Investigate Your World

Nothing in this world is stagnant. Everything changes all the time. Some things like the weather or a scoop of ice cream left out in the hot sun can change very quickly. Other things such as an orange peel decomposing or a tree growing change very slowly over time. Other things may not have a constant rate of change. Instead, such as a baby growing, the baby will grow very fast in the first years, then it slows down the rate of growth. In the adolescent years, the rate of growth speeds up again and then slows into adulthood.

To help yourself learn about the mathematics of change, one of the best projects is to grow your own bean plant (or a plant of any kind that grows up). Keep a chart and record its daily growth. Create a graph showing the slope, or rate of change.  Learn about functions using a made-up “function machine”, compare rates of growth, examine patterns of change, describe how one variable changes in direct relation to another (such as the area of a circle and the length of its radius), be able to explain to someone else the difference between how big something is and the rate at which it grows, and construct bigger and bigger squares out of tile and describe how the area of the square changes in relation to the increasing length of its sides.

Learning about geometry and measurement helps develop your spatial thinking. It also gives you the tools and confidence to be able to build things, cook and bake, set up chemistry experiments, explore historic and modern architecture, paint with structure in mind, calculate the orbits of planets, measure vast distances in outer space using exponents, create fractals on the computer, perform magic tricks, and even play a great game of pool!

Do you want to make a treasure map? How about build a fort? Do you want to know how to give accurate directions? How will you know what size rug will fit in your living room? What size window box will you have to order or make for your plants? Will the leftovers fit in the container you have? Use geoboards (or a square of wood with nails pounded in at even intervals) for learning about fractions and geometric shapes, use household items such as egg cartons and juice packs as arrays to learn about multiplication, learn how to draw 2D and 3D shapes and other objects like buildings, in a creative “cityscape” project, build a model to scale, start a square foot garden, acquire and learn how to use the three most important tools of a mathematician: a pencil, a straight edge (ruler), and a compass. Also useful is a protractor.

Statistics and probability let you evaluate risks in your own life (such as the effects of exercise, playing the lottery, or smoking), data analysis helps you make sense of information you find in the media in order to make informed decisions, and most of all, a solid understanding of statistics helps you know how to ask the right questions to avoid being misled by advertisers, taken advantage of or straight up duped by companies who are trying hard to sell you their product.

How will you decide which political candidate you will vote for? How will you interpret stories you have heard or read in the news? How will you make informed decisions that affect you, your family and the rest of society? Do you have a good chance of winning the lottery? To function in our world and to be an informed and contributing citizen, you need to understand the basics of analyzing (or making sense of) data and the basics of statistics (it’s not that scary of a word!). Start cutting out all the charts, graphs, and maps you can find in your local paper or a magazine. Familiarize yourself with how to read them. Research the relative costs of health care and who pays what, learn the differences between mean, median and mode and how to solve for them, understand “cost-benefit” ratios, and know how an “average” describes your data.

Number sense means understanding how numbers are built and how they relate to each other. Ideas to understand and make games, puzzles and curriculum out of may include: Bigger than, Less than, Equal to (including decimals, real numbers, fractions, irregular numbers, and percentages), Finding numbers on the number line, combining numbers to see what happens, finding patterns, testing numbers by seeing how they react when we do things to them, and how to categorize numbers (such as even, odd, primes, factors, multiples, square numbers, cubed numbers).

Eventually I will post various activities, games and curriculum plans for you to glean from in order to build good number sense in yourself or a child in your life. In the meantime, you may be able to move forward with just this as your jumping off point. Good luck! Problem to try: Put the following numbers in order from least to greatest: 2/3, 60%, and .5