I never give up on a problem and I do my best to get it right.
Task
My Work
Reflections
This task, dealing with the area of circles, aligns with math practice 1 because students are given a small amount of information and are tasked with "analyzing givens, constraints, relationships, and goals" of the problem. Part a in the task is pretty straight forward, although it requires students to determine the radius of the large circle given the radius of a smaller circle. Part b of the task requires several steps get to the answer - area of a smaller circle, area of all 7 smaller circles, area outside the smaller circles, and area of the shaded portion - which call for the student to "plan a solution pathway" as the standard states. Most tasks can be aligned with math standard 1, and this one hits many of the points in this standard as it requires the student to keep going and persevere in solving the problem as they complete each step, gather information, and make a plan for the next step or result.
Students may struggle with this task, at first, because the shaded portion is an irregular shape. They will need to formulate a plan to use the information they have to find the information they need. Students may also get frustrated or overwhelmed by the multiple steps required to solve the problem or the multiple pieces of information they get along the way. A teacher could help scaffold students' learning and comfort with this type of problem by helping them organize the information in a table. The task could be made more accessible by reducing the number of circles inside the larger circle.
This task could be made more engaging having students work in pairs or small groups to formulate a plan and complete the task. To extend the learning, groups could be assigned the same task with different radii and then participate in a class discussion about the relationships between radius of the small circles, the radius of the large circle, the area of the large circle, and the area of the shaded portion for each group.