*Teaching Children Mathematics*,Volume 21, Issue 1, Page 18:

**13 Rules that Expire**

- You cannot take a bigger number from a smaller number.
- Addition and multiplication make numbers bigger.

for Math Teachers (gr 7-12), Prospective Teachers, and Students Who Want to Peek Behind the Curtain

Great article from *Teaching Children Mathematics*,Volume 21, Issue 1, Page 18: **13 Rules that Expire**

…avoid using these…

Overgeneralizing commonly accepted strategies, using imprecise vocabulary, and relying on tips and tricks that do not promote conceptual mathematical understanding can lead to misunderstanding later in students’ math careers.

These are good guidelines for teachers (and students of Math 260).

For example…

- You cannot take a bigger number from a smaller number.
- Addition and multiplication make numbers bigger.

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EEWeb has a very good Math Help page with numerous Quick Reference Sheets

- Algebra – Properties
- Geometry – Shapes and Solids
- Trigonometry – Definition (has unit circle)
- Trigonometry – Laws and Identities
- Calculus – Derivatives and Limits
- Calculus – Integrals

BTW – for printing purposes, it worked better for me to download them (PDF’s) and print from the Adobe Reader than from browser.

Here a two great websites that provide lots of great pattern problems.

These patterns can be used with elementary students (if you just ask number questions) through advanced algebra (if you include questions about functions).

Mathematics is often described as the study of patterns. That is exactly what * Spotting Numbers *and

The interplay of **geometry** and **numbers** and **algebraic thinking** in these questions puts the learner squaring at the core of **mathematical reasoning**. Quite frankly, it doesn’t get much better than this! (OK, my opinion.)

Here are some questions. As a general rule, For Elementary: a-b; Middle School: a-d; Algebra: a-e

a. How many *** are in next figure?

b. How many *** are in next figure after that?

c. How many *** are in pattern n = 10?

d. How many *** are in pattern n = 43?

e. Generalize: How many *** are in pattern n?

This posting provides links to various for this presentation made at the Annual ISMAA Meeting in Dekalb, IL on 3/27/2015. My abstract is here.

- CCSSM is here. PARCC page is here.
- My
**Common Core Math Standards: Information, Links, and Resources**page is here.

The PARCC test has met much criticism (from parents, teachers, whiners, and policy makers) as an assessment tool and a way to measure student mathematical understanding. The PARCC set too high of goals for themselves, and, as an assessment, it has an uncertain future. This session is not about the Pros and Cons of the PARCC, as an assessment.

We want to use the sample items, and CCSSM itself, to provide ideas for classroom tasks – for student learning.

- The Mathematical Practices of CCSSM are helpful. pg 6 of CCSSM I like to emphasize practice 2 (Reason abstractly and quantitatively-the
*decontextualize*and*contextualize*language is great) and 4 (Model with mathematics) - The tables on pages 88 and 89 need to be emphasized. On page 89 the 3 key meanings of multiplication (column 1) are huge. The two key meanings of division (top row right two cells) are huge.
- The idea (stated in the notes near the back of CCSSM) that many of the key ideas for college and career readiness are from grades 6-8 (proportional reasoning and percents) is very good.
- The HS Algebra II PARCC test is very functions and modeling based – as it should be.
- Mental math is important
*(again!)*– We finally have a two-part math test;**with and without a calculator**. - Teachers are saying good things about CCSSM – see http://www.cincinnati.com/story/opinion/contributors/2015/02/22/common-core-transforms-math-learning/23857441/

See http://parcc.pearson.com/practice-tests/math/ Click the bars at the bottom to get them to open up. There are PBA and EOY tests. There are online and print versions.

- Start with Algebra II – PBA-print version
- See #8, 11, 14
- See #18 –
**Compost Problem**wow! Great problem with lots of rates!

- Algebra II – EOY-print version
- #1 – wow!
- #2 “Select
**all**that apply.” - #4 – two parts
- #6 – two parts
- #7 – The need to apply skills and combine skills.
- #11 – average rate of change!
- #18 – formulas and graphs – Select
**all**that apply - #20 – average rate of change from a graph!
- Lots of statistics #24 1.5 standard deviations of the mean; #33
- #27 – note the questions
- Probability #28

parcc-sample-Test-ProblemsforJim – Word document

See this posting on “Spotting Numbers and Visual Patterns” – I think it is very rich mathematically

Posted in CCSSM, PARCC, Uncategorized
Tagged ISMAA
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NCTM statement

http://www.nctm.org/Publications/journal-for-research-in-mathematics-education/2015/Vol46/Issue2/Grand-Challenges-and-Opportunities-in-Mathematics-Education-Research/

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John Maxwell’s minute with Maxwell is on the word Teach.

In a couple minutes he hits the nail on the head.

http://johnmaxwellteam.com/teach-2?i=lLLW

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5 Practical Learning Tips Based On How People Do–And Don’t–Learn

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great information

Another good article:

https://www.theatlantic.com/amp/article/557687/?__twitter_impression=true

It’s time for us to realize that (1) ~~assessment (of student learning) is harder than one might think (harder than we thought) and (2) increasing our ~~~~#~~assessment efforts may not improve student learning.

It’s time we use assessment strategically.

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http://math.ucr.edu/home/baez/six.html

http://math.ucr.edu/home/baez/week79.html

http://www.ams.org/notices/199509/kostant.pdf

http://www.ams.org/notices/199509/index.html

symmetries of the cube: https://www.math.lsu.edu/~verrill/teaching/discrete2020/Spring2005/cubesolution.pdf

http://www.ams.org/samplings/feature-column/fcarc-cubes7

Posted in Geometry, icosahedron, Platonic
Tagged Symmetry
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