Transcript Teaching Ratio & Proportion Problem Solving Using Schema

Teaching Ratio & Proportion
Problem Solving Using SchemaBased Approach
Nikki Stephenson & Katey Long
Population
 The Schema-Based Strategy for
helping solve math word problems is
useful for Middle School Students.
Summary
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Word problems can present
difficulties for students with
or without disabilities.
A schema is a structure that
organizes knowledge and
can help a student
categorize different types of
problems to determine the
best way to solve the
problem.
First it is helpful to identify
the problem type

Change, Group, or
Compare.
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Then by using FOPS, you
can solve the problem.
It is very helpful for
students with disabilities to
figure out the problem type,
organize the information
into a diagram, plan to
solve the problem and then
finally solve the problem.
This strategy could lead to
significant gains in problem
solving skills.
Steps for Solving (FOPS)
 Step 1: Find the problem type
 Step 2: Organize the information
 Step 3: Plan to solve the problem
 Step 4: Solve the problem
Word Problem
 Example:
 The ratio of the number of girls to the
total number of children in Mrs.
Widenhour’s class is 2:5. The number of
girls in the class is 12. How many
children are in the class?
1. Find the Problem Type
 Read and retell problem to
understand it.
 Ask yourself if this is a ratio/compare
problem.
 Ask yourself if the problem is similar
or different from others that you have
seen before.
2. Organize the Information
2. Organize the Information
 Underline the ratio or comparison sentence and
write the ratio value in diagram.
The ratio of the number of girls to the total number of
children in Mrs. Widenhour’s class is 2:5. The number of
girls in the class is 12. How many children are in the
class?
 Write compared and base quantities in
diagram.
 Write an x for what must be solved (what are
you trying to find).
2. Organize the Information
12 girls
2
5
x
Children
3. Plan to Solve the Problem
 Translate the information in the
diagram into a math equation.
 Plan how to solve the equation.
4. Solve the Problem
 Solve the math equation and write
the complete answer.
 Check yourself to see if the answer
makes sense.
Problem Solving Strategies
 Cross multiplication
 12*5=60. 2*x=2x. 60=2x. x=30.
Problem Solving Strategies
 Equivalent fractions strategy
 2 times what is 12? Since the answer is 6 (2 *
6 = 12), we multiply 5 by this same number to
get x. So 6 * 5 = 30.
Potential Difficulties
 Having difficulties recognizing key words in
the word problem such as: less than,
product, and, etc.
 Student may focus more on the diagram and
less on what the problem is actually asking.
 Student may identify the wrong problem
type, causing the answer or diagram to be
incorrect.
 Student may think they do not need to draw
a diagram to get the correct answer.