Reflection: Intervention and Extension Problem Solving with Quadrilaterals - Section 2: Independent Problem Solving

 

I sometimes use the Quadrilateral Practice problem set for scaffolding and extensions within a class.  If students are grouped homogeneously, all of the students in the classroom can work on exactly the same problems, but with different expectations for different groups.  For struggling students, you might ask for less detail in their answers, while for those students who are ready to be challenged, you might make it clear that “all possible information” includes all angle and segment measures whenever possible. 

As an example of this, for Example_1 in the rectangle section students could fill in their diagram so that the opposite sides are congruent and all four angles of the rectangle are right angles.  They could go further and use the Pythagorean Theorem or remember their Pythagorean triples to fill in the length of the diagonal.  Or, as a further extension, students could go even further and find the angle measures created by the diagonals, by using trigonometry.  I suspect that asking students to solve each and every one of the problems to this latter level of detail could become excruciating for the students.  This is where planning ahead and giving careful thought to the problems comes in.  I might, before making copies, for example, write a star next to all the problems on which I would like the more able students (or all of the students) to use trig.  Or I might ask groups of students needing a challenge to select one problem in each section, when possible, to use trig.

There are many possibilities – you just need to be clear in your own mind, going into this problem set, where you want your students to go with it.

  Intervention and Extension: Grouping Students to Challenge Them
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Problem Solving with Quadrilaterals

Unit 8: Quadrilaterals
Lesson 3 of 5

Objective: Students will be able to apply their knowledge of quadrilaterals to numeric and algebraic problem solving.

Big Idea: Students put their knowledge of quadrilaterals to work solving numerical and algebraic problems.

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Subject(s):
Math, Geometry, quadrilaterals, parallelogram, rectangle, rhombus, square, trapezoid, kite, Isosceles Trapezoid, 10th grade
  45 minutes
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