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## Objective

SWBAT figure out a combination of numbers to get to a specified total amount.

#### Big Idea

Different combinations of numbers give you different totals.

5 minutes

In this Introductory Video Road Trip, I explain our objective 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 have private work time to think about and plan how to solve the task.  Next, the students work in groups to explore the concept of the lesson.  Finally, the students share/analyze/and discuss the task as a whole class.  Each student has a copy of the task at their desk and a place value chart.  We have already learned how to use place value to add.

In today's lesson, the students use their understanding of adding with place value to solve this task without direct instruction.  They have to find the answers by adding multi-digit whole numbers using the standard algorithm (4.NBT.4).

I give the students about 5 minutes of independent time to read and plan to solve this Road Trip Task (MP1).  The students should have a place value chart at their desk.  The students can use the place value chart at this time to plan how to solve the task (MP5).   The place value chart will help the students understand that they must line the numbers up according to their places.  Each place has a certain value and they must be lined up according to their values.  After the 5 minutes of independent planning, the lesson goes to the next phase of group exploration.

Ethan’s family is going on a road trip!  They are visiting 3 locations.  His dad named 6 locations that they might travel.  His dad told him that if he adds the miles from their house in Boston to each one of these locations, it would be less than 2,950 miles.  Ethan is trying to figure out which 3 places they are going to visit.  Ethan’s dad loves for him to practice math so he will not tell him the locations.  Can you help Ethan find the 3 locations that they will travel?

 Location Miles from Ethan’s house Destin, FL 1,462 Orange Beach, AL 1,426 Memphis, TN 1,308 Houston, TX 1,840 New York, NY 215 Biloxi, MS 1,464

## Group Exploration/Discovery

20 minutes

During the group exploration/discovery phase, the students work in groups of 3.  Each group has a copy of the task.  The students must work together to complete all requirements of the task.  The students reason abstractly and quantitatively by decontextualizing the information and representing it symbolically (MP2).    During this phase, the students do not receive direct instruction.  In this lesson, they apply skills previously learned.   The students are guided to the conceptual understanding through questioning by their classmates, as well as by me.

The students are required to find the sum of multi-digit numbers (4.NBT.4).  The students communicate with each other and agree upon the 3 locations that Ethan's family traveled.  This takes discussion, critiquing, and justifying of answers by all 3 students (MP3).  Each group has a place value chart.  During this part of the lesson, the students should use the chart to line up the numbers according to place value (MP5).   As the groups discuss this task, they must be precise in their communication within their groups using the appropriate math terminology for this skill (MP6).

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

2.  What is the task asking you to find?  What operation would you use to find the total?

3.  Is there another way to add more than 2 sets of numbers?  How?

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.math-play.com/Addition-Game.html

## Share/Discuss/Analyze

15 minutes

During this phase of the lesson, student solution paths are 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 call groups to the front to share their solutions.  This is 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 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.   I begin with a group that did an excellent job at lining up their problems according to place value. The students share how they lined up their numbers and why they lined them up that way.  From there, we go into talking about adding more than 2 groups of numbers.  I bring out the point that when you are adding more than 2 groups of numbers, you can break them into separate addition problems.  I share an example of this strategy used by one of the groups. Last, we hear the solution to the task.  I call on one group to give us the 3 locations that Ethan and his family traveled. This groups shares that Ethan's family traveled to Destin, Memphis, and New York.

I feel that this is a well rounded lesson on how to add multi-digit numbers using place value because the students are responsible for their own learning.  They have been given the tools and resources necessary to accomplish solving the task.

## Closure

10 minutes

After the share/discuss/analyze phase of the lesson, close the lesson out by having the students do an Exit Ticket Adding Multi Digit Numbers.  This will enable me to see how well the students understood how to use a place value chart to add multi-digit numbers.

The students receive an exit ticket to complete their answers. Upon completion, I collect these exit tickets to evaluate the students' understanding.  Those students who need remediation will work with me in small group the next day