Students enter silently according to the Daily Entrance Routine. Their quizzes are already on their desks and they are instructed to begin promptly. Once students are finished with their quiz they are to stand up, bring me their quiz, and pick up a “Task + Homework” sheet. This is a new procedure I am trying out for quiz days. Since I have multiple students who require extended time on assessments, I create tasks that require little direct instruction. The problems included on paper are to be completed during class or for homework.
The task involves combining rational numbers. The initial questions require that students combine fractions (both positive and negative, with unlike denominators) on a number line. Since students will be working independently on this task (or on their Quiz), I will need to make sure I am checking in with students I know continue to struggle with fraction operations. This is a good time to have chelpers as well, though it should be limited to 2 chelpers to minimize noise. (A chelper is a student who “checks” and “helps” other students with the work).
The last three questions on the back of the sheet are review questions for topics including comparing rational numbers and locations on the number line.
If all students complete their quizzes with time to spare, we will review the answers to the task sheet together. One student would review the answers for questions 3 - 5 on the blackboard and white board, giving another student(s) time to draw the number line models from the front of the sheet on the SMARTboard.
The steps are clearly delineated at the top of the sheet to help students drill the same process and attain mastery of these operations. The two questions I would like to review are #3 and #5. These two examples go beyond calculation and require interpretation on the number line.
Problem #3 includes a number line, leaving the challenge of either memorizing or calculating the repeating decimal for the fraction -1/3. Students must then locate the decimal on the number line. The "distractors" or wrong answers can shed light on the location of breakdown in understanding. Students who elect the values to the right of zero need to be reminded that negative numbers exist to the left. Selecting the answer -0.3 misses the understanding of comparing terminating and non-terminating decimals.
I like Problem #5 because the way students solve, especially those who do it incorrectly, may indicate practical feedback to give the student. For example, a student who answers incorrectly and didn't draw a number line needs to start with that improvement. Anytime you see a problem asking you to compare the values of numbers, draw a number line, plot 0 at at least 4 other points, including those in question.