Quotients - Just the Basics

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SWBAT use drawings to find the quantity unknown in division problems with dividends no larger than 30.

Big Idea

Just like multiplication, addition, and subtraction, division problems involve patterns and there are methodical ways in which manipulatives can be used to solve division problems with small dividends and divisors of 1 through 10.


3 minutes

Today students draw neat models of simple division problems, write the equations, and solve.  While drawing out division problems is not a long term strategy, as least not on a 1 item per one drawing basis (as opposed to graphically resembling larger groups - such as a symbol for 10 or 100), it is an important strategy when children are first grappling with the idea.  

All that is needed for today's lesson is scrap paper and a pencil, or a whiteboard and marker.  I printed out the papers because having the models to look at later in a quiet moment helped me plan for the next day's instruction.  (Misconceptions on paper are very visible).

Guided Practice

6 minutes

Remind students to make certain they are starting with the correct number, and also remind them to move their groups to distinct locations.  I show them several examples, either in these video clips showing 12 stones being divided into different equal groupings  and 18 stones being divided into different equal groupings, or use manipulatives on a document camera, or call students to the carpet and work with real objects.

Examples to model:

18 divided by 3 = 6

20 divided by 4 = 5

12 divided by 3 = 4

15 divided by 5 = 3 

Independent Practice

35 minutes

My goal is that by the the conclusion of this lesson, students will be able to solve division problems with dividends no larger than 30 by drawing out an equal groups model on paper.  In order for them to successful in using this strategy, it's important to closely monitor this independent or partner work.  

While this is rather easy for some students, others struggle with it and fail to make the connection between multiplication and division.  Some students may know how to parrot it, but underneath the words, the understanding is still developing.  If a student is really struggling, I either sit with them as they draw it out, build the model on a white board with them, or go and get some of the manipulatives and then have them draw out their solution after they have built it with cubes.


8 minutes

To close, I place students with a partner or within a small group and ask them to take turns explaining to each other how they used the strategy of splitting up the dividend into equal groups (divisor) to determine the amount in each group (quotient).  

Students are given a scenario for their work together. They are told to pretend that one of them is the teacher, and the other partner pretends they are a 2nd grade student who knows nothing at all about division.


2 minutes

I explain to the students that this homework page has 3 levels. They can choose the one that best suits them.  Version A has smaller numbers and it is recommended for students who are still really struggling with the concept.  Version B is for children who were able to successfully work through the guided practice most of the time. Answers to  questions, such this one where the student is asked to divide 30 as many different ways as possible, can be very informative and give me additional information about who is ready for something more complicated, which they will find on Version C of the homework.