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Responsive Instruction. Teaching & Assessing with the New Curriculum. DISCRETE MATH. Un-packing the Standard
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Responsive Instruction Teaching & Assessing with the New Curriculum
DISCRETE MATH • 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
DISCRETE MATH • 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? • Identify basic elements and assumptions of fair division. • Classify a fair-division game as continuous, discrete of mixed • Apply Divider-Chooser Method • 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.
DISCRETE MATH • 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
DISCRETE MATH • 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.
DISCRETE MATH • 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 projector 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
DISCRETE MATH • 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
DISCRETE MATH • 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