# Comparing and Ordering Numbers with a Number Line

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## Objective

SWBAT use number lines to compare and order numbers according to place value.

#### Big Idea

Putting numbers on a number line is a strategy that can be used to help students compare and order numbers.

## Opener

5 minutes

In this Using Number Lines Video.mp4, I introduce the lesson for today.

I let the students know that today we will do a task.  I remind the students of the structure and routine of a task.  First, the students will have private work time to think about and plan how to solve the task.  Next, the students will work in groups to explore the concept of the lesson.  Finally, the students will share/analyze/and discuss the task as a whole class.  Each student should have a copy of the task at their desk, as well as a number line to help solve the task.  We have already learned to compare numbers according to their place values.

In today's lesson, the students will use their understanding of comparing numbers by place value to solve this task without direct instruction.  They will have to compare multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. (4.NBT.2).

5 minutes

I give the students about 5 minutes of independent time to read and plan to solve this Compare and Order Number Task (MP1).  The students should have a Number Lines at their desk.  The students can use the number line at this time to plan how to solve the task (MP5).   The number line will help the students understand that they must place the numbers on the line according to the value of the numbers.  After the 5 minutes of independent planning, the lesson will go to the next phase of group exploration.

Compare and Order Number Task

Tim, Susan, James, Bobby, and Teresa each own very expensive watches.  I want to put the amounts on one number line in order from greatest to least.    Can you help me put all 5 numbers on one number line from greatest to least?

 Tim Susan James Bobby Teresa \$12,879 \$16,701 \$7,128 \$24,191 \$1,278

1.  Write the numbers in order from greatest to least.

2.  Write equations comparing the numbers using >, <, or =

3.  Write to explain how you solved the problem.

## Group Exploration/Discovery

20 minutes

During the group exploration/discovery phase, the students will work in groups of 3.  Each group will have a copy of the task.  The students must work together to complete all requirements of the task.  The students will have to reason abstractly and quantitatively by decontextualizing the information and representing it symbolically (MP2).    During this phase, the students will not receive direct instruction.   However, to give the students a visual guide, I will have a sample number line on the Smart board (How to use a number line).  I find that if I allow students to explore or figure things out for themselves, they tend to understand it better.   In this lesson, they should apply skills previously learned about comparing numbers using place value.   The students will be guided to the conceptual understanding through questioning by their classmates, as well as by me.

The students will be required to compare and order numbers according to their value by using the >, <, or = symbol (4.NBT.2).  The students must communicate with each other and agree upon the equation.  This will take discussion, critiquing, and justifying of answers by all 3 students (MP3).  Each group will have a number line.  During this part of the lesson, the students should use the number line to order the numbers according to place value (MP5).  Once they have ordered the numbers and written their equation, they must explain the steps in which they came up with their solution.  The written answer must be precise in explaining their steps (MP6).

During the phase, I will monitor and assess the students' progression of understanding through questioning.  Possible questions to help lead to the solution are as follows:

1.  How many digits are there in each number?

2.  What is your benchmark number on the number line?

3.  Is this number greater than or less than your benchmark number?

4.  Did you put your numbers on the number line from greatest to least or least to greatest?

5.  Can you explain the order of your numbers?

Any groups that finish the assignment early, can go to the computer to practice the skill at the following site until we are ready for the whole group sharing:  http://www.ezschool.com/Games/Compare.html

## Share/Discuss/Analyze

15 minutes

During this phase of the lesson, student solution paths will be shared.  While the students were working in groups and I was walking around questioning, I identified solution paths to be shared as a whole class for this phase.

I will call groups to the front to share their solutions.  This will be a teaching opportunity for the few students who may still not know how to add according to place value.  This part of the lesson is lead by the teacher through asking assessing questions.  The students may also have questions that they would like to ask.  I will use a document camera to display the student work on the Smart board for all students to see.

During this phase, I like to organize the sharing of the solution paths in a strategic manner.  For example, I may begin with a group that identified a benchmark number on their number line.  Students will need to understand that benchmark numbers on a number line help you add other numbers to the number line.  From there, I will have a group order the numbers in the correct way.  This should be evident on their number lines.  Next, we  will talk about how to write the equations using the >, <, and = sign.   Last, I will have a group share their written response to the task.

I feel that this is a well rounded lesson on how to use a number line to compare and order numbers.  Students need to know how to use various tools to help them when faced with a task.  The students will have to start taking responsibility for their learning.  When teachers supply the students with the tools and directions that are needed, they should be able to take responsibility for their own learning.

## Closure

10 minutes

After the share/discuss/analyze phase of the lesson, close the lesson out by having the students do an exit ticket.  This will enable me to see how well the students understood how to use a number line to compare and order numbers.

The students will receive an exit ticket (Exit Ticket Compare and Order Numbers with Number line.docx) to complete their answers.  I will collect these exit tickets to evaluate the students' understanding.  Those students who need remediation will work with me in small group the next day.