Task A: Think of a real-life situation that describes the following problem. 52-17= Write the problem and then solve it.We classified this as doing mathematics, which is a high Cognitive Demand Task. This task requires students to explore and understand the nature of mathematical concepts, processes, and relationships. This tasks the students to use past knowledge and own experiences and make appropriate uses of them.
Task I: Your grandmother is 61 years old. Our mother is 37 years old. A) How old was your grandmother when your mother was born? Use any strategy you understand and can explain to solve the problem. B) How could you explain your solution to a first grader using cubes or a 100 chart. We classified this task as doing mathematics because it requires the student to understand the concept and procedure he or she is performing to complete the task. The student is unable to mindlessly proceed through a procedure they don't understand because the task is asking them to explain in terms simple enough, yet effective enough for a first grader to understand.
Procedures With Connection
Task B: Use cubes to model the following problems. Write a number sentence for each problem. Then use words or pictures to explain how you solved each problem.
Connor has 23 cars. He gives 8 cars to Tristan. How many cars does Connor have left?
Connor has 18 cars. How many more cars does he need to have 32 cars?
Connor has 34 cars. Tristan has 52 cars. How many more cars does Tristan have than Connor?
We classified this task as procedures with connections because the student is using the cubes as manipulatives to solve the problem. This task requires cognitive effort when writing the number sentence and explaining how each problem is solved; the student must engage in how many cubes he is starting with and how many he is taking away.
Task C: We classified this task as procedures with connections because cognitive effort is required to solve this; students must engage in the conceptual idea of place value to understand what the 1 means in each problem. They are also explaining the concept instead of mindlessly solving the problem.
Task J: Sean found out that his little sister, Angie could hold 27 popcorn kernels in one hand, he could hold 96 popcorn kernels in one hand. How many less popcorn kernels could Angie hold in one hand? Some people think about this as addition: 27 popcorn kernels in Angie's hand plus 69 more popcorn kernels in Sean's hand. 27+69=96 Other people think about this problem as subtraction: 27 popcorn kernels in Angie's hand, compared with 96 popcorn kernels in Sean's hand, and the difference is 69 popcorn kernels. 96-27=69 Explain why you can find the correct solution using either addition or subtraction. This task is classified as procedures with connections because the student must focus on why addition and subtraction both produce the correct answer and tell the reasoning behind it. The concepts must be explored with cognitive effort by the student, which makes it a high cognitive demand task.