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

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Students learn to estimate the total and find the exact total of decimal numbers with 1 or 2 decimal places.

5.NBT.B.7

It is useful to be able to add decimal numbers with 1 or 2 decimal places exactly, and to be able to estimate the sum, so you can use the estimation as a check for the exact total. You need this if you want to know, for example, about how much you have to pay.

The interactive whiteboard shows a number line from 0 to 1 and a few decimal numbers are given. The students must determine where the numbers belong on the number line and draw a line to that location. Emphasize that numbers with two decimal places is not always bigger than a number with 1 decimal place.

To estimate the sum of decimal numbers with 1 or 2 decimal places, students must be able to round the decimal numbers to whole numbers. Explain that students can do this by looking at which whole number the decimal number is closest to on the number line. You can also explain that it is sometimes easier to round to a tens or hundreds, to make estimation faster. Next, explain how students can add decimal numbers with one decimal place. Show this on the number line adding by splitting the second addend. The first addend is at the start of the number line. Then you add the whole number(number before the decimal point), and then you add the decimal places(number after the decimal point). You can also show students how to add by splitting both addends into whole numbers, and decimal places. You add the whole numbers together, add the decimal places together, and then add those two totals together. Using a story problem, show the different methods of addition again. Have students practice adding decimal numbers with 1 or 2 decimal places again.

To check that students are able to add decimal numbers with 1 or 2 decimals and can give an estimated and exact sum, you can ask the following questions:

- How do you round the decimal numbers to estimate the sum?

- How do you add decimal numbers if you want to know the exact total?

- How do you know if the exact answer is correct?

Students first practice adding decimal numbers with 1 decimal place. Then they practice adding decimal numbers with 2 decimal places. They are finally asked to solve both kinds in story form.

Discuss with students that it is important to be able to estimate the sum so you can check your exact sum as well- as these totals should be close to each other. Check that students are able to estimate the sum and determine the exact sum by splitting the second addend, or by splitting both addends by asking them how they would solve the given addition problems. They are then given two receipts with two purchased items. Students must calculate the estimated and exact sums.

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!---Teaching tips

If students have difficulty with this goal, they can use the number line to add the decimal numbers together, potentially using smaller jumps to add the numbers together.

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