Represent Data in Scaled Bar Graphs

10 min

Narrative

The purpose of this Number Talk is to elicit strategies students have for counting by 2 and 5. These understandings help students develop fluency and will be used later in this lesson when students will use a scale of 2 or 5 to create bar graphs.

When students notice that the number of equal addends are doubled in the second expression, they are looking for and making sense of structure (MP7). When they notice that the pattern repeats in the second pair of expressions and use the pattern to find the value of the sum, they are also looking for and expressing regularity in repeated reasoning (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+22 + 2 + 2 + 2
  • 2+2+2+2+2+2+2+22 + 2 + 2 + 2 + 2 + 2 + 2 + 2
  • 5+5+5+55 + 5 + 5 + 5
  • 5+5+5+5+5+5+5+55 + 5 + 5 + 5 + 5 + 5 + 5 + 5
Solution Steps (4)
  1. 1
    Find 2+2+2+2 by skip counting
    →Count by 2s: 2, 4, 6, 8. Answer: 8
  2. 2
    Find 2+2+2+2+2+2+2+2 using doubling
    →8 twos = double of 4 twos. 8 x 2 = 16
  3. 3
    Find 5+5+5+5 by skip counting
    →Count by 5s: 5, 10, 15, 20. Answer: 20
  4. 4
    Find 5+5+5+5+5+5+5+5 using doubling
    →8 fives = double of 4 fives. 20 x 2 = 40

Sample Response

  • 8: There were four 2s, so I counted by 2 four times: 2, 4, 6, 8.
  • 16: I knew that four 2s was 8, and now there are 2 groups of 8, so I doubled 8 to get 16.
  • 20: I knew that 2 fives is 10 and there are 4 fives, so I doubled 10.
  • 40: I knew that four 5s was 20, and now there are 2 groups of 20, so I doubled 20 to get 40.
Activity Synthesis (Teacher Notes)
  • “How did the first two expressions help you solve the third and fourth expressions?” (I noticed there are double the number of 2s or 5s, so I can just double the sum.)
  • Consider asking:
    • “Who can restate _____’s reasoning in a different way?”
    • “Did anyone use 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
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. <em>For example, draw a bar graph in which each square in the bar graph might represent 5 pets.</em>
  • 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. <span>For example, draw a bar graph in which each square in the bar graph might represent 5 pets.</span>

10 min

25 min