Equivalent Decimals

10 min

Narrative

The purpose of this True or False is to revisit equivalent fractions in tenths and hundredths. The reasoning students do here will be helpful later when students make sense of and identify decimals that are equivalent to given fractions or given decimals.

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 statement.

Student Task

Decide whether each statement is true or false. Explain your reasoning.

  • 50100=510\frac{50}{100} = \frac{5}{10}
  • 2010=20100\frac{20}{10} = \frac {20}{100}
  • 2=1+901002 = 1 + \frac{90}{100}
  • 3110=31103\frac{1}{10} = \frac{31}{10}

Sample Response

Sample responses:
  • True, because 50 hundredths and 5 tenths are both 12\frac{1}{2}.
  • False, because 2010\frac{20}{10} is 2 and 20100\frac{20}{100} is less than 1.
  • False, because 1+901001 + \frac{90}{100} is 1901001\frac{90}{100}, which is less than 2.
  • True, because 3+1103 + \frac{1}{10} is 3010+110\frac{30}{10} + \frac{1}{10}, which is equal to 3110\frac {31}{10}.
Activity Synthesis (Teacher Notes)
  • “What do you know about the relationship between tenths and hundredths that helped you decide whether each statement is true or false?” (One tenth is 10 hundredths and one tenth is 10 times 1 hundredth. There are 10 tenths in 1 whole and 100 hundredths in 1 whole. If we multiply the numerator and denominator of a fraction in tenths by 10, we get an equivalent fraction in hundredths.)
Standards
Addressing
  • 4.NF.5·Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.
  • 4.NF.C.5·Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.<span>Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.</span> <span>For example, express <span class="math">\(3/10\)</span> as <span class="math">\(30/100\)</span>, and add <span class="math">\(3/10 + 4/100 = 34/100\)</span>.</span>

15 min

20 min