Dividing Using Number Lines

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SWBAT to model and explain division using a number line.

Big Idea

Using a number line for division makes sense, once students see that they can represent any number on the line because they can add as many equal "parts" as they need to solve.


10 minutes

To begin this lesson, students review multiplication strategies with area models.  Students are given the task of picking numbers between 10 and 20 to determine an area to represent a space - classroom, library, or the front office of the school.  Working with a partner on whiteboards, students draw the area, label the sides, and then use the distributive property to find the total area.  For example, if the students use the number 15 x 18 they can use the property to find the area with:

(15 x 10) + (15 x 8) or (15 x 10) + (15 x 3) + (15 x 5)

Their diagram is divided to show these areas.  Once the students have successfully created their area model they record their process in their math journal.  I want them to explain how decomposing the multiplier or multiplicand by creating smaller rectangles makes it easier to find larger area measurements. 


10 minutes

Using a number line for division is an important aspect of utilizing the scope of Common Core strategies such as the relationship between multiplication and division or properties of operations (3.OA.7).  A number line is a critical mathematical tool. In this lesson, it helps students understand the structure of division sentences to identify if the unknown factor represents the groups or the number of items in a group. 

I begin with presenting the students with a division number sentence that they cannot calculate in their head.  Because my students are beginning to show mastery of  both division and multiplication facts, I choose numbers that are not easily calculated to keep the students engaged, and also to create a sense of purpose for the use of the number line to solve division problems. 

It is also important to place the numbers chosen in a meaningful context for the students, and I chose books for this lesson.  The library has received 108 books to be used by the third grade students.  Each student will receive nine books for summer reading.  How many students will receive books? 

Counting the number of jumps determines the unknown number of groups which is represented by the number of students receiving books. 

I repeat another example with the students, again using a facts that are not memorized by the students.  

Try It On Your Own

20 minutes

Students will be using number lines to solve division problems on their own.  The context for today's lesson is established by different materials placed in stations around the room.  I gathered different items including craft sticks, plastic counters, paper clips, beads, stickers, and rubber bands. I did not take the time to count out each group of items but rather just assigned an estimated quantity for each items.  Working in groups, the students move to a station with one of the items and use number lines to divide the quantities by 6 and by 3 to find the number of groups.  I chose numbers for the groups to be multiples of 6 and 3 above 100 based on my students' current knowledge.  This can be modified to meet the abilities of any student. 

It is important that students are writing their sentence structure using the format of: 

whole amount  ÷ items = groups

This structure is important because items can not be broken into separate pieces as students begin to encounter remainders with division in future grades.  The remainders represent partial groups rather than partial items. 

Students are given time at each station, and rotate on a given signal.  Students record the item, the number line, and the number sentence.  I kept the pace quick at the stations, and moved students every 3-4 minutes.


5 minutes

To end the lesson I ask the students to write the number line that is represented by how they sit in the classroom.  My room is set up into six different groups with four students.  I ask them to create the number line to show:

how many students are in the class  ÷ number of students at each group = six groups 

or 24  ÷ 4 = 6