1. A Way to Make Math Make Sense NMSA 2011

2. Linda Bridges and Jeanne Simpson Virtual handout at jeannesimpson.wikispaces.com

4. Sometimes teachers have to explain “why” mathematical concepts are true.

5. Why can’t you divide by zero?

6. Why should we write in math class?

7. According to Marilyn Burns there are two major benefits: It supports students’ learning by helping them organize, clarify, and reflect on their thinking. It benefits teachers because students’ papers are invaluable assessment resources. Instructor Magazine, April 1995

8. 1. Write arguments focused on discipline-specific content. 2. Write informative/explanatory texts, including the narration of …scientific procedures/experiments, or technical processes. 3. Write narratives to develop real or imagined experiences… 4. Produce clear and coherent writing… 5. …develop and strengthen writing…by planning, revising, editing, rewriting,…

9. 6. Use technology, including the Internet, to produce and publish writing and present the relationships between information and ideas… 7. Conduct short research projects to answer a question… 8. Gather relevant information from multiple … sources 9. Draw evidence from informational texts to support analysis, reflection, and research.

10. 10. Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for range of discipline specific tasks, purposes, and audiences.

11. Construct viable arguments and critique the reasoning of others. Attend to precision.

12. 6.NS.4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Apply and extend previous understandings of numbers to the system of rational numbers.

13.  Factor  Product  Multiple  Divisibility

14. 1218

15. 3045

17. Explain a way to determine the greatest common factor of any pair of numbers.

19. 6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. 7.RP.3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

20. 7.SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

21. Analyze outcomes when rolling one and two dot cubes “Describe the probability of rolling a sum of 7 in words and in fractions with lowest terms.” Conduct experiments with rolling two dot cubes “Describe the results of your experiment. Compare the results with the theoretical probability of rolling a 2 one time out of every 6 rolls.” “What do you think about the theory of large numbers?” Design an experiment “Describe the results of your experiment.” Analyze combinations using lists and tree diagrams “In what ways do the lists, tree diagrams, and multiplication compare? Which representation is your first choice? Explain.”

24. How can this work in my classroom?

25. Things I learned Things that surprised me Question I still have Virtual handout at jeannesimpson.wikispaces.com