A Picture is Worth a 1000 Problems Joe McNaughton Senior Director of K-12 Mathematics Polk County School Board FAMS President FCTM Curriculum/Best Practice Chair

What question comes to mind? After participants watch the video they are to think of a question that comes to mind. Have them share their question with a table mate. Chart out questions that participants come up with and make sure that if needed you guide them to a question about volume. 1. The Gourmet Gift Baskets team wants to break the record for the biggest coffee cup. Will that cup be enough to break it? How many gallons of coffee do you think will fit inside? 2. Guess as close as you can. Write your guess down. 3. Write down a guess you know is too high. 4. Write down a guess you know is too low. 5. How long do you think it'll take them to fill up the cup? 6. How many regular-size cups of coffee would fit inside that super-size cup of coffee?

Write down a guess you know is too high. Write down a guess you know is too low. Guess as close as you can. Write your guess down. What do you need to know in order to solve? Have participants commit to their guesses and have conversation about what they need in order to solve. Do not go on to the next slide until participants decide on pertinent information they need.

Dimensions Dimensions are 7 feet by 7 feet

1 = 7.48052 Volume Cubic foot US gallon Give participants time to solve with their partner and then share out with the table. Have participants share out different ways that they solved. Facilitator needs to look for groups who solve differently.

Participants can compare their answer to the official answer *Participants can compare their answer to the official answer. Talk about why their answer may differ from the Guinness amount.

Standards MAFS.6.RP.1.3d Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.  MAFS.912.G-GMD.1.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Give participants a moment to read the standard for their own knowledge. NOTE TO FACILITATOR- This is not about what grade level standard we are addressing but rather about the process of learning and the instructional approach taken.

Group Reflection Which mathematical practice(s) did your group demonstrate when solving your task? What is the proof?

5E What it is… What it is not… Instructional model Based on student inquiry Gradual Release

5E

5E Engage Engaging activity to hook the student’s interest and assess prior knowledge.

5E Explore Explore using an activity tied to the concept in the benchmark.

5E Explain Teachers follow up the discussion addressing any misconceptions of the students by providing direct instruction through various means.

5E Elaborate Students apply their understandings of the concept to a real world situation, do further investigations on the concept, and/or read additional texts to support learning.

5E Evaluate Explore using an activity tied to the concept in the benchmark.

How can the mathematical practices come alive in a classroom without student discourse?

What questions would your students have with this picture?

How high is Shamu out of the water? x x

Where will Shamu land?

How long is Shamu on the screen?

How long is Shamu on the screen?

Now your turn… Take a picture that open conversation in the grade/course you teach Write the question your students would ask and what standard(s) it addresses Share your picture, question, and standard on Padlet (password is FAMS)