# Maria's Math News, Vol. 64, July 2012

I love teaching, and I love math. This newsletter is my way of reaching out and helping you to teach it, too.

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Hello! I have news about Math Mammoth grade 3, notices of upcoming sales, and lots of terrific links and sites to share!

~Maria

1. Math Mammoth news
2. Some online measuring games
4. An interactive tessellation tool
5. Tidbits

## 1. Math Mammoth news

Math Mammoth Grade 3 now aligned to the Common Core standards

To see the major changes between the earlier and the new edition, read here. As for the remaining grades, I expect to take about 2 months per grade to finish the alignment.

• Kagi or Homeschool Buyers Co-op: If you purchased a bundle and can wait till I have finished all six grades, please do so. If you want the new version right now, email me.

Then I wanted to answer a question...

Why am I aligning Math Mammoth to Common Core Standards?

I have known of Common Core standards for a few years, but in December 2011 I noticed that nearly all states were or are going to implement them. So, they are in essence providing a framework for a national curriculum in mathematics.

So, I decided to consider them, and to take a closer look at the standards. And I realized that Common Core standards aren't that "bad." They are NOT like most state standards have been, "inch deep and mile wide," with tons of topics per grade.

These are "core" standards, meaning there aren't a huge amount of them per grade. So it's a BIG improvement over many of the states' standards.

I also noticed that some of the "core" standards were already in place in Math Mammoth, such as a focus on single-digit multiplication in third grade, or multi-digit multiplication in 4th, or fractions in 5th.

I liked the fact that the standards explicitly mentioned some mental math!

Also, I am not fundamentally changing the teaching approach or style in Math Mammoth. Aligning to the Common core is more a question of reorganizing topics, moving some topics to a different grade, than anything else.

Yes, I've added a few little things they require such as measuring how much longer one thing is than another, or problems with unknowns shown with shapes, or asking children to divide a shape into quarters. But it is not affecting the development of major concepts.

At the same time, I have also revised many of the lessons and made them better -- this is happening regardless of the standards. It's just when I see my earlier work, I find ways to improve it.

August sales! Homeschool Buyers Co-op will be running a traditional group buy for Math Mammoth bundle products. I will also run a separate sale for the downloads at Kagi store. And, there's been some talks about a sale for the printed copies at Rainbow Resource--but I don't have the details yet.

## 2. Some online measuring games

The Ruler Game
Choose between whole inches, half-inches, quarters, eighths, or sixteenth parts of an inch to measure. Click on the given measurement on a ruler. Timed or not timed versions available.
www.rickyspears.com/rulergame

Sal's Sub Shop
Customers order subs, and you need to cut them to the given measurements - sometimes in metric units, sometimes in inches.
www.mrnussbaum.com/sal.htm

You can illustrate a variety of measuring devices, such as scales, measuring cup, thermometer, and speedometer, and how to read them. Generate examples using different scales on different devices at the press of a button.

Measures
An online activity about metric measuring units and how to read scales, measuring cup, and a ruler. Uses British spelling.
www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/measures

I have a longer list of measuring online games and tutorials here.

## 3. More about Area - a free worksheet for grade 3

Here's a little sample of what is keeping me so busy right now, aligning things to the Common Core standards.

This is a complete lesson (4 pages) about area for grade 3 math. It's not the initial lesson - it assumes the student already knows how to find the area of a rectangle. (Sorry - there is no answer key available for this freebie.)

The lesson is specifically about these two Common Core standards:

3.MD
7.c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

## 4. An interactive tessellation tool

This is just too neat an interactive tool to pass by for creating your own tessellations. Choose a shape (a square, a triangle, or a hexagon), then edit its corners or edges. The program automatically changes the shape so that it will tessellate (tile) the plane. Then push the tessellate button to see your creation!

Interactivate! Tessellate Tool

Also, see one boy's creations with it.

## 5. Tidbits

• Mathematics and scheduling of buses
Whenever mathematics solves a problem in real life, I find it fascinating! This mathematical method "evens out" the headway (the spacing between buses) by holding each bus at the start of the route a specified amount of time. That avoids "bus bunching", and it also makes it where the bus drivers don't need to adhere to any schedule--reducing their stress.

The researcher John Bartholdi says, "The trick is to hold the bus for an adjustable amount of time at one stop. We simply control how long they wait at the end of the route, and then we tell them, 'drive comfortable with the traffic to the other end. Don't worry about where you are. Just flow with the traffic.' "

• Mental math multiplication guide
Rules of thumb and other "tricks" for mental multiplication of two-digit or bigger numbers, conveniently in one place. (This is not about single-digit multiplication; you are supposed to know those by heart of course.)

• Visualizing Probabilities
This is an interesting article about modern visualisation techniques in the context of probabilities. The right picture really can be worth a thousand words.

• Visual representations of the difference of two squares
Not just one, but four different visualizations. And this is not meant to be shown as proof, but as a student activity: they cut a smaller square out of a large square, then dissect the remaining piece, trying to figure out its area.

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Till next time,
Maria Miller