Here are some tips for general patterns...
Following is a meathod for finding the general pattern for a group of speical cases.
Exsample: write the general pattern for the special cases at the right.
Soulution Strategy:
Step 1 write everything that is the same for all of the special cases.
Use blanks for the parts that change.
__________ / 1 = _________
Each special case has divison by 1 and an equal sign .
Step 2 fill in the blanks: each special case has a differnt number , but the number is
the smae for both blanks, so use the same variable in both
Possible soulitions: N / 1 = N , or X / 1 = X , or shape / 1 = shape
Following is a meathod for finding the general pattern for a group of speical cases.
Exsample: write the general pattern for the special cases at the right.
Soulution Strategy:
Step 1 write everything that is the same for all of the special cases.
Use blanks for the parts that change.
__________ / 1 = _________
Each special case has divison by 1 and an equal sign .
Step 2 fill in the blanks: each special case has a differnt number , but the number is
the smae for both blanks, so use the same variable in both
Possible soulitions: N / 1 = N , or X / 1 = X , or shape / 1 = shape
General Pattern to Special Case
-Replace the variables with numbers
Example:
p = 4
p + p = 2 * p (general pattern) to 4 + 4 = 2 * 4 (special case)
If there is more than one varible, each of these variables is replaced with the same number, different variables are replaced with different variables.
Example:
a = 4
b = 3
a * (b - 1) = a * b - a
4 * (3 - 1) = 4 * 3 - 4
-Replace the variables with numbers
Example:
p = 4
p + p = 2 * p (general pattern) to 4 + 4 = 2 * 4 (special case)
If there is more than one varible, each of these variables is replaced with the same number, different variables are replaced with different variables.
Example:
a = 4
b = 3
a * (b - 1) = a * b - a
4 * (3 - 1) = 4 * 3 - 4
Speical Case to General Pattern
~ Find what pieces stay the same and what changes...
- If it is the same in each sentence its stays (fractions, constants)
- If it is a dfferent sentence, it becomes a variable
Example:
7 * (5 - 2) = (7 * 5) - (7 * 2)
7 * (4 - 3) = (7 * 4) - (7 * 3) Those are all special cases
7 * (6 - 1) = (7 * 6) - (7 * 1)
7 * (a * b) = (7 * a) - (7 * b) That is a general pateren
~ Find what pieces stay the same and what changes...
- If it is the same in each sentence its stays (fractions, constants)
- If it is a dfferent sentence, it becomes a variable
Example:
7 * (5 - 2) = (7 * 5) - (7 * 2)
7 * (4 - 3) = (7 * 4) - (7 * 3) Those are all special cases
7 * (6 - 1) = (7 * 6) - (7 * 1)
7 * (a * b) = (7 * a) - (7 * b) That is a general pateren