Modeling Thinking ◆ 111students should also work with vir-
tual tools (see Figure 7.1). For exam-
ple, the students might work with
the physical base ten blocks one day
and then the next time, they might
work with base ten block paper. In
another lesson, the students might
work with base ten sketches and then
on another day they might work
with the virtual base ten blocks.
There are many different ways to
access these virtual blocks. One site
that I like in particular is the NLVM
(the National Library of Virtual^
Manipulatives).
Acting Out and Concrete Materials
Students should be acting out problems with a variety of concrete manipu-
latives. Remember that there are different levels of manipulatives. Some
are more abstract than others. For example, if we are telling division
problems, and we have little plastic people or little paper dolls, this is
different from using cubes to represent the people.
Manipulatives are important when it comes to problem solving. Van
de Walle says that they are “thinking tools” (2007). He cautions us though
to not let the tools become the center of the math. The math should be
the focus of the study. The tools should not overshadow the math or
overscaffold the math. That said, there are some great manipulatives that
are essential for problem solving in the upper elementary grades.
A Closer Look at Math Manipulatives: Bears
Bears are a great tool (see Figure 7.2). They are underutilized in the upper
elementary grades. We should be using them through middle school. In
the primary grades, use them to solve the basic CGI problems. In the upper
Figure 7.1Five great websites for virtual
manipulatives^ are:- Math Playground Math
Bars - NLVM
- Glencoe
- NCTM Patch tool
- Math Learning
Center^ Apps
Figure 7.2http://www.KinderAlphabet.com