Subject: number questions
Name: Liz
Who are you: Parent

Eighth grade teacher is supplementing my daughter's Algebra class with "problems that make you think outside of the box" Question: How can half of 12 be 7? She gave the class the example that half of 11 could be 1 (draw a line between the 2 digits in 11 and each half is "1." I think the answer should be "there is no mathematical way that 7 can be half of 12", but my daughter is reluctant to submit that as an answer. Thank you for your help.

Liz,

I have three responses from my consultants for you.

Harley

Hi Liz.

Use the same idea as the "half of 11" but first write 12 another way (using another numbering system).

Stephen La Rocque.>

Liz,

Teacher's answer is probably to use Roman Numerals. But I agree with you! Let's do mathematics in math classes. Save the party games for recess.

Chris

Liz,

Well there are ways but maybe a bit far out for a grade 8 student.

Normally, that is in base ten, when we write 12 we mean 1x10 + 2x1; the first column on the right is the units column and the second column is the tens column. Thus 25 means 2x10 + 5x1, etc.

There is nothing special about base ten, in fact computers use base two. If we were to use base twelve, then, in base twelve, 12 means 1x12 + 2x1 = fourteen and half of fourteen is indeed seven.

I'm sure there are other ways to solve the problem also.

Cheers,

Penny