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 place value chart to help solve the task. We have already learned how place value can help with addition and subtraction.
In today's lesson, the students use their understanding of 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).
Mr. John lives on a farm. He has 1,265 cows, 432 chickens, and 793 pigs. How many animals are there on Mr. John's farm?
1. Write each number on the place value chart.
2. Write an equation or equations to solve the problem.
3. How many animals are there on the farm?
4. Write to explain how you solved the problem.
I give the students about 5 minutes of independent time to read and plan to solve this 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 will go to the next phase of group exploration.
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 should 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 must communicate with each other and agree upon the equation. 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). Once they have come up with their addition equation, they must give the sum of animals on the farm, as well as 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 can you use the place value chart to help you add?
2. What is the task asking you to find? What operation would you use to find the total?
3. How many numbers will you have in your equation?
4. 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
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. For example, I begin with a group that did an excellent job at lining up their problems according to place value. From there, we go into talking about how to write the equations. 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 student work that shows this example with the entire class. Last, I love for my students to be able to write about what they have done. I have a group share their written response to the task.
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.
After the share/discuss/analyze phase of the lesson, close the lesson out by having the students do an exit ticket. This enables 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 Adding Multi-Digit Numbers to complete their answers. 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.