Responsive Instruction Teaching & Assessing with the New Curriculum

Name of Lesson: Solve Linear Systems by Graphing (7.1) Standard Number(s): DM.4.6 Unpacked Statement of Standard(s): Use fair division techniques to divide continuous objects, ie, objects that can be divided into very small pieces.. Learning targets addressed in this lesson: Engaging Opener: Initial Instruction: Formative Assessment:Process Standard(s): Problem Solving Reasoning & Proof Communication Connections Representation Responsive Instruction (Differentiation): Enrichment:Practice:Re-teach: Formative Assessment:Process Standard(s): Problem Solving Reasoning & Proof Communication Connections Representation Student Learning Summary: Students Exceeding Learning Targets: Students Meeting Learning Targets:Students Reaching for Learning Targets: Un-packing the Standard Divide an object that is continuous, that is, can be divided in infinitely many ways, (like a cake), fairly. The share for each person can theoretically be increased or decreased by very small amounts. Identify elements of the standard used : Identify an object to be divided as continuous, discrete or mixed. Apply divider-chooser method Apply lone- divider method. Note: This standard will be covered over several class periods. Write the standard as it applies to today’s lesson: Use fair division techniques to divide continuous objects, ie, objects that can be divided into very small pieces. Unpacked-standard

Name of Lesson: Standard Number(s): DM.4.6 Unpacked Statement of Standard(s): Use fair division techniques to divide continuous objects, ie, objects that can be divided into very small pieces. Learning targets addressed in this lesson: 1.Identify basic elements and assumptions of fair division Classify a fair-division game as continuous, discrete of mixed 3.Apply Divider-Chooser Method 4.Apply Lone -Divider Method Engaging Opener: Initial Instruction: Formative Assessment:Process Standard(s): Problem Solving Reasoning & Proof Communication Connections Representation Responsive Instruction (Differentiation): Enrichment:Practice:Re-teach: Formative Assessment:Process Standard(s): Problem Solving Reasoning & Proof Communication Connections Representation Student Learning Summary: Students Exceeding Learning Targets: Students Meeting Learning Targets:Students Reaching for Learning Targets: Identify Learning Targets: Unpacked Standard: Use fair division techniques to divide continuous objects, ie, objects that can be divided into very small pieces. What are the distinct skills, processes, and learning outcomes associated with the un-packed standard? 1.Identify basic elements and assumptions of fair division. 2. Classify a fair-division game as continuous, discrete of mixed 3.Apply Divider-Chooser Method 4.Apply Lone -Divider Method One source for identifying learning targets is the heading for each subtopic. Check the headings in sub topics of the text or in the Insider’s Guide to Teaching, which is shown here. The Insider’s Guide is one of the downloadable resources as well as hard copy. Are all of the learning targets addressed?  If not, supplement the text with outside resources, guided questioning, or by enriching student notes.

Name of Lesson: Standard Number(s): DM.4.6 Unpacked Statement of Standard(s): Use fair division techniques to divide continuous objects, ie, objects that can be divided into very small pieces. Learning targets addressed in this lesson: 1.Identify basic elements and assumptions of fair division Classify a fair-division game as continuous, discrete of mixed 3.Apply Divider-Chooser Method 4.Apply Lone -Divider Method Engaging Opener: Read Aesop’s fable on p. 76 Then :(Test p. 81 Example 3.1) On their first date, Damian and Cleo go to the county fair. They buy jointly a raffle ticket, and as luck would have it, they win a ½ chocolate, ½ strawberry cheesecake. Damian likes both chocolate and strawberry equally well, but Cleo hates chocolate. However neither knows about each others likes or dislikes. What is a fair division? Initial Instruction: Formative Assessment:Process Standard(s): Problem Solving Reasoning & Proof Communication Connections Representation Responsive Instruction (Differentiation): Enrichment:Practice:Re-teach: Formative Assessment:Process Standard(s): Problem Solving Reasoning & Proof Communication Connections Representation Student Learning Summary: Students Exceeding Learning Targets: Students Meeting Learning Targets:Students Reaching for Learning Targets: Engaging Opening To create an engaging opening, consider including one of the following resources: Look at “Insiders Guide to teaching” projects workbook. It has many interesting projects with rubrics. Consider finding a problem from the text and making it “come to life”. (See ex.) Most have little scaffolding and are real life. You can play “what if” with some of the given information, to make it more interesting as demonstrated by Dan Meyer in the video clip. Orange Text: Text ResourceYellow Text: External Resource

Name of Lesson: Standard Number(s): DM.4.6 Unpacked Statement of Standard(s): Use fair division techniques to divide continuous objects, ie, objects that can be divided into very small pieces. Learning targets addressed in this lesson: 1.Identify basic elements and assumptions of fair division Classify a fair-division game as continuous, discrete of mixed 3.Apply Divider-Chooser Method 4.Apply Lone -Divider Method Engaging Opener: Test p. 81 Example 3.1) On their first date, Damian and Cleo go to the county fair. They buy jointly a raffle ticket, and as luck would have it, they win a ½ chocolate, ½ strawberry cheesecake. Damian likes both chocolate and strawberry equally well, but Cleo hates chocolate. However neither knows about each others likes or dislikes. What is a fair division?. Initial Instruction: Use ppt presentations that can be downloaded from the Instructor’s Resource Center. Discuss examples in text, Section 3-1, 3-2. Formative Assessment:Process Standard(s): Problem Solving Reasoning & Proof Communication Connections Representation Responsive Instruction (Differentiation): Enrichment:Practice:Re-teach: Formative Assessment:Process Standard(s): Problem Solving Reasoning & Proof Communication Connections Representation Student Learning Summary: Students Exceeding Learning Targets: Students Meeting Learning Targets:Students Reaching for Learning Targets: Initial Instruction Your initial instruction may include a traditional approach: Formative assessment of pre- requisite skills. Look at the “Insider’s Guide” for teaching tips. Delivery of lesson content from the power point presentations provided for many of the lessons from the Instructor’s Resource) Or a constructionist approach: A hands-on activity from the Exercises at the end of the chapter or a project from the Insider’s Guide.

Name of Lesson: Standard Number(s): DM.4.6 Unpacked Statement of Standard(s): Use fair division techniques to divide continuous objects, ie, objects that can be divided into very small pieces. Learning targets addressed in this lesson: 1.Identify basic elements and assumptions of fair division Classify a fair-division game as continuous, discrete of mixed 3.Apply Divider-Chooser Method 4.Apply Lone -Divider Method Engaging Opener: Read Aesop’s fable on p. 76 Then :(Test p. 81 Example 3.1) On their first date, Damian and Cleo go to the county fair. They buy jointly a raffle ticket, and as luck would have it, they win a ½ chocolate, ½ strawberry cheesecake. Damian likes both chocolate and strawberry equally well, but Cleo hates chocolate. However neither knows about each others likes or dislikes. What is a fair division? Initial Instruction: Use ppt presentations that can be downloaded from the Instructor’s Resource Center. Discuss examples in text, Section 3-1, 3-2. Formative Assessment: Complete the first 2 problems from the Math XL Ch 3 test. Process Standard(s): Problem Solving Reasoning & Proof Communication Connections Representation Responsive Instruction (Differentiation): Enrichment:Practice:Re-teach: Formative Assessment:Process Standard(s): Problem Solving Reasoning & Proof Communication Connections Representation Student Learning Summary: Students Exceeding Learning Targets: Students Meeting Learning Targets:Students Reaching for Learning Targets: Formative Assessment Your formative assessment may include observing student performance on: “Exercises” problems from the text at chapter end. Math XL quiz, test items. A written summary of the constructed learning from the mini project or answering the initial problem posed in the engaging opener. Have students come up with their own problems and solutions. (Teaching tip.) A written summary of the constructed learning Dan Meyers task from your instruction (if applicable) X

Name of Lesson: Standard Number(s): DM.4.6 Unpacked Statement of Standard(s): Use fair division techniques to divide continuous objects, ie, objects that can be divided into very small pieces. Learning targets addressed in this lesson: 1.Identify basic elements and assumptions of fair division Classify a fair-division game as continuous, discrete of mixed 3.Apply Divider-Chooser Method 4.Apply Lone -Divider Method Engaging Opener: Read Aesop’s fable on p. 76 Then :(Test p. 81 Example 3.1) On their first date, Damian and Cleo go to the county fair. They buy jointly a raffle ticket, and as luck would have it, they win a ½ chocolate, ½ strawberry cheesecake. Damian likes both chocolate and strawberry equally well, but Cleo hates chocolate. However neither knows about each others likes or dislikes. What is a fair division? Initial Instruction: Use ppt presentations that can be downloaded from the Instructor’s Resource Center. Discuss examples in text, Section 3-1, 3-2. Formative Assessment: Complete the first 2 problems from the Math XL Ch 3 test.. Process Standard(s): Problem Solving Reasoning & Proof Communication Connections Representation Responsive Instruction (Differentiation): Enrichment: Group students who exceeded learning targets. Have them work on “Jogging” or “Running” problems and present to class. Practice: Group students who mastered the concepts will work on a mini project and present to class. If a mini project does not exist, they will create areal life problems and present to the class. Re-teach: Group students who need remediation together and resolve assigned problems using Student Resource. Teacher offers support and clarification table-side as groups work. Formative Assessment:Process Standard(s): Problem Solving Reasoning & Proof Communication Connections Representation Student Learning Summary: Students Exceeding Learning Targets: Students Meeting Learning Targets:Students Reaching for Learning Targets: Responsive Instruction Sources for differentiation in your new text: Remediation & Extension: Student Resource Guide provides hints and additional scaffolding for odd numbered problems. Leveled Practice: Exercises are labeled “Walking” for a basic understanding, “Jogging” for non routine, and “Running “ for above average challenging problems. Math XL resource: Make individualized Study Plans X X X

Name of Lesson: Standard Number(s): DM.4.6 Unpacked Statement of Standard(s): Use fair division techniques to divide continuous objects, ie, objects that can be divided into very small pieces. Learning targets addressed in this lesson: 1.Identify basic elements and assumptions of fair division Classify a fair-division game as continuous, discrete of mixed 3.Apply Divider-Chooser Method 4.Apply Lone -Divider Method Engaging Opener: Test p. 81 Example 3.1) On their first date, Damian and Cleo go to the county fair. They buy jointly a raffle ticket, and as luck would have it, they win a ½ chocolate, ½ strawberry cheesecake. Damian likes both chocolate and strawberry equally well, but Cleo hates chocolate. However neither knows about each others likes or dislikes. What is a fair division? Initial Instruction: Use ppt presentations that can be downloaded from the Instructor’s Resource Center. Discuss examples in text, Section 3-1, 3-2. Formative Assessment: Complete the first 2 problems from the Math XL Ch 3 test. Process Standard(s): Problem Solving Reasoning & Proof Communication Connections Representation Responsive Instruction (Differentiation): Enrichment: Group students who exceeded learning targets. They will complete the Activity Generator lesson for 7.1: Solving Linear Systems Using Tables and present-out to the class Practice: Group students who mastered “solving systems graphically” and using the “graph and check method” correctly. Students will work in pairs to complete one of the word problems on page , create a poster of their solution process, and present their solution to the class. Re-teach: Group students that got “solving systems graphically” wrong. Go to questions 8-10 on page 431. Group students that got “graph & check” wrong. Go to questions on page 431. Teacher offers support and clarification table-side as groups work. Formative Assessment: Have students solve the opening problem as an exit slip for the class period. Use the results to identify groups for next lesson. Process Standard(s): Problem Solving Reasoning & Proof Communication Connections Representation Student Learning Summary: Students Exceeding Learning Targets: Students Meeting Learning Targets:Students Reaching for Learning Targets: Formative Assessment Formative assessment at the end of the class period may take the form of: HW Quiz from the Test Generator (needs to be downloaded from Instructor’s Resources.) Exit Slip formulated from problems provided on the Test Generator’s or the chapter exercises extensive problem bank Student Response System or TI Navigator problem on the SMART Board Students can slip their name into one of three envelopes at the front of the room labeled “Getting it,” “Got it,” and “Need more help!” X X X