56 ◆ Problem Types Across the Curriculum
amount of the whole and not as something that is the same size and the same
shape. So half can look lots of different ways. There is a great activity on PBS
Cyberchase (http://pbskids.org/cyberchase/media/games/fractions/
fractions_intro2.html) and Mathwire (http://mathwire.com/problemsolving/
thirteenways.pdf) called Thirteen ways of looking at half, where students are
challenged to find 13 ways to make a half. I would have the students actually
cut the sandwiches because this is different than having them simply draw
it. They own it in a different way through physically cutting the paper.
Figure 3.25
Grandma Betsy made her 2 grandchildren a turkey sandwich.
Show 4 ways that she could have cut the sandwich so they each
got an equal amount.Decimals
Decimals are scary for students and teachers. Money models are good but
definitely shouldn’t be the only thing we use to teach decimals. Students
should use wheels, bars and grids to think about decimals. Think about
this problem (see Figure 3.26). What would be a good model for students
to use to solve this (to show their thinking)? Have the students reason
about the problem before they solve it. A common error would be for
students to say that 0.125 is bigger than 0.25. So getting students to reason
with tools and models helps to ground their understanding.
Figure 3.26
Jane went to the candy store. She bought 5 bags of sweet candy that
weighed 0.25 of a pound and 5 bags of sour candy that weighed 0.125
of a pound.
Which type of candy did she buy more of?How much more of that candy did she buy?