Using place value to divide

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SWBAT explore patterns in the base ten system and make conjectures.

Big Idea

In this lesson, students use place value reasoning, base ten manipulatives, and proof drawings to divide by ten and see relationships between digits and place value.

Warm Up

15 minutes

I begin this warm up with a fluency practice.  I ask students what fluency or fluent means.  I then lead a brief discussion and explain that in mathematics fluently means quickly and accurately. I use various resources for students to practice fluency.  The resource used in this lesson has students practice multiplying and dividing by 10.  This fluency practice is adapted from

One fluency practice, as used in this lesson is using what you may refer to as fast facts, mad minutes, or sprints.  Since I am a runner, I choose to use the word sprints with my students, often referring to training techniques.   Written directions for the sprints are located in the resources.

Upon completion of the sprints, I remind students of their previous learning by displaying a place value chart to ten thousand.  I write the number 67 in the place value chart and I direct students to use their personal whiteboards to show a proof drawing of 10 x 67. 

Some students may want to simply add a 0, but I encourage the use of the proof drawing to ensure depth of understanding. 

I ask one or two students share responses.

Concept Development

30 minutes

I begin this lesson by posing this situational problem to students; Suppose I had $2,000 to share equally with 10 people.  How might you use a proof drawing or base ten blocks to figure out how much money each person would get?  I give students a few minutes to solve the problem with a partner and then ask two or three students to share their strategies and thinking.

Students should use prior knowledge from previous lessons to relate place value and making smaller units.  2 thousands is equal to 20 hundreds.  20 hundreds divided by 10 is 2 hundreds.  Each person would get 2 hundreds or $200.   As students share, I record their numbers into the corresponding places on a place value chart on the board.  I use arrows pointing to the right with a division symbol to show that 2 thousands is equal to 20 hundreds and that they are dividing by 10 each place value move to the right.

I continue to pose similar problems. For example, I use the numbers 6,000, 3,000 and 7,000. As students solve and share, I observe their strategies and thinking.  After students solve these problems, I pose another situational story in which more than one unit is used.  I tell students, imagine that you have 3,200 legos to share equally with 10 friends for building.  How many legos will each friend get?  I direct students so solve this situational problem with a learning partner using a proof drawing, place value chart, or base ten blocks. When most students are finished, I ask two or three students to share their thinking using the classroom document camera to show the class. 

Students should respond with 3 thousands, and 2 hundreds is the same as 30 hundreds and 20 tens.  30 hundreds divided by 10 is 3 hundreds and 20 tens divided by 10 is 2 tens.  Each person would get 3 hundreds and 2 tens or 320 legos.




Student debrief - Wrap Up

10 minutes

For this lesson, I use an exit ticket as an informal formative assessment.  I direct students to write 5 thousands and 6 hundreds or 5,600 ÷ 10 = _____

Students should respond with 560 or 5 hundreds and 6 tens.  I make two piles of responses, incorrect and correct.  I then go through the incorrect responses and make instructional decisions for those students based on their responses.


Note:  In analyzing this exit tickets, 97% of my students answers correctly.