More Questions about Scaled Bar Graphs

10 min

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for adding groups of 2 and groups of 5. These understandings help students develop fluency and will be helpful later in this lesson when students need to use data in scaled bar graphs to solve one- and two-step 'how many more?' and 'how many fewer?' problems. Students use the structure of the expressions and repeated reasoning when they use methods based on skip-counting by 2 or 5 or counting on 2 or 5 from a previous known value (MP7, MP8).

Launch

  • Display the first 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 strategies.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 2+2+2+2+22 + 2 + 2 + 2 + 2
  • 2+2+2+2+2+22 + 2 + 2 + 2 + 2 + 2
  • 5+5+5+5+5+55 + 5 + 5 + 5 + 5 + 5
  • 5+5+5+5+5+5+55 + 5 + 5 + 5 + 5 + 5 + 5
Solution Steps (4)
  1. 1
    Find 2+2+2+2+2 (five 2s)
    →Skip count by 2: 2, 4, 6, 8, 10
  2. 2
    Find 2+2+2+2+2+2 (six 2s)
    →One more 2 than before: 10 + 2 = 12
  3. 3
    Find 5+5+5+5+5+5 (six 5s)
    →Skip count by 5: 5, 10, 15, 20, 25, 30
  4. 4
    Find 5+5+5+5+5+5+5 (seven 5s)
    →One more 5 than before: 30 + 5 = 35

Sample Response

  • 10: I skip-counted by 2 five times: 2, 4, 6, 8, 10.
  • 12: It is 1 more 2 than the first problem, 10+2=12.10+2=12.
  • 30: I counted by 5.
  • 35: It is 1 more 5 than the problem before this.
Activity Synthesis (Teacher Notes)
  • "What is a strategy that you hadn't used before that you might use in the future?" (Think about 1 more group if I already know part of the problem or skip-count.)
  • Consider asking:
    • "Who can restate _____'s reasoning in a different way?"
    • "Did anyone use the same strategy but would explain it differently?"
    • "Did anyone solve the problem in a different way?"
    • "Do you agree or disagree? Why?"
Standards
Building On
  • 2.OA.4·Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
  • 2.OA.C.4·Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
Building Toward
  • 3.MD.3·Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step 'how many more' and 'how many less' problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
  • 3.MD.B.3·Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step 'how many more' and 'how many less' problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

20 min

15 min