Interpret Relationships

10 min

Narrative

The purpose of this True or False is for students to demonstrate understandings they have for the relationship between multiplication and division. Students will use this understanding in the lesson when they recognize multiplicative relationships between patterns.

Launch

  • Display one statement.
  • “Give me a signal when you know whether the statement is true and can explain how you know.”
  • 1 minute: quiet think time
Teacher Instructions
  • Share and record answers and strategy.
  • Repeat with each problem.

Student Task

Decide if each statement is true or false. Be prepared to explain your reasoning.

  • 276÷3=13×276276 \div 3 = \frac{1}{3} \times 276
  • 276÷3=2766276 \div 3 = \frac{276}{6}
  • (276÷3)×2=23×276(276 \div 3)\times2=\frac{2}{3}\times 276

Sample Response

  • True: 276÷3=2763=13×276276 \div 3 = \frac{276}{3}=\frac{1}{3}\times 276
  • False: It's 276 thirds not sixths.
  • True: I just multiplied the right hand side of the first equation by 2.
Activity Synthesis (Teacher Notes)
  • “How can the relationship between multiplication and division help you justify your reasoning?” (I used the fact that dividing by 3 is the same as multiplying by 13\frac{1}{3}.)
Standards
Addressing
  • 5.NF.B·Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
  • 5.NF.B·Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Building Toward
  • 5.OA.3·Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. <em>For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.</em>
  • 5.OA.B.3·Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. <span>For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.</span>

20 min

15 min