COPIES OF HANDOUTS GIVEN IN CLASS---SEE CALENDAR FOR DATES--- SHOULD BE IN STUDENT'S VIKING BINDER---SCROLL DOWN MORE UNITS--MORE LATER 


ATTENTION:  "VARIABLES AND PATTERNS" IS NOW A 6TH GRADE UNIT.  THE FIRST UNIT USED IN 7TH GRADE WILL BE "STRETCHING AND SHRINKING".      9/09
Variables and Patterns Check Up #1 Study Guide DO NOT LOSE! PUT IN VIKING BINDER

Use these notes, along with your journal, to prepare for the Check-Up Quiz on __________________.  

Some words to describe change or make comparisons in data:

Larger          Smaller         Faster           Slower                   beginning      ending

More            Less             Higher                   Lower          closer           farther

above          below          right            left              forward        backward

Increase        Decrease      expand         contract       up                down

Enlarge         shrink           better          worse           greater than  less than

Same            equal to        unequal        average        linear           non-linear

Variables:

Variables are quantities that change.  We measure two variables to make tables and graphs, for example, time and distance.   How to find them: The names of the variables are written at the top of tables and along the x and y axis of graphs.  If the data is taken down in notes or a story, look for what is being measured.

Making graphs from a table:

Step 1:  Identify the two variables. 

Step 2: Decide which one will go on the x-axis (bottom) and which on the y-axis (side). The dependent variable always goes on the y-axis. “Time” will always go on the x-axis, if it happens to be one of the variables.

 Step 3:  Select a scale for numbering each axis.  You must count by even steps (by 2’s, 5’s, 10’s, 25’s etc).  The numbers are printed on top of the LINES, not in the spaces.

Step 4:   Plot the points.  Start in the lower left corner of the graph.  Using the data off of your table, count over (right) to the first data number, then follow that line up the y-axis to where you estimate the second data number should be.  Put the point (dot) on the line.

Step 5:    You may connect the points with a line if something can be thought of as happening between the points (like a bike trip).  


Making a table from a graph:

Step 1:   Identify the two variables.  They are the labels of the x and y axis on the graph.

Step 2:  Draw a t-table, either vertically or horizontally.      The x-axis variable’s name will go on the left side of a vertical t-table, or on the top of a horizontal t-table.  The y-axis variable will go on the right side of a vertical t-table, or the bottom of a horizontal t-table.                

Step 3:  Find the first point in the lower left corner of the graph.  Count how far over it is and write that number down under the x-axis variable on your table.  Count how far up it is and put that under the y- axis variable.  You will probably have to estimate the number for the y-axis data.  Continue with the next point until you are finished with all the points in order from left to right.

 Finding the most and least progress made on the table:

Compare the difference between each data point.  You may have to subtract one from the other to find the difference.  The largest difference means the most progress was made.  The smallest difference means the least progress was made.  You can also break the table up into larger segments to compare, such as morning vs. afternoon.

Finding the most and least progress made on the graph:

Compare two points on the graph.  Connect them with a line.  The steepest line between two points shows the most progress.  The least steep line shows the least progress. 

Or, estimate the difference on the y-axis between two points.  Compare this with other pairs of points- the bigger number shows the most progress and the smallest shows the least.


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Variables and Patterns Check Up #2 Study Guide- DO NOT LOSE! PUT IN VIKING BINDER

Use these notes, along with your journal, to prepare for the Check Up Quiz on __________________. 
Variables:

Variables are quantities that change.  We measure two variables to make tables and graphs, for example, time and distance.   How to find them: The names of the variables are written at the top of tables and along the x and y axis of graphs.  If the data is taken down in notes or a story, look for what is being measured. 

How to make a table and graph using a rate:

Ex: 55 miles per hour;   $5 per person;   60 seconds per minute

Step 1:  Identify the two variables from the rate given.  For example, if a rate is given of 55 miles per hour, the two variables would be time and distance.  For a rate of $5 per person, the variables would be number of people and $ cost.

Step 2: Decide which one will go on the x-axis (bottom) and which on the y-axis (side). The dependent variable always goes on the y-axis. “Time” will always go on the x-axis, if it happens to be one of the variables.

Step 3:  Draw a t-table, either vertically or horizontally.      The x-axis variable’s name will go on the left side of a vertical t-table, or on the top of a horizontal t-table.  The y-axis variable (dependent) will go on the right side of a vertical t-table, or the bottom of a horizontal t-table. Put numbers under the x-axis variable to get the rate going, such as 0,1,2,3 and keep numbering evenly as far as you want your graph to go.  Pick numbers that make sense for the rate. 

Step 4:   Use the rate to calculate the amount for the y-axis data.  You will probably be multiplying the x-axis variable times the rate to get the y-axis variable.  For example, for 3 people at a rate of $5 per person, you multiply 3x5 to get $15, and write that under the y-axis variable in the table next to the 3.

Step 5:  Create the graph and label the axes.  Use even-step numbers to create the scales for each axis.  Use the two numbers next to each other on the table (the coordinate pair), to plot each point from left to right.

Connecting Points with a Line – Only When it Makes Sense
Connecting points with a line can help you see patterns and compare some parts of the graph with others, but generally it only makes sense to connect the points when some type of action or progress is happening between the points, such as bike riders riding down roads and their distance increasing every minute between the 30 minute points that we plot on the graph.  Another example would be rain falling into a rain gauge.  We could measure and graph it every hour, and connect those points with a line because the rain fell steadily every minute of that hour, not just when we measured it.  This is called continuous data.

An example of when it does NOT make sense to connect the points would be showing the cost per person to get into the movies.  You can find the cost of 1,2, 3 or more people going into the theater, then graph the data, but there is not a reason to find the cost of 1 ½ people going in, which is what a line connecting the points for 1 and 2 people could show.  It just doesn’t make sense.  This is called discrete data.

STRETCHING & SHRINKING STUDY GUIDE
Here's a link to a list of words that you can make into flashcards for studying:
http://www.flashcardexchange.com/flashcards/list/407163


COMPARING & SCALING  STUDY GUIDE FOR UNIT TEST

Do Not Lose-  Put in Viking Binder
Use these notes, along with your journal, to prepare for the Unit Test on ___________.  The unit focused on comparing data using ratios, percents, differences and proportions.  All types of comparisons will be used on the test.

Ratio:  Comparing two parts to each other or comparing part of something to the whole.  For example, if I ask 11 people to vote for the favorite cola, and 8 vote for Pepsi and 3 for Coke, the ratio is “8 to 3” or “8/3” or “8:3”.

 

Equivalent Ratios:  Find the ratio, and then use a scale factor to make both quantities larger.  For example, 8 to 6 can be made into the equivalent ratio of 80 to 60.  You can also reduce the ratios.  For example, 8 to 6 can be reduced by a factor of 2 to become 4 to 3.

 

Fraction:  How many out of the total group-  Ex: 8/11 people like Pepsi, or, part to part- Ex:  the ratio of robins to blue jays in the tree is 9 to 3; the fraction could be written as 9/3.

 

Finding Percent:  Percent means “how many out of 100”.  First, make a fraction out of the data.  Compare the part being counted to the whole thing, or a part to a part.  Then change the fraction to a decimal number, and the decimal to a percent. Change fractions to percents by dividing the numerator by the denominator; the first two numbers after the decimal point are the percent.  Ex:  3 out of 11 like Coke, so the fraction is 3/11.  Next, 3 / 11 = 0.27272.  This equals 27%.

 

Difference:  How much more or less (subtract!).  The difference between the Pepsi and Coke votes is 5.  (8-3=5), so 5 more people like Pepsi.

UNIT RATE:   Use DIVISION to find the unit rate, (or how much ONE thing is), like 55 miles per hour; 2 hotdogs per person; 1.6 gallons of syrup per tree.

Example A:  the ice-cream store uses 19 gallons of ice cream in 8 hours. To find how much ice cream is used in 1 hour, divide 19 by 8.  19 / 8 = 2.38       gallons per hour.

 To find the 2nd unit rate possible, divide the opposite way. 

Example B:  to find out how many hours 1 gallon of ice cream lasts, divide 8 by 19.  8 - 19 =  0.42 hours per gallon (less than half an hour!).

 

Changing minutes to hours:  There are 60 minutes in one hour.  Set up equivalent fractions to convert the number of minutes to 60, and then multiply the other part of the fraction by the same number. Ex:  Joe can eat 6 hot dogs in 15 minutes.  What number can he eat in an hour?

 7/15 =  ___ / 60; 15 x 4 = 60, so 6 x 4 = 24 He can eat 24 hot dogs in 1 hour.


Comparison Statements:  greater, more, faster, slower, less, same, higher, lower, equal, etc.

Ratios:  Our school is winning the game by a ratio (score) of __ to __ .

Percents:  ___ % more (or less) were sold on Friday.

Differences:  The difference between this and that is ____; or, use more than and less than.

 

­Comparing Two Ratios to Each Other:

One way to compare two different ratios is to find the unit rate for each one.  Then it is easier to see which is more or less. 

Ex:  CD’s at MusicCity cost 5 for $50.  CD’s at Sun Records are 7 for $65.  The unit rate (using division) for MusicCity is 50 / 5 = 10 dollars each.  Sun Records unit rate is 65 / 7 = 9.29 dollars each.  CD’s at MusicCity cost $ .71 more than at Sun Records.

 

After getting the unit rate you can multiply it for larger quantities.

  Ex:  11 CD’s at MusicCity cost $110 ( 11 x 10), and 11 CD’s at Sun Records cost $102.19 ( 11 x 9.29).