# Decimals – Adding and Subtracting

## Learning Objectives for all Adding and Subtracting Decimals lessons in Unit 12.

**Introduction to Decimals**

The student will be able to:

- Define decimal, mixed number, whole number, fraction, place value, expanded form, decimal digits and equivalent decimals.
- Identify the whole number and fractional parts of a decimal.
- Identify the purpose of using decimals.
- Recognize connections between decimal numbers and place value.
- Write decimals in expanded form.
- Write whole numbers as decimals.
- Recognize that writing a decimal with a zero in the one’s place helps us remember that the number is less than one.
- Recognize that the decimal point is used to separate the whole number part from the fractional part.
- Apply decimal concepts to complete five interactive exercises.

**Reading and Writing Decimals**

The student will be able to:

- Define equivalent fractions.
- Write mixed numbers as decimal numbers.
- Write phrases as decimal numbers.
- Recognize that decimal places change by a factor of ten.
- Recite and write decimal numbers using words.
- Distinguish between the value of two hundred thousand, two hundred thousandths and two hundred-thousandths.
- Distinguish between the written phrases decimals such as for 0.110 and 0.0100.
- Apply reading and writing of decimals to complete five interactive exercises.

**Comparing Decimals**

The student will be able to:

- Identify the equality and the inequality symbols used to compare two decimals.
- Compare two decimals using a place-value chart.
- Express the comparison using the proper symbols.
- Recognize the importance of writing one decimal below the other when comparing two decimals.
- Recognize that writing one or more zeros to the right of the last digit of a decimal does not change its value.
- Compare two decimals without a place-value-chart.
- Describe the procedure for comparing two decimals.
- Apply the procedure for comparing two decimals to complete five interactive exercises.

**Ordering Decimals**

The student will be able to:

- List three or more decimals in order from least to greatest using a place-value chart.
- Recognize the need to compare decimals two at a time when ordering three or more decimals.
- List three or more decimals with varying places in order from least to greatest.
- Recognize the need to write one decimal beneath the other when ordering decimals.
- Recognize the need to place a number in a circle to the right of each decimal when ordering decimals.
- Solve non-routine and open-ended problems by comparing and ordering of decimals.
- Describe the procedure for ordering three or more decimals from least to greatest
- Apply the procedure for ordering three or more decimals to complete five interactive exercises.

**Estimating Decimal Sums**

The student will be able to:

- Define estimate, overestimate and underestimate.
- Describe the front-end and rounding strategies for estimating decimal sums.
- Apply these strategies to estimate decimal sums.
- Recognize that the use of different strategies can result in different estimates.
- Determine if an estimate is an overestimate or an underestimate by comparing it with the actual sum.
- Explain the difference between an overestimate and an underestimate.
- Apply estimation strategies to complete five interactive exercises.

**Adding Decimals**

The student will be able to:

- Examine examples of adding two decimals with varying places after the decimal point.
- Examine examples of adding three decimals with varying places after the decimal point.
- Examine examples of adding currency.
- Describe how to carry when adding decimals.
- Examine examples of adding decimals in which carrying is performed more than once.
- Describe the procedure for adding two or more decimals.
- Perform addition of two or more decimals to find the sum.
- Recognize the importance of lining up all the decimal points in a column before adding.
- Connect decimals and money.
- Apply decimal addition strategies to complete five interactive exercises.

**Estimating Decimals Differences**

The student will be able to:

- Recognize that estimation is an important tool in our daily lives.
- Estimate decimal differences by rounding to various places.
- Determine whether an estimate is reasonable or unreasonable.
- Develop a sense of which place to round to when estimating decimal differences.
- Recognize that estimates may vary for the same problem.
- Recognize, when estimating differences, the estimate should not exceed the original numbers.
- Apply estimation strategies to complete five interactive exercises.

**Subtracting Decimals**

The student will be able to:

- Examine simple examples of subtracting two decimals in which borrowing is performed.
- Examine examples of subtracting two decimals with varying places, and in which borrowing is performed.
- Recognize the importance of writing one or more extra zeros to the right so that both decimals have the same number of decimal digits.
- Describe the procedure for subtracting decimals.
- Examine examples of subtracting currency.
- Perform subtraction of decimals
- Connect decimals and money.
- Apply decimal subtraction strategies to complete five interactive exercises.

**Solving Decimal Word Problems**

The student will be able to:

- Examine examples of real-world problems involving decimals.
- Examine the solution presented for each problem.
- Examine five interactive exercises with real-world problems involving decimals.
- Analyze each problem to identify the given information.
- Formulate a strategy for solving each problem.
- Apply decimal strategies to solve problems.

**Practice Exercises**

The student will be able to:

- Examine ten interactive exercises for all topics in this unit.
- Determine which strategies and procedures are needed to complete each practice exercise.
- Compute answers by applying appropriate decimal strategies and procedures.
- Self-assess knowledge and skills acquired from this unit.

**Challenge Exercises**

The student will be able to:

- Evaluate ten interactive exercises with word problems for all topics in this unit.
- Determine which strategies and procedures are needed to complete each exercise.
- Apply decimal strategies and procedures to solve routine and non-routine word problems.
- Synthesize all information presented in this unit.
- Connect decimals to the real world.
- Develop problem-solving skills.

**Solutions**

The student will be able to:

- Examine the solution for each exercise presented in this unit.
- Identify which solutions need to be reviewed.
- Compare solutions to completed exercises.
- Identify and evaluate incorrect answers.
- Amend and label original answers.
- Identify areas of strength and weakness.
- Decide which strategies and procedures need to be reviewed from this unit.