Math Mammoth Grade 5-A Complete Worktext

Finally! Grade 5-A is available for the LightBlue Series (the complete curriculum series). The part A of 5th grade focuses on

• multi-digit multiplication and long division
• simple equations
• problem solving
• place value with large numbers and the judicious use of a calculator
• all operations with decimals
• statistics and graphing

Please see the table of contents and samples for a complete lesson list, and read more info here.

Another problem solving book

I know there already exist books that teach problem solving and contain lots of word problems. Well, there is a new one on the block, now: Solving Math Problems by John R. Dixon. It contains math problems with extremely detailed solutions for middle school, high school, and (some) for college level.

He's made available a superb collection of samples from his book. Each sample has three completely solved problems. There's a sample file for pattern recognition problems, counting problems, word problems, optimization problems, and fun or "recreation" problems.

Even if you're not planning to buy any math books, I encourage you to check his samples and read them through, just for your own learning (and of your students). It isn't often that one finds such detailed expositions on how to solve word problems.

I'm a firm believer in the "apprentice" principle, when it comes to learning problem solving. In other words, one of the best ways to learn to solve problems is to observe an "expert" doing so. (This is why I've often solved word problems here on my blog.) These example solutions can be very enlightening to parents and teachers who might not had much opportunity to witness the thinking that goes into solving even simple problems. For those who can solve word problems easily, such thinking seems to come easily and becomes automated. But for others, it doesn't, and so reading up well-written detailed solutions can help you.

In fact, it would be even more enlightening to witness and expert problem solver solve a problem from scratch and follow his thinking through the incorrect solution paths, as well. You know, all of us, when solving a problem, might (or will) start working on the problem and go down a path that will eventually be a dead end. Good problem solvers monitor their progress on a "meta" level, and "turn back" from those dead ends when they notice them to be so - and try to take a fresh approach.

All too often, youngsters simply give up when such happens! Wrong solution paths are valuable as well. They're just about inevitable when you tackle a non-routine problem!

The book is offered as a softcover for $19.95 and as a download (ebook) fo $9.95. The author claims it's written for middle and high school math teachers, but I feel he shouldn't market it that way — the book has a lot of value for us parent-teachers as well!

Multiplication family group

The information below is from another Maria, namely MariaD from NaturalMath.com. I'm posting it here with her permission, as it might interest some of my readers.

Hello!

My name is MariaD, and I love multiplication. Natural Math is starting a research and development family group about this topic. You are cordially invited! Please forward this invitation to other families who may want to join.

There are three main benefits. You receive individual family math coaching. You access a community of other parents sharing questions and ideas. And you contribute to a beautiful and much needed web resource for the future. There are two main responsibilities. At least weekly, you will run custom family math activities you select. As needed, you will talk with me or other group members about your activities. We can talk by email, chat, voice, or face-to-face in Cary, North Carolina, USA. At this early stage, we need active group members. If you plan to be a quiet fly on the wall, please wait until the next round of development. Time estimate is that the group will provide your family at least an hour a week of math and community activities.

Multiplicative reasoning is the capstone of arithmetic: it ties all the parts together. It is the cornerstone of algebra and the basis of pattern thinking. It is also one of the most badly taught areas of math. People spend a lot of effort and many years on times tables, division, fractions, and proportions. Still, many struggle with these multiplication topics for the rest of their lives. I am a strong believer in multiplication. A kid who "gets" multiplicative reasoning will probably be just fine with algebra and math in general. Based on this faith, I've spent more than twelve years collecting, researching and creating multiplication-related lore.

My collection includes psychology of multiplication. It explains why 7*8 and 6*7 are hard to memorize without gimmicks, or how doubles relate to our innate sense of health, beauty and order. There are tidbits about multiplication from histories of many cultures: Ancient Greek music of the spheres, and medieval Chinese secret finger codes for trades. The collection has a lot of modern children folklore. It includes rhymes, finger tricks for times nine and all times tables beyond five, silly pictures and jokes. There are all kinds of contraptions: abacuses, mirror books, bead strings, and Napier bones. There is software: powerful Excel, or small applets for a kaleidoscope, a snowflake creator, or a base two calculator. There is cutting-edge as well as classic research: hundreds of articles, conference presentations and books. Some of these are actually useful, but most are ever read by just a handful of academia people. Speaking of which, there are also people in my collection! Among our contemporaries, there are parents, researchers, designers, and writers who love multiplication, too. This collection of multiplication stuff, and people, can help us start.

I envision a "multiplication planet" map, connected by a web of many paths. Each family can start at a different entry point, depending on their goal. If you want to memorize times tables in three hours, your will probably trek through algebraic shortcuts, memory tools and work with patterns. If you want to have rich, deep experiences connecting many human endeavors, you will also visit algebraic shortcuts. But then you will travel to geometric explorations, history-centered projects, or psychological experiments. If you want arts and crafts, you'll head for drawing, cutting, or computer animation activities. This first stage of research has five main goals for the map.

1. Develop and find major multiplication activities to put on the map. As all Natural Math activities, they will be centered on creating something.
2. Develop paths between activities, following each family's travels.
3. Find out what kinds of families use each path, and for what. Use this knowledge to start a guide for new families joining us.
4. Find out what support people need in their journeys.
5. As we do all of the above, plan web tools that can help us do it better.

Please contact me if you are interested.

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Cheers,
Maria Droujkova, PhD