Lib of Links – old journal entries from SS

Teaching Algebra

Teaching Calculus and Advanced math Earlier?


Thinkering Day Math planning

This book has some amazing problems on the last 30 pages for getting elementary students to think algebraically:

You can see all of the problems on the Amazon “Take a Look”, but no way to copy – still beats buying the book!



We are going to be doing a unit study on evolution in the next month or so, and here are a few of the websites we will be using:

Someone on BAGHS recommended this Open Yale course, which is a course taught by a Yale University professor available for free on the internet:

Evolutionary Biology Online Course

This is one of the premier education sites about evolution:

Berkeley’s Evolution Website

We have been watching Earth:The Biography to get started, but with our schedule slowing down for the summer, I’d like to do a lot more! Luke has really been enjoying the Earth:The Biography series, so I’m planning for him to join along in our studies.

Studying for AP Biology

Chance has been studying furiously for the upcoming AP Biology exam, and here are some recent websites with great review resources and old exams:

A teacher’s website with some nice lab reviews:

A top-notch site with tons of resources:


Restoration Ecology and Habitat Restoration

We are taking part in YSP, and I’ve found some great links about restoration ecology:



A high school biology class’ science blog

This is a cool example of what can happen when a bunch of kids work together:

Extreme Science Blog

A debate website

Some cool blog posts from around the web

Some math fun

This is from the Homeschool Math blog I subscribe to:

The New Year 2009

By Maria Miller

I hope you all have had some happy family time (or otherwise) during these Christmas days! Now, I’m already going to turn your thoughts towards the changing of calendar year.

We’re about to change from 2008 to 2009. If you’d like to have some mathematical fun with a new year’s theme, check out MathNotation’s Get Ready for Happy 41*7^2.

Basically, what you do for this “game” is try to find something special about the number 2009. Like the title of Dave’s post tells us, 2009 factored is 41 × 72. So one thing you can do is ask the kids to factorize 2009.

Then, it’s just up to you – or the students – to find anything interesting or special about the number 2009. Maybe they can explore the remainders when 2009 is divided by various numbers and find something that sounds “special”. Maybe they can explore what kinds of sums they can make with it (it’s 1004 + 1005 for example). Or, how about this sum: 2009 = 777 + 29 + 92 + 209 + 902. Or, you could simply ask students to write 2009 as a sum of four (or five or seven) whole numbers that are as close together as possible.

Read also Dave’s post.

Classic reading

A Stanford Dickens page

Math Contests

This is a blog published by a 10 year old homeschooler who lists all sorts of math contests for individual homeschoolers:

Natural History

This is a naturalist site, which might make our hikes a lot more educational!

Another site which is about estuaries:

Natural History is the study of things in our world, so it includes plants, animals, fossils, etc. Some other great sites include:

American Museum of Natural History

Natural History Magazine

Smithsonian Magzine

Life Photos Archive

This the archive created by Google containing millions of Life Magazine photos, since never published before. WHat could we do with these?


I just found this website:

Reduced Shakespeare

It looks like a lot of fun, can you guys check it out and tell me what you think?

Open Courseware

These are free! university and high school level courses on almost any topic you might care to learn about. Some of the best are at MIT, but Berkeley has some great ones, too, and the lower links are for finding courses anywhere.

MIT OCW homepage:

Some specific classes:–IAP–2005/Projects/index.htm

Berkeley Resources:

A newer blog:

Words, words words

Hmm, a visual thesaurus, I wonder what that could be?

Thinking math problems

grade 8 (DRAFT)

20 Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics
Algebra: Analyzing and representing linear functions and solving linear equations and systems
of linear equations
Students use linear functions, linear equations, and systems of linear equations to represent, analyze, and
solve a variety of problems. They recognize a proportion (y/x = k, or y = kx) as a special case of a linear
equation of the form y = mx + b, understanding that the constant of proportionality (k) is the slope and the
resulting graph is a line through the origin. Students understand that the slope (m) of a line is a constant rate
of change, so if the input, or x-coordinate, changes by a specific amount, a, the output, or y-coordinate,
changes by the amount ma. Students translate among verbal, tabular, graphical, and algebraic representations
of functions (recognizing that tabular and graphical representations are usually only partial representations),
and they describe how such aspects of a function as slope and y-intercept appear in different representations.
Students solve systems of two linear equations in two variables and relate the systems to pairs of lines that
intersect, are parallel, or are the same line, in the plane. Students use linear equations, systems of linear
equations, linear functions, and their understanding of the slope of a line to analyze situations and solve
Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using
distance and angle
Students use fundamental facts about distance and angles to describe and analyze figures and situations in
two- and three-dimensional space and to solve problems, including those with multiple steps. They prove
that particular configurations of lines give rise to similar triangles because of the congruent angles created
when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety
of problems, including those that ask them to find heights and distances. They use facts about the angles that
are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a
triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students
explain why the Pythagorean theorem is valid by using a variety of methods—for example, by decomposing a
square in two different ways. They apply the Pythagorean theorem to find distances between points in the
Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.
Data Analysis and Number and Operations and Algebra: Analyzing and summarizing data sets
Students use descriptive statistics, including mean, median, and range, to summarize and compare data sets,
and they organize and display data to pose and answer questions. They compare the information provided by
the mean and the median and investigate the different effects that changes in data values have on these
measures of center. They understand that a measure of center alone does not thoroughly describe a data set
because very different data sets can share the same measure of center. Students select the mean or the
median as the appropriate measure of center for a given purpose.
Algebra: Students encounter some nonlinear functions
(such as the inverse proportions that they studied in
grade 7 as well as basic quadratic and exponential
functions) whose rates of change contrast with the
constant rate of change of linear functions. They view
arithmetic sequences, including those arising from
patterns or problems, as linear functions whose inputs
are counting numbers. They apply ideas about linear
functions to solve problems involving rates such as
motion at a constant speed.
Geometry: Given a line in a coordinate plane, students
understand that all “slope triangles”—triangles created by
a vertical “rise” line segment (showing the change in y), a
horizontal “run” line segment (showing the change in x),
and a segment of the line itself—are similar. They also
understand the relationship of these similar triangles to
the constant slope of a line.
Data Analysis: Building on their work in previous
grades to organize and display data to pose and answer
questions, students now see numerical data as an
aggregate, which they can often summarize with one or
several numbers. In addition to the median, students
determine the 25th and 75th percentiles (1st and 3rd
quartiles) to obtain information about the spread of data.
They may use box-and-whisker plots to convey this
information. Students make scatterplots to display
bivariate data, and they informally estimate lines of best
fit to make and test conjectures.
Number and Operations: Students use exponents and
scientific notation to describe very large and very small
numbers. They use square roots when they apply the
Pythagorean theorem.

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