 ## Grade 5 Math: Adding and Subtracting Decimals

### Adding Decimals: All Steps

In earlier lessons, students learn to add whole numbers using the standard algorithm. In this lesson, they extend what they learned in those lessons to add decimal numbers to hundredths.

They first learn to set up the problem in the vertical format, lining up like place values. When adding decimal numbers, this process starts with lining up the decimal points. When this is done, all the place values for the numbers will be lined up by like value.

When the problem is set up, adding proceeds from the smallest place value to the largest place value, which is right to left, as it does for whole numbers. Since students already know how to make a ten in any place, they use this strategy for regrouping. They regroup hundredths into tenths and tenths into units.

In doing the addition problems students are required to show the results of regrouping as notations at the top of the problem. Each digit in the answer and the regrouping notations are evaluated separately, and feedback is specific to each digit in the answer and the regrouping notations.

### Adding Decimals: Answer Only

In this lesson, students solve the same kinds of addition problems for decimals as in the prior lesson.

The only difference is that in doing the addition problems students are not required to show the results of regrouping as notations at the top of the problem, but only enter their final answer, which is evaluated in its entirety.

### Subtracting Decimals: All Steps

In earlier lessons, students subtract whole numbers using the standard algorithm. In this lesson, they extend what they learned in those lessons to subtract decimal numbers to hundredths.

They first learn to set up the problem in the vertical format, lining up like place values. When subtracting decimal numbers, this process starts with lining up the decimal points. When this is done, all the place values for the numbers will be lined up by like value.

When the problem is set up, subtraction proceeds from the smallest place value to the largest place value, which is right to left, as it does for whole numbers. Since students already know how to regroup by breaking a ten in any place, they use this strategy for regrouping when needed for subtraction. They regroup by breaking hundredths into tenths and tenths into units.

In doing the subtraction problems students are required to show the results of regrouping as notations at the top of the problem. Each digit in the answer and the regrouping notations are evaluated separately, and feedback is specific to each digit in the answer and the regrouping notations.

### Subtracting Decimals: Answer Only

In this lesson, students solve the same kinds of subtraction problems for decimals as in the prior lesson.

The only difference is that in doing the addition problems students are not required to show the results of regrouping as notations at the top of the problem, but only enter their final answer, which is evaluated in its entirety.

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