Goodbye April.... Topics for April 27th

Algebra I

Today we discussed
Our discussion has moved into roots and radicals.  We discussed what a square root is and reviewed all our perfect squares from 1 to 144.

Sections Covered in Textbook
1) 12-2: Square Roots (pages 477-481)

Video Tutorials
1) Finding the square root of a perfect square
http://www.virtualnerd.com/sat-math/fundamentals/exponents-square-roots/perfect-square-square-root
2) How to find the square root of a fraction
http://www.virtualnerd.com/algebra-1/algebra-foundations/powers-square-roots/square-roots/fraction-square-root

Assignments
1) Chapter Test on Page 471 #'s 1-16 all
2) Page 480 #'s 27-53 odd.

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
We took our discussion of proportions and included the special proportion for percents.  Remember per-cent means per-100 or out of 100.   You are comparing a percentage of a base number with 100.

Sections Covered in Textbook
1) 9-4: Using the Percent Proportion

Video Tutorials
1) What is a percent proportion?
http://www.virtualnerd.com/middle-math/ratios-proportions-percent/percent-number/percent-proportion-definition
2) Using the percent proportion to find a part of a whole.
http://www.virtualnerd.com/middle-math/ratios-proportions-percent/percent-number/proportion-for-part-of-whole

Assignments
1) Chapter 8 Test.
Download Test Here.
2) Set 9C on Page 608 #'s 1-10 all

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

Topics for April 25th

Algebra I

Today we discussed
We finished our discussion about solving systems of equations and tackled some more complicated equations with rational numbers.  From there we graphed systems of inequalities to determine the solution - as with all inequalities, there are many possible solutions so the key is to find where the two graphs intersect.

Sections Covered in Textbook
1) 11-5: Elimination Using Multiplication (pages 457-461)
2) 11-5: Graphing Systems of Inequalities (pages 463-467)

Video Tutorials
1) How to Solve Systems of Equations by Graphing

• http://www.virtualnerd.com/algebra-1/systems-equations-inequalities/inequalities/solving-systems-inequalities/inequality-solve-by-graphing
• https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/graphing-inequalities/v/graphing-systems-of-inequalities-2

Assignments
1) Page 460 #'s 22, 24, 31
2) Page 465 #'s 13-33 2nd Column only


**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
We have finished our unit on graphing and now have moved into ratios, proportions and percents.  We defined a ratio as a comparison of two numbers by division.  Ratios can be expressed in three ways:

2 is to 3       or       2:3      or 2/3

A rate is defined as a ratio that compares two numbers with different measures like mile/hour.

Proportions can be formed by setting two ratios (fractions) equal to each other.  If we have a missing number, we can solve by multiplying the means and extremes and solving for the variable (missing value).

Sections Covered in Textbook
1) 9-1: Ratios and Rates (pages 324-325)
2) 9-2: Proportions (pages 327-329)

Video Tutorials
1) How to solve a proportion.
http://www.virtualnerd.com/pre-algebra/ratios-proportions/proportionality/solving-proportions/proportion-cross-multiply-example

Assignments
1) Look over chapter 8 to see if you have any questions (skip section on systems of equations)
2) Page 329 #'s 26-37 all

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

Algebra I

Today we discussed
Systems of Equations continues to be our topic of discussion and how to best solve them.  We've now covered three methods for solving systems, and have discussed the limitations of each method:

1. You may solve by graphing.  The limitation is we are prone to error and unless graphs are constructed very carefully, it is easy to make a mistake and not have line lines cross where they should.  There are tools available  to help with this method, including spreadsheets and graphing calculators  (Click here to try this online graphing calculator to check your work.)
2. You may solve by substitution.  Limitations for this method include equations that are in standard form must first be manipulated to solve for a variable, requiring an extra step, and equations with fractions require more cumbersome arithmetic.  
3. You may solve by elimination.  The goal of this method is to eliminate one of our variables so we and use it to find the second variable.  Most people agree that elimination is the preferred method because it works for every type of system.  

Sections Covered in Textbook
1)  11-4: Elimination Using Addition and Subtraction (pages 452-453)

Video Tutorials
1) Solving systems of equations using elimination method.
http://www.virtualnerd.com/algebra-1/systems-equations-inequalities/elimination/elimination-by-addition-subtraction/equations-solution-by-elimination-addition

Assignments
1)  Make any needed corrections to your graphing test on a separate sheet of paper.
2)  Page 455 #'s 13-31 odd, 37

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
Our discussion graphing moved on to graphing inequalities.  We reviewed the difference between strictly less than or greater than (< , >) and less than or equal to or greater than or equal to (≤, ≥), and whether to include the line or not in the graph of the solution.  You can find another lesson on graphing inequalities by going here:

http://www.mathsisfun.com/algebra/graphing-linear-inequalities.html

Three Methods for Graphing Lines

How to Graph Inequalities

Sections Covered in Textbook
1) 8-11: Graphing Inequalities (pages 315-317)

Video Tutorials
1) Graphing Inequalities

• http://www.virtualnerd.com/algebra-1/linear-inequalities/two-variables-graphing/graphing-coordinate-plane/coordinate-plane-graphing-example
• https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/graphing-inequalities/v/graphing-linear-inequalities-in-two-variables-example-2

Assignments
1) Page 317 #'s 9-19 odd, 25

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

April 18th

Algebra I

Today we discussed
Our conversation about systems of equations moved on to solving the equations to find the exact point or points of intersection.  Recall that lines can intersect at a single point, no point at all (parallel lines) or at infinitely many points (same line).  The answer(s) you get when you solve the equations mathematically by substituting one of the variables is where the lines intersect.

Sections Covered in Textbook
1) 11-3: Substitution (pages 447-451)

Video Tutorials
1)  Solving systems of equations using substitution method
http://www.virtualnerd.com/algebra-2/linear-systems/solve-algebraically/solve-by-substitution/equations-solution-by-substitution

Assignments
1) Pages 450-451 #'s 17-33 odd, 41

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
Our discussions about graphing moved on to intercepts.  Intercepts are where a line crosses either the x- or y-axis.  The x-intercept can be found when y=0 and the y-intercept can be found when x=0.  Because it take only two points to determine a line, a line can be graphed by using both the x-intercept and y-intercept and connecting those points.

Sections Covered in Textbook
1) 8-9: Intercepts (pages 308-309)

Video Tutorials
1) Graphing using the x-intercept and y-intercept
http://www.virtualnerd.com/algebra-1/linear-equation-analysis/intercept/intercept-examples/x-y-intercepts-graph-standard-line

Assignments
1) Page 309 #'s 14-22 all, 27

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

Concepts for April 13th

Algebra I

Today we discussed
We did a full review of all things functions and graphs and put it all together.  From there, we moved to systems of equations, and for the sake of this course, they will be two lines.  There are three possibilities for two linear equations.

1. The lines may cross at a single coordinate point.  This point will make both equations true at the same time!
2. The lines may not cross at all.  Said another way, the lines may be parallel.  Recall that parallel lines have the same slope, but a different y-intercept.
3. The lines might intersect infinitely many times, or at every point on the same line.  In this case, we really have equations that represent the same line.  

Sections Covered in Textbook
1) 11-2: Graphing Systems of Equations (pages 442-446)

Video Tutorials
1)  Solving Systems of Equations by graphing

• http://www.virtualnerd.com/algebra-2/linear-systems/graphing/solve-by-graphing/equations-solution-by-graphing
• http://www.mathplanet.com/education/pre-algebra/graphing-and-functions/solve-systems-of-equations-by-graphing

Assignments
1) Pages 445-446 #'s 17-32 1st column, 43.
2) Complete Test on Functions and Graphs.
    Download a copy of the test here.

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
No discussion of graphing is complete without slope.  Slope or steepness is how quickly something rises or falls compared to (or divided by) how far something travels.  It is the rise of  line divided by the run, or the change in y-values divided by the change in x-values.  Positive slopes start low at the left and rise as they move right, and negative slopes are just the opposite - they start high and end lower.

Sections Covered in Textbook
1) 8-8: Slope (pages 305-307)

Video Tutorials
1) What is the Slope of a Line?
http://www.virtualnerd.com/algebra-1/linear-equation-analysis/slope-rate-of-change/understanding-slope/slope-definition
2)  Slope Formula
http://www.virtualnerd.com/algebra-1/linear-equation-analysis/slope-rate-of-change/understanding-slope/slope-formula-definition
3)  Find Slope from Two Points
http://www.virtualnerd.com/algebra-1/linear-equation-analysis/slope-rate-of-change/slope-examples/slope-from-two-points

Assignments
1) Page 307 #'s 7-18 all; 23-28 all

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

Welcome Back! Concepts for April 11th

Algebra I

Today we discussed
Midpoints of lines was the topic of discussion today.  Finding the midpoint is really as simple as finding the average of the x-coordinates of the end-points and the average of the y-coordinates of the end points.

Sections Covered in Textbook
1) 10-7: Midpoint of a Line Segment (pages 428 - 431)

Video Tutorials
1) How to find the coordinates of the midpoint of a line segment.
http://www.virtualnerd.com/algebra-1/radical-expressions-equations/distance-midpoint-formulas/midpoint-formula/midpoint-between-coordinates

Assignments
1) Page 430 #'s 17-47 odd

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
Today we took our process of finding solutions to equations with two variables and used it plot the points we found on a graph.  Because we have the power to pick whatever values we want for "x", we talked about what made good choices to keep the equations as easy as possible to solve.

Sections Covered in Textbook
1) 8-6: Graphing Equations (pages 299-301)

Video Tutorials
1) How to graph an equation using a table.
http://www.virtualnerd.com/algebra-1/relations-functions/graphing-linear-equations/graphs-examples/linear-equation-graphing-method

Assignments
1) Page 301 #'s 11-25 odd

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

REMINDER!!

I hope everyone has a wonderful Spring Break!

There will be NO CLASSES this week.

We will get together again on April 11th.  See you then!