Prompt 27: Common Misconceptions in Algebra

Questions:

  1. Are all of these misconceptions directly addressed through explicit curriculum objectives, or is it luck as to whether they are addressed whilst doing algebra? i.e. Is there a specific lesson or sequence of lessons about the difference between (a+b)/a, and a/(a+b)?
  2. For each of the prompts, how exactly would you set up a pedagogical sequence to address and teach students the correct manipulations?
  3. Are there any other common misconceptions you can think of?

Additional common misconceptions:

Additional sources:

  1. @MathCurmudgeon shared: Do this and a Bunny Dies
  2. @ProdctvStruggle shared: Twitter Comment
  3. @greg_roberts86 shared: Classic Mistakes

Prompt 24: Length Scale Factors

Questions:

  1. Which methods leads most seamlessly to area scale factors and volume scale factors?
  2. Is there an argument for method 2 being helpful to practice algebraic manipulation?
  3. Imagine you had a scenario in which there was a missing length on both similar shapes. Which method might be least confusing in this case?
  4. Which method connects most effectively to scientific concepts learnt in school regarding scaling things up or down – i.e. Antman is made 100 times smaller in length. How will this affect the strength of his muscles?

Prompt 21: Solving Linear Equations

This is a task I gave to a Year 8 mixed attainment class which I think would be a nice pedagogy prompt given the question set below:

Questions:

  1. How do you show balance operations between steps? Is this consistent between department members? Should all department members use a consistent approach?
  2. Do you explicitly reference all variants of linear equations in curriculum documentation? i.e. I can solve a linear equation with unknowns on both sides when one or both unknown terms are negative, or, I can create a linear equation given the solution.
  3. Do you teach only one method for an equation like this? How do you approach different methods? Is this student led or do you explicitly instruct on a range of methods?

Prompt 20: Order of Operations

Which approach do you utilise to help students understand the order of operations?

Some interesting blog posts to back up this post:

  1. Cell 4: Dani Quinn (@danicquinn) – Tried and Tested: GEMS
  2. Cell 2: Colin Foster (@colinfoster77) – Higher Priorities Article in favour of BIDMSA
  3. Cell 5: David Butler (@DavidKButlerUofA) The Operation Tower
  4. Cell 6: Chris McGrane (@ChrisMcGrane84) – Order of Operations Area Model (A task which highlights that BIDMAS is not required).

Prompt 18: Exponential Growth – Comparison with Linear

Additional Fun:

Questions:

  1. Even if simple interest does not appear in the curriculum, would you still utilize it in order to make a direct comparison between linear and exponential growth?
  2. Do you show the entire curve to begin with, or would you build up as in the 3 pictures given in the prompt?

Further examples of exponential growth:

a. My Geogebra Applet on Bacterial Growth.

b. Nrich Task – Modelling an Epidemic (Nice kinaesthetic starter). You could also have an interesting discussion about how gossip could be modelled very simply with exponential growth.

Source: Unknown

c. Grains of Rice on a Chessboard Problem (The video is quite old but I love it).

d. Towers of Hanoi Puzzle (NCTM Applet)

e. Paper Folding TED Talk.

f. Dan Meyer’s Domino SkyScraper.

g. Human Population through Time (exceptional video on population growth shared by @atulruna on twitter)

h. How often do real world phenomena actually follow exponential growth indefinitely?

Source: Unknown