standard_description: Interpret multiplication as scaling (resizing), by:
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
problem_activity: Narrative
The purpose of this True or False is for students to demonstrate the strategies and understandings they have for dividing by powers of 10. In this lesson they will convert from a smaller metric unit to a larger unit which means dividing by an appropriate power of 10. The problems here are selected so that students can begin to see how the value of the digits in a number change when that number is divided by 100 or 1,000.
Launch
Display one equation.
“Give me a signal when you know whether the equation is true and can explain how you know.”
1 minute: quiet think time
Activity
Share and record answers and strategy.
Repeat with each equation.
Student Facing
Decide if each statement is true or false. Be prepared to explain your reasoning.
\(5 \div 1,\!000 = 0.05\)
\(36 \div 100 = 0.36\)
\(1,\!328 \div 1,\!000 = 1.328\)
Student Response
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Activity Synthesis
“How did you find the value of
\(1,\!328 \div 1,\!000\)
?” (I thought of it as 1,328 thousandths and then wrote that as a decimal.)


aligns: no