Divide and Conquer

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SWBAT to show what they know about adding, subtracting, and multiplying rational numbers by completing Quiz #5. SWBAT divide rational numbers.

Big Idea

Students take their weekly assessment and work independently to divide rational numbers

Do Now - Quiz

30 minutes

Students enter silently. Quizzes are on their desks and they are to begin as soon as possible. They are allowed to spread out and sit at empty tables. Instructions on the board direct students to stand up and turn in their quiz to receive their “Task + Homework” sheet.

Task + Homework

20 minutes

The front of the sheet reviews division of fractions and decimals. All of the steps in these processes are included so that most students can practice independently. During this time, students with extended time provisions will also complete quizzes. By structuring the worksheets this way on quiz days, I am free to help small groups of 3-4 students who need additional support with rational number operations. 

The back of the worksheet includes the actual problems for students to solve. The word multiplicative inverse is used in the directions for the problems, but the front uses the word reciprocal. It will be necessary to write the following on the board:

“Reciprocal – the multiplicative inverse of a fraction”


10 minutes

If all students complete their quizzes with time to spare, we will review the answers together. Students waiting for everyone in class to finish can copy their work and answers for targeted questions 12, 16, and 21 on the blackboard and white board at the front of the class. I pre-selected these specific problems to review because they each represent a skill(s) that are central to today's task. For example:

  • problem 12 will allow us to review the vocabulary term multiplicative inverse (reciprocal) as well as the process for writing a mixed number as an improper fraction, and THEN flipping the numerator and denominator to identify the reciprocal. As always, it is very important to use these opportunities so that students, not the teacher, are using the vocabulary to explain these processes. Scaffolding questions that could be used to guide students include:
    • what is another word for the multiplicative inverse? what is it?
    • if we have to "flip over a fraction" what should we do first? should we flip the fraction in this mixed number alone? what about the whole number in front of the fraction?
    • what mistake are you likely to make and how will you avoid making this mistake after you've turned the mixed number into an improper fraction? did anyone make the mistake of forgetting to flip the fraction after turning the mixed number into an improper fraction? how can we avoid making this mistake?
  • problems 16 and 21 will allow us to once again review writing mixed numbers as an improper fractions, as well as dividing signed fractions. 
    • what step should we do first? can we divide mixed numbers without turning them into improper fractions?
    • how do we divide fractions? Take 30 seconds to revisit the notes in front of the sheet.
    • what about the signs? are they different or the same? if they are different what does that mean about the answer? what if they are the same? 
    • did anyone forget to consider the signs? how can we avoid making this mistake?