Estimating Products & Quotients

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Students will be able to use estimation to increase fluency when calculating decimal problems.

Big Idea

Decimal Round Up!: Using estimation to solve problems involving decimal quantities.

Curriculum Reinforcer

5 minutes

For today’s warm up exercise, I will have my students calculate the following problems:

  1. 3.78 x 2.4 =
  2. 3.02 - 1.7864 =
  3. 1.935 divided by .09 =

As my students are working on this warm up, I will be checking to see if my students are able to calculate with decimals properly when dealing with different operations. Often times, when students are calculating decimals using different operations, they get confused as to what to do with the decimals. For example, when multiplying they line up place values as if they were adding and when adding they count the digits behind the decimals as if they were multiplying. 



5 minutes

Today, I will facilitate a discussion concerning the meaning of estimation.

Guiding Questions:

  • What is estimation?
    • Students should respond that estimation involves rounding and provides a way to calculate using numbers that are easier to work with.
  • How do we estimate? What is the process of estimation?
    • Students should respond that you round the numbers that you are calculating with and then perform the operation presented in the problem.
  • Is rounding estimation?
    • Students should respond “no” but will probably say “yes.” What you want to convey to students regarding this questions is that rounding is only part of estimation.
  • Is estimation more than just rounding?
    • Students should respond “yes.” They should be able to tell you that you use numbers that have been rounded to calculate. The answer to that calculation that used rounded numbers is an estimation.


Instruction & Teacher Modeling

10 minutes

Using the opening discussion, I will segue into instruction concerning estimation. I will begin instruction with an activity that shows students how to round numbers.


Using three strips of paper, have students draw three number lines, one on each strip of paper. Using the number lines, the students will round the following quantities: 4.8, 75.4, and 9.5. The students will do this by placing each number on the number line where it belongs, in between the nearest whole number that is greater than the quantity and the nearest whole number that is less than the quantity.

After completing this activity, I will explain to students that now that they understand what it means to round quantities, now they can estimate sums, differences, products, and quotients. I will further explain that the purpose of being able to estimate in 6th grade is so that as a student you can check your calculations when calculating with decimals. If you are calculating 3.12 x 39.3 = you can look at this and use estimation to understand that your answer should be somewhere near 120... Why? Because 3 times 40 is 120. If you get something that is nowhere near 120 then, you know you did something wrong. I use this lesson to show my students how to check their decimal calculations for accuracy.


Try It Out

10 minutes

For the guided practice, I will have my students re-do the warm up problems using estimation.

Students will calculate the following problems using estimation.

  1. 3.78 x 2.4 =
  2. 3.02 - 1.7864 =
  3. 1.935 divided by .09 =

I will then begin a discussion by asking my students which way they thought was easier and why.


Independent Exploration

20 minutes

Students will complete a task (Estimation is the Root of Fluency) in which they will explore the significance of estimating. The students will complete this task individually. As they complete the task, I will travel the room to observe and assess students. I will be looking for common misconceptions and their ability to thoroughly explain their thinking in writing.


Closing Summary

20 minutes

I will select three students to present their work on the task. The manner in which I will make my selections will be based upon how the students answered the questions in the task. In particular, I will be looking for those students who provided thorough and correct explanations and accurate calculations. The selected students will place their work under the document camera so that all students are able to see their answers. They will discuss their answers and the process by which they came to their answers. The selected students will answer the questions that I will ask as well as those questions that their peers ask.

During the summary of this lesson, I will make sure to emphasize the fact that estimation is to be used to help students to assess the accuracy of their answers when calculating with decimals. Estimation is not a 6th grade standard and therefore, it is important to show students the relevance of this lesson to the 6th grade curriculum.