My son finished his very first formal online math class at age 14. We started at a grade 8 level which seems to bridge elementary and high school math concepts nicely. He learned integers, fractions, decimals, prisms, pythag, variables, relations, graphs, etc. He did very well in understanding how to do math on paper, but he needs much more practice in learning which operation to apply to which problem. That is going to take life practice…to meld the paper math with the mental math. But my other 4 kids did it. He will too. Now he is going to take another year off and fully unschool (play video games) again and then take
grade 10 math for a high school diploma. I think that math grade 8 is a good start for more formal math foundations if your child is heading to a career in STEM. My other 5 children also began their formal, on-paper, math studies at either grade 7, or 8, depending on how willing they were to start, although they had been using mental math from the time they were toddlers, applying math concepts to real life problems. Math is just learning tools to solve problems and young children are good at solving problems.
Here is an example. We ordered a half cheesecake for a birthday party. When we opened the box, we had a problem – it didn’t visually look like half a cheesecake. We wanted to prove our hypothesis. So we had a mini-lesson on using Pi to measure if we had a problem. It was a piece of cake using Pi to determine that we had a case to complain. Happily, the cafe gave us another half cake to compensate! The key is that the kids learned a tool to help them solve a real life problem, and that is what make math come alive – not doing 25 problems in a workbook.
Can a child really learn grades 1-8 math concepts on paper in one year when they are 13? Yes! But they are not really starting from grade 1. They have learned the concepts, by living life and hands on applications and are ready to apply them to paper by age 13, when their pre-frontal cortex is gaining critical thinking and analytical skills. My kids learned decimals by buying and selling items. They knew the concept and when they were teens, then they easily learned how to add, subtract, multiply and divide fractions on paper. Just like a child can toilet train in one day at age 4 when they are fully developmentally ready, a child can learn 8 grades of math in one year at age 13-14 when they are developmentally ready.
Here are some handy ways children can learn mental math without a workbook:
Adding and subtracting – Play board games such as monopoly, etc. Selling items and making change at a garage sale or lemonade stand. Paying for items in stores and noticing change.
Multiplying and dividing – Cooking, baking, sewing, workshop projects, and art projects. Sharing food and items among friends.
Greatest Common Multiples – Skip counting jumps on the trampoline.
Fractions – Baking and cooking from recipes. Dividing up food with siblings. Deciding how much quantity of food to buy per person for hosting dinners.
Decimals – Shopping. Splitting restaurant cheques.
Percents – Calculating tips, taxes and sale prices while shopping.
Estimation – Shopping. Tracking travel miles.
Perimeter – Measuring for baseboards.
Area – Measuring for carpet, paint or floor coverings. Sewing.
Volume – Measuring parcels for the post office.
Least Common Factors – Lego pieces are named 2×2’s or 2×8’s so figuring out how many pieces needed to build a model.
Integers – Monitoring temperature changes. Counting money. Counting zero pairs with lego pieces.
Algebra – Computer games such as Graal, Minecraft etc. Shopping for packaged food items for a certain number of people. Figuring out problems. Balance scale.
Variables – Figuring out symbols that stand in for concepts.
Place value – Sorting and grouping toys and items. Measuring liquids, distances, and weight using the metric system that is based on 10. Counting money in games such as Monopoly. Writing out cheques. Cooking.
Coordinates and Ordered Pairs – Play Battleship.
Rounding – Figuring out how much allowance one has to pay for things. Estimating price total when grocery shopping.
Angles properties – Making a sundial. Studying astronomy. Visiting historical sites where people made ancient contraptions to measure time and seasons.
Degrees – Formatting photos and learning about astronomy. Questioning why the Xbox is a 360! Playing Hide and Seek
Temperature – Bake and cook. Monitoring the weather.
Time – Figuring out the clocks at hospitals and airports help children learn the 24 hour clock.
Roman numerals – Read “Asterix and Obelisk” books.
Reading graphs, pie charts, and figures – Reading magazines such as The Economist and MacLeans. Checking out newspaper articles to see how units on graphs can be manipulated to one’s advantage.
Even and Odd numbers – Reading maps and house numbers on a street.
Properties of geometric solids – Playing with blocks and nets.
Slides, turns, rolls and flips – Formatting photos on the computer. Playing with blocks.
Symmetry – Playing with mirrors, objects and prisms.
Perfect squares – Examine a multiplication table and visually see the patterns. Making paper squares for cutting snowflakes and other paper projects. Seeing how squares fit into other squares.
This is a model of X^2 + 4X + 3, and the best part is that you can eat it after!
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Excerpted from Chapter 18 of “Unschooling to University” by Judy Arnall