To begin Early in a child’s learning, values are expressed in groups of 10s:
• 10 pennies make a dime.
• 10 dimes make a dollar.
• 10 “one-dollar” bills make 1 ten dollars, and 1 ten–dollar breaks down to 10 “one–dollar” bills
• 100 pennies make a dollar.
• 100 dimes make ten dollars.
• 10 hundreds make a thousand.
• 1,000 thousands make a million.
Some things ”make sense” to cut in half: a candy bar, a piece of wood, numbers... Other things don’t: people, pennies, cars... To diagnose the correct approach, assess the subject matter. Use the examples below as guidance.
• If twice as many people as you expected come on a picnic, then you will need twice as much food.
But, if you are baking bread, twice the regular heat will not get the job done twice as fast.
• When you double the number of pieces, the size of each piece is half as much as it was. (This is the inverse relationship: when one thing goes up, the other goes down.)
Contrary to its reputation, Math is not all numbers, in fact, word prefixes play a large role in setting the numerical value. Take these examples:
• “mono–”means 1: The monorail at Disneyland runs on 1 rail.
• “bi–” means 2: A bicycle has 2 wheels.
• “tri–” means 3: a Triceratops has 3 horns.
• “qua–” means 4: a quartet has 4 players
• “dec–” means 10: a decade is 10 years
• “cent–” means 100: percent means “for each 100”
• “mil–” means 1,000: a millennium is 1,000 years—a mile is “1,000 paces”
Finally, I touch on a few points of knowledge for your student (if this is for parents, “parents have kids… teachers have student) that will assist him or her build the base for understanding the previously dissected, whole and parts method.
• A quarter of an hour is 15 minutes (not 25).
• There are 4 quarts in one gallon. A “quart” is a quarter of a gallon.
• Whole basketball and football games have 4 quarters.
• Four quarters make a whole dollar.
• One half dollar is the same as 2 quarters.
• Half-time in a basketball game comes after 2 quarters.
These basic understandings set the cornerstone for laying the foundation of knowledge to continually build and evolve your student’s mind, the Mathnasium way.