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 CaliforniaMathematics Content Standards -Grade8 9 10 11 12
Algebra II
Standard
4. Students factor polynomials
representing the difference of
squares, perfect squares, trinomials,
and the sum and difference of two
cubes.
Skills (Note: none listed for science standards)
Teacher Strategy
Have students multiply polynominals such as (x +y)(x y))and (2x +3y)(2x 3y))and (3x2 +1)(3x2 1)by FOIL and ask them if there is a pattern.Then assign them problems in the reverse direction and ask them to factor them. Have students multiply (x +2)2 .Ask them how they would go about doing it.They should understand that squaring means multiplying a number by itself.Repeat with (x 2)2 .Ask them what changes;see if they can come up with a general formula.
Have them multiply (x +3)(x2 3x ++9)and (x 3))(x2 +3x +9).Again ask them what the pattern is.
Student Tasks or Scientific Investigation/Experimentation
Assign students problems when they are familiar with the difference of two squares formula in expanding a factor.
1.m2 81
2.16x2 100b 2
3.x2 49Give students algebra tiles or graph paper where they can explore perfect square trinomials.The following are suggested (x +1)2 , (2x +1)2 ,(3x 1)2 ,(2x y)2 .This should be similar to the first student task on Standard 3.
Have students work on trinomials where the first term has a coefficient of 1 and they have to figure out the factors.See example below:
Assessment or Scientific Application/Assessment
Have various problems where students factor
either trinomials,difference of squares,sum and
difference of cubes.Have students factor x 3 +1.Hint:If needed,
write as x 3 +1 3 .Have students draw a cube of side x and shade
a cube of side 1.They can actually use graph
paper and make their cubes and determine what
the remaining volume is if a cube of side 1 is cut
out.This way,they know how to derive the
formula.They may need/want to explore this
first with 3-D Algebra Lab Gear.Have various problems where students factor either trinomials,difference of squares,sum and difference of cubes.Have students factor x 3 +1.Hint:If needed, write as x3 +13 .
Have students draw a cube of side x and shade a cube of side 1.They can actually use graph paper and make their cubes and determine what the remaining volume is if a cube of side 1 is cut out.This way,they know how to derive the formula.They may need/want to explore this first with 3-D Algebra Lab Gear.
Resources and Technology
Resource:Algebra Lab Gear helps students visualize algebraic concepts with concrete two-and three-dimensional models.Three- dimensional model fits together to model (x +y)2 .Sets for the overhead are also available.These materials are carried by most companies providing manipulatives for 6-12th grades. Technology:Bradford Algebra Software : Exponents,Roots and Radicals, William K.. Bradford Publishing.
This page is taken from the Santa Clara Office of Education.