investigation involves the students in a research project dealing with
pictures such as those commonly found in primary levels of elementary
school mathematics textbooks and workbooks. The students conduct a
survey of people representing various age groups to determine what
number stories such pictures bring to their minds. Completing this
activity will (1) sharpen students' appreciation of the need for
standardized methods of data collection; (2) reinforce the concept that
a picture without a number story can match with a variety of number
sentences, and (3) illustrate that several different interpretations of
the operations of addition and subtraction are possible.
To start the lesson, bring five people to the front of the room, and
then call three more. Ask the group of five to stand on one side of the
room; ask the group of three to stand on the other side of the room.
Encourage the class to tell mathematics stories about the situation
at the front of the room, and ask for number sentences to match each
Write all number sentences generated by the students on the chalkboard. Possible number sentences include:
5 + 3 = 8
3 + 5 = 8
8 – 3 = 5
8 – 5 = 3
After several stories and number sentences have been identified,
arrange students in groups of two. One student should draw a simple
story, similar to the one enacted in class. The other student should
write a number sentence that corresponds to the story. Both students
should discuss other possible number sentences. The students then
switch roles and repeat the activity.
Using story books from the classroom library, try to find an
example of such problems. These books typically have one number
sentence that is supposed to match each picture. Show the examples to
the children, and ask them if they can think of other stories and
number sentences that might match the picture
Ask students what they think it means to be a researcher? Discuss
the students' responses. Ask students how a survey is used. Once again,
discuss the students' responses.
Show students an overhead of What's the Story? activity sheet.
Ask students what kind of data could be collected by showing
people these pictures. As the class discusses survey questions, guide
the students into these two main questions:
- What types of responses do different people give to the pictures?
- Do people of different ages give different types of responses?
Distribute copies of the What's the Story?
activity sheet and data recording sheet. Read the directions at the
bottom of the What's the Story? activity sheet. After each direction,
ask the children to explain why they think each of these directions is
important. Suggested responses to each direction follow:
- The more people we survey, the more data we will have. The more
data we have, the easier it will be to see patterns to help answer our
- If people who are surveyed hear other people's responses, they may be
tempted to respond in the same way.
- It will be interesting to see if the mathematics story matches the number sentence.
- Adults might interpret the pictures differently than children
do. Also, all the information from one person needs to be on one piece
of paper so that all the data are kept together.
After discussing each point, you may wish to pair the children and
ask them to role play the parts of researcher and subject. Researchers
ask questions and record responses without comment; subjects "read" the
pictures and give responses.
Assign the survey for homework, asking for all data to be returned
after two or three days. Students should find at least two people to
survey. One of these people should be an adult, and the other person
should be a child. Each student will need at least two copies of the
Data Recording Sheet, which is found in the same file as the What's the Story? activity sheet.
When all surveys have been completed, place the children in
groups of three or four to share their data from the first picture (the
Ask the children to make a list or table of addition and
subtraction number stories or number sentences that their subjects told
them while looking at the rabbits picture, along with the number of
people who told each kind. A sample data table follows:
|Rabbit Story |
|Addition Story (16 People) |
|3 + 1 = 4||6 People|
|1 + 3 = 4||10 People|
|Subtraction Story (12 People) |
|4 - 1 = 3||6 People|
|3 - 1 = 2||5 People|
|4 - 3 = 1||1 Person|
Ask each group to share its data with the rest of the class. On the chalkboard or on chart paper, make a class list of results.
Discuss all stories and number sentences to make sure that they are
mathematically correct. Justifiable number sentences for the first
problem include the following:
4 ‑ 1 = 3
3 + 1 = 4
3 ‑ 1 = 2
1 + 3 = 4
4 ‑ 3 = 1
These results can lead to a discussion of many different topics, including:
- Commutative property ("order property"); 3 + 1 = 1 + 3
- Number families
- Different meanings for subtraction
- Take away: 4 ‑ 1 = 3; how many are left?
- Comparison: 4 ‑ 1 = 3; how many more are in the bigger group
If you see little variety in the data collected by your
students, you might wish to offer some of these number sentences to
encourage discussion among your students.
Challenge the children to analyze their data again—first in
their small cooperative groups, and then as a class—to determine
whether a relationship exists between a subject's age and his or her
choice of number story or sentence. You may wish to have each group
record the results of these analyses on the reproducible Picture This data sheet.
After the entire class has shared their results, place the compiled class data on a clean version of the data sheet.
Follow the same procedure for the second problem.
Possible solutions for this problem include:
4 + 2 = 6
6 - 2 = 4
6 - 4 = 2
6 - 2 = 4
2 + 4 = 6
6 - 6 = 0