Homeschool Math Blog

Fact families on a whiteboard

2009-11-08T13:53:00.004-04:00

I just found this picture that I took of the fact families my 4-year old wrote on the whiteboard - totally on her own.

There was a time she loved writing fact families like this every day. Being able to choose different color markers plus it being on the whiteboard seemed to be the main motivating factors, because she didn't want to write them on blank paper... Kids are funny.

Then again, it allows us teachers to use colorful markers as a "motivational tool" : )

Anyway, I was really happy that she had grasped the concept.

Review of Math Apprentice

2009-11-02T06:46:00.000-04:00

Math Apprentice is a new free website, meant to show students how math is used in real world. In the game, you are like an apprentice at various companies, applying your math skills to challenges similar to those encountered in the real world and real companies.

Main Street - Click to enlarge

To begin, you click the button on the home page of the site that says "Explore the Math". Then choose your character, and you'll be on the main street (see screenshot above) . Then use arrow keys to move right or left, and click to select a company to visit.

The companies you can visit are:

Sweet Treat Cafe - baking pies

Sweet Treat Cafe - Click to enlarge

Wheelworks - constructing bicycles and exploring gear ratios
Game Pro! - keep track of the distance between superhero and the villain in a computer game, using Pythagorean Theorem
Spacelogic - study speed of a spacecraft & slope, and then angle & distance commands to get the space rover where it needs go.
Trigon Studios - Explore the usage of sine and cosine functions to create rhytmic or repeating motion of animated objects.
Doodles - explore polar curves created with sine and cosine. These can be like stars, flowers, or spirals.

Doodles - Click to enlarge

Builders, Inc. - calculate areas and perimeters of shapes

Builders, Inc. Click to enlarge

Adventure Rides - study the angle of elevation and height of a roller coaster

While the site is targeted to grades 4-7, many of the mathematical ideas are actually far more advanced than that. In the simulations involving sine and cosine, for example, all you have to do is change the values in the equations using sliders and observe. Also, in some activities there are instructions given how to calculate things.

It says the about page: "Some of the mathematics in Math Apprentice may seem advanced for its targeted age group, grades 4-7. That's ok. It's important for students to interact with math concepts beyond the standards. This is where the joy of math can often be found."

Nevertheless, I feel some activities are definitely best reserved for students who have studied the concept (such as Pythagorean Theorem in Game Pro! company).

In general, I think Math Apprentice has well-made and interesting activities, and kids are sure to enjoy it!

Percentages with mental math

2009-11-01T13:38:00.003-04:00

(This is an older post that I have revised plus added a video to it.)

In this article I want to explore some ideas for using MENTAL math in calculating percents or percentages.

I have made this video of percent & mental math strategies as well:

And here are the ideas:

Find 10% of some example numbers (by dividing by 10).
Find 1% of some example numbers (by dividing by 100).
Find 20%, 30%, 40% etc. of these numbers.
FIRST find 10% of the number, then multiply by 2, 3, 4, etc.
For example, find 20% of 18. Find 40% of $44. Find 80% of 120.

I know you can teach the student to go 0.2 × 18, 0.4 × 0.44, and 0.8 × 120 - however when using mental math, the above method seems to me to be more natural.
Find 3%, 4%, 6% etc. of these numbers.
FIRST find 1% of the number, then multiply.
Find 15% of some numbers.
First find 10%, halve that to find 5%, and add the two results.
Find 25% and then 75% of some numbers. 25% of a number is 1/4 of it, so you find it by dividing by 4. For example, 25% of 16 is 4. To find 75%, first find 25% and multiply that by 3.
Calculate some simple discounts. If an item is discounted 20%, 15%, 25%, 75% etc., then find the new price.

For example, a book costs $40 and is discounted by 15%. What is the new price?
First find 15% of $40 (10% of $40 is $4 and 5% of $40 is $2... so 15% of it is $6). Then subtract $40 - $6. So the new price is $34.
"40% of a number is 56. What is the number?" - types of problems.

You CAN do this mentally: First FIND 10% of the number, and then multiply that result by 10, and you'll get 100% of the number - which is the number itself.

So if 40% is 56, then 10% is 14 (divide by 4). Then, 100% of the number is 140. This result is reasonable, because 40% of this number was 56, so the actual number (140) needs to be more than double that.
"34% of a number is 129. What is the number?" (A calculator will help here.)

You don't need to write an equation. You can just first find 1% of this number, and then find 100% of the number.

If 34% of a number is 129, then 1% of that number is 129/34. Find that, and multiply the result by 100.

Hope you enjoyed these little mental math ideas! They also help students understand the concept of percent where they don't end up relying too much on mechanical calculations or equations.

Cell size and scale

2009-10-30T11:40:00.004-04:00

Just a neat link my hubby found this morning...

http://learn.genetics.utah.edu/content/begin/cells/scale/

You can zoom in to see these various things starting from a coffee bean and down to a skin cell, human egg, red blood cell, bacteria, viruses, hemoglobin, glucose and molecules, etc., all the way "down" to a carbon atom.

In measuring scale, you go from millimeters (0.001 or 10^-3m) to micrometers (0.000001 or 10^-6m) to nanometers (0.000000001 or 10^-9m) to picometers (0.000000000001 or 10^-12m).

American Math Challenge

2009-10-24T16:35:00.003-04:00

The American Math Challenge is an online math challenge or "competition" where students aged 9-14 from across America can compete in a safe, multiplayer game environment.

This is from the same folks as the World Math Day, if you happen to remember that.

Students will have the task of answering as many correct questions as they can in 60 second mental arithmetic challenges LIVE, against other students. Or, they can also solve questions based on the national curriculum at their own pace.

Why would you take part?

It's about having fun with math. In fact, there's a good chance your students/children will love it.
It's absolutely free. Nothing to lose if you participate. In fact, during the practice week you can find out if your kids like it or not.
If your children or students really get into it, they can vastly improve their mental arithmetic and basic facts.

Week 1: Nov. 2-8 is Practice week
Week 2: Nov. 9-16 is the actual American Math Challenge

Register at www.americanmathchallenge.com

Wolfram|Alpha homework day

2009-10-21T08:48:00.003-04:00

Today October 21st is a Wolfram|Alpha Homework Day. I am not quite sure myself what all this entails, but it is a LIVE interactive event on the web, revolving around what can be done with Wolfram|Alpha search engine.

Here are some highlights (from the website) of what will be happening over there today:

A special Homework Day Welcome from Stephen Wolfram
A demonstration by a forward-looking elementary school teacher of lesson plans that use Wolfram|Alpha
A conversation with the creator of "Shift Happens" about tech trends and their impact on education
A fun experiment with Wolfram|Alpha's mad scientist Theodore Gray
Several live, interactive Q&A sessions where Wolfram|Alpha scholars and experts help you tackle your homework questions
A special live Q&A session tackling the toughest math questions

A thought-provoking in-depth conversation with an internationally known actor and education advocate
A live interview with the creator of the Ning social networking group Classroom 2.0
An insightful dialog with an award-winning physics professor and best-selling author of several popular science books
A vibrant panel discussion of teaching with technology led by noted journalist Elizabeth Corcoran
Several live, interactive Q&A sessions where Wolfram|Alpha scholars and experts help you tackle your homework questions
A special live Q&A session tackling the toughest math questions

An interview with a renowned theoretical physicist, best-selling author, and frequent PBS contributor
A special live Q&A session tackling the toughest science questions
A live concert by Common Loon
A demonstration of Wolfram|Alpha examples from an innovative college professor
Several live, interactive Q&A sessions where Wolfram|Alpha scholars and experts help you tackle your homework questions
A recap of the best highlights of Wolfram|Alpha Homework Day

http://homeworkday.wolframalpha.com/

Math Teachers At Play carnival #17

2009-10-16T16:29:00.002-04:00

Math Teachers At Play #17 carnival is posted at Math Recreation. LOTS of stuff there this time!

Here are some of my picks: Circle of fifths and roots of two is of interest if you have studied music. This post explains the difference between equal temperament and Pythagorean tuning, from a mathematical point of view. All about A4 explores this common paper size and its special properties. And Pat's post You Might Be a Mathematician IF... was quite funny.

NAEP math test results are in

2009-10-15T09:53:00.002-04:00

The National Assessment of Educational Progress (NAEP) math tests given early in 2009 show that the US fourth graders scored the same as in 2007, and 8th graders gained a little over 2007 tests. This is commonly called "the nation's report card".

I guess it shows things haven't changed since 2007 in the realm of math education; however the test results are better now than when they first started administering the test in 1990's.

If you are interested, NAEP Mathematics 2009 website has charts and much more information.

10/10 and the Metric Week

2009-10-10T12:12:00.005-04:00

Photo courtesy of Miss Colleen

Today is 10th of October or 10/10. As we know, the metric system is based on number 10. Thus, the week ending today has been designated as the metric week..

The National Council of Teachers of Mathematics (NCTM) started the National Metric Week tradition in 1976. Please read a little bit more about the history of the Metric Week here.

You could celebrate the Metric Week doing some metric units puzzles and quizzes. Here's a link to postal stamps and cards celebrating the metric system.

NCTM has tons of related resources so I'll mainly point you there.

I grew up using the metric system, and so I've actually had to learn the imperial system while authoring math materials. These days, it seems, I know the U.S. system better than the people around me... But the metric is sure easier, as far as calculations and conversions go, since you just have to remember it goes by 10s.

In fact, to fully operate in this world, it seems it's best to know both.

Converting between metric and U.S. measuring systems

Here are a few helpful guidelines if you find yourself having to switch between one or the other. I have these conversion factors memorized from much of use. Not that everyone else would actually use these all as much as I do, being in the business of authoring math materials, but anyway:

1 quart ≈ 1 liter, but 1 quart is slightly less.
1 liquid ounce ≈ 30 ml. From this, one can figure out that 1 cup ≈ 240 ml and 4 C ≈ 960 ml.

1 inch = 2.54 cm
It's an awkward number but I need to use this conversion factor constantly, when working with images on my computer, which has a resolution of 96 pixels per inch... but I need the image to print out as 5 cm long or whatever.
You could use 1 inch ≈ 2.5 cm.

Another way is to think about those typical student rulers which are 12 inches = 30 cm. So... 4 inches is 10 cm.

Also... 1 inch might very well be the length of your thumb's last bone (the bone that contains the nail). Check! And 1 cm might very well be the width of any of the other fingernails. Check!

1 yard ≈ 1 meter; better yet 1 yard ≈ 90 cm and 1 meter = 100 cm. You see, that student ruler was 12 inches = 1 foot ≈ 30 cm.

1 mile ≈ 1.6 km. Or, 5,000 meters or 5 K is a popular running distance... about 3 miles.

1 pound is about 450 g, but actually it's easier to remember 1 kg = 2.2 lb.

It's fairly easy to multiply by 2.2. I have a metric scale; I might weigh about 55 kg. 55 x 2 = 110 and 55 x 0.2 = 11. So I weigh about 121 lb.

And 1 ounce ≈ 30 g. Just like 1 liquid ounce was about 30 ml.

To convert anything, go to Google and type

25 lb to kg
8 m to inches
22 km to miles
etc.

Math contest for homeschoolers (elementary)

2009-10-07T10:55:00.002-04:00

Noetic Learning is holding a math contest for elementary students that homeschoolers can take part in. Here are some details about this contest:

Registration deadline: October 18,2009 (coming up soon!)
Contest Date: October 26-30 2009
Who: any students (grades 2 - 5)
Location: your home
Fee: $8 per student per contest

My daughter is taking part. We will see how it goes. The purpose of a math contest is definitely NOT to discourage a child or to put additional burden on him. I'm basically checking to see if this contest can be a means of inspiration and motivation for my daughter.

www.noetic-learning.com/mathcontest/homeschool.jsp

Spread of H1N1 (swine) flu and mathematics

2009-10-03T13:58:00.004-04:00

I came across an interesting blog post by Murray Borne titled H1N1 and the Logistic Equation. It explains how a logistic function can be used to model the spread of a virus or a disease in a given population.

Now, maybe you don't know what is logistic function or equation. It is shown in the blogpost; it uses the exponential function as a part of it. Basically, it is like an exponential growth function but it is limited after a certain point so that the growth tapers off, and approaches a certain (upper) limit.

Murray shows the graph, and then shows a real-life example about the spread of swine flu in Mexico last spring. It's a great, yet fairly simple, example of how mathematics is used for modeling real-life situations.

You could definitely use it as such an example with your students, even if you don't understand a THING about logistic equations. You see, seeing how math is used is definitely inspiring and motivating to a lot of students - especially when it ties in with some current "hot topic" such as the H1N1 flu.

Understanding basic division

2009-09-30T10:58:00.002-04:00

Denise has made a good post on the concept of division, which I heartily recommend. She deals with a study where Finnish researchers gave this problem about division and remainders to high school students and pre-service teachers:

We know that:

498 ÷ 6 = 83.

How could you use this relationship (without using long-division) to discover the answer to:

491 ÷ 6 = ?

[No calculators allowed!]

I really like the question. To solve it, you need to TRULY understand what DIVISION and remainders are all about!

Now, let's think about it. Have you ever seen a pattern in division and remainders, like the one below?

20 ÷ 4 = 5
21 ÷ 4 = 5 R1, or 5 1/4
22 ÷ 4 = 5 R2, or 5 2/4
23 ÷ 4 = 5 R3, or 5 3/4
24 ÷ 4 = 6
25 ÷ 4 = 6 R1, or 6 1/4
26 ÷ 4 = 6 R2, or 6 2/4
27 ÷ 4 = 6 R3, or 6 3/4
28 ÷ 4 = 7
29 ÷ 4 = 7 R1, or 7 1/4
30 ÷ 4 = 7 R2, or 7 2/4
31 ÷ 4 = 7 R3, or 7 3/4

Students need to see and do such patterns when they are first learning basic division.

The pattern shows that every fourth number is evenly divisible by 4, and the ones in between have remainders 1, 2, or 3 in order. If the answer is given as a mixed number, the remainder is the numerator.

Back to 498 ÷ 6 = 83. Since 498 is divisible by 6, so is the number just 6 less than 498, or 492. In fact, 492 ÷ 6 = 82, or in other words, the quotient is one less than 83.

This makes sense when thinking of division as, "How many times does it fit?" If 6 fits into 498 exactly 83 times, then it fits into 492 one less time, or 82 times.

Continuing, also 492 − 6 = 486 is divisible by 6, and this time 486 ÷ 6 = 81.

We can now build the pattern from 486 onward until we have 491 on our list:

486 ÷ 6 = 81
487 ÷ 6 = 81 R1 or 81 1/6
488 ÷ 6 = 81 R2 or 81 2/6
489 ÷ 6 = 81 R3 or 81 3/6
490 ÷ 6 = 81 R4 or 81 4/6
491 ÷ 6 = 81 R5 or 81 5/6
492 ÷ 6 = 82

So, 491 ÷ 6 = 81 R5 or 81 5/6. Problem solved.

Review of Mangahigh games

2009-09-25T13:11:00.006-04:00

I got an advance notice of a new games website called Mangahigh.com. It's more than just simple math games, though. These games are designed extremely well, both from mathematical and "enjoyment" perspective. Mangahigh is led by a team of mathematicians, educationalists, and games designers so the games feature commercial-quality gameplay.

I wanted to highlight two of the free games here:

Flower Power
This is the one that I liked most... it's addictive! Grow flowers and harvest them to make money. Practice ordering decimals, fractions, and percentages. The game starts with ordering decimals (daisies), and proceeds into fractions (tulips or roses) and percents. Each time you get a full stem, you need to decide whether to pick the flowers to sell (earn money) or to let them be pollinated and thus get more flowers to grow. Grades 3-8.

Save Our Dumb Planet
Defend Earth from deadly meteorites using missiles. A team of dumb scientists are on hand to suggest possible trajectories. Practice drawing lines, quadratic curves, and some harder curves using their equations. The game has many levels, and you can stay at the easier levels if you so wish. Don't listen to the dumb scientists' talk - they mislead you! Grades 8-11 (algebra).

If I understood right, the games that are there now is just the beginning, and there are more to come.

Lastly, Mangahigh also has a powerful game called Prodigi. This is a math learning engine (or a math practice environment) that has thousands of maths problems with worked solutions and hints that adapt to each student's ability and learning speed. You can try Prodigi for free; however, only on a certain "easy" and set level. To enjoy the full possibilities of Prodigi, you need to subscribe.

Carnival time

2009-09-18T22:12:00.002-04:00

"Math Teachers at Play" carnival #15 is posted at mathfuture.wikispaces.com/Math+teachers+at+play. Lots of interesting posts, once again. Go check it out!

Strategies for basic addition and subtraction facts

2009-09-16T06:31:00.002-04:00

In this video I show several strategies for learning the basic addition and subtraction facts:

finding all the possible sums for a certain number; e.g. for 6, these would be 0 + 6, 1 + 5, 2 + 4, and 3 + 3;
writing out all the fact families where the sum is a certain number;
the 9 "trick"; 9 + 7 is the same as 10 + 6 (9 wants so badly to be 10 so that it "steals" one from 7);
doubles and the accompanying addition facts;
number rainbows and how to use them to practice subtraction;
a structured drill for addition facts.

Enjoy!

Strategies for Addition and Subtraction Facts - Video

Unit studies in math - States by the Numbers

2009-09-10T18:51:00.005-04:00

There is a book for
each state of the US.

Each book has 38 pages
(80 activities)

Price per book:
$2.99 PDF download

Free Sample (PDF):
North Dakota

Bundle of 50 workbooks $19.99
($0.40 per state)

Your order is secure
Shopper help at Kagi

Recently I've had the pleasure of adding to MathMammoth.com a series of workbooks titled States by the Numbers, by Make It Real Learning company.

States by the Numbers is a series of workbooks where the problems in each workbook are based on data from the Census Bureau's 2008 Statistical Abstract of the United States.

These workbooks offer a real-data math adventure across the United States! You can use the workbook for your state along with other resources as a unit study about your own state, or your other favorite states. Meanwhile the students will also learn and practice place values, rounding, estimation, fractions and percentages.

There are 50 workbooks in the series — one for each state. Each workbook includes basic instruction and 80 practice problems. The problems can be used on grades 3-7; probably the best fit is for grades 4-6.

Since the activities teach both mathematics and social studies, many teachers and families enjoy using the workbooks to reinforce mathematics across the curriculum. Although the activities may be effectively used in a formal teaching setting, they are designed specifically for the independent learner.

Please see this page for a list of mathematical objectives in each of the books.

Math Teachers At Play - Sep 4, 2009 edition

2009-09-04T06:32:00.002-04:00

Welcome to another edition of "Math Teachers At Play"! It is again a very engaging and interesting assortment of posts, so feel free to stay a while and relax. Thank you for everyone who submitted!

We'll start out in the early years of kindergarten. What happens when a research mathematician goes into a kindergarten class? Something interesting, creative ... and best of all, kids love it. Go check Sequences and Creative Math for Kindergartners.

Next in line, kids in the elementary school (grades 1-4) spend a lot of time with math facts. Consider the fun Joey-Joey math game to help them practice!

We advance to 5th grade. With "Math Buddy" you can explore Fractions as part of life.

"Discrete Ideas" presents The Shortest Path - or mental math multiplication shortcuts for all of us. As a tie-in, I provide a PROOF for one of those shortcuts, which could be used as an exercise in algebra class.

Next, we advance to middle school. Quadrilateral Property Combo Chart shows how the Number Warrior finally untangled the dilemma of explaining the relationships between the quadrilaterals.

Tom from "I Want to Teach Forever" offers us an Erasing Debt Activity with a printable activity sheet. This is based on real-life data (actually offers he's received in the mail), and can get students really engaged in comparing the various options for paying back a debt. For middle school on up.

And lastly, time for miscellaneous math teaching articles.

What is the shape of the Earth? Do you think it's a sphere (a ball)? John Cook from "The Endeavour" answers the question. He also submitted Three algorithms for converting color to grayscale. It actually sounds pretty simple!

Well, now we get off math for a bit. An urban, high school mathematics teacher rambles on about something annoying... but gives us a glimpse to the issues teachers face.
From "Math and Logic Play" we get The Woman, Dog, and Flea riddle.
A complex-sounding question has a surprisingly simple answer.

We end the carnival with something fun. Here's something that most of us have probably not tried... using SKITS to teach math! From "I Want to Teach Forever"...

Thanks for reading - I hope you enjoyed something! Here's where you can submit to the next carnival.

Math trick and its proof: square a number ending in 5

2009-08-28T09:39:00.004-04:00

I will be hosting the blog carnival Math Teachers at Play next week. (You can send in submissions here.)

One submission I got about various multiplication tricks or shortcuts got me inspired to write a proof of the particular trick.

You could definitely use this in algebra class. First explain the shortcut or trick itself. Then ask students to prove it, or to explain WHY it works, using algebra.

You could also explain this to younger students as an additional "neat trick" and let them explore and play with it.

THE "TRICK"

If a number ends in 5, then its square can be calculated using this "trick" (I like to call it a shortcut because there's nothing magic about it):

Let's say we have 75 × 75 => Go 7 × 8 = 56. Then tag 25 (or 5 × 5) into that. You get 5625.

Let's say we have 35 × 35 => Go 3 × 4 = 12. Then tag 25 into that. You get 1225.

Let's say we have 115 × 115 => Go 11 × 12 = 132. Then tag 25 into that. You get 13,225.

Let's say we have 245 × 245 => Go 24 × 25 = 600. Then tag 25 into that. You get 60,025.

So, you simply take the digit or digits in front of the 5 and consider those as a number in itself. Multiply that by the next number. Then "tag" 25 to the answer you got in the previous step.

Photo by Lazy butterfly

PROOF

Any whole number that ends in five is of the form A + 5, and A is a multiple of 10. Since A is a multiple of 10, we can write A = 10b, where b is now some whole number. So, our number is of the form 10b + 5. Now, let's square it.

(10b + 5)(10b + 5) and we use the distributive property to multiply this out.

(10b + 5)(10b + 5) = 100b² + 50b + 50b + 25 = 100b² + 100b + 25

Now, notice those 100b's there. We can gather that as a common factor for the first two terms:

= 100 b (b + 1) + 25

This is now essentially in the form that the trick is using.

The trick says to take b, or the number formed by the digits in front of the 5. That corresponds exactly with our b! (For example, in number 645, b is 64. Our number 645 is 10b + 5, or 640 + 5.)

So we take b, multiply it by (b + 1) which is the next number, and also by 100, and lastly add 25.

Now, b × (b+1) is the part of the trick where you multiply the digits in front of the 5 by the next number. To "tag" 25 to those digits means you add 25 only after having multiplied the number by 100 so that it would end in "00". Once it ends in "00" you can add 25 (or any two-digit number) and it is the same as "tagging" 25 to the digits without the "00".

I hope this is clear enough.

By the way, I do not feel all students must learn this shortcut for finding the square of numbers ending in 5. It is a nice addition to one's mathematical knowledge, but not any necessity. However, it is useful as an algebra problem, and of course has been used as such over the course of centuries, I'm sure.

A math review or reference book for adults & students

2009-08-24T10:55:00.004-04:00

I just stumbled upon the book Math on Call: A Mathematics Handbook:

Based on the reviews and from the "Look Inside" feature at Amazon it looks like a GREAT math reference book. I've been on the lookout for something like this, because I get emails from adults who want to review or refresh their basic math before going to college or some other course they're taking. So now I have something to refer them to.

The table of contents includes these chapters:

NUMERATION

The Base Ten System
Rational Numbers
Irrational Numbers

NUMBER THEORY

Factors and Multiples
Powers and Roots

COMPUTATION

Addition
Subtraction
Multiplication
Division

ALGEBRA

Algebraic Notation
Properties
Relations and Functions
Equations
Inequalities

GRAPHS AND STATISTICS

Gathering Data
Organizing and Summarizing Data with Statistics
Displaying Data in Tables and Graphs
Interpreting Data

GEOMETRY

Elements of Geometric Figures
Angles
Plane Figures
Solid Figures

RATIO, PROPORTION, AND PERCENT

Ratio
Proportion
Percent

PROBABILITY AND ODDS

Permutations and Combinations
Probability
Odds

ALMANAC

Prefixes
Suffixes
Problem Solving
Study Tips
Using a Computer for Math
Geometric Constructions
Test-Taking Skills
Handy Tables

The Metric System
The Customary System
General Measurement
Fraction/Decimal Equivalents
Multiplication Table
Square and Cube Roots
Right-Triangle Ratios
Prime Numbers Less Than 500
Mathematical Symbols

Number Patterns
Number Systems

YELLOW PAGES

Glossary of Mathematical Formulas
Glossary of Mathematical Terms

INDEX

A total of 608 pages. I can hardly believe how good reviews it has!

I was unclear if Math on Call contained exercises or not, but I'm thinking not, since I didn't see anyone mentioning such in the reviews or the description.

Math Teachers at Play Carnival

2009-08-21T12:42:00.002-04:00

There is lots of interesting stuff today at Math Teachers at Play Carnival #14 at Math Mama Writes. Quite a nice assortment - surely something for everyone!

I particularly recommend Three Applications of High, Abstract Math. We teachers can always use other ideas as to how mathematics is useful in real life.

Learn to recognize coins

2009-08-14T12:23:00.004-04:00

Image by Stopnlook

In the past few days I decided it's time for my younger girl to start learning how to recognize coins and learn the cent-values of various coins. She's generally been doing kindergarten-1st grade addition and subtraction and I figured she's ready.

First, I got a pile of pennies, a pile of nickels, and a pile of dimes (no quarters at first). We played where I told her to make a certain amount, such as "Make 24 cents." She made it, I checked. Then she told me to make some amount. We just take turns.

It's like a game, and great fun for her! I figure it'll work the same with other kindergarten or 1st grade kids.

Since she did pretty good, I was able to introduce quarters the next day. I showed her that two of them makes 50, and we practiced making 62 or 58 or other such amounts that use 2 quarters.

Then I showed her a quarter and a nickel, and we figured out how much that was. That's always a difficult thing - to combine just one quarter with other coins. I soon asked her to make 30 cents, or 32 - and she was able to use the quarter and nickel combination to make 30 cents.

One important thing I've done is that I have deliberately NOT yet introduced the words "nickel", "dime", and "quarter". She's heard of the penny so much that she was fine with that. I want to scaffold the teaching so that we'll first learn the coin values, and later the customary names.

So, in essence, for now I've been calling them as "5-cent coin", "10-cent coin", and "25-cent coin". Has anyone else done that?

Review of Algebra Unplugged

2009-08-13T15:59:00.006-04:00

Algebra Unplugged by Kenn Amdahl and Jim Loats is not a textbook, nor does it have any exercises. Instead, it is filled with verbose, often humorous explanations of algebra 1 concepts for those who would rather hear or read math explained in many words, instead of in a few symbols.

Algebra Unplugged also often explains the reasons behind some peculiar mathematical notations or terminology, and in general, tells the students WHY things are done the way they are done in your "Real Algebra Book".

Note: the cover image doesn't directly have to do with the contents of the book... the book is not about music, nor graffitis. I think it's just conveying the idea that just like musicians might "jam" freely after the practice, with this book you'll get to experience algebra "freely" after the class.

Excerpt:

The Associative Principle

Organizing your singers into sections won't affect how many are in your choir. Grouping them is creating associations. The associate law recognizes the benefits of confining your tenors to one easy-to-patrol area. Fifteen tenors in a corner is no different from fifteen scattered throughout room. It's just safer.

If all you're doing to a series of numbers is adding them, you can add them one at a time, or you can put them in groups, then add the totals of each group.

I certainly enjoyed reading through the book, and feel it can be very helpful for algebra students who feel "lost" and want to understand more thoroughly how to navigate in the maze of rules, symbols, terminology, and unknowns.

Here's another fun little excerpt to get you a "taste":

Why They Make You Factor

Factoring is, on the surface, a foolish waste of time. You will read many books and factor many polynomials before you have a clue why you are doing it. The next sentence in this book will save you two months of confusion.

We factor to take advantage of some neat properties of zero.

In addition and subtraction problems, zero is powerless. You can add or subtract zero to a number for the rest of your life and you won't change the number at all. But zero become an all-powerful super-hero once you move into the domain of multiplication.

When you multiply any number by zero, you get zero. A million times zero equals zero.

When you divide zero by any number, you get zero. Zero divided by a million equals zero.

But you can't multiply any other two numbers together and get zero. And you can't divide any other number by anything and get zero. If the answer to a multiplication problem is zero, one of the numbers you multiplied must also be zero. And, if the answer to a division problem is zero, your original numerator was zero.

That's why we factor.

By all means, click to Amazon and "click to look inside" the book to read some more and see if you like the style. I did - but I never know if others do, or if teenagers do.

The authors have definitely succeeded in keeping the conversation on a lighthearted level. They make light of mathematicians and mathematics and tenors (of course, some might not like that). The book often uses apples, bananas, rats, kangaroos, catbox, jabberwocky, etc. as variables, instead of always resorting to x, y, and z. The authors let Little Weenie Numbers show us the way when things get complicated (these are 1, 2, 3, 4, 5, 6 and other small, easy-to-handle numbers).

The only complaint I have is that the book could have given a bit more attention to graphing with more graphs and actual visual illustrations. The author Kenn Amdah confesses he is not a visual person, so that is why.

Check also for used copies. The book is listed at both Amazon and Barnes & Noble

The same authors have also written Calculus for Cats, a clear and entertaining introduction to the mysteries of calculus. It is written with similar goals in mind. It doesn't contain exercises. For some reason, the analogies to the world of cats didn't quite "jibe" with me as well as the writing in the algebra book. This doesn't mean that that book is not useful; it can be tremendously useful for people who feel intimidated or even dismayed by calculus. It just didn't feel quite as fun to read as the algebra book to me.

This book is also listed at Amazon and Barnes & Noble.

Multiplication Mountain songs CD - a review

2009-08-08T13:41:00.003-04:00

It has been proven that music can help children memorize things. There is something about the music or the rhythm or both that changes or improves the way our brain works. I haven't studied this effect in-depth; I'm just familiar with the general idea.

So, using music to memorize math facts—or in this case, multiplication tables—is definitely a sound idea.

Multiplication Mountain is a CD by Hap Palmer, filled with songs for the multiplication tables. For each table, there is one song, but it is presented twice on the CD: once sung completely, and the second time without the answers sung. That way, the child can try to fill in the answers while listening to the song from the second track.

I found the songs to be pleasant and jolly, easy to listen to. The musical style varied somewhat so that one song was more jazzy, another was bluegrass, another a waltz, and so on. But they all were melodic, harmonic, and had a medium beat—easy to sing along. My favorite was the song for the sixes times table.

The songs are presented in a particular order: the easiest tables first. Learning all the tables is compared to climbing a mountain: you start at the bottom with the 2s, 5s, 10s, and 11s. You gradually climb up till you reach 7s as the top of the mountain — and then you reach for the sun (the 12s)!

You can listen to samples at www.myspace.com/happalmer (the songs for nines and twos) and at CdFreedom website.

Here's yet another sample of his music from YouTube. It's called Bean Bag Alphabet Rag. It's not from the Multiplication Mountain CD. I just put the link here in case you want to check out the musical and singing style of this artist.
Bean Bag Alphabet Rag by Hap Palmer .

Multiplication Mountain is not the only CD I have that has songs about multiplication tables. I have gotten one other CD in the past, but much disliked that one, because its musical style was rap with quite heavy beats - reminded me of heavy rock. Hap Palmer's music is quite the opposite of that, so I liked it much better (of course, all of us have VERY varying tastes of music).

My older child already knew the multiplication tables when I got the CD, so I could not test how much she would learn with it, and the younger one is not quite ready for that yet. But, in a nutshell, I feel the CD is well done and there is no reason why it wouldn't be effective in helping children to learn the tables.

I would definitely recommend it for anyone interested in trying musical approach to learning the tables and for elementary teachers & tutors in general. Also, if your child has ADD/ADHD or any learning disability, I would suggest that you try music-enhanced learning simply because of the special effect music has on our brain.

Here's a link to Multiplication Mountain CD at Amazon.com.

Disclaimer: I was given this CD for free to review it. I'm not receiving any monetary gain from the company, however.

Math Mammoth Grade 5 Complete Curriculum now available

2009-08-06T19:42:00.002-04:00

163 pages
147 lesson pages

218 pages
179 lesson pages

5-A contents and samples
5-B contents and samples

Finally it is ready! I know some folks have been waiting for the 5-B part to get finished, and now it is here!

Math Mammoth Grade 5 complete curriculum consists of two student worktexts (A and B), a separate answer key for each, chapter tests and an end-of-year test, cumulative reviews, and an easy worksheet maker (Internet access required) to make extra practice worksheets when needed.

The two books (worktext part A and part B) for 5th grade deal with

multi-digit multiplication and long division
simple equations
problem solving
place value with large numbers and the judicious use of calculator
all operations with decimals
statistics and graphing
all fraction operations
geometry: classifying and drawing triangles & quadrilaterals; calculating the area of rectangles, triangles, parallelograms, and compound figures; surface area and volume of rectangular prisms
introduction to integers
introduction to percent

You can purchase the whole curriculum as a download, or as printed copies.

The downloadable curriculum is available at Kagi and at Currclick. The printed copies are made by Lulu (see links on this page, under the cover image).

Free e-books from Sylvan Dell

2009-07-31T17:08:00.004-04:00

Sylvan Dell publishing is allowing the public to view for FREE their new line of ebooks.

These ebooks are animal-themed picture storybooks for children with beautiful illustrations and text. They can be used to learn language or science.

The neat thing is, they are bilingual (English/Spanish). You can switch the language while you're reading one page and it'll stay on that page. Plus you can have the book read to you (audio) in either English or Spanish.

Here is the link:
http://www.sylvandellpublishing.com/ebooktrials.php?e=MSBL9J

Click, and then click the button that says "Validate access code".