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Five-Star Educational Resources
for Homeschooling Families and Others Too!
Maths Resources
- Miquon Math. Miquon is nominally a K-3 math program. Basically it's a "guided discovery" math program using cuisenaire rods as its main manipulative. It's visually uninteresting, old and inexpensive. On the surface it looks boring and ordinary. There are a set of 6 workbooks and three parent/teacher resources. I happen to think it's brilliant in the way it leads kids to high levels of conceptual understanding of fundamental math operations and numbers without really doing a whole lot of direct teaching. It's very light on practice and there's no drill. Although the workbooks seem, at a first glance, to be the backbone of the program, they aren't. The most important part is the activities in the Annotations manual that introduce the ideas and patterns and relationships. Miquon is well-suited for hands-on learners. It's conceptually fairly advanced, for example introducing multiplication in the first half of the first book.
Erin did Miquon between ages 5.5 and 8. She completed the program and moved onto a more conventional math program at the ~4th grade level with no difficulty. Noah did the beginning of Miquon at age 6-7 but didn't find it terribly inspiring, since he seemed to have already "got" the conceptual links and patterns. Sophie started Miquon at 4.5, at her persistent insistence, and did very well with it until about halfway through when she got more interested in the Singapore program her siblings were doing. I really enjoy it too. We used Miquon (and our other math programs) in unschooly ways, whenever the kids seem interested in doing a bit of math bookwork, but not otherwise. It's a nice supplement to life learning for us... it gives the kids a chance to see how their real-life math translates into symbols on paper.
Some parents find Miquon chaotic because it's not a nicely laid-out compilation of exercises for ensuring young children will easily perform math computations. Instead it's more about the why of math, giving a menu of activities and approaches for introducing the thinking behind the numerical relationships. It's very flexible and creative.
- Singapore Math . Singapore Math complements Miquon Math very well, I think, and many families use the two together. We've generally done either/or, beginning with Miquon and then moving into Singapore when the kids have wanted something more sequential and visually appealing. What impresses me so much is the way Singapore builds up clear, logical,
flexible mathematical thinking. In the Primary (Gr. 1 - 6) series, every new concept is introduced in three stages... pictorial, diagrammatic, then symbolic. The pictorial works well with manipulatives for hands-on learners,
and the diagrammatic representations are brilliant stepping-stones to mental math. The kids are given tools for assembling images and schemes in their heads which make sense of a variety of problems.
The workbooks are extremely light on drill and busywork. The four timestable in 2nd grade for example gets about one page of "practice" before moving on. In schools in Singapore there's lots of supplemental practice that goes on, and that's dead simple to create on your own if necessary. But it's not in there padding out the program if your child doesn't need it. If you've been using Saxon I think you'd be astonished by how little busywork there is in Singapore. My kids tend to work at math for 30 minutes at a sitting. At that pace they get through about 2 lessons a session. There are about 100 lessons per grade level. So that's fifty days of small doses of math work to get through a year's worth of curriculum that is considerably more advanced than Saxon's. (Singapore 3B is approximately at the same level as Saxon 65.)
The type of problem-solving that's included in Singapore is also a breed apart. Examples typical of early-third-grade level...
"There are 428 adults and 789 children at a concert. 129 of the people at the concert are wearing glasses. How many people are not wearing glasses?" "A farmer has 7 ducks. He has 5 times as many chickens as ducks. How many more chickens has he than ducks?"
It's basic two-stage problem-solving, and simple-enough math. But you simply can't do it if you don't understand clearly the nature of the problem and the nature of the operations. A rote-memory cookbook approach doesn't work. That's okay, because Singapore teaches the understanding.
- Novels about math eg. "The Man Who Counted" by Malba Tahan, "The Number Devil" by Hans Enzenberger, "The Phantom Tollbooth" by Norman Juster.
- Books about math Picture books and others, especially Theoni Pappas' books like "Penrose the Mathematical Cat"
- Manipulatives and geometric building toys played with in a free-form way: tangrams, cuisenaire rods, pattern blocks, K'nex, Lego, fraction circles, fraction overlays, 10x10 counting frame, origami paper and books and the Page-a-Day Origami calendar
- CD-ROMs especially the Singapore Math ones and Zoombinis
- Spatial and pattern-based games and toys such as chess, checkers, Set Game, Labyrinth, Tetris (on the computer), Rush Hour or Blokus.
- Arithmetical games like dominoes, Monopoly, Yachtzee,
- Pedagogical math games from the "Box Cars and One-Eyed Jacks" books using card games and dice (see BoxCarsandOneEyedJacks.com)
- Sophie's Cuisenaire Discovery Book, my own pedagogical math games that use Cuisenaire Rods, suitable for kids from 4-8 (some will continue to intrigue older kids too). I developed this booklet and set of cards to use with Sophie who was begging for a "real math book" at age 4. I was hoping to delay her starting formal math. In fact she kept asking and we started Miquon Math after only a month or two of play with this book. But I was amazed at how well prepared she was for Miquon thanks to the work we'd done. You can download the Acrobat (.pdf) files here: Booklet, Cards, and print your own copy. If you don't have a colour printer, use this link for B&W Cards and get out your pencil crayons.
- Real-life math including tracking and graphing fish-tank chemistry, figuring out the logarithmic basis of pH and star magnitudes, participating in the accounting for fund-raising ventures, managing a laying-hen business, baking (doubling and halving recipes, dealing with fractions), woodworking (measuring, dealing with angles), saving and spending money, calculating tax and tips, sewing/weaving/quilting/knitting (textile allowances, stitch patterns, angles, etc.) and lots I'm sure I've forgotten.
- Music, which, as Pythagorus knew, was based on math.... learning to read and notate music requires a lot of math, and the relationship between intervals and frequencies is mathematical as well.
- Pattern blocks, combined with two unbreakable frameless locker-mirrors hinged together with duct tape are a lot of fun for making patterns and reflections. The blocks themselves are colourful and fun to play with. There's an applet here that gives you a taste of the blocks in an on-line format.
- Tesselations are a fascinating way to explore geometry. There's an out-of-print program called "TesselMania" that I think you can download a demo of here. And a library book filled with M.C. Escher's art gives a fascinating glimpse at some pretty complex tesselations, as well as a lot of other neat visually puzzling art.
- Designing and sewing quilt-blocks.
- MSW Logo. There's a very old computer programming environment (think early-1980's) called Logo that was developed for children. It's been adapted as freeware for the Microsoft Windows environment. Basically you control the trace pattern of a point (a "turtle") on a screen using computer commands. It uses conventional angles in the definition. So you tell the turtle to go foward 20 paces, turn 90 degrees left, go forward 20, turn 90 degrees left, go forward 20, etc. and you've created a square. There's a free downloadable children's book called "The Great Logo Adventure" that's excellent. They're all available for free on this page.
- Woodworking is another hobby that involves tons of geometry.
- Geometer's SketchpadThis is a robust computer program that is a geometry drawing tool for the computer. I just bought it for Erin to accompany her Singapore Math high school program, so we haven't delved into it seriously at all. It's the sort of program that might require some structured teaching to introduce the tools and basic operations its capable of. SpectrumEducational carries it in Canada, as well as many guides and manuals and additional modules. In the US, Key Curriculum Press is the publisher and supplier
- Geometric art. A "math set" of compass, protracter and rulers, some pencils and pencil crayons are great fun. We quite like the Triman Safety Compass too -- it has some neat advantages over a traditional compass. Dover Publications has some neat books on geometric art. There's Mosaic and Tessellated Patterns: How to Make Them (with 32 plates to colour) and Kaleidoscopic Designs and How to Create Them. They also have lots of geometric pattern colouring books.
- Maps. There's a lot of overlap with geography here. A child who has a comfortable familiarity with maps and with how they relate to actual movement on the earth's surface has gained a lot of comfort with manipulating planes in his mind, rotating mental images and changing perspectives. A topographical map of one's immediate area (1:50,000 scale is nice) can spark a lot of interest.Passing the kids a road map when we're driving somewhere is probably also a useful habit. I can ask them questions and give them the role of navigator: "Here's the Highway 31 exit. How far now until we get to the Smallville exit? Do we need to go right or left after the exit?" We've also had lots of fun with map work. We use a GPS receiver to do a high-tech form of orienteering treasure-hunts called Geocaching . We've created our own maps of our property, of fantasy worlds portrayed in novels, and of completely imaginary worlds of our own. Every map presents its own geometry challenges. Here is a Searchable database of Canadian topo maps . You Americans will have to find your own ;-)
