Methods for Multiplying Decimals

5 min

Narrative

This Warm-up prompts students to carefully analyze and compare multiplication expressions. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminologies that students know and how they talk about multiplication and equivalent expressions.

Launch

Arrange students in groups of 2–4. Display the expressions for all to see. Give students 1 minute of quiet think time. and ask them to indicate when they have noticed three expressions that go together and can explain why. Next, tell students to share their response with their group and then together to find as many sets of three as they can.

Teacher Instructions
 

Student Task

Which three go together? Why do they go together?

A

(0.1)⋅2⋅3(0.1) \boldcdot 2 \boldcdot 3

B

3⋅(0.2)3 \boldcdot (0.2)

C

(0.1)⋅3(0.1) \boldcdot 3

D

6⋅1106 \boldcdot \frac{1}{10}

Sample Response

A, B, C go together because they all have 3 and a decimal as factors.

A, B, D go together because they all have a value of 6 tenths or 0.6.

A, C, D go together because they all have 1 tenth as a factor.

B, C, D go together because they all involve only one operation.

Synthesis

Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations, and ensure that the reasons given are correct.

During the discussion, prompt students to explain the meaning of any term that they use, such as “factor,” “product,” “equivalent,” or “commutative,” and to clarify their reasoning as needed. Consider asking:

  • “How do you know . . . ?”
  • “What do you mean by . . . ?”
  • “Can you say that in another way?”
Extension
 
Extension Response
 
Standards
Building On
  • 5.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.
  • 5.NBT.B.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.
  • 5.NF.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
  • 5.NF.B.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

20 min

15 min