Math is one of those topics that I didn’t really expect to be learning new things about this year. After all, my oldest son is just six years old and although I wanted him to get a good basis on math I figured he’d be learning things I had learned years ago. But when I sat down to start teaching him, I discovered there’s lots for him to learn that I had never thought about. This past year we’ve learned a lot of math strategies, played plenty of math games, and even done some math crafts. We’ve talked about different number systems and learned about both modern abacuses and historic counting boards. It has been fun, and I thought I’d put together a list of some of the resources that have been helpful to us.
I cannot say enough good things about this program. It is based on the idea that counting is an inefficient way of doing math and it encourages children to think of numbers in terms of groups of five and ten. Eight is five and three. Nine is five and four. So 8 + 9 = two fives plus three and four or seventeen. It probably sounds awkward explaining it but once you get used to the system of thinking it is very quick and easy.
Suddenly all of math becomes about trying to find patterns and shortcuts. If I had any doubt about the method of doing math it disappeared on a day when my son was worried we wouldn’t have time to do math because we were doing errands, so I started quizzing him on math questions in the car. I started with easy multiplication questions like the 2s and 3s, but then not thinking I called out 6 x 7. When a few seconds later M answered correctly I started asking him other multiplication questions we had never practiced, and each time he could answer it and explain how he got there using another question he did know, such as taking 5 x 7 and adding 7, or for 9 x 7 he took 10 x 7 and subtracted 7. That at six years old he could start making these connections impressed me. If he had to memorize the questions, he could forget, but knowing how to figure them out will last. And the speed and memory comes now with the practice through games.
The emphasis of the RightStart Mathematics course is on understanding not memorizing, although the expectations for what the student should learn to do mentally quite high. The student is introduced to a new idea or concept, given three or four days worth of lessons approaching it in different ways and then the idea is reinforced in the warm-up exercises for lessons to come. Extra practice is achieved primarily through games, rather than drill although level C does contain a fair amount more worksheets than level B. A book of games and the various card decks to play them with are available separate from the main curriculum for those who want to supplement a different program instead.
One of the real joys of the program is the extras it includes. Level C teaches the student how to use a drawing board, T-square and triangles to draw triangles, hexagons and stars. One worksheet in the same level involves coloring patterns in a tessellation of a hexagon. My kids insisted I photocopy this worksheet over and over so they could color many different patterns.
The Rightstart Mathematics course is a complete course in itself. It doesn’t “need” to be supplemented. Yet there were times doing it where we felt like we wanted a break and we found a number of other resources helpful. These are some of the things we borrowed from libraries to provide even more variety and practice to our math studies this year.
Grapes of Math by Greg Tang
This book is an exercise in grouping and strategies so it fits in great with the Rightstart Mathematics program and is probably best at about level C when students are learning multiplication. Each page is a separate practice question with a poem and a picture. Greg Tang’s other math books are also excellent, all emphasising strategy rather than memorization.
Math in a Cultural Context
This one was available from the local university education library. It is a program designed in Alaska meant to teach mathematics and wisdom of the Yup’ik elders. We worked through three of the grade two math modules, not doing all the activities but those that seemed appropriate. One of the joys of going through this is the emphasis on story and culture gave me a way to include my three year old too. He could sit and color copies of the coloring book while I read the story and discussed the math. Patterns and Parkas led to some fun days of cutting and pasting colored paper. Going to Egg Island involves making a small abacus based off of the Yup’ik way of counting hands and feet to twenty, and that led to discussions about what a hypothetical alien with only three digits would count like and an introduction then to number systems based off of other numbers. The units are designed for school classrooms and not necessarily worth buying for individual families, but excellent if you can borrow one for a while.
History of the Abacus by J. M. Pullman.
I borrowed this book from the library, and it isn’t a children’s book. It is a book for adults, so maybe it is weird I list it here but I will anyway because it helped me understand Roman numerals, abacuses and counting boards, and thus it helped me to teach that to my son.
I’m including a picture here that doesn’t really go with any of the above resources but was one of our math projects we did. This paper craft was part of exploring fractions. We started with a square and folded all the corners into the middle, then discussed how the smaller square was exactly half the size of the larger unfolded shape. We cut a yellow sheet the size of the smaller square and did the same thing over and over till the squares were too small to easily fold. As we did it we discussed the relationships of the shapes. The orange is a quarter of the red, and before we glued the orange sheet into the center of the yellow we could put it in the corner of the red one to see how it filled the space. So if the red was 1, then the orange is 1/4. But what if the orange was our standard? Then the orange is 1, the yellow 2, and the red 4. We also discussed what would happen if we took the colored sheets and tried to color the red one. Could we use all the smaller sheets to do so? The yellow would cover 1/2 of it, the orange 1/4, the blue 1/8 and so on and so on. In this way we explored one of Zeno’s paradoxes and talked about how at some point the remaining area would be too small to be of significance.