A sequence is an arrangement of things or events in a particular order. When you are asked to sequence
objects or events within a group, figure out what comes first, then think about what should come second. Continue to choose objects or events until all of the objects you started
out with are in order. Then, go back over the sequence to make sure each thing or event in your sequence logically leads to the next.
A sequence with which you are most familiar is the use of alphabetical order. Another example of sequence would be the steps in a recipe, as shown in Figure 2. Think about
baking bread. Steps in the recipe have to be followed in order for the bread to turn out right.
If you were taking an automobile trip, you would probably take along a road map. The road map shows
your location, your destination, and other places along the way. By looking at the map and finding where you are, you can begin to understand where you are in relation to other
locations on the map.
A concept map is similar to a road map. But, a concept map shows relationships among ideas (or concepts) rather than places. A concept map is a diagram that visually shows how
concepts are related. Because the concept map shows relationships among ideas, it can make the meanings of ideas and terms clear, and help you understand better what you are studying.
There is usually not one correct way to create a concept map. As you construct one type of map, you may discover
other ways to construct the map that show the relationships between concepts in a better way. If you do discover what you think is a better way to create a concept map, go ahead
and use the new one. Overall, concept maps are useful for breaking a big concept down into smaller parts, making learning easier.
Tree Look at the concept map about U.S. currency in Figure 3. This is called a network tree. Notice how some words are in rectangles while others are written across
connecting lines. The words inside the rectangles are science concepts. The lines in the map show related concepts. The words written on the lines describe the relationships between
When you are asked to construct a network tree, write down the topic and list the major concepts related to that topic on a piece of paper. Then look at your list and begin to
put them in order from general to specific. Branch the related concepts from the major concept and describe the relationships on the lines. Continue to write the more specific
concepts. Write the relationships between the concepts on the lines until all concepts are mapped. Examine the concept map for relationships that cross branches, and add them to
the concept map.
Events Chain An events chain is another type of concept map. An events chain map, such as the
one describing a typical morning routine in Figure 4, is used to describe ideas in order. In science, an events chain can be used to describe a sequence of events, the steps
in a procedure, or the stages of a process.
When making an events chain, first find the one event that starts the chain. This event is called the initiating
event. Then, find the next event in the chain and continue until you reach an outcome. Suppose you are asked to describe what happens when your alarm rings. An events chain map
describing the steps might look like Figure 4. Notice that connecting words are not necessary in an events chain.
Cycle Map A cycle concept map is a special type of events chain map. In a cycle concept map, the series of events does not produce a final outcome. Instead, the last
event in the chain relates back to the initiating event.
As in the events chain map, you first decide on an initiating event and then list each event in order. Because
there is no outcome and the last event relates back to the initiating event, the cycle repeats itself. Look at the cycle map describing the relationship between day and night in
Spider Map A fourth type of concept map is the spider map. This is a map that you can use for
brainstorming. Once you have a central idea, you may find you have
a jumble of ideas that relate to it, but are not necessarily clearly related to each other. As illustrated by the homework spider map in Figure 6, by writing these ideas
outside the main concept, you may begin to separate and group unrelated terms so that they become more useful.
Making and Using Tables
Browse through your textbook and you will notice tables in the text and in the activities. In a table, data or information is arranged in a way that makes it easier for you to
understand. Activity tables help organize the data you collect during an activity so that results can be interpreted more easily.
Most tables have a title. At a glance, the title tells you what the table is about. A table is divided into columns and rows. The first column lists items to be compared. In Figure
7, the collection of recyclable materials is being compared in a table. The row across the top lists the specific characteristics being compared. Within the grid of the table,
the collected data are recorded.
What is the title of the table in Figure 7? The title is "Recycled Materials." What is being compared?
The different materials being recycled and on which days they are recycled.
Making Tables To make
a table, list the items to be compared down in columns and the characteristics to be compared across in rows. The table in Figure 7 compares the mass of recycled materials
collected by a class. On Monday, students turned in 4.0 kg of paper, 2.0 kg of aluminum, and 0.5 kg of plastic. On Wednesday, they turned in 3.5 kg of paper, 1.5 kg of aluminum,
and 0.5 kg of plastic. On Friday, the totals were 3.0 kg of paper, 1.0 kg of aluminum, and 1.5 kg of plastic.
Using Tables How much plastic, in kilograms, is being recycled on Wednesday? Locate the column
labeled "Plastic (kg)" and the row "Wed." The data in the box where the column and row intersect are the answer. Did you answer "0.5"? How much aluminum, in kilograms, is being
recycled on Friday? If you answered "1.0," you understand how to use the parts of the table.
Making and Using Graphs
After scientists organize data in tables, they may display the data in a graph. A graph is a diagram that shows the relationship of one variable to another. A graph makes interpretation
and analysis of data easier. There are three basic types of graphs used in science-the line graph, the bar graph, and the circle graph.
Line Graphs A line graph is used to show the relationship between two variables. The variables being compared go on two axes of the graph. The independent variable
always goes on the horizontal axis, called the x-axis. The dependent variable always goes on the vertical axis, called the y-axis.
Suppose your class started to record the amount of materials they collected in one week for their school to
recycle. The collected information is shown in Figure 8.
|Materials Collected During Week
You could make
a graph of the materials collected over the three days of the school week. The three weekdays are the independent variables and are placed on the x-axis of your graph. The amount
of materials collected is the dependent variable and would go on the y-axis.
After drawing your axes, label each with a scale. The x-axis lists the three weekdays. To make a scale of
the amount of materials collected on the y-axis, look at the data values. Because the lowest amount collected was 1.0 and the highest was 5.0, you will have to start numbering
at least at 1.0 and go through 5.0. You decide to start numbering at 0 and number by ones through 6.0, as shown in Figure 9.
Next, plot the
data points for collected paper. The first pair of data you want to plot is Monday and 5.0 kg of paper. Locate "Monday" on the x-axis and locate "5.0" on the y-axis. Where an imaginary
vertical line from the x-axis and an imaginary horizontal line from the y-axis would meet, place the first data point. Place the other data points the same way. After all the points
are plotted, connect them with the best smooth curve. Repeat this procedure for the data points for aluminum. Use continuous and dashed lines to distinguish the two line graphs.
The resulting graph should look like Figure 11.
Bar Graphs Bar graphs are similar to line graphs. They compare data that do not continuously
change. In a bar graph, vertical bars show the relationships among data.
To make a bar graph, set up the x-axis and y-axis as you did for the line graph. The data is plotted by drawing vertical bars from the x-axis up to a point where the y-axis would
meet the bar if it were extended.
Look at the bar graph in Figure 11 comparing the mass of aluminum collected over three weekdays. The
x-axis is the days on which the aluminum was collected. The y-axis is the mass of aluminum collected, in kilograms.
Circle Graphs A circle graph uses a circle divided into sections to display data. Each section
represents part of the whole. All the sections together equal 100 percent. Suppose you wanted to make a circle graph to show the number of seeds that germinated in a package. You
would count the total number of seeds. You find that there are 143 seeds in the package. This represents 100 percent, the whole circle.
You plant the seeds, and 129 seeds germinate. The seeds that germinated will make up one section of the circle
graph, and the seeds that did not germinate will make up the remaining section.
To find out how much of the circle each section should take, divide the number of seeds in each section by
the total number of seeds. Then multiply your answer by 360, the number of degrees in a circle, and round to the nearest whole number. The section of the circle graph in degrees
that represents the seeds germinated is figured below.
129/143 * 360 = 324.75 or 325 degrees (or 325°)
Plot this group
on the circle graph using a compass and a protractor. Use the compass to draw a circle. It will be easier to measure the part of the circle representing the non-germinating seeds,
so subtract 325° from 360° to get 35°. Draw a straight line from the center to the edge of the circle. Place your protractor on this line and use it to mark a point
Use this point to draw a straight line from the center of the circle to the edge. This is the section for
the group of seeds that did not germinate. The other section represents the group of 129 seeds that did germinate. Label the sections of your graph and title the graph as shown
in Figure 12.