Amanda & Jackie
Connecting Different Representations
After students have worked on the Triangles task, Jackie and Amanda each share their solution methods. Cindy asks the class if the two methods can be connected to each other.
Amelia’s Approach
Using Structural Thinking
Amelia explains how she came up with her equation for Schemel's Logo from the visual model. Jason tells how he found the equation from the table, and Amber comments that Jason's table shows that Schemel's Logo is not linear.
Angel’s Question
Examining Slope and Y-Intercept
As students discuss a variation of the Growing Dots task in which the starting point is shifted, one student shares that when the first dot is at time 0, the rule is 4x – 3. Another student, Angel, asks, “Where is the –3 in the picture?”
Breanna & Cody
Representing Mathematical Thinking
After having worked individually to predict the number of faces for a line of 10 connected cubes, the class discusses their predictions attending to two particular student methods--one using repeated addition and the other using multiplication.
Casey & Irma
Examining Slope Across Representations
After working on a variation of the Growing Dots task in which the starting point is shifted to several different times, students share what their graphs look like for several different starting points, and the discussion moves on to focus on connections across the graph, table, and equation.
Chase’s Question
Discussing Mathematical Thinking
As students discuss their approaches, Chase asks Cody where the 4 comes from in his idea. Cody responds, "Which 4? There are a whole bunch of 4s." As the discussion continues, Kyle, Nicholas, and Jasmine add their ideas.
Comparing Logos
Examining Linear vs. Quadratic Growth
After discussing several equations for Regina Logo (linear function) and Schemel's Logo (quadratic function), students consider how the two tasks are similar and different. As the lesson closes, the teacher asks them to do a journal write on how the graphs of the two functions compare.
Debra’s Question
Exploring Mathematical Equivalence
After small groups share three different equations to determine the number of 1 x 1 tiles needed to form a border for a square pool with side length x, Debra asks, "Are these equations the same?"
Different Equations
Looking for Geometric Structure
After Debra's class has determined y = 4x + 4 as one equation for solving the Pool Border task, Debra asks them to work in small groups, exploring visually to find as many other equations as they can.
Discussing 5 by 5
Framing a Pattern Task
Debra (the teacher) asks students to consider how many 1 x 1 tiles would be needed to create a border for a 5 x 5 pool. The class then discusses the different approaches students took to counting the tiles, both correct and incorrect.