Lesson 18
Paint Splattered Bar Graph (optional)
Warmup: Number Talk: Subtract within 1,000 (10 minutes)
Narrative
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
Activity
 Record answers and strategies.
 Keep expressions and work displayed.
 Repeat with each expression.
Student Facing
Find the value of each expression mentally.
 \(530420\)
 \(530426\)
 \(535420\)
 \(535426\)
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
 Consider asking:
 “Who can restate _____’s reasoning in a different way?”
 “Did anyone have the same method but would explain it differently?”
 “Did anyone approach the problem in a different way?”
 “Does anyone want to add on to _____’s method?”
Activity 1: Student Population (15 minutes)
Narrative
The purpose of this activity is for students to analyze a given bar graph and answer questions involving addition and subtraction within 1,000 (MP2). Students may notice that some of the information for the grade 1 population on the bar graph has been hidden by a paint splatter.
In the last part of activity, students come up with their own mathematical question that can be answered using the graph. It is okay if some students come up with questions that require more than the given information. This is addressed in the next activity.
Launch
 Groups of 2
Activity
 “Oh no! Paint fell on the poster of the bar graph Clare and Priya created. Take a minute to look at their graph.”
 1 minute: quiet think time
 “Work with your partner on the questions about the bar graph.”
 7 minutes: partner work time
 Monitor for students who:
 write addition and subtraction equations.
 are able to reason why there is not sufficient information to compare the number of grade 1 students to grade 2 students.
 are able to use the features they can see in the graph to make assumptions about how many more students are in grade 2 than grade 1.
 ask questions that can be answered by adding and subtracting.
Student Facing
Oh no! Paint fell on the poster of the bar graph Clare and Priya created.
Answer the questions that you can with the graph. If a question cannot be answered, explain how you know.

What is the total number of students in grades 3 and 4?

How many more students are in grade 2 than in grade 1?

How many more students are in grade 3 than grade 2?
 Write at least 2 mathematical questions that can be answered using the bar graph.
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
 Invite previously identified students to share how they compared the number of students in each grade and what they noticed when comparing grade 2 and grade 1.
 Invite a few students to share one of their mathematical questions and give students a chance to discuss them with their partner.
 “You’ll each get a chance to ask your classmates one of your questions in the next activity.”
Activity 2: Asked and Answered (25 minutes)
Narrative
The purpose of this activity is for students to use information in a bar graph to answer their peers' mathematical questions.
In this activity, students exchange the questions they wrote in the previous activity and go through 3 rounds of answering new questions. Students may notice some questions require more than the given information and cannot be answered or cannot be answered precisely. For example, if students create a question that requires the grade 1 data, some students may argue that the question cannot be answered. However, others may decide to estimate based on the given information. Encourage students to justify their reasoning to convince others (MP3).
Advances: Conversing
Supports accessibility for: Memory, Organization
Launch
 Groups of 4
Activity
 “Trade a question that you came up with in the last activity with another partner. Answer each others’ question.”
 “If you cannot answer a question, be prepared to explain why you cannot answer the question based on the given information.”
 “If you have time, trade another question with a different partner.”
 Give students 3–4 minutes with each partner.
 9–12 minutes: partner work time
 Monitor for students who are able to reason why a question cannot be answered.
 Monitor for addition and subtraction expressions students write during the rounds and record a few on the board.
Student Facing
For each round:
 Trade one question you came up with in the last activity with a partner.
 Answer the question. Show or explain your reasoning.
 If you have time, trade another question with a different partner.
Round 1:
Round 2:
Round 3:
Student Response
For access, consult one of our IM Certified Partners.
Activity Synthesis
 Invite previously selected students to share their questions.
 “How did you decide if you had enough information to answer a question?”
 Point to the expressions recorded earlier.
 Consider asking:
 “What does this expression represent?”
 “How might you solve it?”
Lesson Synthesis
Lesson Synthesis
“Today, we analyzed a bar graph and answered questions using the information from the graph.”
“How did you know when you could answer a question by adding or subtracting?”