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The last day, day three was fantastic! The day fo cused the elaboration E phase of the 5E lesson model. It allowed an opportunity students to move beyond typical calculations as they built their win dows. The students saw their learning and efforts transform into a practical application and a con crete product. The students were ready eager to build their designs. The building process was im plemented in one step increments as a whole class activity. First, the students were instructed to get out their designs. The plastic pocket paper protec tors were handed out. They inserted their design in to a plastic pocket protector (8.5x11) and set it aside. Next, they traced all lines from their graph paper on the exterior pocket protector using a black sharpie and a ruler. After the design was traced, the students colored the open space areas using colored sharpies. They placed their completed colored pocket protector in a safe place. Figure 3 shows de sign components preassembled. Next, the frames were passed out and the students carefully took the backing off of the frame. Pieces of aluminum foil, slightly larger than 8.5x11, were handed out. The students were asked to ball it up gently then straighten it out on a flat surface. The students wrapped the interior backing of the frame with the crinkled aluminum foil and set it aside. They turned their attention to the completed colored pocket protector and retraced any black lines on their design that may have faded. Next, they took the graph paper out of the pocket protector and re placed it with the aluminum foil wrapped frame backing. Then they placed their designs into frame and lock it into place. There were so many great designs and the students were so proud of what they accomplished that they wanted to show all their peers. The joy of math was in the eyes and it was magical. The final step was making a placard that described their prototype.

The final “ evaluation ” phase for the 5 E model was the public presentation of their products. The stu dents completed a 3 - 2 - 1 exit ticket: 3 - types of slopes, 2 - things they learned from the lesson that they did not know before, and 1 - thing they liked about the lesson. Assessment Students were assessed each day and throughout the lesson. The initial prior knowledge assessment was given at the beginning of day one with the “ Linear Equation Warm - up ” worksheet. T benefit of the PBL framework is anticipating and knowing the students were going to research, investigate, and discover a deeper meaning of linear equations and slopes throughout the process. Furthermore, each of the stations were paired with a worksheet to serve as formative assessments. Since the stu dents were working in small groups for the first three stations, it was easy to peruse the class and give guidance as needed. The class went outside for station 4 and were able to see slopes of lines in the real - world. As they were returning to the class room, they were asked to show each of the four types of slopes with their bodies or arms. The con nection to the real - world objects and their individu al bodies gave some students the coveted “ ah - ha ” moments. On day two, the students began the sum mative assessment, which was the design of their window. Using the “ Stained Glass Equation Work sheet ” and graph paper, the students had to create their own design and use a minimum of ten linear equations. This assessment was critical to the PBL lesson and to the students understanding, because they could connect algebra to a real - world situa tion, which strengthen their new understanding. By plotting y - intercepts and deciding on the slope in order to find the equation for the lines, the students interacted with the algebra rather than memorizing formulas and plugging in numbers. The last day of the lesson was building the prototype and the stu dents were given a small summative 3 - 2 - 1 assess ment at the end of the day. Since they were work ing individually on their design, discussions flour ished with students one - on - one where they were asked to explain their designs, reasoning and what if scenarios. The combination of the PBL lesson framework within the 5E model, resulted in a suc cessful student learning experience, where students deeply connected to the content. Evidence of Student Learning Student learning was apparent throughout the les son. It began on day one with the prior knowledge assessment “ Linear Equation Warm - Up ” worksheet

Figure 3: Student designs components before assembly

Virginia Mathematics Teacher vol. 46, no. 2

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