Reasoning About Problems ◆ 89might tell the students it’s an addition problem or a subtraction problem
and have them practice those. In the upper grades, also use multiplication
and division. For example: The answer is 5 marbles and it was a division
problem.
Sometimes, I’ll tell the students to write a one-step or two-step prob-
lem. Other times, the students will write problems and then we will sort
those problems and decide what was the operation as well as how many
steps. Templates help to outline the criteria. They also lead nicely into
using the rubric to check the work. The templates hold the students
responsible for all the parts of writing word problems. Notice that in the
templates, there is an emphasis on a set-up equation and a solution equa-
tion. Part of reasoning is that students understand how to show the
problem with equations.
Equations
From first grade up in many of the standards, students are expected to
be able to write an equation with a symbol for the unknown. They are
also expected to compare numbers using symbols for greater than, less
than and equal to. For example: Sue had 15 cm of string. She bought 27 cm
more. How much does she have now?
15 + 27 =?Another example: Sue has 57 cm of string. Tara has 34 cm of string. Who
has more and how much more?
57 > 34Students should be able to show that comparison using symbols:
57 > 34. It is crucial that students understand mathematical symbols and
when and how to use them when explaining their reasoning. Make sure
that in the word problem work, there is an emphasis on students knowing
how to show what they know with numbers and symbols (see Figures 6.1
and 6.2). Students could count up or back to find the difference.
Using Graphic Organizers to Write a Word Problem
Work with structure, meaning work on a specific type of word problem.
For example, you could tell the students you are going to work on divi-
sion problems. Then, on the board, do a group graphic organizer of all
the elements of the word problem (see Figure 6.3).