Compare and Order Decimals in Different Notations

10 min

Narrative

This Number Talk encourages students to rely on what they know about tenths and hundredths and about equivalent fractions to mentally solve problems. The reasoning elicited here will be helpful later in the lesson when students compare and order fractions and decimals.

Launch

  • Display one expression.
  • “Give me a signal when you have an answer and can explain how you got it.”
  • 1 minute: quiet think time
Teacher Instructions
  • Record answers and strategy.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 510+50100\frac{5}{10} + \frac{50}{100}
  • 510+55100\frac{5}{10} + \frac{55}{100}
  • 610+50100\frac{6}{10} + \frac{50}{100}
  • 610+65100\frac{6}{10} + \frac{65}{100}

Sample Response

  • 1: 510\frac{5}{10} is equivalent to 50100\frac{50}{100}, and 50100+50100=1\frac{50}{100} + \frac{50}{100} = 1
  • 105100\frac{105}{100} (or equivalent): 510\frac{5}{10} is equivalent to 50100\frac{50}{100}, and 50100+55100=105100\frac{50}{100} + \frac{55}{100} = \frac{105}{100}
  • 1110\frac{11}{10} (or equivalent): 50100\frac{50}{100} is equivalent to 510\frac{5}{10}, and 610+510=1110\frac{6}{10} +\frac{5}{10} = \frac{11}{10}
  • 125100\frac{125}{100} (or equivalent): 610\frac{6}{10} is equivalent to 60100\frac{60}{100}, and 60100+65100=125100\frac{60}{100} + \frac{65}{100} = \frac{125}{100}

Synthesis

  • Consider asking:
    • “Who can restate _____’s reasoning in a different way?”
    • “Did anyone have the same strategy but would explain it differently?”
    • “Did anyone approach the expression in a different way?”
    • “Does anyone want to add on to _____’s strategy?”
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>

25 min

10 min