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Homeschooling the Middle & High School Years

Chaotic Bliss Homeschooling

Math
Greater Than; Less Than; Equal
Category: Math
Tags: greater than less than comparing numbers greater than less than worksheet greater than less than symbols

This Illuminations Lesson provides printable mat, fish and clam figures for doing number comparisons using greater than, less than and equal symbols. 

ABCya Online Game for comparing numbers.

Worksheets for comparing numbers.

Math Problem
Category: Math
Tags: real world math algebra in the real world high school math

It's a valid question educators are asking themselves more and more in the face of dismal test scores and the fact that many high school students have never gotten a good handle on basic math, the stuff we use everyday. 

Yet despite the fact that most people will not go into engineering or use higher math in any way in their lives, it continues to be forced on students and hinders many from pursuing their true interests. Why should passing Algebra be such a determining factor in a person's future? (Homeschoolers, too, are affected by this either through state  graduation requirements, or via college entrance exams).

This math teacher for the middle- and high school grades doesn't think that makes any sense: 

"Too many of the nation’s 14-year-olds inadvertently narrow their college options before they’ve even settled into high school." The reason? They can't get past the "gateway" course, Algebra 1. Many fail a second time and never become proficient at it.

Some argue that the reason students are unsuccessful is because the course as it is generally taught is badly designed.

"Algebra, as we teach it, is a death march through endless disconnected technical tools and tips, out of context....The course has no big ideas, no direction, no purpose. And when was the last time you had to graph inequalities?"

Others argue Algebra must be taught because it is necessary for developing critical thinking. But there are alternatives, both to the way Algebra is taught, (relate it more to real-world problem solving), and for the course itself (rigorous courses in statistics and probability, or philosophy and logic to develop reasoning and analytical skills).

And wouldn't we be serving students better if we made sure they had a good, working understanding of things like decimals and percents, how to measure square footage, budgeting and personal finance, how loan amortization works -- you know, some practical stuff? 

I don't think Algebra and other higher maths should be scrapped completely from high school courses of study. I just don't understand why these courses are a requirement for everyone. Hopefully, this will change.

In the meantime, the next time one of your kids asks, "Why do I have to learn this?" or "What am I ever going to use this for?", here are two sites that attempt to provide some answers:

Math Apprentice 

Get the Math 

Math Puzzles and Visuals
Category: Math
Tags: math puzzles symmetry 3d objects lines of symmetry 3d shapes dot-to-dot puzzles free dot-to-dot

I came across some interesting math puzzles over at MathPickleMy daughter likes doing dot-to-dot puzzles, but on this site, you'll find these puzzles with a twist: you use a ruler and only connect the pairs of dots that are a specific distance apart. For example, the puzzle starts out looking like this: 

And if you connect all the dots properly, (in this case, those that are 5 cm apart), you'll get a design like this: 

This is one of the easy ones. There are 23 progressively harder puzzles, with solutions, that you can download from this pagealong with other puzzles. 

We've also been looking at symmetry: 

and the way 3D shapes look when they are flattened out (noting things like the number of surface faces, sides, and vertices):

You can find both of these free downloads at Nyla's Crafty Teaching.

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