What Kinds of Shoes Are We Wearing?
BIG IDEA Data Relationships
CURRICULUM EXPECTATIONS
Students will:
• collect objects or data and make representations of their observations, using concrete graphs (e.g., conduct simple surveys and use graphs to represent the data collected from questions posed; use a variety of graphs, such as graphs using people to represent things, bar graphs, pictographs; use tally charts) ;
• respond to and pose questions about data collection and graphs.
MATERIALS
– shoes worn by students
– 3 sets of cards made from DRK.BLM1a–b: What Kinds of Shoes Are We Wearing? – chart paper
– interlocking cubes
– DRK.BLM2: What Kinds of Shoes Are in Our Home? (1 per student)
ABOUT THE MATH
Creating people graphs in which students themselves represent the data allows Kindergarten students to experience physically how information can be categorized. When students create people graphs, they are able to easily recognize the quantities of students in different groups and can readily compare quantities (e.g., “This group is larger than that group”).
Kindergarten students also learn that data can be represented in concrete graphs (e.g., bar graphs made with interlocking cubes). By observing, counting, and comparing the quantities in different parts of the graph, students can describe information presented in the graph.
In this activity, students create a people graph in which they themselves represent data, and then create a concrete graph using the same data. This experience helps students to understand that the same data can be represented in different ways.
KINDERGARTEN LEARNING ACTIVITY: DATA RELATIONSHIPS
GETTING STARTED
Begin a discussion about shoes by telling the following story to the class:
“Last weekend, I went shopping for a new pair of shoes. At the store, the salesperson showed me many different shoes. Some had laces just like [Jolene’s] shoes, others had sticky straps just like [Sunja’s] shoes, and others had buckles just like [May’s]. There were also some shoes that didn’t have fasteners – you just slip them on your feet. “After looking at so many different shoes, I began to wonder: What kinds of shoes do the students in this class have? How many students have shoes with laces? with sticky straps? with buckles? How many students have shoes that they just slip on? I had so many questions.
“I wonder if you can help me find the answers to questions about shoes in our class. How can I find out how many students in our class are wearing each kind of shoe?” Have students explain how they might find the number of students wearing each kind of shoe. For example, they might suggest that students create groups according to the kinds of shoes they are wearing, and then count the number of students in each group. Try the strategies students suggest and discuss whether they are good ways to find the number of students wearing each kind of shoe.
WORKING ON IT
Explain that creating a people graph is a way to find the number of students who are wearing each kind of shoe.
Show cards labelled “Laces”, “Sticky Straps”, “Buckles”, and “Slip On” (made from
DRK.BLM1a–b: What Kinds of Shoes Are We Wearing?) and discuss the kind of shoe that is represented by each card. Place the cards in a row, and ask students to stand in a line behind the card that represents the kind of shoe they are wearing. After students are standing in the appropriate line, have them sit down in their line.
Ask: “How could we find the number of students who are wearing shoes with laces? with sticky straps? with buckles? that just slip on?” Together, count the number of students in each line, and record the results on chart paper.
What Kinds of Shoes Are We Wearing?
Laces: 10
Sticky Straps: 6 Buckles: 1 Slip On: 5
KINDERGARTEN LEARNING ACTIVITY: DATA RELATIONSHIPS
Ask:
• “Which kind of shoe are most students wearing? How do you know?” • “Which kind of shoe are fewest students wearing? How do you know?” • “Are there more shoes with laces or with buckles? How do you know?”
Extend the activity in order to help students understand that the data about different kinds of shoes can be represented in different ways. Show the class four bowls labelled with a second set of cards made from DRK.BLM1a–b: What Kinds of Shoes Are We Wearing? Give students each an interlocking cube, and ask them to place their cube in the bowl that corresponds to the kind of shoe they are wearing. Ask: “How many cubes are in the bowl labelled ‘Laces’? How do you know?” Recognize that some students may be uncertain about the number of cubes in the bowl; they might not fully understand the one-to-one correspondence between each student and each cube. It is important to have students count the cubes and to connect the count with the data recorded earlier on chart paper. Discuss and count the number of cubes in the other bowls, and relate these numbers to the data recorded on chart paper.
Next, snap together the cubes in each bowl, and create a concrete bar graph. Use a third set of cards made from DRK.BLM1a–b: What Kinds of Shoes Are We Wearing? to label the bars.
Help students understand that the concrete bar graph contains the same data that students represented in the people graph they created earlier. Ask:
• “According to our concrete bar graph, how many students are wearing shoes with laces? with sticky straps? with buckles? that slip on?”
• “How do we know that the number of cubes in the ‘Laces’ bar is 10?”
• “How can we know the number of students in each group without counting the cubes?”