Unit 3 Multiplying and Dividing Decimals
Standards:
MCC5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number
by powers of 10, and explain patterns in the placement of the decimal point when a decimal is
multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
Perform operations with multi-digit whole numbers and with decimals to the hundredths.
MCC5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models
or drawings and strategies based on place value, properties of operations, and/or the
relationship between addition and subtraction; relate the strategy to a written method and
explain the reasoning used.
STANDARDS FOR MATHEMATICAL PRACTICE
Students are expected to:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
ESSENTIAL QUESTIONS
• How can we use models to demonstrate multiplication and division of decimals?
• What happens when we multiply decimals by powers of 10?
• How can we use exponents to represent the value of larger numbers?
• How can we describe the relationship between the number of zeroes and the exponent for
base ten?
• How do the rules of multiplying whole numbers relate to multiplying decimals?
• How are multiplication and division related?
• How are factors and multiples related to multiplication and division?
• What happens when we multiply a decimal by a decimal?
• What happens when we divide a decimal by a decimal?
• What are some patterns that occur when multiplying and dividing by decimals?
• How can we efficiently solve multiplication and division problems with decimals?
• How can we multiply and divide decimals fluently?
• What strategies are effective for finding a missing factor or divisor?
• How can we check for errors in multiplication or division of decimals?
Prerequisite Skills
l Place value of whole numbers, tenths, and hundredths
l Multiplication of whole numbers (2 digit by 2 digit and 3 digit by 2 digit)
l Division of whole numbers (using 1 and 2 digit divisors)
l The meaning of "product" and "quotient"
l Estimation concepts
l Decimal concepts
EVIDENCE OF LEARNING
 Students should demonstrate a conceptual understanding of
operations with decimals as opposed to a purely procedural
knowledge. For example, students should understand that if they
are multiplying tenths by tenths, the product must be expressed as
hundredths. (i.e., 1/10 x 1/10 = 1/100).
 Students should also know to round to the nearest whole number
and estimate to place the decimal
 using the estimate to determine the reasonableness of an answer,
rather than only knowing to count the digits after the decimal point
to place the decimal point in the answer.
By the conclusion of this unit, students should be able to demonstrate
the following competencies:
 understand place value
 use whole number exponents to denote powers of 10
 compare decimals
 model multiplication and division of decimals
 multiply and divide decimals by powers of 10
 use estimation when multiplying and dividing decimals
 multiply and divide decimals with fluency
 determine relationship between quantities algebraically
 recognize student errors in multiplication and division of decimals
 use decimals to solve problems