Algebra II
Standard
|
| Skills (Note:
none listed for science standards)
|
Teacher
Strategy
|
Student
Tasks or Scientific Investigation/Experimentation
|
Assessment
or Scientific Application/Assessment
|
Resources
and Technology
|
|
The California Mathematics Content Standards -Grade8 9 10 11 12
Algebra II
Standard
11. Students prove simple laws of
logarithms.11.1 Students understand the inverse
relationship between exponents and
logarithms,and use this relationship to solve
problems involving logarithms and
exponents.11.2 Students judge the validity of an argument
based on whether the properties of real
numbers,exponents,and logarithms have
been applied correctly at each step.
Skills (Note: none listed for science standards)
Teacher Strategy
Review relations and functions and their domains and ranges.Start by having students plot the graph of y =2x +1 and its inverse x =2y +1. It is important for them to plot the inverse function by interchanging the components of the ordered pairs of each of the points for the original function.Ask them to come up with an alternate way of graphing the inverse of the function.Repeat and have them plot y =x2 +1 and its inverse function. The concept of undoing:
y =2x +1
Step 1:Multiply a number by 2
Step 2:add 1Finding the inverse:
x =2y +1.Solve for y.
Step 1:Subtract 1 from the number
Step 2:Divide by 2
From the previous section students should know how to convert from logarithm form to exponential form and vice versa.They should be able to solve a variety of equations this way. Remind students that the log number on the calculator is base ten.
Student Tasks or Scientific Investigation/Experimentation
Have students graph a function and its inverse. After students are taught graphs,have them graph x =10y and y =log x .They should discover that it is the same graph and that x = 10y and y =log x are equivalent.
Have students find the log of 10,100,1000 and come up with a general statement of log bx=x.
Have students simplify logs.For example,log 2 8, and convert from log to exponential form.Ex: logx 8 =3
Have students solve various equations where they have to convert from logarithmic form to standard form.
Note:y =3x log3 y =x
1.The base number stays as the base.
2.The exponent becomes the answer.
3.The response number becomes the log
number. 4.The x and y change places.
Assessment or Scientific Application/Assessment
Have students graph y =3x ,x =3y ,and log3 y =x on the same graphs. Have students report on real-life applications of logs such as determining the strength of an acid by its pH or the magnitude of an earthquake.
Have students explain the relationships between exponents and logarithms in both word and (number)examples.
Resources and Technology
Resource:Have students explore how to use a
log table to determine the mantissa of the log
and its characteristics.They should check their
answers with the calculator.Technology:Ask students to see if the log and
the In keys are the same and have them
explore the differences between them.Students judge the validity of an argument
based on whether the properties of real
numbers,exponents and logarithms have
been applied correctly at each step.Have students work out various problems where
they solve equations which are in exponential
form using logarithms with the help of a
calculator.
This page is taken from the Santa Clara Office of Education.