Add, Subtract, and Multiply Fractions

10 min

Narrative

This Number Talk encourages students to think flexibly about numbers to multiply. The understandings elicited here will be helpful throughout this unit as students build toward fluency with multiplying fractions and whole numbers.

Students use what they know about fractions and equivalent fractions to apply the properties of operations to find the products (MP7). 

Launch

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

Student Task

Find the value of each expression mentally.

  • 5×1055 \times \frac{10}{5}
  • 9×639 \times \frac{6}{3}
  • 8×1148 \times \frac{11}{4}
  • 6×12106 \times \frac{12}{10}

Sample Response

  • 505\frac{50}{5} or 10:
    • I know that 105\frac{10}{5} is 2 and 5×25 \times 2 is 10.
    • If 5 fifths is 1, then 50 fifths is 10.
  • 543\frac{54}{3} or 18:
    • 6 thirds is 2, and 9×29 \times 2 is 18.
    • If 3 groups of 6 thirds is 18 thirds, which is 6, then 9 groups of 6 thirds is 3 times as much, which is 18.
  • 884\frac{88}{4} or 22:
    • 8×118 \times 11 is 88, so there are 88 fourths. I know 80 fourths is 20 and 8 fourths is 2, so 88 fourths is 20+220 + 2.
    • 114\frac{11}{4} is 11×1411 \times \frac{1}{4}. To find 8×11×148 \times 11 \times \frac{1}{4}, I multiplied 8 and 14\frac{1}{4} first, which is 84\frac{8}{4} or 2, and  2×11=222 \times 11=22.
  • 7210\frac{72}{10} or 72107\frac{2}{10} or 7157\frac{1}{5}:
    • 6 times 10 is 60, and 6 times 2 is 12, so 6 times 12 tenths is 72 tenths.
    • I know that 1210\frac{12}{10} is 12101\frac{2}{10}. I found 6×16 \times 1, which is 6, and 6×2106 \times \frac{2}{10}, which is 1210\frac{12}{10} or 12101\frac{2}{10}, and then I added them.
Activity Synthesis (Teacher Notes)
  • “How is the last expression different from the others?” (Sample responses:
    • The denominator in the fraction is not a factor of the whole number.
    • The whole number is not a multiple of the denominator in the fraction.
    • The value of the product is not a whole number.)
  • 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 problem in a different way?”
    • “Does anyone want to add on to _____’s strategy?”
Standards
Addressing
  • 4.NF.4·Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
  • 4.NF.B.4·Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

15 min

10 min

10 min