Shifts 6, 7, and 9 Accessible Mathematics Day 2. Review of Day 1.

Accessible Mathematics Day 2

Shifts 6, 7, and 9Accessible MathematicsDay 21Review of Day 1What do you remember from Day 1? Review the 10 shifts. Some of these we are already doing. Remind of Shift 8: Minimize what is no longer important (referring to the Major Work document).2Butterfly FractionsMilking the dataInstructional Shift 6:What does this data stand for?27,52521,44036,53028,28023,50029,065Ford Edge27,525Ford Escape21,440Ford Expedition36,530Ford Explorer28,280Ford F-15023,500Ford F-25029,065What can we do with this data? Charts and tables are a major part of the curriculum (especially part of the mathematical practices Practice 4: Model with Mathematics).5What if I presented the data like this?Describe what that looks like in a classroom.Why is the So? strategy so powerful?

Allows the kids to make conjectures and pull from their own experiences. Forces critical thinking skills.7How does using data to launch a lesson support quality instruction?Gets the kids thinking right off the bat.8So What Should We See in an Effective Mathematics Classroom?An abundance of problems drawn from the data presented in tables, charts, and graphs.Opportunities for students to make conjectures and draw conclusions from data presented in tables, charts, and graphs.Frequent conversations, with and without technology, of data in tables and charts into various types of graphs, with discussions of their advantages, disadvantages, and appropriateness.Mathematical Practices addressed?9Tie the math to such questions as How big? How much? How far? To increase the natural use of measurement throughout the curriculum.Instructional Shift 7:What do you think?This classroom is in pretty bad shape so one of the things I want to do is paint the walls. I have 1 gallons of Carolina Blue paint. Do I have enough? Get with a partner to determine the answer.

What questions do you have? What questions do you think the students will have? Would students be able to develop an understanding of how to find surface area by doing this first? What tools could be used to find this (refer to referent)? What are some additional things we could look at using this problem (How much will it cost to paint the room? What if I want to put up chair molding and have the top part in Carolina Blue and the bottom part in white?)11Which would be more engaging? The previous problem or the following problem:

Find the surface area of the rectangular prism with the given dimensions: L 12 ft, W 8 ft, and height 9 ft.Which would lead students to really gain an understanding of surface area?12So What Should We See in an Effective Mathematics Classroom?Lots of questions are included that ask: How big? How far? How much? How many?Measurement is ongoing part of daily instruction and the entry point for a much larger chunk of curriculum.Students are frequently asked, to find and estimate measures, to use measuring, and to describe the relative size of measure that arise during instruction.The teacher offers frequent reminders that much measurement is referential-that is, we use a referent (such as your height or a sheet of paper) to estimate measures.Mathematical Practices addressed?13Embed the mathematics in realistic problems and real-world contexts.Instructional Shift 9How many of you have been asked the question by a student: When are we ever gonna use this?Ask yourself: When do normal human beings do the mathematics I am teaching? What situations arise in daily life where people use this mathematics? Pretend were in a math class and Im the teacher. We are going to go over last nights homework.15Ashrita Furman of the United States holds the world record for sack racing.

What would you like to know? 1 mile in 16 min. 41 sec. done in Mongolia on May 19, 2007.How would you explain Find the quotient of 12.5 and 1.23. and how would you make this simple problem more engaging for the students?16What is Mr. Leinwands secret to raising mathematics achievement?Who are the most successful students in our mathematics classes?High-quality instruction in important and relevant mathematical content.(page 67)The students who can memorize the formulas.17But once again, the critical question is Why bother? Teaching this way is harder to do. This type of instruction takes longer to plan and it is often very messy as we share instructional power with our studentsSo, why should we bother?Look at examples on page 68.18So What Should We See in an Effective Mathematics Classroom?Frequent embedding of the mathematical skills and concepts in real-world situations and contexts.Frequent use of So, what questions arise from these data or this situation?Problems that emerge from teachers asking, When and where do normal human beings encounter the mathematics I need to teach?Mathematical Practices addressed:19For next time, please read Chapters 4, 5, and 6.Any questions about what we talked about today?20