Goodies for teachers and all

Just a few items of interest:

1) Math Goodies CD from www.MathGoodies.com has been updated earlier this year; I got to see it, and updated my review of the CD. It's full of good math lessons with interactive exercises, printable worksheets, crossword puzzles and more.

2) I've added a free online equation editor to my site. This would be most useful for teachers or others who write math content and need images for complex symbols and math expressions.

3) Those of us who use math a lot might also enjoy a free calculator/graphing program called SpeQ Mathematics. You can type complex expressions into it, define variables to be used in later calculations, and make plots.

Mnemonic helps for multiplication tables?

...regarding my third grader. We are still slogging through learning the times tables. To liven it up, I decided to order Times Tales (I ordered the deluxe version that includes division as well).

I have read different opinions about using mnemonic devices to learn math facts. Some say that mnemonic devices actually slow the student down, and one even went as far to say it was like counting on fingers. I don't want to use Times Tales if it's going to slow her down, and I do want to make sure she knows her math facts cold.

I, myself, remember I didn't know 8x8=64 in seventh grade, and I just figured it in my head, 8+8=16, 16+16=32, 32+32=64 -- 8x8=64. I did this until I realized how slow I was and decided to commit the facts I didn't know to memory. What do you think about Times Tales and other "helps" for math facts?

Mnemonic helps in themselves are not bad. We use them all the time, in everyday life situations. You have a phone number, you divide it to 2-digit numbers, maybe remember it has successive numbers, or doubles, etc.

I once memorized a certain 4-digit pin number by dividing it to two 2-digit numbers, and remembering that the latter was 9 less than the first... but after a while I remembered it without that.

On Times Tales. It's a fine program in itself. It associates a silly story and picture with each "difficult" upper times tables fact. You've probably seen samples. I don't think it is going to hinder... Basically, if it works for your kid, let's say you will show 8 x 7 to your your kid. He will see 8 x 7 and suddenly also see the silly picture of lady eight and the character 7 driving in a car, in his mind, and remember "It's 56."

It's not too much different from using a rhyme such as "5, 6, 7, 8, fifty-six is seven times 8."

Such a program can be a confidence booster as well.

Now, for some kids it doesn't work because they don't easily remember silly stories, and then it can cause frustration. Or, they're older and don't enjoy the silly stories anymore.

All these "helps" are fine in their place, but you have to be sensitive to your child so that the mnemonic "help" does not end up being an additional burden in itself... such as if the child cannot easily remember the stories or the song or whatever the "help" is.

So it's totally up to you. Try it first with the free sample they offer on their website... and see how your child reacts.

That program is an additional resource of course, and doesn't replace studying multiplication concept itself.

Help for house cleaning with kids

This is a special offer for May only:

Trigger Memory Systems is offering a FREE Bedroom Cleaning For Kids Clean N' Flip (a $7.95 value) if you buy either their Times Tales Deluxe OR Zone Cleaning For Kids Clean N' Flip.

Times Tales Deluxe is a collection of short stories that provides a mnemonic aid to learn the upper multiplication tables. The "Deluxe" means that the book has story/picture pages for corresponding division facts as well.

Zone Cleaning For Kids Clean N' Flip is a fun & unique system designed to help children visually and systematically work through cleaning the three main rooms of a house independently, and with ease.

Bedroom Cleaning For Kids Clean N' Flip is a sturdy, spiral bound, 8.5" X 5.5" flipchart that walks children quickly and easily through the process of cleaning their room. It takes an overwhelming process and breaks it down into simple parts. Complete a step and flip the page.

-> Buy a Times Tales Deluxe OR Zone Cleaning For Kids Clean N' Flip - and receive a free Bedroom Cleaning For Kids Clean N' Flip.

Type code FREEFLIP in comments at checkout. Offer ends May 31.

Math Mammoth news

I've made a partnership with Scott from Softbasics to offer additional bonus software for those who buy any Math Mammoth CD product or the Blue Series download.

In essence, by buying any of the CDs, or the Blue Series download, you will also get a bundle of 7 software products (math, L&A, testing):

The Soft-Pak contains:

• Math Maker - printable worksheets/activities with answer keys.


• Math Master - same activities as Math Maker, but on-screen.


• Math User - on-screen program for solving the 900 multi-level word problems (also printable in Math Maker) with a built-in calculator.


• True/False Math Challenger - on-screen program for answering math questions that are either True or False using motivational activities. Includes math "facts" that are either true or false.


• Language Arts Master - covers spelling and reading (over 4000 words included) plus usage, writing mechanics, reading speed and recall, and a non-threatening grammar section: parts of speech, subjects and predicates, phrases and clauses, and sentence structure. Printable activities with answer keys.



• Test Maker - used to CREATE personal word lists for use in LA Master spelling and reading. Also used to create True/False and Multiple Choice activities for use in Test Master.


• Test Master - on-screen program for answering the True/False and Multiple Choice questions created in Test Maker. Any subject (geography, history, science, foreign language etc may be addressed). Printable activities as well.

See more info and screenshots.

Otherwise I've been busy preparing the complete curriculum for 1st, 2nd, and 3rd grade that will be sold at Winterpromise. It going slower than I thought... Well, that probably happens to many people who start new projects. You never quite anticipate all the hurdles and how much time this or that takes.

It took me a long time making the measuring / geometry section for 2nd grade. I was trying hard to think what kind of lessons would get kids familiar with inches, kilograms, pounds, milliliters, etc.

You know, I don't think you get a good feel of measuring if you don't go do it and measure! Just doing paper and pencil problems won't get you there. So I tried to think up little measuring projects and things that mothers and children can do at home, and that help the children learn about various measuring units.

Right now I'm writing something way easier, which is early multiplication lessons. In comparison, it's a breeze.

Also, I am overseeing all this translating work that's happening all around me (it seems). One person is translating the books to Spanish, another to French, and a third one is checking and fixing the layout after all those looonnng Spanish and French words are in there. You know, they don't always fit into my 'boxes', pages flow over etc.

So I'm keeping busy. Anticipate several new products in June!

Basic abacus as a manipulative

I don't want to leave out one of the best manipulatives there is for grades 1-2: a simple "school" abacus that has 10 wires and 10 beads on each wire.

I'm not talking about a Chinese or Japanese abacus with a special counting system. I'm talking about using a simple 100-bead abacus for counting, and treating each bead as 1. You don't have to learn any of these sophisticated systems that have been in use with various abacuses. Just consider each bead being 1, period.

Then you have 10 tens, or a hundred, in your abacus, and that goes a long way explaining tens and ones or 2-digit place value to first graders.

To help a child learn the numbers up to 100, you can play a simple game with the abacus. When it's your turn, you say a number, and the child "makes" it or shows it on the abacus. Then your child says a number for you to show on the abacus.
You can also show the child other things, such as how the subtractions
10 − 5
20 − 5
60 − 5
are similar, or let the student find sums of 2-digit numbers, such as 23 + 45. He can move 2 tens and 4 tens, then 3 and 5 individual pieces — you can show how to add the tens and ones separately.

You can let the child explore what happens with 28 + 9.

It's better if the abacus has the first five beads colored differently from the next five, in each row, like in this silly picture.

Then the child will easily recognize 6, 7, and 8 beads without counting. Also, let's say you choose 6 beads on one wire and 8 on the next one. You can show how the five and five on those two wires makes ten, and some are left over.

You can also model multiplication: move 4 beads on each of the 5 neighboring wires, and there you have 5 times 4!

So this is not rocket science; it is very easy. You don't need to learn any special abacus systems.

Here's a picture of an old school abacus.

Wikipedia has info on all different kinds of abaci, including this kind of usage of the school abacus.

You can browse Amazon's abacus selection here.

Performing well below grade level

I am leading a training next week on how to introduce grade level concepts/standards when the students are performing well below grade level, and I am sure that math is going to be an issue. Any suggestions?

These are my 2 cents on teaching under-performing students.

Let's imagine we have an 8th grader performing on 3rd grade perhaps.

I would dismiss for starters geometry and measuring topics, and concentrate on this train of topics, in THIS ORDER:

addition
subtraction
multiplication
division
fractions
decimals.

... the goal being to cover the basic arithmetic up to pre-algebra.

Think of mathematics as a building. You need to have the foundation building blocks before you can go forward.

Maybe the child stopped understanding the math on 2nd grade or 3rd. We need to find the exact point after which he has not understood everything.

You can gauge this by the way by asking the child simple questions such as,

• I give you an addition 8 + 2 = 10, you give me a subtraction sentence (1st grade knowledge).


• How much do you need to add to 600 to make a thousand? (2nd grade place value)


• Draw a picture of 4 x 3 (3rd grade knowledge)


• There are 293 flowers and 145 are red. How many are not red - how do you find that? (using subtraction in finding parts)


• Draw a picture of 20 : 4. (division concept, 3rd grade)

etc.

So for such imaginary 8th grader, I'd make up a separate curriculum that goes through addition, subtraction, multiplication, division, fractions and decimals, in this order.

A teenager can go through those topics in 1 year, and understand it all, if he wants to. Obviously you'd want to show the student the train of topics too so they know what's coming next. You'd want to motivate them that hey, in one year I can learn all this basic math. You'd want to show them how the basic topics lead to the next ones.

Addition: you'd start at adding single-digit numbers, then memorizing addition facts, then 2-digit addition, then multi-digit addition.

If the student does NOT know addition facts, then spend a week practicing them! But not in random order. Like I do in my books (Addition 1 and Subtraction 1) you need to put those facts into contexts, study them in systematic, logical fashion such as sums of 5, sums of 6, etc. (using fact families). Or, adding to 9, adding to 8, etc.

Not knowing the addition facts makes the student SLOOOOOWWWW in doing simple addition problems, and makes it hard to get into subtraction or multiplication. So it is important, even if he's on 8th grade, and it is 1st grade stuff.

On to subtraction. Cover the three situations where subtraction is used, even if it is 1st grade stuff. Cover multi-digit subtraction. Shouldn't take many weeks.

Then multiplication concept. Times tables. Multi-digit. Absolutely remember to show what principles 23 x 38 is based on (multiplying in parts). Spend several weeks here.

And so on.

In a school year's time, it absolutely is possible to cover the basic arithmetic if the student is a teenager. I just would cover it all, including 1st grade topics, to make sure to catch those points where the student "dropped" off.

Any comments anyone?

Maria Miller

New games website

Again! Games sites certainly abound on the internet.
I didn't try all the games but I liked the tangram puzzle game.

SchoolTimeGames.com - Mathematics

On their home page are links to other school subjects as well.

The good side of manipulatives

Update: read also Mama Squirrel's excellent blogpost on the issue; basically there is probably a balance in this, as in everything.

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If you haven't, go pay a visit to the National Library of Virtual Manipulatives.

Lots of good stuff there!

So, why would I suddenly turn around and praise manipulatives, if I just mentioned how they're not the "ultimate thing" in math education?

It's just one of those things that can be good, if used right, in its rightful place.

Manipulatives do help students to understand concepts, initially, on a concrete level. But they shouldn't stop there. Kids need to learn to make generalizations. That is where the power of mathematics is.

For example, maybe you'd use The Base Blocks Addition to illustrate the concept of "carrying" to tens and hundreds (or "trading") in addition.

Once the student understands that, they should be able to translate their knowledge into bigger and smaller place values (including decimal addition).

So it's the age-old truth; there is balance in everything.

Or, what do you think?