Interpret Equations

10 min

Narrative

The purpose of this What Do You Know About ____? is for students to share what they know and how they can represent the number 32\frac{3}{2}. This will be useful when students write equations to represent the relationship between a division expression and a fraction in a later activity. Record answers on a poster because students will revisit their answers to the Warm-up during the Lesson Synthesis.

This is the first time students experience the What Do You Know About ____? routine in IM Grade 5. Students are familiar with this routine from a previous grade, however, they may benefit from a brief review of the steps involved.

Launch

  • Display the number.
  • “What do you know about 32\frac{3}{2}?”
  • 1 minute: quiet think time
Teacher Instructions
  • Record responses.
  • “How could we represent the number 32\frac{3}{2} ?”

Student Task

What do you know about 32\frac{3}{2}?

Sample Response

Sample responses:

  • It is more than 1.
  • It is equal to 1121\frac{1}{2}.
  • It is 3 groups of 12\frac{1}{2}.
  • It is 3÷23\div2.
Activity Synthesis (Teacher Notes)
  • “What diagrams can I draw to represent 32\frac{3}{2}?” (A number line, shaded rectangles, or a tape diagram.)
  • Draw the diagrams.
  • “How are the diagrams the same and different?”
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>

20 min

15 min