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Chaotic Bliss Homeschooling

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Christmas 2016
Category: Misc.
Tags: Christmas 2016

Merry Christmas and Happy Holidays to all. Here are some free holiday and winter-themed activities:

Winter Math and Problem-Solving Activities

The winter-themed labs in this video illustrate several chemistry concepts, highlighting viscosity and density, polymers, and polar and non-polar reactions:

Here are activities similar to the video that you can reproduce at home:

Snow Globes: (viscosity and density)

Snow Balls: (polymers)

Marbled Holiday Cards: (polar and non-polar reactions)

Make these Christmas-themed games to learn about electrical circuits and forces: 

Christmas Games, Interactives, Skills Practice

Fractions, Decimals, Percents, Ratios, Proportions
Category: Math
Tags: multiplying fractions how to multiply fractions multiplying fractions with whole numbers multiplying fractions worksheets

Several years ago, when my son and I were working on multiplying fractions, we were doing some work with multiplying a whole number by a fraction, specifically a proper fraction, where the numerator is less than the denominator. The example was 5/8 x 12, and the focus of the lesson was supposed to be that in order to multiply a fraction and a whole number, you change the whole number into its equivalent improper fraction, in this case, 12/1, then solve. (Cross cancel, multiply the numerators, multiply the denominators, get your answer).

Okay, so he had no problems with the process. What did bother him was when he got the answer and saw that it was less than what he started with.  At first, this didn’t make sense to him because, as he put it, “Doesn’t multiplication mean more?” 

So we talked about it, and with a little more contemplation:  

  • he understood that, yes, when you multiply whole numbers, you get more (except when one of the factors is 1 or 0
  • he remembered that when you multiply by 1 (which is like multiplying by a fraction with the same numerator and denominator) the number stays the same
  • by Jove, he then realized that when you multiply by a fraction that’s less than 1, you’re taking less than 1 of what you started with, so the answer is smaller.
  • he then extended the thinking a bit more by relating that when you multiply by an improper fraction (where the numerator is bigger than the denominator) you’re multiplying by more than 1, so the answer would be bigger

Now, I realize this example demonstrates a rudimentary understanding of numbers, but, to me, this also illustrates a problem I think kids can run into when it comes to learning math: the difference between knowing how to perform the steps of a particular process versus understanding why an answer does or does not make sense. Sometimes, we can learn a process mechanically without thinking about what we're doing in concrete terms. Maybe the pondering comes later – or maybe it never comes at all.

I suspect this may be one reason why kids that do great in basic math and pre-algebra seemingly hit a brick wall when they get to Algebra.  Could it be because when studying Algebra, you may learn to mechanically follow steps to solve complex equations without really comprehending the underlying logic? Or maybe some kids never get a good enough grasp of the basics to sufficiently tackle “higher math?” 

I’m not sure where the breakdown occurs, but I do know that some people have a great facility with numbers (I am, unfortunately, not one of these people), while others may struggle all their lives with math, and others are somewhere in between. Is the facility with numbers from having been taught well, a result of some innate trait, a combination?  How do you determine if your child has a sufficient understanding of math principles? Do you assess with worksheets and tests or use another method? Please leave a comment. And, if you need some free resources for learning fractions, decimals, percents, ratios and proportions, take a look at these:

MathMammoth: videos and worksheets on a variety of fraction topics

Fraction Video Tutorialson reading, writing and reducing fractions

Math Games, Videos, Worksheetson fractions, decimals, and percentages

Dining OutHere are free activities you can use for a co-op or group. Get the kids working with fractions, decimals and percents by figuring tax, tips and discounts when ordering food at restaurants.

Fraction Worksheets and Printables

Math AnticsFree videos with access to some free worsheets.

Yummy Math:  This site stands out from many on the Web, in that it focuses on relating math to real life. There’s more emphasis on concepts and critical thinking than on memorization of steps. For more on the YummyMath philosophy, read this post.

Math SnacksShort animations and games for teaching math concepts in grades 3 - 8. Includes accompanying worksheets (with answer keys).

And for additional math resources, visit our math page.

 

 

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Self-Paced Lessons for Middle School
Category: Academics
Tags: middle school lesson plans teaching resources social studies lesson plans 7th grade science

The PBS Learning Media Middle School Collection features 40 self-paced lessons for grades 5 - 8 in the core subjects. Some of the topics include: energy, plate tectonics, nutrition, and Newton's law; civil rights, building the Erie Canal, and the Trail of Tears; language arts topics such as symbolism and personification; and math topics such as ratios and proportions, multiplying fractions, and graphing distance and time.

The slideshow lessons incorporate video and interactive activities. Learners take notes, answer questions (multiple choice, matching, drag and drop), learn new vocabulary, and complete writing assignments.

Each lesson also includes a teaching guide with an overview of the lesson, and a summary of what's on each slide.



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