# Inside Mathematics

illustrative mathematics Illustrated Standards Count to 100 by ones and by tens. (see illustrations) Count forward beginning from a given number within the known sequence (instead of having to begin at 1). (see illustrations) Write numbers from 0 to 20. Understand the relationship between numbers and quantities; connect counting to cardinality. 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. Understand that the last number name said tells the number of objects counted. Understand that each successive number name refers to a quantity that is one larger. Count to answer “how many?” 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. Compare two numbers between 1 and 10 presented as written numerals. Fluently add and subtract within 5. Recognize area as additive.

Would You Rather? | Asking students to choose their own path and justify it Home Page Teachers Primary Pupils Secondary Students Events and PD "It gave me some good ideas to use in the classroom and ... a link that I can get all of the activities from." Book NRICH Bespoke PDBook Forthcoming EventsBook our Hands-on Roadshow Your Solutions Space Math @ NASA ! An Interview with Grant Wiggins: The Power of Backwards Design When Grant Wiggins and Jay McTighe wrote Understanding by Design (UbD) they did what no other educator had ever accomplished. They unequivocally cast assessment in the central role of teaching and learning by making the forceful argument that testing should not be the afterthought of instruction, but the central point of instruction. After all, how do we know students have learned anything after we have taught them if we don't assess them on what we hope they have learned? As a result, I had a very encouraging chat with Dr. Edutopia: Dr. Grant Wiggins: Elementary teachers seem to do a much better job of this than secondary. Edutopia: What are some ways to get around that difficulty? Grant Wiggins: Some high school teachers use Socratic Seminars to provide students with feedback on their thinking and literacy -- similar to an athletic coach that has to stand on the sidelines while the athletes perform. Let's consider the Common Core sixth-grade content in fractions and decimals.

Standards for Mathematical Practice "Does this make sense?" Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Illustrations Kindergarten Grade 1 Grade 2 Videos CCSS Chairs in Hall (High School) from Math Department on Vimeo.

Yummy Math The Best Resources On Differentiating Instruction My colleague Katie Hull-Sypnieski is leading a February 1st Education Week Webinar on differentiating instruction, and I would strongly encourage people to participate. Katie’s the best teacher I’ve ever seen…. In addition, Katie and I have co-authored a piece for Education Week Teacher on the topic that will be appearing there soon (it’s appeared: The Five By Five Approach To Differentiation Success), and an upcoming post in my blog there will be talking about it, too (that two part series has also appeared). I also did a second two-part series in Ed Week on differentiation. Also, check out The Best “Fair Isn’t Equal” Visualizations. Given all that, a “The Best…” post was inevitable, and here it is. Here are my choices for The Best Resources On Differentiating Instruction: The Best Places To Get The “Same” Text Written For Different “Levels” Busting Myths about Differentiated Instruction is by Rick Wormeli. Reconcilable Differences? Deciding to Teach Them All is by Carol Ann Tomlinson.

3-Act Problems | Teaching Outside the Norm CSU NGSS community: Science and Literacy Learning Web Resources in STEM Education-Examples Created by CSU Faculty Dr. Ivan Cheng, Department of Secondary Education, CSU Northridge This site contains archived presentations by Ivan Cheng from recent California Mathematics Council (CMC) meetings. You will find information on how assessments under CCSS-M will shift, advice on teaching with a “non-Common Core” text book, and example activity sheets that support development of the mathematical practices required under CCSS-M. Click Here to view Dr. Responsive Teaching in Science Dr. Responsive Teaching refers to the practices of attending and responding to the substance of students' thinking. "Surveys Fail to Measure Grasp of Scientific Practice" Dr. Dr. There is debate in the science education literature about how best to improve students' understanding of the nature of science: Can an "immersion" experience in the process of doing science like scientists outperform explicit instruction on the nature of science? Dr. Chicago Lesson Study Group

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