EEWeb has a very good Math Help page with numerous Quick Reference Sheets
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 Visual Patterns do.
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.)
Questions to Ask
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.
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/
PARCC Sample tests
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
From Bob Mann
parcc-sample-Test-ProblemsforJim – Word document
Spotting Numbers and Visual Patterns
See this posting on “Spotting Numbers and Visual Patterns” – I think it is very rich mathematically
Grand Challenges and Opportunities in Mathematics Education Research
John Maxwell’s minute with Maxwell is on the word Teach.
In a couple minutes he hits the nail on the head.
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.
symmetries of the cube: https://www.math.lsu.edu/~verrill/teaching/discrete2020/Spring2005/cubesolution.pdf