Estimated and exact sum with decimal numbers with 1 and 2 decimal places

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Students learn to add decimal numbers with 1 and 2 decimal places and to estimate the sum and calculate the exact sum.

5.NBT.B.7

It is useful to be able to estimate and give the exact sum of decimal numbers with 1 and 2 decimal places so you can check if your exact answer is correct by using the estimated total. You need this to calculate about how much something weighs in total.

The interactive whiteboard shows three decimal numbers. Students must determine which of the three decimal numbers is the largest number. They can write the letter A, B, or C. Emphasize that a number with two decimal places is not always larger than a number with one decimal place.

To estimate the total of decimal numbers with one and two 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 and 2 decimal places, it is useful to transform the number with 1 decimal place into a number with 2 decimal places. You do so by adding a 0 at 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 add decimal numbers with 1 and 2 decimal places by asking the following questions:

- How do you round decimal numbers if you want to estimate a 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 decimal place to decimal numbers with 2 decimal places?

Students first practice adding decimal numbers with 1 and 2 decimal places. Then students are asked to calculate using a story problem.

Discuss with students that estimating the sum is useful because it gives an indication of what the exact sum should be- providing you a check for your exact total, as they should be quite close to each other. Check that students are able to calculate the estimated and exact sum by adding a 0 to the end of a decimal number and by splitting the second addend or both addends. As a class, solve the addition problem with weights given on the interactive whiteboard.

If students have difficulty with this learning goal, they can use the number line to add. Encourage them to take smaller jumps in their addition to help support their learning.

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