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Developed by Ogle (1992) for the purpose of scaffolding readers' prior
knowledge to new knowledge, the KWHL strategy initiates active engagement
in the reading/learning task. The strategy creates an instructional framework
where students list (1) what they know, (2) what they want to find out, (3) how
they plan to find new information, and (4) what they have learned or still want
to learn. This activity can be used individually, in small groups , and with whole
class activities. This strategy allows students to share what they learn with
others, learn that there are many sources where information can be found, and
to summarize their findings .

In this story the number devil addresses some rather complex math concepts
which are suitable for 7th graders but can be used to address Algebra 2 concepts
such as factorials or expanding polynomials ( multiplying a polynomial with 2 or
more terms with another that contains 3 or more terms). He does it in a way
that is easy to understand and engaging. This activity will help the students
connect the mathematics in the text with the deeper development of the
concepts in the course and the world.

STEP ONE .—Hand out the KWHL worksheet to the students and instruct
them to brainstorm on the topic of polynomials (or the topic of your choice,
see a list of topics at the end of this document). Explain what each of the four
boxes on their worksheet stands for and prompt them with some of the
following questions:

• What do you know about polynomials?
• What kinds of applications do polynomials have ?
• Who are the contributors to the development of polynomials in history?

• What do you want to know more about?
• What questions would you like answered ?

• How can you find out?
• Where can you look for answers?

Initiate the discussion as a class and then have the students first complete the
worksheets on their own. Let them know that they will be coming back to the
final box (“Learn”) later. Let them discuss ideas with peers if needful.

STEP TWO .—After students have completed their worksheets individually,
compile a class list on the board of some of the things students wrote in each
category. Tell the students they can add to their worksheets as they hear
something new that interests them.

STEP THREE.—Instruct students to pick at least one of their questions that they
would like answered. At this point, you should assign a follow-up assignment
such as one of the following:
• Students read an article on the topic that interests them and write a
• Students write a research paper on the topic that interests them
• Students research more information about a topic and give a
presentation or mini -lesson in front of the class.

STEP FOUR.—After students have completed their own individual research,
return to the KWHL worksheet and have them fill in the “learn” column.
Prompt them with the following questions:

• What did you learn?
• Which ideas are most important?
• What kinds of real world applications might these concepts have?

Open up to a class discussion on ideas students learned in their research. Then,
tie ideas into those presented in the novel and discuss what they are now able
to understand better. Finally lead into a mathematical unit addressing more
fully the concepts discussed in class expanding the Learn column periodically.
Try to answer (or let the students answer) as many of the questions as possible
from the “Want to find out” section of the KWHL.

The teacher will use the activity to informally assess what the students already
know about polynomials. Then the teacher will be able to use this information
to scaffold learning and teach new concepts. Students should be given credit
for completing their KWHL worksheets and associated projects. Assessments
for the related research projects will vary, depending on the type of project.

Alternative Topics
In the explanation for this strategy I used the topic of polynomials as the
subject of the KWHL inquiry. As there are various topics in math and various
courses to which they may be applicable I thought it would be useful to suggest
a list of other topics that could be investigated in relation to this book. The list
is not meant to be comprehensive; it is merely given as a list of suggestions

Number Systems
Geometric Shapes
Geometric Proofs
Pythagorean Theorem
Series and sequences
Combinations and permutations
Pascal’s Triangle
Uncountable sets (set theory)
Imaginary Numbers

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