Homeschool Math Newsletter, Vol. 23
October 2008
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Greetings! This is Maria Miller from HomeschoolMath.net and MathMammoth.com.
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In this month's newsletter:
Last time I asked people to write me back, and tell how they liked the newsletter, or give suggestions. Someone wanted more abacus stuff, another wanted algebra stuff. So this time I'm including those.
And this time also, feel free to hit the "reply" button to tell me how you like this month's newsletter and what you'd like to see in the future.
1. Math Mammoth news
2. Algebra problems to solve
3. Abacus and basic division concept
4. Mean & mode freebie download
5. Tidbits
1. Math Mammoth News
There are two new books available in the Blue Series:
1. Math Mammoth European Money is a worktext that covers money-related topics usually encountered during grades 1-3, using euro coins.
The book starts with counting coins with cent-amounts and easy problems about change. From there, the lessons advance toward practicing with euro amounts, and figuring out total bills and change.
2. Math Mammoth Early Geometry covers geometry topics for the early elementary grades (approximately grades 1-3).
The first lessons in this book have to do with shapes - that is where geometry starts. Children learn the names of the common shapes, and also put several shapes together to form new ones, or divide an existing shape into new ones. They practice using a ruler to draw various shapes and are introduced to tilings.
Next children learn the concepts of parallel lines and lines that are at a right angle (perpendicular lines). The book also has beginner lessons about symmetry, area, perimeter, and solids.
Apart from those books, I'm happy to report (for those of you who are waiting) that LightBlue Series grade 5-A is coming along... I've finished writing the lessons and answer key is done. I am waiting for a proofreader to finish his job, plus I still need to write tests and a worksheet maker. I expect it to be ready in the latter part of October! (Then I'll start the B part.)
2. Algebra Problems
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The following is a quite typical "algebra" word problem... but there's an easier way to solve it - without using algebra!
Todd, Chris, and Rod have 30 birds. Rod has five times as many as Todd. Todd has one fourth the number Chris has. How many birds do they each have?
The numbers in this problem are so small that I won't make any equations -- it is QUICKER to use guess and check!
- The following problem is just the other way around: easier to solve WITH algebra than without... but you can solve it several different ways (see the blogpost and its comments).
There are some marbles in Box A and Box B. If 50 marbles from Box A and 25 from Box B are removed each time, there will be 600 marbles left in Box A when all marbles are removed from Box B. If 25 marbles from Box A and 50 marbles from Box B are removed each time, there will be 1800 marbles left in Box A when all marbles are removed from Box B. How many marbles are there in each box?
- And one more, where algebra is definitely the way to go.
Andy has $200 more than Peter. Andy gives 60% of his money to Peter. Peter then gives 25% of his money to Andy. In the end, Peter has $200 more than Andy. How much did Andy have at first?
The solution is here.
3. Abacus and basic division concept
Let's be reminded first of all that there are two basic "interpretations" of division:
- Sharing division. In it, you think that 16 / 2 means "If there are 16 beads divided between 2 people, how many does each one get?
- Quotative division. In it, you think how many groups of the same size you can form. Or, "how many times does the divisor fit into the dividend?" For example, 16 / 2 is interpreted as: "If you have 16 beads, how many groups of 2 beads can you make?"
Sharing division is easy to understand as a concept, but it's hard to do without the knowledge of multiplication tables. Just imagine, if a child who doesn't know their times tables is trying to find the answer to the question, "If there are 56 strawberries and 8 people, how many will each one get?" It'll take some guesswork, trying and checking.
But quotative division is easy for children to do with the help of manipulatives (or by drawing pictures). Just make a group of 56, and start forming groups of 8 out of it. Once you're done, check how many groups you got. There's no guessing. It's just repeated subtraction - each group the child forms is "subtracted" or set apart.
And this activitity lends itself perfectly to the 100-bead abacus, as well.
See how it's done!
4. Mean & mode freebie download
This free lesson about mean and mode will get you a foretaste for my upcoming 5-A Complete Curriculum from the LightBlue Series.
Download it here:
Mean, Mode, and Bar Graphs - lesson for 5th grade.
In the lesson I highlight the idea of mode versus mean (average) and when you can calculate the mean. Students also graph the data in bar graphs.
Check also my list of online statistics resources for mean, median, mode, bar graphs, line graphs, and more.
5. Tidbits
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Credit card math - resources to help kids learn about credit card basics and misleading credit card advertising.
- Free math software: math911.com - this offer will only last till the end of January so take advantage of it while you can.
- A simple ratio problem: If a:b = 1:3 and b:c = 3:4, find a:c. This is very very simple, but I also discuss a variant of this problem with harder numbers.
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My decimal worksheets generator just got better. Now you can vary the number of decimals randomly in the problems. Also, the page now includes a bunch of ready-made worksheets that you generate just by clicking on links. This generator makes worksheets for decimal addition, subtraction, multiplication, and division.
Let me know if the resources in this newsletter were interesting and/or benefited you in some way - or if not! Just hit "reply" in your email program and write me back.
I wish you success in your math teaching!
Maria Miller
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