Ways to Look at Triangles

10 min

Narrative

This Number Talk encourages students to use their understanding of mixed numbers and properties of operations to mentally solve problems. The strategies elicited here will be helpful as students develop their fluency in performing operations on fractions.

Launch

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

Student Task

Find the value of each expression mentally.

  • 12+12+7512 + 12 + 75
  • 1212+1212+7512\frac{1}{2} + 12\frac{1}{2} + 75
  • (2×1212)+(4×1212)(2 \times 12\frac{1}{2}) + (4 \times 12\frac{1}{2})
  • 7×12127 \times 12\frac{1}{2}

Sample Response

  • 99: 24+7524 + 75 is 1 less than 25+7525 +75, which is 100. One less than 100 is 99.
  • 100: 2×12=12 \times \frac{1}{2} = 1 and this sum is 1 more than the previous sum, which was 99.
  • 75: 2×12122 \times 12\frac{1}{2} is 25 and 4×12124 \times 12\frac{1}{2} is twice 25, which is 50. Adding 25 and 50 gives 75.
  • 871287\frac{1}{2}: 7×12127 \times 12\frac{1}{2} is 121212\frac{1}{2} more than 6×12126 \times 12\frac{1}{2}, which is 75. Adding 121212\frac{1}{2} to 75 gives 871287\frac{1}{2}.
Activity Synthesis (Teacher Notes)
  • “How is each expression related to the one before it?”
  • “How can the first three expressions help us find the value of the last expression?”
  • 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 expression in a different way?”
    • “Does anyone want to add on to _____’s strategy?”
Standards
Addressing
  • 4.NF.3.c·Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
  • 4.NF.4·Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
  • 4.NF.B.3.c·Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
  • 4.NF.B.4·Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

25 min

10 min