One of the wonderful things about teaching is when you find a better
way of explaining, presenting or demonstrating something that is
difficult for students to grasp.

When teaching about the different types of simple math problems (as defined by Thomnas Carpenter) I use the phrase 'how many" in all of the problems except one in which I use "how much". The students always tell me, when they come to theat problem that I have made a mistake. When I ask why they think that they always say something like "well, it just doesn't make sense to say how much pennies of how much hours, or how much buckets". When I tell them that it is not I who have made the mistake but them they always look somewhat confused.

To clarify, the problems are set out with no referents next to the numbers ush as "I I have 6 ___________ and you give me 8 more ________________, how many _____________ do I have now? Their task is to fill in the referents so that the problem makes sense. So the odd problem similar to the one above ends with "how much ____________ do I have now.

The key to success with this particular problem is to change the referent from a discrete one such as pennies or hours or candies to a continuous variable such as money, time or sand. A discrete variable refers to things that come in single units whereas a continuous variable can be divided in an infinite number of ways.

Yesterday in class I made two vertical lists on the board ; one of continuous variables and another next to it of related discrete variables.

Next time you visit your local supermarket check to see if the express lane says "10 items or less" or the more mathematically correct "10 items or fewer.

When teaching about the different types of simple math problems (as defined by Thomnas Carpenter) I use the phrase 'how many" in all of the problems except one in which I use "how much". The students always tell me, when they come to theat problem that I have made a mistake. When I ask why they think that they always say something like "well, it just doesn't make sense to say how much pennies of how much hours, or how much buckets". When I tell them that it is not I who have made the mistake but them they always look somewhat confused.

To clarify, the problems are set out with no referents next to the numbers ush as "I I have 6 ___________ and you give me 8 more ________________, how many _____________ do I have now? Their task is to fill in the referents so that the problem makes sense. So the odd problem similar to the one above ends with "how much ____________ do I have now.

The key to success with this particular problem is to change the referent from a discrete one such as pennies or hours or candies to a continuous variable such as money, time or sand. A discrete variable refers to things that come in single units whereas a continuous variable can be divided in an infinite number of ways.

Yesterday in class I made two vertical lists on the board ; one of continuous variables and another next to it of related discrete variables.

Next time you visit your local supermarket check to see if the express lane says "10 items or less" or the more mathematically correct "10 items or fewer.

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