Teacher apprecation week is coming

I myself have enjoyed the downloadable resources from these Learning A-Z websites in the past, so I thought you might take a look, too. It's all going to be free for a week! Here's their blurb:

To thank the world's teachers during Teacher Appreciation Week from May 3-7, we're opening up all six of our PreK-6 Learning A-Z websites — for free. Sites include Reading A-Z, Raz-Kids, Writing A-Z, Science A-Z, Vocabulary A-Z, and Reading-Tutors.

Nearly 50,000 teachers took advantage of our Open House last year and pre-registration for this year is now open. Just go to http://www.learninga-z.com/openhouse — and then pass it on to your friends and colleagues!

Shopping City game hints

My daughter asked me to check out Shopping City game at HoodaMath.com, and so I did. Well, I became hooked... it's one of those "addictive" types of games. I spent nearly a week playing it every day, until I was able to finish all 9 levels.

I decided to write this blogpost about the gameplay because in the end, to be able to finish the last level, I had to do some serious analyzing of various factors in the game, which definitely reminds me of solving and analyzing math problems.

On each level, you are shown an empty street map, and your task is to build stores and to earn a certain amount of money in a given amount of days. As the levels progress, the street map gets more complex, you have a bigger goal to achieve and more days to do it. In the last level, you need to earn a million dollars in 29 days.

Then once you start the game, people start walking in from various directions, visiting the shops, and spending their money.

Click to enlarge

For the most part, I played the game kind of randomly, building different kinds of stores randomly here and there - toy stores, boutiques, pet stores, restaurants, jewelry stores, and so on. That strategy seemed to work alright in the beginning... but then the game got harder.

I was not able to finish the last level without thinking about and analyzing several things. I even wrote out how many percent I earned each day, and if I was falling behind my "best play", I would quit and start that level over (which you can do by pressing the "menu" button). I reached 96% or 97% several times before succeeding in reaching 100% in the 9th level.

I'm going to share some tips now for playing the Shopping City game. Warning: if you want to figure out these things yourself, don't read on! Just go play it. Of course, part of the fun IS when you figure out the strategy yourself. In fact, you could even use this game TO teach analyzing skills to youngsters.


Hints for the Shopping City game

The game itself gives you some instructions, such as the fact that the customers won't go to two of the same kind of stores, but they will visit a store and an upgraded version of the same store. Or, that corners are important locations.

1. On day 1, no matter what level, your shoppers have only $30 to spend, and they can spend it all in a pet store. On day 2, they have $60 to spend and they can still spend it all in a pet store. A pet store happens to be the best store to start with. On day 3 and 4, having a pet store and boutique is enough for them to spend all their money (as long as all the people can visit a boutique and a pet store on their walking path). If on any particular day, all your customers spend all their money, you get a $1000 bonus. This is important to get for the first few days on level 9.
   
   
2. The game tells you how much the customers spend in each particular store (before it's upgraded). Some stores are not nearly as cost-effective as others. For example, a restaurant costs $10,000 and a boutique costs $2,500, yet customers spend the same amount of money in both. Study carefully how much people spend in each store. Some stores look like fun to get, but they won't bring you in the most money.
   
   
3. When you upgrade a store the first time, customers will spend 1.5 times as much money there than before upgrading. When you upgrade a store the second time, customers will spend 2 times as much money there than before upgrading at all.
   
   
4. For best play, observe carefully the walking paths of the customers. They come from various directions and go off at several different exits. You want to choose the location of the best stores so that most people can visit them. Usually the corners work best for that. In level 9, I found out (eventually) which few locations worked best. If I put a pet store (for example) to two specific locations, I could be sure that everyone would visit one or the other. This is one of the most important things to analyze in the game.
   
   
5. As the days progress on any particular level, you will need to sell the smaller stores in the best locations in order to build the better-performing stores in those locations. For example, if you put a pet store in the best location at first, later on when you can buy a jewelry store, it should go to one of the best location. Then you can rebuild the pet store somewhere else.
   
   
6. You won't need the fire station or police station in the early levels.
   
   
7. When a store needs repaired, if you can upgrade it (if you have enough cash), it gets repaired for the upgrading fee, so that becomes more cost-effective than simply repairing it.
   
   
8. If a fire comes and you don't have a fire station, you can sell that particular store before it burns down and you lose it.
   

Hope this helps!

British Money and Fractions & Decimals 3 - New Math Mammoth books

I have two new books available for the Math Mammoth Blue Series:

1) British Money

Math Mammoth British Money is a worktext that covers money-related topics usually encountered during years 2-4. The book contains both textbook explanations and exercises, and is designed to be very easy to teach from, requiring very little teacher preparation (you do need to find practise coins before the lessons).

Please read more, and see free sample pages.


2) Fractions & Decimals 3

Math Mammoth Fractions & Decimals 3 continues the study of fraction and decimal topics, on the 6th grade level. This book assumes the student already has studied fractions and decimals in the past, for example using Math Mammoth Fractions 2 and Math Mammoth Decimals 2. The goal of the book is to go through all of the fraction and decimal arithmetic, using up to six decimal digits and larger denominators in fractions than what is commonly encountered in 4th and 5th grade materials.

Read more, and see free sample pages.

Carnival time again

Please check out Math Teachers at Play #25!

I especially liked the fun math game provided by Pumpkin Patch blog, and the fun(ish) algebra worksheets from The Exponential Curve blog. There's even a murder mystery included...

Coupon code for free shipping at Lulu

If you'd like to purchase a printed version of any of Math Mammoth books at Lulu, use the coupon code FREEMAIL305 to get $3.99 off the shipping charge (that is the shipping charge for one single book within the US). Only applicable for US addresses. Offer expires May 1, 2010.

Teaching long multiplication a.k.a multiplying in columns)

The two videos below show how you could teach multi-digit multiplication, or the multiplication algorithm, or multiplying in columns to students.

Teaching multiplication algorithm

Multiplication algorithm with a 2-digit multiplier

I approach this in steps. First, to teach students to multiply 4 × 87 or 5 × 928 (one factor is single-digit):

1) Teach students to multiply single-digit numbers by whole tens and hundreds.
2) Teach them the partial products algorithm;
3) Use the above as a stepping stone and teach the usual multiplication algorithm.

Then we can go on to the two-digit multiplier:

4) Teach the partial products again.
5) Teach the regular form of the algorithm.


Let's look at these steps in more detail.

Step 1. This means teaching students to multiply 5 × 80 or 7 × 400 or 3 × 40 or 9 × 900 (mentally!). The shortcut is to multiply without the zero or zeros, then tag the zero or zeros to the result.

But, where does it come from? For example, 5 × 80 is the same as 5 × 8 × 10. We first multiply 5 × 8 and then multiply that result by 10.

Step 2 is the partial products algorithm. Here, we write the numbers under each other, just like in the regular multiplication algorithm. But the multiplying is done in two (or three) parts: first the ones, then the tens, and then the hundreds (if any).



Step 3. After this, you would teach the usual multiplication algorithm. Point out to students how the two multiplications and the addition (the carry) are done at the same time, instead of as separate calculations.

This step needs practiced quite a bit before moving on so that students become confident in the carrying process.

Step 4a has to do with learning to multiply 50 × 46 or 70 × 352 or 600 × 529 in columns, using the regular algorithm. It is like multiplying 5 × 46 and tagging a zero, or multiplying 6 × 529 and tagging two zeros, but we place those extra zeros in the result first, before multiplying.

    3                 1 5
    4 6               5 2 9
x   5 0           x   6 0 0
--------        ------------
2 3 0 0         3 1 7 4 0 0

The bolded and underlined zeros are placed there before multiplying. The second video makes this maybe even clearer.

Step 4b has to do with multiplications by a 2-digit multiplier, such as 45 × 89. Here, we'd first multiply 40 × 89, then 5 × 89 (using the regular algorithm), and then add the two results. So this means, first of all, three separate calculations.

Step 5: We show students the regular form of the multiplying in columns with a two-digit multiplier, and point out how those three separate calculations are now compactly written under each other.

That's it in a nutshell! Please watch the videos to make this even more clear.

More new worksheet generators

At HomeschoolMath.net, you can now make free worksheets for place value & scientific notation (such as write a number in expanded form or in scientific notation), and also for proportions, including simple proportion word problems.

The links are:
Place value & scientific notation worksheets
Proportion worksheets