BUILDING FORMULAS
GOALS
1.
Represent
a visual pattern with words, symbols, and numbers.
2.
Describe
visual patterns using recursive and direct formulas.
3.
Generate
and use a table of values and/or graph.
4.
Use
and construct recursive and direct formulas.
5.
Square
and find the square root of a number.
6.
Understand
the distributive property.
7.
Recognize
the advantages & disadvantages of different representations (tables, direct
& recursive formulas, and visual models).
8.
Understand
the inverse relationship between square and square root.
9.
Recognize
equivalent representations for the same situation.
10.
Appreciate
the usefulness of formulas.
11.
Use
formulas to solve simple problems.
12.
Generalize
a particular situation by means of a general formula.
1.
You
can leave out the “x” when multiplying.
T=4xL-1 is the same as T=4L-1.
2.
When
adding or multiplying, you can change the order. T=(P+1)x3+2 is the same as T=3(P+1)+2.
1.
If
you have to repeat a calculation over and over, using a formula can be helpful.
2.
A
formula with parenthesis can be written without parenthesis. 2(4S+3L) is the
same as 8S+6L
3.
A
formula without parenthesis can be written with parenthesis. 6S+3L is the same
as 3(2S+1L)
SECTION C: AREA
1.
A
number is a perfect square if its square root is a whole number.
2.
Unsquaring
allows you to find the length of a side of a square if you know the square’s
area. It also allows you to find the
radius of a circle whose area is known.
SECTION D: FORMULAS…Can be used
to:
1.
describe
a situation, as was the case with the Egyptian art, for which formulas describe
how drawings were made.
2.
solve
problems, such as how to convert temperatures.
3.
investigate
possibilities within certain constraints, such as staircases.
4.
Information
in formulas can also be given in pictures, stories, graphs, tables, or other
formulas.
5.
When
solving problems, be sure to choose the best way to organize and represent the
information.