"teaching" base 10 concepts
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i really like to think of the concept of base x as containers.
in our number system, base 10, each digit is like a container that can hold 0 to 9 units before overflowing and requiring another digit to hold the extra unit. with computer stuff, i also tend to work in base 2, 8, and 16 fairly often. they math is all the same concept as in base 10, just with different sized containers: 0-1, 0-7, and 0-F respectively.
this can all be visualized with something like jars and ping pong balls or vials and marbles. the jars represent the digits and their capacity to hold units. each ball would be a unit. for base 10, the jars should hold only 9 balls before overflowing. for base 8 they should hold 7, etc. this can help visualize how the digits can represent different values in different bases, and you can always get the actual value (in our native base 10) by counting the balls at first. later the multiplication and addition will hopefully be more intuitive.
did that make sense?
how old are your learners?
in our number system, base 10, each digit is like a container that can hold 0 to 9 units before overflowing and requiring another digit to hold the extra unit. with computer stuff, i also tend to work in base 2, 8, and 16 fairly often. they math is all the same concept as in base 10, just with different sized containers: 0-1, 0-7, and 0-F respectively.
this can all be visualized with something like jars and ping pong balls or vials and marbles. the jars represent the digits and their capacity to hold units. each ball would be a unit. for base 10, the jars should hold only 9 balls before overflowing. for base 8 they should hold 7, etc. this can help visualize how the digits can represent different values in different bases, and you can always get the actual value (in our native base 10) by counting the balls at first. later the multiplication and addition will hopefully be more intuitive.
did that make sense?
how old are your learners?
Have you ever seen the base 10 blocks sold in educational stores/catalogs? The blocks measure 1x1x1, 1x1x10 and 10x10x10. (In other words, you get one's, ten's and hundred's.)
I don't know how old your child is, but if he/she is pretty young you can glue 10 pinto beans to a popsicle stick to create ten's, and then use individual beans for one's. I have some of these made up for DD and we play around with them now and then.
I don't know how old your child is, but if he/she is pretty young you can glue 10 pinto beans to a popsicle stick to create ten's, and then use individual beans for one's. I have some of these made up for DD and we play around with them now and then.
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