 2: Teacher Role Teacher facilitates Teacher Questions, Prompts, Cues appropriately Teacher provides Corrective Feedback Provide Enrichment Opportunities as needed Student Role Students communicate thinking and understanding Students will problem solve and reason Students will process, justify, explain, prove, critique, etc. (Utilize mathematical practices) Students will use and discuss strategies to extend/deepen understanding of learning Engage in Collaborative Conversations and use Language Functions ( Develop within PLC and embed within steps): 20
Resources Grade Level Expectations(Progressions) Pre-K students will have learned to count to five. students will have used multiple manipulatives and have rote counted to 10. students will have used multiple manipulatives and have counted groups with different amounts of objects. Grade 1 Standards count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. (1.NBT.1) compare two two digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. (1.NBT.3) extend the counting sequence by counting to 120 starting at any number less than 120. SBAC Claims Claim 1 Concepts and Procedures Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency Claim 2 Problem Solving Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. Relevant Verbs: Understand, Solve, Apply, Describe, Illustrate, Interpret, Analyze Claim 3 Communicating Reasoning Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. Relevant Verbs: Model, Construct, Compare, Investigate, Build, Interpret, Estimate, Analyze, Summarize, Represent, Solve, Evaluate, Extend, Apply Claim 4 Modeling and Data Analysis Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems. Relevant Verbs: Understand, Explain, Justify, Prove, Derive, Assess, Illustrate, Analyze Classroom environment: Grade Level Domains 1. Students engage in mathematical discourse (collaborative conversations) 2. Students will explain, justify, reason, and critique the work of others through oral or written responses 3. Students use problem solving strategies to solve real world and mathematical problems 4. Students persevere and find different solution pathways 5. Students attend to precision by calculating efficiently and accurately http://bcsd.com/cipd/files/2011/11/questions-to-development.pdf Grade Level Domains CC- Counting and Cardinality NBT- Number and Operations in Base Ten G- Geometry OA- Operations and Algebraic Thinking MD- Measurement and Data 21
Required Fluencies for Grades K-6 Grade Standard Required Fluency K K.OA.5 Add/subtract within 5 1 1.OA.6 Add/subtract within 10 2 3 2.OA.2 2.NBT.5 3.OA.7 3.NBT.2 Add/subtract within 20 (know single-digit sums from memory) Add/subtract within 100 Multiply/divide within 100 (know singledigit products from memory) Add/subtract within 1000 4 4.NBT.4 Add/subtract within 1,000,000 5 5.NBT.5 Multi-digit multiplication 6 6.NS.2,3 Multi-digit division Multi-digit decimal operations 22