Estimated and exact sum with decimal numbers with 3 decimal places

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Students learn to add decimal numbers with up to 3 decimal places and to estimate the sum and calculate the exact sum.

CCSS.Math.Content.6.NS.B.3

It is useful to be able to calculate the estimated and exact sum of decimal numbers with 3 decimal places, so you can use the estimated total as a check to your exact sum. You need this to determine about how much objects weigh together, for example.

The interactive whiteboard shows decimal numbers with 1, 2, and 3 decimal points. Students must determine their order and set them in order from least to greatest. You can drag the numbers to the circles on the interactive whiteboard. Emphasize that a decimal number with 3 decimal places is not always greater than a decimal number with 1 or 2 decimal places.

To estimate the total of decimal numbers with three decimal places, students need to be able to round decimal numbers to whole numbers. Explain to students that they do so by looking which number a decimal number is closest to. You can also explain that with larger numbers, it can be useful to round to the tens or hundreds, to make estimation quicker. Next explain to students that that when adding decimal numbers with 1, 2, and 3 decimal places, it is useful to transform the number with less decimal place into a number with the same amount of decimal places. You do so by adding a 0, or 00 to the end. Then show how to add the two decimal numbers. First add by placing the first addend at the start of the number line, and then splitting the second addend. Add the whole number, and then the decimal places. Next show students that they can split both addends into whole numbers and decimal places, add those together and then add the totals. Using the story problems, have students practice both kinds of addition.

Check that students are able to calculate the estimated and exact sum of decimal numbers with 3 decimal places by asking the following questions:

- How do you round decimal numbers to determine the estimated sum?

- How do you add decimal numbers if you want to determine the exact sum?

- What is useful to do when adding decimal numbers with 1, 2 and 3 decimal places?

Students first practice adding decimal numbers with 2 and 3 decimal places. Then they are asked to solve using a story problem.

Discuss again why it is important to be able to calculate the estimated and exact sum of decimal numbers with 3 decimal places. By using the estimated sum to act as a check of your exact sum, you addition becomes quicker, easier and more accurate. Check that students are able to add the decimal numbers by splitting the second addend or by splitting both addends by doing the exercises on the interactive whiteboard as a class. Finally students must determine which child has thrown their spear the furthest. Ask how they determined their answer.

Students who have difficulty with this can be supported by adding on a number line. Encourage them to take smaller jumps in adding so they understand the progression.

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