Problem Solving Revamped

An example of what I am talking about with this 'blending':

Firstly, students opened up their packs of Cuisenaire Rods, given time to play with their 'new' materials prior to starting the learning process. 
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​The aim of this mini session was to explore how we can represent basic fractions. That is, showing themselves and one-another representations of a half, a third, and a quarter. Once they were able to do this effectively, convincing their 'skeptic' partner who needed convincing, they then devised a way of showing this in notation form. 
​Next, students were shown a street sign as per Robert Kaplinksy's task 'How Far Apart Are the Freeway Exits?' I posed the questions:

• How can you tell which exit is closest to you?
• How can you tell which exit is farthest from you?
• How would you show how far apart the freeway exits are on a map?
• Which exits are closest together?
• How far apart are the freeway exits?

Then, I asked students to blend their skills by asking them to represent the road and the exits using Cuisenaire Rods, explaining their reasoning to their skeptical partners, using their skills from Jo Boaler's 'Prove it to Me' approach (attached below). Next step is to ask students to represent these in different ways. I will also pose the question 'What if a different color was equal to one kilometer?' 

Thank you for reading and please do leave comments/suggestions/feedback - would love to connect!

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