## We Are Having a Party! Part I

### Kristy RousseauBay District Schools

#### Description

Students follow a problem-solving plan to answer a class question. They generate, collect, organize, display, and analyze data to find the range of responses. This analysis is used to predict and justify reasonable answers.

#### Objectives

The student writes notes, comments, and observations that reflect comprehension of content and experiences from a variety of media.

The student solves problems by generating, collecting, organizing, displaying, and analyzing data using histograms, bar graphs, circle graphs, line graphs, pictographs, and charts.

The student determines range, mean, median, and mode from sets of data.

The student uses statistical data about life situations to make predictions and justifies reasoning.

#### Materials

-Small sticky notes (one per student)
-Chart paper or poster board for graph
-Copies of Individual Graph Template (See Associated File)
-Crayons or colored pencils
-Data Diaries (a math journal)

#### Preparations

1. Collect chart paper and sticky notes.
2. Make sure student groups have plenty of crayons or colored pencils.
3. Run copies of the Individual Graph Template. (See Associated File)
4. Make sure the problem-solving steps are highlighted on a visible poster or chart. (A master may be downloaded from the Associated File.)
5. Pre-label one sheet of chart paper with the title, "When should we have the party?" and another sheet with "Why do we need to know the range of a set of data?"

#### Procedures

PREREQUISITE KNOWLEDGE: Students should be familiar with reading bar graphs and the following problem-solving steps:
Step 1: Understand the problem
Step 2: Decide on a plan
Step 3: Carry out the plan
Step 4: Look back and review

1. Ask students what questions have to be answered in order to plan a party. Generate and record a list of their ideas on the board or chart paper. Explain that data analysis skills can be used to plan the perfect party. (Depending on the time of year when this lesson is completed, students could focus on The Perfect Birthday Party, or The Perfect Halloween Party, or The Perfect End-of-the-Year Party, etc.)

2. Tell the students that today we will follow our problem-solving steps to try and answer the question, “When should we have the party?” Review with them that Step 1 states we must make sure that we [Understand the Problem]. Ask, “What is the problem we will try to solve today?” (Answer: When should we have the party?)

3. State that Step 2 reminds us that we need to [Decide on a Plan]. Our plan is to gather data and make informed predictions and decisions based on the information collected. Let them know that today we will conduct an in-class survey to generate the needed information to answer the question, “When should we have the party?”

4. So, let's [Carry out the Plan]! Say, “Write on the sticky note the time of day that you think would be best to have the party. When you are finished, give the notes to the group manager who will then come and place them on this chart. (Chart paper should be labeled with the question “When should we have the party?”)

5. After group managers have placed the notes on the chart, give them copies of the Individual Graph Template (See Associated File) to distribute to each member of their group.

6. After all notes have been posted on the chart, ask the students if they see any patterns in the data. (If students fail to raise the issue that the data must be organized to reveal patterns, be prepared to lead them to this issue.)

7. Ask the students how they would organize the data. Guide them to see the need to develop a bar graph. Have the students use their Individual Graph Template to label the graph title and axes (Horizontal axis: Time of Day; vertical axis: Number of Responses) as you model on the chart paper.

8. Begin grouping the times on the chart paper by stacking up the sticky notes. As you build the graph on the chart paper, the students should be coloring in the grid boxes on their templates.

9. After the data has been organized and displayed, ask the students again for any patterns that they see. (They will probably identify the most popular answers, etc.)

10. Tell the students that today you are going to teach them how to “read” the graph like a mathematician. Explain that one part of the graph that mathematicians look at is the range of the data.

11. To access prior knowledge, and hopefully derail any misconceptions, ask students where they have heard the word “range” used before. Explain that mathematical ranges focus on the distance covered between the high and low values of a graph.

12. Direct the students' attention back to the bar graph and ask them to identify the low value on the graph. In the white space above the bar, have them draw an arrow and label it “low value.” (Beware: Some students may indicate the smallest bar as the lowest value. If for instance 10:30 only has one response and students identify this as the low value, ask them if there is another time that comes before 10:30 that was also listed. Help them to see that the low value is referring to the [first value] found along the horizontal scale.)

13. After identifying the low value, ask the students to identify the high value of the data. In the white space above the bar, have them draw an arrow and label it “high value.” (Hopefully they will recognize that it is the [last value] on the horizontal scale, but be ready to re-emphasize the fact that it is not the highest bar on the graph.)

14. Have the students draw a connecting line between the low and high value arrows, and label this area with the word “RANGE.” Reinforce that the range of a set of data is the distance, or area, covered between the highest and lowest values.

15. Ask the class to figure out how many hours are actually covered on this graph from the low value to the high value. (Allow students time in their groups to formulate answers.)

16. Solicit answers from the students and the process they used to find the number of hours. Explain that mathematicians subtract the highest and lowest value in order to identify the range with one number. Model this process by writing the math sentence on the chart as you think through the steps out loud. Tell the students that, “In our case, we would say the range was ____ hours.”

17. Along the line labeled “RANGE,” have the students write the math sentence used to describe the range. (i.e., RANGE = 6:00pm - 10: 30 am = 7.5 hours) Note: Finding the range for times may be more easily discovered using military time, so that 6 p.m. becomes 1800. Therefore, RANGE=1800-1030=730.

18. Ask students to discuss in their groups why they think mathematicians, and even ordinary people, would need to know the range of a set of data. Have guided questions prepared if groups are stumped. (i.e., “What does the range of our graph tell us?” “How does this information help us plan?” “When would be the earliest we could have our party?” “When would be the latest?” “Would we want to have the party at a time that falls outside the range of our data? Why or why not?”)

19. Solicit from each group a rationale or reason for finding the range. Discuss their responses as you list them on another sheet of chart paper.

20. Explain that tomorrow they will be working in stations to conduct simple experiments in order to generate, collect, organize, display, and analyze data for the range of responses.

#### Assessments

Have the students respond in writing to the following prompts on the bottom half of the Individual Graph Template:

·How did we solve our problem today?
·What does the range tell us about this set of data?
·Based on the data, when do you think we should have the party?
·Be sure to explain your answer.

Assess students' graphs and writing based on the following formative assessment criteria:

Students solved the problem by:
·generating a graph as modeled,
·determining the range as modeled,
·making a prediction based on the data, and
·explaining the reasons for their prediction.

Review their responses after class in order to gather evidence of misconceptions or understandings that need to be corrected and strengthened in part two of this lesson on range.

After reviewing the graphs and writing for their current understandings on how to determine the range and what the range tells us, have students store their completed Individual Graph Templates in their Data Diaries.

#### Attached Files

This file contains the Individual Graph Template and the Problem-Solving Steps.     File Extension: pdf