Grades 3-5 Math Problem Solving in Action_ Getting Students to Love Word Problems

Modeling Thinking ◆ 125

With math story mats, I would start by acting out the stories with
manipulatives. Later, I would have the students draw out the stories.
Finally, I would have them write the words and symbols connected to the
stories. For this step, I would have number cards and math symbols so
the students could show the number models. I would also have them
write out the number models. Sometimes I would have them match the
story problem with the number model and then model it on the math mat.
Grouws and Cebulla (2000) found that working with partners for
problem solving increases student achievement. They also found that
long-term use of manipulatives increases math achievement. With story
mats, you can have students working with partners and using manipula-
tives to represent their thinking.

• Have stories written on task cards. The students pull the cards and
  model the story with manipulatives to solve^ it.


• Have students work in partners and one partner tells a story while
  the other one represents it on the math^ mat.


• Have students tell their own story and represent it on the math
  mat as they are telling it and others listen.


• Have a student tell a story and the group represents and solves it
  on their own individual math^ mats.


• Remember to always have a small group discussion after the practice
  so students can concretize their learning. Grouws and Cebulla (2000)
  found that this discussion helps to raise student achievement because
  students get to hear others and think about their own reasoning.
  Math mats are an abstract scaffold. They provide a context but are
  much more open than the other tools previously mentioned.

Drawings and Sketches

After the students have worked extensively with the concrete materials,
have them draw what they are doing. It is important to teach the students
to do “mathematical sketches,” rather than to have them spend hours
drawing a marble.

(Bar/Tape/Strip) Diagrams

After the students have practiced using pictures and drawings, they should
be doing diagrams. Bar/strip/tape diagrams are important in terms of
unpacking word problems. Most of the time, once students have set up
the strip diagram, the calculations are easy because they actually under-
stand what they are doing.