Math

Note:

Although these materials may all be used as early as preschool, most are intended for a rather broad age range and can be used well beyond the preschool years. Also see: Homeschoolstories.com Preschool and Math

Why mental math?

The authors state that "two common problems found in all levels of math classes are the inconsistencies of math terminology and the lack of self confidence in students when answering simple math questions." This series of books was written to address these problems and to provide practice in solving math problems both mentally and quickly. The use of terminology from standardized tests is also beneficial; my children have been confused by different terms even when they understood the concepts well. To a first-grader, "add" doesn't always mean the same thing as "plus". This series of math supplements is available for grades 1 to 5, and is designed to be used each day of the school year for the first 10 minutes of math class. These courses provide practice and review, but no direct instruction; this is not a complete math program. In addition, these courses require the active participation of the teacher; Mental Math cannot be considered an independent program. From my perspective, this is a particular strength for homeschoolers. Many students work on their math independently, and these courses give the homeschool teacher an opportunity to casually and regularly assess the progress of their student. First graders begin in the second semester of the school year while the other grades start at the beginning of the school year. With the exception of the first grade book, each book begins by reviewing material from the previous grade level. The instructions for each book clearly state that the teacher is to read the questions to the student twice and then to go on to the next question. The student is not permitted to ask questions, to talk, or to request that the problem be repeated. The student is also not permitted to use scratch paper. Because these courses were designed for the classroom, the student is instructed to write the answer. In a homeschool setting, the answers could be given orally as well. The only confusing part of the program to me was the numbering system used on the daily worksheets. Each sheet is coded with the grade level and the types of problems being practiced. A key is provided to explain it, and the system makes sense, but I floundered a bit until I developed some experience. This is done to provide flexibility; the program does not have to be used in a specific order. My children have enjoyed these books, and they look forward to showing me just how much they have learned. Sometimes they are quicker to find a solution than I am. Reviewed by S.K.

A Million Dots

Author(s): 
Andrew Clements
Illustrator(s): 
Reed, Mike
Number of pages: 
48 pages
Copyright: 
2005
ISBN: 
9780689858246
Publisher: 
Simon & Schuster Books for Young Readers
Subject(s): 
Grade / Age level: 
Resource Type: 
Review: 

There are indeed a million dots in the book, although the book states it would take over eleven days for the reader to actually count them! On each page one of the dot numbers is highlighted and a large illustration depicts what that number represents. For instance, dot number 265,000 represents the number of different kinds of moths and butterflies on earth, and dot number 615,100 represents the number of words in the Oxford English Dictionary.

Kids and adults alike will like this book. Interesting, fun facts aided by the colorful illustrations over the dots provide a way to better understand how much a million really is!

Reviewed by: 
First reviewed: 
Mar 27, 2009

Addition Songs

Copyright: 
1998
Publisher: 
Audio Memory
Subject(s): 
Review: 
Audio Memory offers math audio tapes and CDs for practicing "Math Facts" in Addition, Subtraction and Multiplication. (Sold separately from each other). These are Math drills set to music (of the synthesized variety). Although these make for an easy memorization aid, I found the songs almost unbearably sappy. (My children did like them though.)
Reviewed by: 
First reviewed: 
5-13-2000

Algebra I: A Teaching Textbook

Book cover: 'Algebra I: A Teaching Textbook'
Author(s): 
Greg Sabouri
Shawn Sabouri
Number of pages: 
654 pages
Copyright: 
2004
Publisher: 
Teaching Textbooks
Binding: 
Spiralbound
Subject(s): 
Grade / Age level: 
Review: 
Over the years I have used several different Algebra programs with my children. With Peter, this is the fourth Algebra program we have tried. For various reasons, they have never met our expectations. At long last with Teaching Textbooks Algebra I, we have found one that works.

Before writing a review, I wanted to wait until Peter had completed most of the textbook, so that I would avoid any unpleasant surprises. Right now, he has completed about 2/3rds of the text and my opinion has not changed. This program is a homeschool mom's dream come true.

Designed for homeschool students, there are many reasons to like this program. The material is written in a friendly, conversational tone. The text is laid out in an easy to understand fashion without dumbing down the problems. The pace is not rushed. The story problems often use silly examples, which keep the student's interest as he learns important concepts. The best part of the program are the Solutions CDs. They are like having your own personal Algebra tutor.

Algebra I covers 18 Chapters with 129 lessons for a total of 654 pages. This book is long because the authors take the time to thoroughly explain each new lesson. A sampling of chapter topics includes simple equations, negative numbers, longer equations, powers, and roots. Much more is covered. Lesson 85, for example, is "Completing the Square."

Each "lesson" includes the lesson, practice, and problem set. Each lesson portion presents a new topic written in a conversational tone. Important points are highlighted (literally slightly darkened). The lesson material also covers sample problems of the topic introduced in the lesson. In other words, he does not just talk about the topic; he walks the student through the problems step by step. Similar to any other good Algebra text, the lessons build on previously learned knowledge. The lesson may also include a humorous story problem.

For Peter, he just reads the lesson. There is a lecture CD available for the student to watch and listen to the teacher go over the lesson material. This would be helpful for the student who learns best by hearing or incorporating as many senses as possible. This is the same material as in the lesson.

The next section is the "practice," which includes problems that review the material just covered in the lesson. The last section is the "problem set." This includes previously covered material from other lessons. Just like Saxon Algebra, the problem set covers a variety of topics. The last problem in the "problem set" is a silly story problem. For example, here is the story problem in problem set 7. "The husband and wife toy makers named their son Ken and their daughter Barbie. If 19,125 people in the couple's hometown--exactly 75% of the population--think the couple is crazy, what is the total population of the town?"

What makes this Algebra program a homeschool mom's dream come true are the Solutions CDs. These allow the student, for the most part, to work independently, freeing me to work with my other children. Now there are times when my son does ask me questions. He may want to know if he is doing a problem correctly or why a problem is coming out wrong. He could ask me or he could go to the Solutions CD, which explains the problem. The times he asks me, however, are few and far between. And if he asks me a question that I can't answer (I'm terrible with story problems) or if I am busy working with another child, he can always pull out the Solutions CD.

There are Solutions CDs for all the problems: the practice problems, the problem set problems, and the chapter test problems. If a student doesn't know how to work out a problem, or after correcting his lesson or the chapter test, the answer is wrong and he doesn't know why, he pulls out the CD he needs and pops it into the computer. There is a menu and he chooses the exact lesson and problem. He doesn't waste time looking for the answer. The answer begins with the problem displayed. The teacher then builds the answer from there, explaining the answer line by line. It is as if the teacher is standing at the head of the classroom, working through the problem. You hear the teacher's voice as he writes out the problem step by step on the "board" (screen). His voice is pleasant and very relaxed, which helps when you are dealing with a frustrated student.

Since the answer key only includes the final answers, the Solutions CDs are essential. There is no solutions manual. The answer key book includes practice set answers, problems set answers, and chapter tests with answers.

I won't say Peter doesn't get frustrated at times. Algebra and math are not his favorite subjects. But I will say his frustration level is far less than if he had used some of the programs we had used in the past. Also, I will add that this program won't work, just like any other math program, if the child does not correct and redo his work daily, since new material is based on previously learned concepts. If foundational concepts are learned incorrectly, the student will dig himself into a deeper and deeper hole. Sometimes, all that is necessary is for a parent to ask the student to show her his daily corrected work to see that he is on task.

This Algebra program has made my job as a homeschool mom so much easier. It is like having an Algebra tutor whenever I need him. Teaching Textbooks now has available Pre-Algebra, Algebra I, Geometry, and Algebra II. You can preview sample lessons, sample lectures, sample solutions, the table of contents, and more at www.teachingtextbooks.com. The complete package includes spiral bound student textbook, answer key & test bank, lecture and practice CDs, Solutions CDs, and Test Solutions CD.

A comment from another reviewer (Suchi Myjak): The book's explanation of the associative property as given for both addition and multiplication is wrong. The property described in the book as the "associative property" is actually a combintation of the associative and the commutative properties. Please see my post on Unity of Truth for more details and the correct definitions of the properties. In Lesson 26, page 126, the book explains the associative property of addition in these words:
You already know the rule that two numbers can be added in any order (the commutative property of addition). Well, it turns out that this rule can actually be extended to longer strings of numbers. ... So our new rule is that a string of numbers (however many) can be added in any order. The technical name for this rule is the associative property of addition.
This, unfortunately, is wrong. The associative property is not the commutative property "extended to longer strings of numbers." It is a completely separate and independent property. Nor is it the rule "that a string of numbers (however many) can be added in any order," although it is one of the properties that makes that rule possible. After the above quote, the book correctly lists the equation defining the associative property, but then goes on to say things like:
That means the expression 3 + x + 4 + 1 can be rearranged any way you want and its value won't change. So 3 + x + 4 + 1 and x + 3 + 4 + 1 and 1 + 4 + 3 + x are all equivalent.
This example concretely shows the confusion on this topic by moving the operands around. This is possible only with the commutative property. The associative property does not allow rearranging of operands. Later, page 131 (Lesson 27), says the following about the associative property of multiplication:
In fact, no matter how many numbers are in a string, they can be multiplied in any order without changing the answer. This rule is called the associative property of multiplication.
This is also wrong, and for the same reasons. Please see an explanation on the commutative and associative properties here. You may wish to print it out to share with your student.
Additional notes: 

Answer Key & Test Bank, 111 pages, softcover

8 CDs total - divided into Lecture and Practice CDs and Solutions CDs (over 120 hours total)

Reviewed by: 
First reviewed: 
5-5-06

An Easy Start in Arithmetic

Book cover: 'An Easy Start in Arithmetic'
Author(s): 
Ruth Beechick
Number of pages: 
28 pages
Copyright: 
1986
Publisher: 
Arrow Press
Binding: 
Stapled Softcover
Subject(s): 
Grade / Age level: 
Review: 
I've really enjoyed using Ruth Beechick's suggestions in this little booklet for introducing Mathematics to my young children. I think she does an excellent job of explaining how children learn and understand Math. She also lays out a very natural way of encouraging an interest in Math. This little booklet, which can be read rather quickly, also includes activities for learning Math from Pre-K through 3rd grade! In Designing Your Own Classical Curriculum, Laura Berquist recommends using this book for Kindergarten.

Available in a set called The Three R's that also includes A Home Start in Reading and A Strong Start in Language.

Reviewed by: 
First reviewed: 
1999

Anno's Counting Book

Book cover: Anno's Counting Book
Author(s): 
Mitsumasa Anno
Number of pages: 
32 pages
Copyright: 
1975
ISBN: 
9780590446754
Publisher: 
Harper Trophy
Binding: 
Softcover
Subject(s): 
Grade / Age level: 
Review: 
This is a charming Counting Book with a colorful two page spread for each number from zero through twelve. The pictures show the beginnings of a town. For zero, you see a snowy field with a river running through it. The next page has one house built, one snowman, one person skiing, one pine tree, one crow, one dog, etc. Each month another building is added as more people come to the town. Young children, who often enjoy small details in pictures, can find how many things on each page can be counted up to the same number. Some of the details are quite creative, such as the clock on the church showing the appropriate time for the particular page.

Reviewed by: 
First reviewed: 
3-25-2000

Ask Albert Einstein

Author(s): 
Lynne Barasch
Number of pages: 
40 pages
Copyright: 
2005
ISBN: 
9780374304355
Publisher: 
Farrar, Straus and Giroux (BYR)
Binding: 
Hardcover
Grade / Age level: 
Resource Type: 
Review: 
Back flap of book

So maybe your elementary school age child will not learn much Math with this book--the one problem shown involves the Pythagorean theorem and it shows the external tangent line touching two circles--but she may learn a few related things: who is Albert Einstein, why he came to America, where he worked and study, ... and how he actually helped some kids with their Math homework!

My husband enjoyed the allusion to Archimedes in Annabelle's bathtub scene... and my favorite pages in the whole book are the inside pages of the front and back covers: Einstein's own quotes each illustrated with adorable drawings of Einstein doing all sort of things. Here are a couple: "When the solution is simple, God is answering," and. "Joy in looking and comprehending is nature's most beautiful gifts." A very cute story, based on real events, this book enchanted our 10 year old Math-challenged artistically oriented student.

Reviewed by: 
First reviewed: 
May 01, 2009

Catholic Math Activities

Book cover: 'Catholic Math Activities'
Author(s): 
Mary Ann Grobbel
Number of pages: 
102 pages
Copyright: 
1999
Publisher: 
Catholic Heritage Curricula
Binding: 
Stapled Softcover
Subject(s): 
Resource Type: 
Review: 
If you're looking for a way to liven up your math program or to bring in some painless math review you have to pick up this book. Catholic Math Activities provides dozens of math games that children actually enjoy playing and almost all of them only require dice and simple home-made material. The author makes use of children's interests by revolving the games around things such as baseball cards and animals. What really pleased me about this program is the clever way our Catholic faith was brought into these games. Some of the games revolve around a short story involving our faith, bible stories (e.g. Noah's Ark and 2 by 2) and simple Catholic sayings to name a few. I was especially delighted that this book provides games for such a wide range of ages and with a text that is simple enough that an older sibling can read the instructions and then go on to play the game with the younger child. Topping off the program are 40 nicely hand-drawn illustrations of saints. Each saint is accompanied with a short biography and math problems which, when solved, give the child information as to how the picture should be colored. This is definitely a new twist on color by number and one that my children have enjoyed.
Perspective: 
Catholic
Reviewed by: 
First reviewed: 
3-9-01

Cuisenaire Rods

Publisher: 
ETA/Cuisenaire
Subject(s): 
Grade / Age level: 
Resource Type: 
Review: 
When I first researched homeschooling products and resources, I spent quite some time looking at different math manipulatives. For one thing, there are so many, and for another, I love math. I remember wondering whether these colored rods would really be worth purchasing, as they are on the expensive side. And my math education, as far as I could remember, had been accomplished without a single manipulative. Then I found Miquon Math, and immediately liked the concept. Miquon uses Cuisenaire rods as their primary manipulative, so with some trepidation, I acquired a starter set. I needn't have worried. The rods made math so much easier for my very concrete, hands-on son to grasp. That was almost a decade ago, and now my youngest enjoys doing his math with the rods. The concept behind the rods is simple. Each rod color is a specific length, representing a particular number of units. White rods are "units" 1cm long, reds are twice as long and represent the number 2, and so forth. A starter set comes with several of each rod from 1-10, with more of the smaller rods. The child then uses the rods in combination to visualize basic math concepts. Perhaps it is obvious that addition can be modeled using such rods, simply by putting them end to end in a "train." However, they can also be used for subtraction, multiplication, and division, and even fractions, areas, and more. Using the Cuisenaire rods, quite young children can understand what multiplication means and can work out simple problems. We actually own a lot of math manipulatives, including both store-bought and homemade ones, but these are the ones I use the most.
Reviewed by: 
First reviewed: 
5-5-2009

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