For today's Warm Up, I provide a list of categories of rational and irrational numbers (like proper fractions and repeating decimals) and ask students to classify each one into one of those two categories. I remind them to use the academic vocabulary wall or their notes to decide. When the timer sounds, I select student 'volunteers' from a cup with sticks of student names. Once they tell me how they classified the category, I ask for class agreement/disagreement with a thumbs-up or thumbs down signal. Once we have sorted the whole list, I move directly to today's activity.
For this review activity, each student is given 8 blank note cards. Their job is to write an example of each type of rational and irrational number listed in the warm-up. I model this task by pointing to number one, repeating decimals, and writing .45 with a repeat bar over the top on a note card. I ask for needed clarification and then move about the room while the students complete their cards. While doing so, I am on the lookout for any misconceptions that arise.
Once the student and his/her partner have finished creating their individual cards, they exchange cards and then sort their partner's cards into stacks of rational and irrational. Once finished, they exchange with the other students at their table so that they have 3 opportunities to practice sorting numbers.
When the timer sounds, I ask students to place all their cards in one pile at their tables. I then distribute today's RationalIrrationalQuiz A.
Today's short formative assessment was created as a common assessment by the team of 8th grade math teachers at my school.
We organized this assessment with five questions ordered by complexity. The first two questions tested the student's ability to classify numbers as rational or irrational. Then, students had to show they could order numbers on a number line. Next, students had to describe how they knew a given number was rational or irrational. Finally, students had to explain whether an irrational number added to any other number was rational or irrational.
As always, if students finish the assessment before time is called, they are allowed to work on their weekly homework, work on optional challenge problems, or read for pleasure.
Once the assessments are graded, we each bring our item analysis (e.g. most commonly missed questions) to the next team meeting to discuss. We use this data to make any needed changes in either the assessment or our curriculum for the future.