## Up on Top

In this lesson students generate bar graphs. Posing and answering questions using the graphs gives them an opportunity to apply their reasoning and communication skills. They also consider whether a given category is likely, certain, or impossible.

Invite the students to name the different colors of hair they have seen in the school. Then have the students write their hair color on an index card and form groups according to their hair color. (Creating a human graph, as done in the previous lesson on eye color, can help the students with various learning styles to make essential connections.) Display a blank horizontal bar graph on the board, and select students to title the graph and to fill in the row names with hair colors represented in the class.

**The Color of Our Hair**

Blond | |||||||||

Brown | |||||||||

Black | |||||||||

Red |

Ask one student from each group to tell how many are in his or her group. Then ask for a volunteer to color in bars representing the number of students in his or her hair-color group and label the row with the appropriate number. When the bar graph is completed, call out two hair colors and ask which has the longer bar. Ask the students what it means when you compare the two bars. Invite the students to tell which hair color appears most frequently. Then ask them to find the range and mode for this data set.

Project the Create a Graph Tool and select the "Bar Graph" option from the drop-down menu found near the bottom of the page. Ask a student to enter the data into the recording section. Call on students to choose a name for the bar graph and the colors of the bars. Choose the orientation [horizontal] of the graph to match the graph that is on the board. Then select a student to hit the "Generate graph" command.

In the example above, 4 students had blond hair, 6 had brown hair, 9 had brown hair, and 3 had red hair.

Ask the students to tell what they can learn from the chart about the colors of hair represented in the room. Ask the students to write two questions under the graph that can be answered by using the data displayed on the graph. When they have done so, call on various students to read their questions for the rest of the class to answer.

Next, ask the students to put their index cards upside down in a pile where all can see them. Select one of the cards at random, and call on students to tell which color they think it will be. Repeat several times.

Next, ask whether they think there is any color of hair that could not come up when a card is drawn. (Impossible hair colors will vary according to the colors represented in your class.) Tell the students that they are describing impossible events.

In order for students to experience certain probabilities, ask whether there is any color of hair that is sure to come up when a card is drawn. (Whether or not any hair colors are certain depends on the hair colors represented in your class.) Tell the students that they are describing events said to be certain.

To acquaint students with the likelihood that an event will occur, ask the students whether there are any hair colors that occur frequently in the class. Introduce the word "likely" by saying, "If I draw a card without looking, is there any color that you think will be more likely than others to come up?"

Ask the students to look at the graph to see whether the graph can help them answer the question. [The hair colors represented by the longer bars are more likely to come up.] Then ask what "certain" means and whether any of the hair colors are certain to come up. Repeat with "impossible." You may wish to begin these discussions with outrageous impossible events (for example, there is a live elephant in class today) and clearly certain events (for example, a given student is breathing). Call on several volunteers to name a hair color and tell whether it is likely, certain, or impossible to come up when an index card is drawn.

- Crayons
- Index cards
- Paper
- Create a Graph Tool

**Assessment Options**

- You may wish to make entries on the Class Notes recording sheet concerning the progress of the students toward the learning goals of this lesson. You might also attach notes to work samples of individual students who demonstrate competence with the mathematical concepts of this lesson or students who need additional practice with specific concepts. Keeping these observations about their strengths and needs can provide information for future instructional planning and feedback for a variety of audiences.
- You may wish to collect the graphs generated by the students for their unit portfolios. Save one copy of the bar graph for use in Lesson Four.

**Extensions**

- On Create a Graph Tool site, you can also generate a pie chart. Although the students at this level may not be able to construct a pie chart, they may enjoy seeing this popular graph. To generate it, choose the "Pie Chart" option when you get to the site. You may wish to have students compare these two forms of representation. They might say, for example, that a bar graph is a graph that uses bars to show data, whereas a pie chart uses sections or slices of a whole to show data.
- Alternatively, you may compare two data sets. Tell the class
they will visit another class and collect two pieces of data from one
or more students in that class--the color of each student's eyes and
hair. After they have returned to their own classroom, divide the class
into two groups. Assign one group to make a bar graph with the
eye-color data and the other group to make a pictograph with the
hair-color data from the students in the buddy class.
Now display the bar graph from their own class survey on eye color and ask them to compare it with the buddy class bar graph. Call on volunteers to describe any similarities and differences they see. If they do not mention the range and the mode, prompt these responses. Repeat with the hair-color graphs

- Move on to the last lesson,
*Look at Me: Making Glyphs*.

**Questions for Students**

1. How many different hair colors can we see in the classroom? How does this information help us make a bar graph?

[Answers will depend upon the class data set.]

2. What words did we use to describe this set of data?

[Range and mode.]

3. Suppose that a new child came into the class and he had red hair. How would that change our graph? (Repeat with other scenarios.)

[Answers will depend upon the class data set.]

4. Suppose that a brown-haired child in the class moved away. How would that change our graph? (Repeat with other scenarios.)

[Answers will depend upon the class data set.]

5. How many students had black hair? Brown hair? How can you tell that from looking at the graph?

[Answers will depend upon the class data set; By looking at the lengths of those corresponding bars.]

6. What is the mode of our data set? The range? How would you tell a student from another class how to find those answers?

[Answers will depend upon the class data set; Look at the longest bar; Compare the shortest and longest bars.]

7. If one of our class index cards for hair color were drawn without looking, are there any hair colors that would be impossible to draw? Are there any colors that would be certain? Are any colors more likely to be drawn than the other hair colors?

[Answers will depend upon the class data set.]

**Teacher Reflection**

- Which students remembered how to construct a bar graph? Which remembered how to find the range and the mode? Were they able to use this vocabulary correctly?
- Were all the students able to form questions that could be answered by looking at the bar graph? Were they able to answer the questions posed by other students?
- Could the students name events that were certain and impossible? Could they identify likely events?
- Which students could justify their answers clearly and correctly?
- Would I make any adjustments the next time that I teach this lesson?

### Freckle Face

### The Eyes Have It

### Making Glyphs

### Learning Objectives

Students will:

- Create bar graphs.
- Find the range and mode of a data set.
- Determine whether an outcome is possible, likely, or certain.

### NCTM Standards and Expectations

- Pose questions and gather data about themselves and their surroundings.

- Represent data using concrete objects, pictures, and graphs.

- Discuss events related to students' experiences as likely or unlikely.

### Common Core State Standards – Mathematics

Grade 1, Measurement & Data

- CCSS.Math.Content.1.MD.C.4

Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Grade 2, Measurement & Data

- CCSS.Math.Content.2.MD.D.10

Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.