More Perimeter Problems

10 min

Narrative

This True or False? routine prompts students to recall what they know about addition of fractions with a common denominator and about fractions that are equivalent to whole numbers. The understandings elicited here will be helpful later in the lesson when students find sums or differences of two fractions, or of a whole number and a fraction, to solve problems about the perimeters of rectangles with fractional side lengths.

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 strategies.
  • Repeat with each statement.

Student Task

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

  • 812+312+912+412=2\frac {8}{12} + \frac{3}{12} + \frac{9}{12} + \frac{4}{12} = 2
  • 204+104+64=8\frac{20}{4} + \frac{10}{4} + \frac{6}{4} = 8
  • 2=59100+41100+89100+111002 = \frac{59}{100} + \frac{41}{100} + \frac{89}{100} + \frac{11}{100}
  • 2=38+38+1282 = \frac{3}{8} + \frac{3}{8} + \frac{12}{8}

Sample Response

  • True: (812+412)+(312+912)=1+1=2\left(\frac{8}{12} + \frac{4}{12} \right) + \left(\frac{3}{12} + \frac{9}{12}\right) = 1 + 1 = 2
  • False: 204+(104+64)=5+4=9\frac{20}{4} + \left(\frac{10}{4} + \frac{6}{4} \right) = 5 + 4 = 9
  • True: (59100+41100)+(89100+11100)=1+1=2\left(\frac{59}{100} + \frac{41}{100} \right) + \left(\frac{89}{100} + \frac{11}{100}\right) = 1 + 1 = 2
  • False:
    • 38+38+128=188=228\frac{3}{8} + \frac{3}{8} + \frac{12}{8} = \frac{18}{8} = 2\frac{2}{8}
    • There are 2 groups of 88\frac{8}{8}s in 188\frac{18}{8}, with 28\frac{2}{8} left over.
Activity Synthesis (Teacher Notes)
  • “In each equation, how do we know that the sum of the fractions can be written as a whole number? For example, how do we know that 2412\frac{24}{12} and 364\frac{36}{4} each can be written as a whole number?” (There are 2 groups of 1212\frac{12}{12} in 2412\frac{24}{12} and 9 groups of 44\frac{4}{4} in 364\frac{36}{4}.)
  • “How do we know if any fraction is equivalent to a whole number?” (The numerator is a multiple of the denominator.)
Standards
Building On
  • 4.NF.3.b·Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.
  • 4.NF.B.3.b·Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. <span>Examples: <span class="math">\(\frac38 = \frac18 + \frac18 + \frac18\)</span>; <span class="math">\(\frac38 = \frac18 + \frac28\)</span>; <span class="math">\(2 \frac18 = 1 + 1 + \frac18 = \frac88 + \frac88 + \frac18.\)</span></span>

15 min

20 min