Number Talk

10 min

Narrative

This Number Talk encourages students to rely on the properties of operations and what they know about multiplication of a fraction and a whole number to mentally solve problems. The understandings elicited here will be helpful later in the lesson when students complete or create their own Number Talk.

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.

  • 6×146 \times \frac{1}{4}
  • 6×346 \times \frac{3}{4}
  • 18×3418 \times \frac{3}{4}
  • 180×34180 \times \frac{3}{4}

Sample Response

  • 64\frac{6}{4}, 1241\frac{2}{4}, or 1121\frac{1}{2}: 4×14=14 \times \frac{1}{4} = 1 and 2×14=122 \times \frac{1}{4} = \frac{1}{2}, so 6×14=1126 \times \frac{1}{4} = 1\frac {1}{2}.
  • 184\frac{18}{4}, 4244\frac{2}{4}, or 4124\frac{1}{2}: 34\frac{3}{4} is 3 times 14\frac{1}{4}, so it is 3 times the last product or 3×1123 \times 1\frac{1}{2}, which is 4124 \frac{1}{2}.
  • 544\frac{54}{4}, 132413 \frac{2}{4}, or 131213 \frac{1}{2}: 18 is 3 times as much as 6, so this product is 3 times as much as the last product. 3×412=1232=13123 \times 4\frac{1}{2} = 12\frac{3}{2} = 13\frac{1}{2}
  • 5404\frac{540}{4}, 130204130 \frac{20}{4}, 130102130 \frac{10}{2}, or 135: 180 is 10 times as much as 18, so this product must be 10 times as much as the last product. 10×13=13010 \times 13 = 130, 10×12=102=510 \times \frac{1}{2} = \frac{10}{2} = 5, 130+5=135130 + 5 = 135
Activity Synthesis (Teacher Notes)
  • “Today we are going to write our own Number Talk. Imagine the writer of this Number Talk started with ​6×146 \times \frac{1}{4}​. What did you notice about how each expression changed? What do you think the writer was trying to get you to notice?” (Each expression had a factor that changed by multiplying by 3 for the first two expressions and then by 10 for the last expression. I think they were getting us to notice how we can look for ways to make each expression easier to solve by using products we've already found.)
  • As needed: “How is each expression like the expression before it? How can you use that change to find each new value?” (Each expression has one factor that changes. If we think about how many times greater the factor is than the factor before it, we can use that to find the product.)
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.

20 min

15 min