Share More Sandwiches

10 min

Narrative

The purpose of this Estimation Exploration is for students to use what they know about fractions to estimate how much of the tape is shaded. Students use what they know about division to determine how much of the bar is shaded.

Launch

  • Groups of 2
  • Display the image.
  • “What is an estimate that’s too high? Too low? About right?”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 1 minute: partner discussion
  • Record responses. 

Student Task

The whole rectangle represents 1. What fraction of the rectangle is shaded?

Rectangle. Less than 1 fourth shaded blue. 

Record an estimate that is:

too low about right too high

Sample Response

Sample responses:

  • Too low: 0 to 110\frac{1}{10}
  • About right: 16\frac{1}{6} to 15\frac{1}{5}
  • Too high: 13\frac{1}{3} to 12\frac{1}{2}
Activity Synthesis (Teacher Notes)
  • “How did you make your estimate?” (It looks like there are about 5 of those shaded pieces in the whole rectangle so that’s about 15\frac{1}{5}.)
Standards
Building Toward
  • 5.NF.3·Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. <em>For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?</em>
  • 5.NF.B.3·Interpret a fraction as division of the numerator by the denominator <span class="math">\((a/b = a \div b)\)</span>. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. <span>For example, interpret <span class="math">\(3/4\)</span> as the result of dividing <span class="math">\(3\)</span> by <span class="math">\(4\)</span>, noting that <span class="math">\(3/4\)</span> multiplied by <span class="math">\(4\)</span> equals <span class="math">\(3\)</span>, and that when <span class="math">\(3\)</span> wholes are shared equally among <span class="math">\(4\)</span> people each person has a share of size <span class="math">\(3/4\)</span>. If <span class="math">\(9\)</span> people want to share a <span class="math">\(50\)</span>-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?</span>

15 min

20 min