Math Goodies: Developing Proficiency with Signed numbers

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SWBAT apply prior knowledge and develop proficiency with integers.

Big Idea

Students compete with thought-provoking tasks that improve their fluency with signed numbers.


10 minutes

As students walk into the class I hand each a Launch Ticket which serves as an "applying prior knowledge task". It's also a prelude to the "goodies" tasks they will be doing later in the lesson. I ask that each student work independently. Before letting students start, I call on someone to read the task intro and directions out loud, and then give the class a few minutes to complete it.  

I want to gauge student's mastery of the signed number rules, as well as refresh their knowledge of integer operations. Students should be done in about 5 to 7 minutes, and then I call on volunteers to share what they wrote for each operation with respect to Janiya's statement. I motivate students to express any doubt or ask any questions on the responses, allowing other students to answer their classmate's questions as much as possible.

In the task, Janiya makes a common mistake many students make, which is, not being totally clear when expressing themselves mathematically, omitting crucial terms or words. This may indicate lack of concept grasp. I inform students that this is a major issue when being assessed, because on any exam, the teacher cannot evaluate what is not written. I tell students that any written work on math assessments must be clear and precise. The teacher cannot guess what the students is thinking. Therefore, if it isn't written properly, then the student is not saying it, and hence, not answering the question. 

Activity / Application

50 minutes

For this activity I set up 5 stations, one at a desk, or at several desks pushed together, with enough chairs for small group of students (for two pairs of students in my case). I place a Station Task Sheet.docx containing two tasks at each station and hand each student a Task Worksheet.  

When a group (pair) of students arrives at a station, they should work together to solve the task,  yet each student should record the answers on his or her own worksheet to record the group's work. This helps keep students engaged in the activity and gives each student a record of the activity for future reference.

For this activity pairing up students according to similar ability is convenient, and I ask that they stay together and discuss each task among themselves, writing down answers only when both agree on them. I also inform them that either of students can be called to explain the task at the end of the activity.

Each station’s tasks should take approximately 8 minutes with a two-minute interval for moving from one station to the next. I find it is always helpful to give students two or three minute warning before it is time to change stations. At the end of the activity, I collect the worksheets to tally them up before our next class.

During our next class period I hand back worksheets with their scores and hold a brief discussion. At this time, I encourage students pose any questions they had about the tasks, but before responding, I ask if students in other groups encountered the same difficulty or if they have a response to the question. The class discussion is also a good time to reinforce issues or ideas related to the tasks.