Proportional+Reasoning

=Proportional Reasoning=

- Who doesn't love an M&M mini-lesson!

- I had students explore these problems before giving them any strategies about how to solve them. It was interesting to see the different strategies partners came up with to find the solutions. I used this after unit rates so I definitely saw a lot of those in student work.

- A second paper to use for students to explore proportional reasoning.

[|Goldilocks and the Three Bears]- An activity from NRich.maths.org on proportional reasoning and determining sizes of the furniture and bowls, etc at the house of the 3 bears.

Idea borrowed from an NCTM Message board (posted by Kai Henneman): "I fill a pint size mason jar with two kinds of beans in a specific ratio. The kind of beans and the ratio changes from year to year, but I usually keep the ratio fairly simple--1:2, 1:3, or 2:3. I ask my pre-algebra students to find a valid, elegant mathematical process for estimating the number of each bean in the jar without opening the jar. I do not give them any tools or additional information unless they ask for them. Students eventually figure out that they need a scale, an empty jar, the ratio of the beans in the jar, and a smaller, but not too small, sample of beans in the same ratio that they can weigh and count. They then put the data together in a proportion to find an estimate for the total and a system of equations to find the estimates for each kind of bean. The jar remains in the back of classroom for the duration of the project, and other than a few minutes during a couple classes to brainstorm ideas, students come in on their own time to complete the project and write their report."