Download Using Models to Solve Equations – Balance Scale Model

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Equations of motion wikipedia, lookup

Van der Waals equation wikipedia, lookup

Equation of state wikipedia, lookup

Differential equation wikipedia, lookup

Calculus of variations wikipedia, lookup

Derivation of the Navier–Stokes equations wikipedia, lookup

Two-body problem in general relativity wikipedia, lookup

Itô diffusion wikipedia, lookup

Exact solutions in general relativity wikipedia, lookup

Partial differential equation wikipedia, lookup

Schwarzschild geodesics wikipedia, lookup

Transcript
Using Models to Solve
Equations


An equation is a statement that says the value of one
expression is equal to the value of another expression.
Solving equations is the process you used to
determine the value of the unknown that makes the
equation true. This is called the solution.
Herman is in the last round of the spell-a-thon in his school. A contestant receives 3 points for every
word spelled correctly. Herman has 42 points. How many words has he spelled correctly?
Let h represent the number of words Herman has
spelled correctly.
Then, the number of points is 3 times h, or 3h.
Since Herman has 42 points, the algebraic equation is
3h = 42.
Use a balance-scales model to represent this equation.
On the left side, show masses to represent 3h.
On the right side, show a mass to represent 42.
Since there are 3 identical unknown masses in the left
pan, replace 42 g in the right pan with 3 equal masses.
Each mass is 14 g.
So, each unknown mass is 14 g.
h = 14
Herman has spelled 14 words correctly.
Check:
3h = 42
3(14) = 42
42 = 42
The solution is correct.

Jodee is also a contestant in the spell-a-thon. A contestant receives 3 points for every word spelled
correctly. Because of a technical penalty, Jodee loses 5 points. She now has 19 points. How many words
has Jodee spelled correctly?

Let j represent the number of words Jodee has spelled correctly.

Then, the number of points she receives is 3j.

When the penalty is considered, the number of points is 3j - 5.

So, the equation is: 3j – 5 = 19
The solution is j = 8.
Jodee has spelled 8 words correctly.
Check: 3j – 5
3(8) – 5
24 – 5
19
= 19
= 19
= 19
= 19
Solution is correct.
Draw the equation and then solve:
2x + 4 = 8
X
Remove 4 blank squares from both
sides.
Now there are 2 identical
unknown masses on the left side
and need to arrange the weights
into 2 equals groups.
x = +2
X
Draw the model then solve
x – 3 = -6
x +4 = -7
x = -11
x = -3
-1 +x -2x +2 -5 = 3x -2 +3
-2x +2 = -4x -4
x = -3
x = 1.25
Page 324-325 #6,7,8