The purpose of this True or False is for students to demonstrate strategies they have for relating division of two whole numbers to multiplication of a fraction by a whole number. The reasoning students use here helps to deepen their understanding of the relationship between multiplication and division. It will also be helpful later when students find the area of rectangles with mixed number side lengths.
Launch
Display one equation.
“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 if each statement is true or false. Be prepared to explain your reasoning.
10÷3=10×31
10÷3=1031
310=5×32
Sample Response
True: There are 10 groups of 31 in 310.
False: 1031 is greater than 10 and much greater than 10÷3.
True: 5 groups of 32 is 310.
Activity Synthesis (Teacher Notes)
“How can you explain your answer to the last statement without finding the value of both sides?”
Standards
Addressing
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
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Fractional Side Lengths Greater than 1
10 min
Narrative
The purpose of this True or False is for students to demonstrate strategies they have for relating division of two whole numbers to multiplication of a fraction by a whole number. The reasoning students use here helps to deepen their understanding of the relationship between multiplication and division. It will also be helpful later when students find the area of rectangles with mixed number side lengths.
Launch
Display one equation.
“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 if each statement is true or false. Be prepared to explain your reasoning.
10÷3=10×31
10÷3=1031
310=5×32
Sample Response
True: There are 10 groups of 31 in 310.
False: 1031 is greater than 10 and much greater than 10÷3.
True: 5 groups of 32 is 310.
Activity Synthesis (Teacher Notes)
“How can you explain your answer to the last statement without finding the value of both sides?”
Standards
Addressing
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>