Mortgages Wrap-up and Additional Scaffolding

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Objective

Students will be able to reflect on their mortgage payment calculation activity and independently work through additional problem solving applications surrounding arithmetic and geometric series.

Big Idea

A time of reflection over an in-depth mathematical investigation - coupled with additional practice and skill building.

Reflection

15 minutes

Independent Work Time – Additional Scaffolding on Problem Solving with Series

28 minutes

Now that we have wrapped up the mortgages activity, it is time to put the students through some additional practice dealing with series applications.  Attached you will find a worksheet that I use for this.  I ask the students to work INDEPENDENTLY on this worksheet until they are stuck.  Once they are stuck, I have established a protocol for receiving support.  This format really challenges students to make sense of problems and persevere in solving them (MP1).  See below:

  • Designate 3-4 areas of the room as “help space” – this space should have enough elbow room to work with 3-4 students at a time.
  • Students will report to one of these areas of the classroom when they need help. 
  • The first student at the help space will write the problem # that they are working on
    • I use easels and it works really well!  Be creative and use what you can, however.
    • As other students arrive who are also stuck they are able to collaborate with each other to see what pieces they are confused about. 
    • The role of the teacher is to be patient and wait until 3-4 students are all at a dead end at one of the help stations before going over and offering support. 
    • Once the student has resolved their issue they must leave the help station and return to their seat to work independently.    

Closure

2 minutes

To close class I direct the student’s attention to #8 and the final two challenge problems.  Many times, kids are intimidated by the final problems of the worksheet, especially if they seem abstract and “disconnected” from the more structured problems.  I like to have the students quickly fill in the final box of the triangular numbers diagram so that they feel like they have at least gotten the problem rolling.   I then clarify what the questions are asking them to do, and give a little history on Plutarch, who is mentioned in Challenge Problem #2.  Hopefully, this “de-intimidates” the kids and they are able to view the challenge problem as something that really can be conquered!