SCORE Mathematics

Standards Connections

Sorting Through Spiders

Helen Jo Morse

 

Education means developing the mind, not stuffing the memory.
- Anonymous

Grade levels: K-3 (This lesson was written with 2nd grade standards in mind but it may be adapted to several other grades.)

Introduction:
Children need extensive opportunities to think about, question, discuss and manipulate data in order to learn how to ask and answer the whys in mathematics. In this activity, children will utilize their own drawings of spiders to analyze and sort the attributes that each child drew. I leave it very open-ended for the students to choose the categories from which to sort.

Objective:
Introduce children to analyzing and classifying data in different ways.
       I. Sorting in general groups
       II. Introduction to Dichotomous Keys
       (Optional: Assess students' scientific knowledge of spiders)

Evaluation:
Student observation is the key to assessment as this is a group activity. Can the students sort the illustrations into logical groups and explain why they did so? Can students make observations, generalizations, comparisons, and extensions regarding the data collected? If written evidence is preferred, children may write what they observe and/or draw a representation of the sorting strategy used.

Prior Knowledge:
Experience with sorting, graphing and the language connected to both is helpful, but this lesson may be used as an introduction to these concepts.

Learning Advice:
Any illustration or object may be used, not just spiders. Use your curriculum or the students' interests to generate ideas. With kindergarten or 1st grade, I would begin with concrete objects (teddy bears, shoes, hats, etc.) It could even be a good way to get to know each other at the beginning of the year by asking children to draw their favorite activity, sport, book character, or themselves. This lesson may be used for a purely mathematical purpose, without the science. However, I prefer to integrate and make learning as meaningful as possible, hence the science connection. I have used the drawing technique as a pre- and a post-assessment of knowledge. Save all the illustrations to show growth in understanding of a concept.

I broke the lesson into 3 days (or sessions) because of depth of understanding I hope to achieve. Depending on the focus, it could be a one or two day activity. Hopefully, the concepts will be revisited several times during the year with a different object to be analyzed. Also, depending upon the size of your class, you may choose to only use 10-12 pictures at a time or work in smaller groups.

Dichotomous keys are tools used by scientists and naturalists to identify specific names of natural objects, such as trees, ferns, wildflowers or insects. "Dichotomous" means "divided into two parts", so there are always two choices in a step to identification, usually in the form of a positive and a negative. That is, if looking at spiders, you may begin by sorting them into "spiders who are black" and "spiders who are not black". In science, a single object is taken through these steps until an identification is made. I've turned this around to be able to have a group contribute and sort several items at once.
       Sample sites for other dichotomous key lessons:
      Dichotomous Key - An AskERIC Lesson Plan http://www.eduref.org/cgi-bin/printlessons.cgi/Virtual/Lessons/Science/Process_Skills/SPS0002.html
      Dichotomous Plant Key  http://www.nps.gov/goga/parklabs/library/plantkey.htm

Activity Resources:
All these items are optional dependent upon how you approach the activity:
       objects to sort
       drawing paper
       pens, pencils, markers and/or crayons
       floor graph
       long pieces of yarn to create sorting circles
       butcher paper to chart out key
       large index cards or sentence strips

Spider Resources (for the teacher):

"Spider Pages" has good cross-curricular activities
http://www.powerup.com.au/~glen/spider.htm
Letsfindout Kid's Encyclopedia to search for information on specific spiders
http://www.letsfindout.com
O. Orkin Insect Zoo
http://www.mnh.si.edu/museum/VirtualTour/Tour/Second/InsectZoo/
Myths, stories, poems, songs and art of spiders
http://www.arachnology.org/
This has more links
http://www.austmus.gov.au/spider/li.htm
More unit ideas
http://www.viking.stark.k12.oh.us/~greentown/spiders.htm
And one last link to classroom activities
http://www.sedl.org/scimath/pasopartners/spiders/background.html

Process:

Day One: Introduction and Creation of Materials
1. Ask students to draw a spider and include details they know about them. Preferably, pictures should be larger than life (full page) so others can see them when presented to a group.
2. Have children share and describe their pictures either in small groups or with the whole class.
3. Are the children beginning to notice similarities or differences between other students' work? If not, prompt them to begin discussing what they notice.
4. Collect the pictures or have the children keep them in their desks until Day Two.

Day Two: Sorting and Graphing Activities
1. Redistribute or ask children to take spider pictures out of their desks.
2. Gather on carpet in circle, with pictures on floor in front of the students.
3. Lay floor graph or two sorting circles on carpet in center of children. Ask the class: What is a way we can sort/graph our spiders? Children will choose groupings but you may need to help them narrow it down. The more ways the children have of looking at and analyzing the information before them the better their learning will be. Write labels for the groups on the index cards or sentence strips (better yet - have the child who chose the grouping write the label). Each student will then place their picture where they think it is appropriate. Problem solve as a group any discrepancies that arise. Do more groups need to be added? Discuss what they notice when activity is complete. If needed, question them to compare data or ask "What if.." to bring them to a higher level of thinking. Honor different students' ideas by resorting the pictures several times. You may wish to keep the headers that are written to put on the wall for the children to refer to and read.
4. If you began with sorting circles, try laying out the pictures on a floor graph or just sort them in straight lines on the carpet. Children need not only the practice thinking about data, but need experience organizing it in different ways. Reuse the circles to create Venn diagrams, too. Much more than one day could be spent on these activities.
5. At this time, there is a choice in how to continue the lesson depending upon your purpose:
       a. Go on to Day Three.
       b. Create KWL chart (a 3 part chart: what we KNOW, what we WANT to know, and what we LEARNED) from the information shown and discussed about spiders. Fill in what we KNEW and what we want to LEARN from this point on. Use this information to begin spider unit. Revisit chart and re-illustrate spiders at end of unit, then key the (hopefully) more detailed spiders out.
6. At the end of the session, put the pictures away once more, or post the bar graph up on a wall. We have a magnetic bulletin chalk board, so we leave it up with magnets for a day or two.

Day Three: Dichotomous Keys
1. Look at spider illustrations yet once again. Review some of the attributes that were noticed and discussed the last time they were graphed and sorted. If you kept the category or header cards, this would be helpful.
2. Choose ONE attribute to focus on. Have children divide themselves into two groups, those that have this attribute and those that do not. Use butcher paper, or just a chalk board, to record this. Begin at the center top with a box entitled "Spiders". Draw two diagonal lines in different directions down from it and connect to additional boxes with the "has" and "has not" attributes your class has chosen.
3. Choose a second attribute. Both of the previous two groups will subdivide into two more groups by this attribute (so now there should be four groups). Add the new information to the chart, then continue on and sort out each group as many times as possible. For example, if you began sorting the pictures by spiders who are "black" and "not black", there should be two groups. Then, the class may decide to group by spiders who are "in webs" and "not in webs". Both the black spiders and not black spiders will divide again and four groups are created: black spiders in webs, black spiders not in webs, not black spiders in webs and not black spiders not in webs. Can the children sort themselves out so each child is in a group by themselves? Can the children remember their list of attributes they were sorted by? The pictures themselves my be sorted at the end and put on a bulletin board with the appropriate headings.

Extensions: Can a pattern be created with the pictures? Try to have the children find a way to do this without using colors.
Use the illustrations at a center for the children to continue exploring ways to sort and graph the pictures.
Have commercial dichotomous keys available for the children to use. Take a "field trip" around your school and identify trees, plants or critters. I know in California they are written for specific regions. The keys are very inexpensive (usually $3-$4) and are available at local bookstores in the nature section.

Conclusion:
Just have fun with these activities! It is very exciting for me to listen to the children talk mathematics. In doing activities of this kind, the discussions and reasoning of the students is a wonderful insight into how they really see and understand the concepts of analyzing and sorting data. Sometimes their suggestions may seem at first to be quite far-fetched, but have them explain why they think this, and you have a much more in depth assessment of a child than any standardized test will ever give you.


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California Academic Content Standards:

Grade 2:
Statistics, Data Analysis, and Probability
1.0 Students collect numerical data and record, organize, display, and interpret the data on bar graphs and other representations:
1.2 Represent the same data set in more than one way (e.g., bar graphs and charts with tallies).
1.4
Ask and answer simple questions related to data representations.

Mathematical Reasoning
1.0 Students make decisions about how to set up a problem:

1.1 Determine the approach, materials, and strategies to be use.

2.0 Students solve problems and justify their reasoning:

2.1 Defend the reasoning used and justify the procedures selected.

 

Optional Science Standards if a complete study of spiders is undertaken

02 life 2a: Organisms reproduce offspring of their own kind The offspring resemble their parents and each other.
02 life 2b: The sequential stages of life cycles are different for different animals.
02 life 2c: Many characteristics of an organism are inherited from the parents. Some characteristics are caused by, or influenced by, the environment.
02 life 2d: There is variation among individuals of one kind within a population.
02 iexx 2c: Compare and sort common objects based on two or more physical attributes.
02 iexx 2d: Write or draw descriptions of a sequence of steps, events, and observations.
02 iexx 2e: Construct bar graphs to record data using appropriately labeled axes.
02 iexx 2f: Write or draw descriptions of a sequence of steps, events, and observations, and include the use of magnifiers or microscopes to extend senses.
02 iexx 2g: Follow verbal instructions for a scientific investigation.

NCTM Standards:

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January 2000 / Revised June 19, 2000
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