Mastering Rational Numbers

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SWBAT set a mastery goal of 80% for a chosen number sense skill needed in this unit: Ratios and Proportional Relationships.

Big Idea

students use results to diagnostic to choose skills which they need to work on to prepare for our ratios unit

Do Now

10 minutes

Students enter silently according to the daily entrance routine. Their Do Now assignments await them at their seats. Students are instructed to enter their answers into clickers as they complete the assignment. They are given 6 minutes to complete 5 questions. The results will be used to determine which worksheet students will collect to practice skills important to the ratio unit.

I stop the assessment after 6 minutes and view the results with students on the SMARTBoard. Questions 3 and 5 come up consistently, in all three of my 7th grade sections, as the least mastered questions. For question 3, ask students to visualize the positions of the numbers on a number line:



For question 5, as always, I am emphasizing neat work and following the order of operations:


After reviewing the solutions to these two problems, the top 4 scoring students will be allowed to move into booths to work for the rest of class.

All students will be asked to get ready to receive directions for the next section of class.

Intro to Activity

15 minutes

Students will receive a copy of the following slides from the Fraction and Decimal Skills Powerpoint: #3 – #7. The last three slides in this resource are offered as bonus questions for students to complete for homework. All of these slides are attached in the resource section of this lesson as PPT student resource.  I will begin the power point presentation by displaying the 3rd slide and reviewing the skills students encountered during the Do Now. It will be explained to students that they must choose two different skills from the list on this slide. Then I will ask students to view the next slide (#4 from the ppt) with me. This slide details the expectations of work that must be completed during class. There are three CW sheets with three stars marked across the top of each sheet. Each student must choose one of the following:

  • Operations with Decimals (a worksheet created using Kuta software)
  • Comparing Rational Numbers (a worksheet created using Kuta software)
  • Equivalent Fractions (worksheet attached and found in the Book of Fractions, a readily available resource online)

I printed out a total of 22 worksheets for students to choose from (all included in the resource section of the Independent Practice section), including the three listed above. For their second choice, students may select any other worksheet. I also make sure to push students to make their selections based on their performance on the exit ticket. For example, if a student missed questions 1 and 5, I may ask, “what skill do these questions cover according to the notes in the power point?” This way, students reflect on their performance and use it to inform themselves about the skills they need to continue practicing.

It may be a good idea to ask students to volunteer as models for how to choose their worksheets. I will bring up 1 – 2 students who do not mind sharing their results to the Do Now and explain which worksheets will push their mastery.

The goal is to save 5 minutes at the end of this section for student questions or to find a way to help students make selections quickly in order to move on to independent work time.

Independent Practice

20 minutes

All worksheets are displayed horizontally on a table(s) and students are sent in groups of 5 to make their selections. Students waiting for their turn should look back to their Do Now results and have an idea about the worksheets they will be selecting. After selecting their worksheets students are given instructions to return to their seats and begin working independently. All work must be shown on a separate sheet of paper complete with a heading and a title.

Once all students have made their selections they will be reminded that they must only complete 10 problems from each sheet and that this work will be turned in for a grade. Those who finish within class time, mastering 80% of the questions on each worksheet, will be receiving a HW pass.

Students are also encouraged to ask questions by raising their hands. I will be walking around with a whiteboard and dry erase marker to help any students I see struggling or asking for help. This is a good time to pair students strategically to help each other as well. Students showing work and completing the assignment quickly may be paired with students struggling and sent to a booth to work together.

All will be allowed to complete this assignment for homework if they are not able to finish during class.

Once a student finishes the work they will be instructed to come see me for a Work Completion Report . Before class I used a mail merge to include students’ names at the top. As students finish I will be giving them a completion report which I will sign to serve as a HW pass for any other future assignments. I will collect their work. Students who do not finish by the end of class will not receive this report and it will serve as a reminder of the students who have yet to turn in the assignment. 

As students continue to practice skills with rational numbers they may begin to notice the patterns within the processes of each operation (including comparing rational numbers through the use of a number line). This is MP8 in action. For more examples and descriptions of the Mathematical Practices check out this website.


10 minutes

Once there are 10 minutes left in class, I will hand every student an Exit Ticket. I will be using the results to inform my Do Nows and spiraled homework material to give all students. Any problem where more than 40% of the students are failing to master will continue to be spiraled and reviewed during class warm up and remediation periods.

If students complete this Exit Ticket before the end of class they may continue working on the class work. I will be completing reports for students who have not yet finished and/or answering any last minute questions about today’s class work. Homework will be distributed and the Exit Tickets will be collected once there are 3 minutes left in class.