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Learning Math Home
Data Session 10, Grades K-2: Solutions
 
Session 10 Session 10 K-2 Part A Part B Part C Part D Homework
 
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A B C D 

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Solutions for Session 10, Part B

See solutions for Problems: B1 | B2 | B3 | B4 | B5 | B6


Problem B1

Here are some possible statements that children might make:

 

There is a clump of data from 29 to 35.

 

I can see a bump at 30.

 

There is big gap from 15 to 20.

 

There are four holes in the data.

 

The data are spread out from 14 to 35.

<< back to Problem B1


 

Problem B2

 

The clump from 29 to 35 tells us that lots of boxes had this number of raisins.

 

The bump at 30 is the number of raisins that occurred most often when we were counting how many raisins were in a box.

 

The gap from 15 to 20 tells us that no boxes had 15, 16, 17, 18, 19, or 20 raisins in them.

 

The holes in the data tell us that at each point where there's a hole, there are no boxes with that number of raisins.

 

The "spread" of the data tells us that the smallest number of raisins (the "minimum") in a box is 14, and the largest number (the "maximum") is 35.

<< back to Problem B2


 

Problem B3

To get at the idea of "outliers," you might ask students whether there are any unusual data points on the graph. To focus on the variation in the data, you might ask students to talk about intervals where the data are clustered or concentrated, or where they are spread out. To introduce the concept of the median, you could ask students to try to find the center of the data set.

<< back to Problem B3


 

Problem B4

a. 

A sample answer is that the first graders are likely to notice that the mode for Mr. Mitchell's class is 34, whereas their mode was only at 30. They are also likely to point out that they had a "really low number" of raisins at 14, which was "a lot lower" than the lowest number from the second-grade class, 26. Students might also notice that their raisin data is more spread out with a larger range than the raisin data from Mr. Mitchell's class.

b. 

The first observations compare individual pieces of the data. The second observation compares the whole data sets to each other.

<< back to Problem B4


 

Problem B5

As data may be displayed in many ways, answers will vary; the representations listed here are only one option:

Question

Type of Data

Data Displays

a.

How many raisins are in a box?

quantitative (numeric)

line plot

b.

How far can you jump?

quantitative (numeric)

line plot

c.

Who is your favorite author?

qualitative (categorical)

bar graph

d.

How did you get to school today?

qualitative (categorical)

bar graph

e.

Are you 6 years old?

qualitative (categorical)

bar graph

f.

How many people are in your family?

quantitative (numeric)

line plot

g.

Will you go on the field trip to the zoo?

qualitative (categorical)

bar graph

h.

How many pockets do you have?

quantitative (numeric)

line plot

i.

How tall are you?

quantitative (numeric)

line plot

j.

Do you like chocolate milk or white milk better?

qualitative (categorical)

bar graph

k.

What is your favorite restaurant?

qualitative (categorical)

bar graph

l.

Which apple do you like best: red, green, or yellow?

qualitative (categorical)

bar graph

<< back to Problem B5


 

Problem B6

One example of a question that involves collecting quantitative (numeric) data and that often interests students in first or second grade is, "How many teeth have you lost?" An example of a question that involves collecting qualitative (categorical) data is, "What is your favorite pizza topping?"

<< back to Problem B6


 

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