Decimals Part II

Learning Topics: 

Estimate products, multiply decimals & whole numbers, multiply decimals, estimate quotients, divide decimals by whole numbers, round quotients, divide decimals, solve word problems.

This page lists the Learning Objectives for all lessons in Unit 13.


Estimating Decimal Products

The student will be able to:

  • Define estimate, product, factors, estimation and compatible numbers.
  • Examine several strategies for estimating decimal products.
  • Examine examples using these strategies to estimate decimal products.
  • Recognize that estimates will vary depending on the strategy being used.
  • Determine if an estimated product is an overestimate or an underestimate.
  • Determine if an answer is reasonable using estimation.
  • 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 estimation strategies to solve problems.

Multiplying Decimals and Whole Numbers

The student will be able to:

  • Define powers, decimal digits and partial products.
  • Examine how a decimal number changes when it is multiplied by powers of ten.
  • Examine how a decimal number changes when it is divided by powers of ten.
  • Recognize, each time we multiply by a power of ten, the decimal point is moved one place to the right.
  • Recognize, each time we divide by a power of ten, the decimal point is moved one place to the left.
  • Examine examples in which a decimal is multiplied by a whole number.
  • Identify the number of decimal digits in a decimal.
  • Recognize that placement of the decimal point is very important
  • Examine detailed examples in which the product is estimated and computed.
  • Compare the estimate with the product to verify the answer makes sense.
  • Explain how (two) partial products are found.
  • Examine examples in which three partial products are found.
  • Describe the procedure for multiplying a decimal by a whole number.
  • Examine patterns of numbers being multiplied, and list each product using mental arithmetic.
  • Perform multiplication of a decimal and a whole number.
  • Identify where to place the decimal point in the product.
  • Apply multiplication procedures to complete five interactive exercises.

Multiplying Decimals

The student will be able to:

  • Recognize, when multiplying two decimals that are each less than one, the product will be less than each of the factors.
  • Examine detailed examples in which the product of two decimals is estimated and computed.
  • Compare the estimate with the product to verify the answer makes sense.
  • Connect decimal multiplication with place value.
  • Recognize that the sum of the number of decimal digits in each factor will yield the number of decimal digits in their product.
  • Describe the procedure for multiplying two decimals.
  • Perform multiplication of two decimals.
  • Evaluate a product by comparing it with an estimate.
  • Identify where to place the decimal point in the product.
  • Apply decimal multiplication procedure to complete five interactive exercises.

Estimating Decimal Quotients

The student will be able to:

  • Define quotient
  • Examine examples that use compatible numbers to estimate decimal quotients.
  • Recognize why compatible numbers is a good strategy for estimating decimal quotients.
  • Determine if an estimated quotient is an overestimate or an underestimate.
  • Determine if an answer is reasonable using estimation.
  • Connect overestimates and underestimates with the real world.
  • Estimate decimal quotients.
  • Apply estimation strategies to complete five interactive exercises.

Dividing Decimals by Whole Numbers

The student will be able to:

  • Identify the divisor, the dividend and the quotient in examples presented.
  • Examine detailed examples in which the quotient of a decimal by a whole number is estimated and computed.
  • Compare the estimate with the quotient to verify that the answer makes sense.
  • Describe the procedure for dividing a decimal by a whole number.
  • Recognize that the divisor can be greater than the dividend in a division problem.
  • Examine detailed examples in which the divisor is greater than the dividend.
  • Describe the procedure for dividing a decimal by a whole number when the divisor is greater than the dividend.
  • Examine patterns of numbers being divided, and list each quotient using mental arithmetic.
  • Perform division of a decimal by a whole number.
  • Identify where to place the decimal point in the quotient.
  • Apply division procedures to complete five interactive exercises.

Rounding Decimal Quotients

The student will be able to:

  • Examine detailed examples in which decimal is divided by a whole number.
  • Recognize when to round a decimal quotient.
  • Recognize, when rounding decimal quotients, we must divide to one more place than we are rounding to.
  • Describe the procedure for dividing a decimal by a whole number and then rounding the quotient.
  • Perform division of a decimal by a whole number and then rounding the quotient.
  • Apply decimal division strategies to complete five interactive exercises.

Dividing Decimals By Decimals

The student will be able to:

  • Recognize that multiplying both the divisor and dividend by the same power of ten maintains the equality of an expression.
  • Examine detailed examples in which two decimals are divided to find the quotient.
  • Examine detailed examples in which two decimals are divided, and the quotient is rounded.
  • Examine division problems that involve currency.
  • Describe the procedure for dividing two decimals.
  • Apply decimal division procedures to complete five interactive exercises.

Solving More 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 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.