Teaching Math and a Giveaway

Mental Arithmetic in the Public School of S. Rachinsky by Nikolay Bogdanov-Belsky, 1895

The topic for today’s post was prompted by

Catherine Oliver

, who recently commented in her post, “I am still completely baffled at the discovery that two rectangles of the same perimeter can have different areas. Can someone explain this in the comments?” (Check out the comment section here for some insightful and comprehensive answers). In my many years of homeschooling, I have met countless parents who are “rediscovering” math in the process of teaching their children.

Math was not one of the subjects I looked forward to teaching. This was likely so because my high school teacher in Switzerland once told me, “You are excellent in all subjects and in math you cannot get any worse”. So as you can imagine, teaching math (especially the higher grades) was an intimidating idea for me, as it is for many parents (and even school teachers)¹. Yet, over the years I discovered a great variety of excellent math curricula that provided not only a solid foundation for my children, but were a pleasure to teach. Indeed I feel that I have received a whole “re-education”, finally clicking with certain Algebra concepts that had left me completely baffled when I was in school.

No matter how you may feel about math, there are some definite advantages in being your child’s math instructor:

• As a homeschool parent you have the advantage of selecting a program that fits your child’s learning style.

• You can move as quickly or slowly as you wish, allowing your child to progress at their own pace.

• You have the opportunity of helping your child develop strong mental math skills. Students who are able to smoothly navigate addition, subtraction, multiplication, and division are better prepared for abstract thinking skills required in higher math.

• Students in schools are allowed to use calculators very early on, and often lack a true understanding of math fundamentals, leaving them helpless with more difficult or innovative problems.

• For older students, you have the opportunity of incorporating real life math including calculating discounts, adding up bills, learning about taxes, investments, and budgeting.

Today I’ll share some of the math curricula our family has used over the years.

But first…

Mini Math Games Giveaway

I want to offer you encouragement in not just surviving math, but developing true enjoyment of the subject.

I will thus be giving away four small game sets from the Right Start Math collection!

The Corners game has been our family’s favorite for years, and my kids have played it quietly in solitaire mode, happily with grandparents, eagerly with siblings, as well as large, rowdy co-op speed math groups. You can see a sample of the Corners Games here and the Multiplication Card Games here. (I’ll talk a bit more about using these math games in the post below).

If you would like to enter the giveaway², simply reply in the comment section with a note about what math curriculum (or method) you use and what you love (or loathe) about it.

The winners will be chosen the old-fashioned way: I will write all names on a piece of paper, place them in a hat, and draw four winners. Note: As a special Thank You, paying subscribers will have their name entered on two pieces of paper :)

Winners will be announced on Oct. 15th.

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Math Curricula We Have Used Over the Years:

Right Start Math (Grade 1-8)

We first started using Right Start Math after a year of a horribly failed experience with Saxon Math (I know this is a favorite for many, but for my daughter it was unfortunately an utter mismatch). This is a complete elementary and middle-school program that “uses visualization of quantities, de-emphasizes counting, and provides strategies and games for learning the facts”. A unique tool that students learn to use is the AL Abacus, a specially designed two-sided abacus that adds both kinesthetic and visual learning dimension. Students learn to see numbers without counting and learn to trade quantities when adding numbers into the thousands (helpful especially for students who struggle with understanding place value).

Here you can find a placement test as well as sample lessons.

There are two levels dedicated to Geometry, which include lots of drafting and working with three-dimensional models. Making the a gigantic soccer ball or dodecahedron was particularly fun!

Something a bit different

I have used Right Start Math games for over a decade, and they are incredibly versatile, promote solid mental math skills, and can be used to supplement any math curriculum.

The kit includes everything needed to play math games: Math Card Games book with clear and easy explanations, six special decks of cards, two laminated fraction charts and an AL Abacus. The book includes 300 games providing practice in numeration, addition, subtraction, clocks, money, multiplication, division, and fractions and can be used for students starting in Kindergarten all the way up to middle school. This is also an excellent resource for remedial work. 

In our homeschool co-op I teach speed math games to elementary and middle school students. They absolutely love these games, and the class often erupts into uproarious laughter and yelps of eager competition. One of their favorites is “corners speed” (image on right), where players have to match their cards as quickly as possible to make sums of 5, 10, 15, or 20.

Math Mammoth (Grade 1 to 8)

Math Mammoth is one of the most affordable math programs out there. It is solid and provides clear instructions. The program consists of two student worktexts (A and B), a separate answer key for each, tests, mixed revisions, and in the download version, an additional worksheet maker (Internet access required) to make extra practice worksheets when needed. There are instructional videos for each of the concepts as well as a variety of additional online practice exercises for each chapter. You can view samples of the curriculum here . If you would like to have a live online class to go along with this curriculum you can find one at The Potter’s School here (used for Grades 5 to Pre-Algebra).

• focuses on understanding of mathematical concepts

• uses clear explanations, lots of visual exercises and pattern exercises

• mastery oriented: concentrates at length on a topic, with very few topics per grade

• emphasizes mental math skills and developing number sense

• very little teacher preparation needed

Math Mammoth also offers a free two-week math teaching course with topics such as: How to help a student who is behind in math; The value of mistakes in math learning; Principles of deeply effective math teaching etc. Here you can find a placement test and there a lots of samples and freebie available on their webpage.

Singapore Math

We have used this curriculum only briefly, but quite liked it. It is a traditional math program taught in a direct, easy to understand manner. The right amount of repetition, uncluttered pages, and a concise teaching style have made this program a popular choice. Singapore’s Primary Mathematics is more advanced than most math programs used in the U.S. Curriculum reviewer Cathy Duffy: “Primary Mathematics has taken the homeschool market by storm, and with good reason. This program teaches children to think mathematically rather than just having them memorize the mechanics of problem solving. Primary Mathematics lays a solid foundation for conceptual understanding using a three-step process, taking children from concrete, to pictorial, then abstract approaches to learning. Concepts are addressed from a number of directions that challenge students to think and understand.”

Beast Academy

Beast Academy is a dream come true for all kids who long to study math with a comic book to guide them. The program was created to “help kids ages 8‑13 build their problem-solving skills while learning elementary math. Students learn new topics from the graphic-novel-style Guides, and then master math topics by solving engaging problems and challenging puzzles. Beast Academy can be used either as a set of physical books, as an Online program (which also offers access to videos and chapter tests), or as a mix of both.” Here you can find a placement test. Beast Academy is the elementary math curriculum created by the Art of Problem Solving (see below).

Here is what a sample page of the guide book looks like:

Teaching Textboooks (Grade 3-12)

This program seems to check all the boxes, but I have to admit that my children dubbed it the “kill-me-now” curriculum. However, if you are looking for a simple program that is “hands-free” you may want to try some of their sample lessons. This is an online math curriculum that uses step-by step tutorials. Each lesson begins with a brief lecture, provides thorough explanations for each problem, and provides grading for each lesson as well as assessments for each chapter. This curriculum does not require any parental instruction. As a math program, it is a bit more simple than other math curricula and students will likely be able to start at a grade level higher (you can use the placement tool to determine the best starting point). Teaching Textbooks provides a free trial period so that you can assess whether it fits with your expectation and your student’s learning style.

Art of Problem Solving AoPS Curriculum

(Grade 7-12 – Competition Math)

If you have a high-achieving math student, who is interested in math competitions or a future career with an emphasis on mathematics, then this curriculum is an excellent choice. The text is quite dense, but includes concise instructions and explanations for all problems. AoPS is specifically designed for high-performing math students in grades 5-12 and presents a much broader and more in-depth study of challenging mathematics than a typical curriculum. The program demonstrates how students can apply their knowledge and problem-solving skills to difficult problems. These skills are particularly helpful for mathematics competitions (such as MATHCOUNTS and the AMC) and future careers with math emphasis.

Life of Fred

This is a great favourite of many homeschoolers! It is most definitely the most unique math program out there as each text is written in the style of a novel with a humorous story line. (My teenage son was interested in completing the higher levels in his free time merely because he wanted to find out what was happening in the story !) Each section tells part of the life of Fred Gauss and how, in the course of his life, he encounters the need for math and learns the needed concepts. The program was written by Dr. Stanley Schmidt with the intent to make math come alive with lots of humour, clear explanations, and silly illustrations that make the learned concepts stick.

Over the years we have used Life of Fred as “fun math” on Fridays or when we needed a little bit of a change, although some homeschoolers use it as their main math program.

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There are many other popular math programs including Math-U-See , Saxon Math, Khan Academy, CTC Math that we have not used ourselves, but you may also want to explore.

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What math curriculum do you use?

Which ones have you loved or loathed?

Have you used different curricula for different learning styles?

Please share your experiences or questions in the comments below!

Be sure to indicate whether you are interested in entering the Right Start Math Games giveaway :)

1. While one might expect trained teachers to be capable educators, many are not necessarily well-equipped to teach math. The Ontario Institute for Studies in Education tested every student teacher in Ontario in 2018, and despite being top university graduates, a full one-third were unable to pass the sixth-grade EQAO standardized test in mathematics for Ontario children.

2. This giveaway is open to participants in the US, as international shipping can be quite ghastly. If you live outside the US and are willing to cover the shipping costs, I’ll be happy to add your name to the hat :)