The "Home Depot Garden Club Photo" investigation described in an earlier post has been dubbed the "Berry Bush Problem" by my students, likely in an effort to conserve syllables. Another reason for the renaming is due to the mislabeling of a plant at the Home Depot: what we thought was a blackberry bush was actually a blueberry bush. The activity associated with the photograph will be the basis for my presentation on 9/30 in Kearney at the **N**ebraska **A**ssociation of **T**eachers of **M**athematics (**NATM**) Annual Meeting. The description in the conference listing reads:

CCSSM Practice Standards 2 and 4: Using Images to Maximize Student Engagement:This session will model how to use an image as a hook and build a lesson which engages students in the listed practice standards. Participants will formulate questions and conduct investigations based on these questions. The featured image is one the presenter took while shopping at Home Depot. Geogebra will be used in this session. Topics may include, but are not limited to, volume, area, linear functions, temperature, and modeling. Participants would benefit from bringing a laptop or tablet device with wireless capability.

For reference, here are the two Standards for Mathematical Practice featured:

**CCSS.Math.Practice.MP2 Reason abstractly and quantitatively. **Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to *decontextualize*—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to *contextualize*, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

**CCSS.Math.Practice.MP4 Model with mathematics. **Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

I learned a great deal from working alongside my students and acting as a facilitator. Here is a subset of the outcomes I saw in my classroom:

**Transfer of mathematical authority from teacher to student.****Ownership and intrinsic motivation in the revision process.****Students developing healthy strategies for working through point of frustration.****Procedure viewed as process rather than the culmination of the mathematics.****Rich discussion regarding potential sources of error, particularly roundoff error in Geogebra.****Collaboration and mentoring between experienced and inexperienced math students.****Understanding we make sacrifices in modeling that may be revisited later.**

**Initial student video:**

Andrew, Matt, Nik, Ryan

At** the NATM talk, I will show examples of Geogebra sheets and PDFs written by other students in class and provide insight on these students' mathematical backgrounds. I will also offer information on how I assess such a project in a way that encourages revision.**

**Revised student video:
**Andrew, Matt, Nik, Ryan

** **