That's a Wrap! Concepts for our Final Class!

Algebra I

Today we discussed
Today we practiced our quadratic graphing and used the discriminant to determine the nature of our roots.  From there we discussed direct and inverse variation.

Sections Covered in Textbook
1) 4-8: Direct Variation (pages 162-165)
2) 4-9: Inverse Variation (pages 166-169)

Video Tutorials
1) What is direct variation?
http://www.virtualnerd.com/algebra-1/linear-equation-analysis/direct-variation/direct-variation-definition/direct-variation-proportionality-formula
2) What is inverse variation?
http://www.virtualnerd.com/algebra-1/rational-expressions-functions/inverse-variation/inverse-variation-examples/inverse-variation-indirect-proportionality-formula

Assignments
1) Please complete the Virginia State Algebra Exam.  This is a VERY large file there are 50 problems and only one problem per page.  I suggest using your computer to download this file and work your problems out on a separate sheet of paper.  There is one concept we did not cover:  standard deviation.  Just do the best you can on those - I will not be counting those problems.  Please record your answers on the answer sheet and submit it to me by no later than noon on Monday, May 29th.  Good luck and thanks for a great year!

Download Exam here.
Download Answer sheet here.

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Pre-Algebra

Today we discussed
Today we discussed probability.  We talked about many different possible events including tossing coins, rolling dice and picking a card out of  deck.

Sections Covered in Textbook
1) 9-4: Probablity

Video Tutorials
1) What is probability?
http://www.virtualnerd.com/middle-math/probability-statistics/probability/definition-probability

Assignments
1) Exploring Probability by Rolling Two Dice activity.  Please complete and email to me by no later than noon on Monday, May 29th.  
Download Worksheet here.

HAVE A WONDERFUL SUMMER!!!

Almost Done! Topics for May 23rd

Algebra I

Today we discussed
Today we looked a little closer at the Quadratic formula at what is called the discriminant.  By analyzing the discriminant, we can know a lot about potential roots for a quadratic equation.

Sections Covered in Textbook
1) 13-6: Using the Discriminant

Video Tutorials
1) What is the discriminant
http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/discriminant-quadratic-formula/discriminant/discriminant-definition
2) Use the discriminant to find the number of solutions to a quadratic equation
http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/discriminant-quadratic-formula/discriminant/discriminant-determine-solution-number-example

Assignments
1) Pages 544-545 #'s 11-37 odd, 42

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
Today we moved into a discussion about possible outcomes.  First we used tree diagrams to list our possibilities.  Then we used the counting principle to find the number of possibilities, and finally, we used the permutation and combination formulas to calculate outcomes.  Remember, a permutation is a list of possible outcomes in which the order matters (like a school schedule of classes) versus a combination where order does not matter (items on a pizza).

Sections Covered in Textbook
1) 11-1: Counting Using Tree Diagrams (pages 400-402)
2) 11-2:  Counting using Multiplication (pages 403-405)
3) 11-3: Permutations and Combinations (pages 407-409)

Video Tutorials
1) Using Tree Diagram to Count Outcomes
http://www.virtualnerd.com/texas-digits/texas-digits-grade-7/acquire-and-demonstrate-mathematical-understanding/display-explain-and-justify-mathematical-ideas-and/sample-space-count-outcomes-using-tree
2) Using Counting Principle to find outcomes
http://www.virtualnerd.com/algebra-2/probability-statistics/permutations-combinations/counting-outcomes/sample-space-count-outcomes-using-fundamental-principle
3) What is a factorial?
http://www.virtualnerd.com/pre-algebra/probability-data-analysis/permutations-combinations/factorials/factorial-definition
4) Permutation Formula
https://www.khanacademy.org/math/precalculus/prob-comb/combinatorics-precalc/v/permutation-formula
5) Combination Formula
https://www.khanacademy.org/math/precalculus/prob-comb/combinations/v/combination-formula

Assignments
1) Page 409 #'s 16-25 all, 29. 30, 32

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

Topics for May 18th

Algebra I

Today we discussed
Today we investigated the Quadratic Formula.  We also reviewed three different ways to determine the roots of a quadratic equation:

1. Factor the equation
2. Complete the square
3. Use the Quadratic formula

Sections Covered in Textbook
1) 13-5: Solving quadratic equations by using the quadratic formula (pages 536-540)

Video Tutorials
1) Solving equations using the quadratic formula
http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/discriminant-quadratic-formula/quadratic-formula/solve-by-quadratic-formula
2)  Using quadratic formula with irrational solutions
https://www.youtube.com/watch?v=Nwx4ZO9Hopk

Assignments
1) Page 539 #'s 21-37 odd, 45.  Also, pick two problems and solve by completing the square.  Ensure that your answers to both methods are the same.

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
We continued on with our discussion about data sets and how our sets can have similarities, but also vary.  We used the range, maximum values, minimum values, upper and lower quartiles to build box-and-whisker plots to visually represent a data set.

Sections Covered in Textbook
1) 10-4: Measures of Variation (pages 374-377)
2) 10-: Box-and-Whiskers Plots (pages 378-381)

Video Tutorials
1)  What is the interquartile range?
http://www.virtualnerd.com/middle-math/probability-statistics/measures-variation/interquartile-range-definition
2) What is a Box and Whiskers Plot?
http://www.virtualnerd.com/pre-algebra/probability-data-analysis/central-tendency-variation/measures-variation/what-is-a-boxandwhisker-plot

Assignments
1) Page 380 #'s 4-22 all

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

Concepts for May 16th

Algebra I

Today we discussed
Today we discussed how to use the method of completing the square to solve quadratic equations.  The goal is to get a perfect square trinomial so that we can take the square root of both sides of the equation to get the solution.

If the leading coefficient is more than 1, see example below.

We did not have time to work on these in class.

Also see video tutorial below for another example worked out.

Sections Covered in Textbook
1) 13-4: Solving Quadratic Equations by Completing the Square (pages 531-535)

Video Tutorials
1) Solving by Completing the Square
http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/completing-the-square/completing-the-square-solutions/completing-the-square-solution-example
2) Completing the square when leading coefficient not equal to 1.
https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-by-completing-the-square/v/completing-the-square-to-solve-quadratic-equations

Assignments
1) Pages 534-535 #'s 17-39 odd; 40-43 all

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
Today we learned how to put a large set of numbers into a format that is easy to read and understand - Stem and Leaf Plots.

Sections Covered in Textbook
1) 10-3: Stem and Leaf Plots (pages 371-373)

Video Tutorials
1) What is a stem and leaf plot?
http://www.virtualnerd.com/middle-math/probability-statistics/stem-leaf-plots/what-is-a-stemandleaf-plot
2) How do you read a stem and leaf plot?
http://www.mathplayground.com/howto_stemleaf.html

Assignments
1) Page 373 #'s 11-18 all; 22, 24

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

May 11th

Algebra I

Today we discussed
Today we moved back into a discussion about quadratic functions.  We reviewed what roots are and how they relate to the function's graph.  We also found the axis of symmetry as well as solved so we could find the coordinates of the vertex.

Sections Covered in Textbook
1) 13-1: Graphing Quadratic Functions (pages 518-522)

Video Tutorials
1) Find the axis of symmetry
http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/graphing/graph-basics/axis-symmetry-example
2) How to graph a quadratic function
http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/graphing/graph-basics/how-do-you-graph-a-quadratic-function

Assignments
1) Radicals Practice Worksheet - circled numbers only.
Download worksheet and answers here.
2) Pages 521-522 #'s 15-30 1st column only; 36-42 all

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
Our discussion moved into data, statistics and measures of central tendency.  We talked about three types of "averages" that we use that represent the data we are analyzing.

Sections Covered in Textbook
1) 10-1; Gathering and Recording Data (pages 363-365)
2) 10-2: Measures of Central Tendency (pages 367-370)

Video Tutorials
1) Finding the mean of a set of numbers:
http://www.virtualnerd.com/middle-math/probability-statistics/mean-median-mode-range/mean-data-set
2) Finding the median of a set of numbers:
http://www.virtualnerd.com/middle-math/probability-statistics/mean-median-mode-range/median-data-set
3) Finding the mode of a data set
http://www.virtualnerd.com/middle-math/probability-statistics/mean-median-mode-range/mode-data-set

Assignments
1) Chapter 9 Test
2) Page 369 #'s 10-26 all

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

May 9, 2017 Topics

Algebra I

Today we discussed
We discussed how to solve equations with radicals.  Most notably, we must isolate the radical so that we can square both sides (using inverse operations again to solve equations!).  We also reviewed simplifying radical expressions - recall that radicals in the denominator are not permitted if an expression is to be in simplest form.

Sections Covered in Textbook
1) 12-7: Radical Equations (pages 501-505)

Video Tutorials
1) Solving radical equations.
http://www.virtualnerd.com/algebra-2/radical-functions/expressions-examples/solve-equations/solving-example
2) Solving radical equations with a variable in the radicand.
http://www.virtualnerd.com/algebra-2/radical-functions/expressions-examples/solve-equations/solve-radical-equation
3) Solving radical equations with extraneous solutions.
https://www.khanacademy.org/math/algebra2/radical-equations-and-functions/solving-square-root-equations/v/extraneous-solutions-to-radical-equations

Assignments
1) Pages 503-504 #'s 19-35 odd; 39-45 odd

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
We used a practical application of percents today by calculating percent of change.  When we get a negative answer, it means we have a decrease so negative answers are perfectly fine.

Recall that percent of change is calculated as follows:

Sections Covered in Textbook
1) 9-10: Percent of Change (pages 354-355)

Video Tutorials
1)  What is percent of change?
http://mmu.virtualnerd.com/viewtutorial/Alg1_4_18

Assignments
1) Page 355 #'s 10-18 all

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

May the 4th Be With You....

Algebra I

Today we discussed
We expanded on our discussion of simplifying radicals and discussed how to mathematically remove radicals from the denominator of a fraction.  For an expression to be in simplest form, there must be no radicals in the denominator. We discussed what a conjugate is, and also how to simplify radical expressions so that they may be added or subtracted.

Sections Covered in Textbook
1) 12-5: Simplifying Square Roots - part 2 (pages 494-496)
2) 12-6: Adding and Subtracting Radical Expressions (pages 497-500)

Video Tutorials
1) Simplifying radical expressions using the conjugate.
https://www.youtube.com/watch?v=7oWUgtFneco
2) Combining radicals
http://www.virtualnerd.com/algebra-1/radical-expressions-equations/operations/adding-subtract/subtract-unlike-radicands

Assignments
1) Absolute Value Graphing Activity.
Download worksheet here.
Download graph paper here.
2) Page 496 #'s 39-53 odd
3) Pages 499-500 #'s 17-39 odd; 40 & 41

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
Today we reviewed percent proportions and setting them up to solve them. Then we discussed what a discount is and what interest is, and how to calculate it.

Recall:  Interest = principal * rate * time
principal  = amount of money invested
rate = percentage rate expressed as a decimal, so 2% = 0.02
time = amount of time in years, so 6 months would be 0.5 years

Sections Covered in Textbook
1) 9-8: Discount and Interest (pages 349-351)

Video Tutorials
1) Percent Discount
https://www.youtube.com/watch?v=b82OUB_30lI
2)  Finding Simple Interest
http://www.virtualnerd.com/algebra-1/linear-equations-solve/isolate-variables-formulas-examples/formulas-examples/simple-interest-formula-definition

Assignments
1) Percent Problems Worksheet - set up the proportion for each problem.  Solving is optional.
Download worksheet and answers here. 
2) Page 351 #'s 8-19 all

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

Hello May! Concepts for May 2nd

Algebra I

Today we discussed
Today we talked about the Pythagorean theorem and the relationships between the legs of a right triangle and its hypotenuse.  In addition, we worked on simplifying radical expressions using the product and quotient properties of square roots.

Sections Covered in Textbook
1) 12-5: The Pythagorean Theorem (pages 482-486)
2) 12-5: Simplifying Square Roots - Part 1 (pages 492-495)

Video Tutorials
1) What is the Pythagorean Theorem?
http://www.virtualnerd.com/pre-algebra/real-numbers-right-triangles/pythagoream-theorem/right-triangles-pythagorean-theorem/pythagorean-theorem-definition
2) How to simplify radicals using the product property
http://www.virtualnerd.com/algebra-1/radical-expressions-equations/simplify/multiply-divide/square-root-non-perfect-square-simplification
3) What is the Quotient Property of Square Roots?
http://www.virtualnerd.com/pre-algebra/real-numbers-right-triangles/squares-square-roots/squares-square-roots-properties-definitions/square-root-quotient-property-definition

Assignments
1) Page 485 #'s 17-33 odd; 39
2) Page 495 #'s 19-37 odd

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
We reviewed using the percent proportion to solve problems. From there we went though  comparison of fractions, decimals and percents and how to convert numbers among these formats.

Sections Covered in Textbook
1) 9-5: Fractions, Decimals and Percents (pages 338-341)

Video Tutorials
1)  Turning percents into fractions
http://www.virtualnerd.com/pre-algebra/percents/decimals/basics/fraction-conversion
2)  Turning decimals into percents
http://www.virtualnerd.com/pre-algebra/percents/decimals/basics/decimal-to-percent-conversion
3) Fractions, Decimals and Percents
https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates/pre-algebra-percent-decimal-conversions/v/representing-a-number-as-a-decimal-percent-and-fraction

Assignments
1) Worksheet on Percents.
Download worksheet and answers here.
2) Pages 340-341 #'s 21-57 divisible by 3 (so, 21, 24, 27, 30, 33, etc...)

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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!

Concepts for March 30th

Algebra I

Today we discussed
Our discussion about functions and graphing is almost complete.  Today we introduced the concepts of parallel and perpendicular lines. Students should be able to take a set of ordered pairs and determine if they are a function, what the slope of the line is that contains the two points, and how to put the equation into point-slope form, slope-intercept form, standard form, function notation, and determine the x- and y-intercepts as well as find parallel and perpendicular lines.

Sections Covered in Textbook
1)  10-6:  Parallel and Perpendicular Lines (pages 423-426)

Video Tutorials
1) What are Parallel Lines?
http://www.virtualnerd.com/pre-algebra/geometry/points-lines-planes-angles/points-lines/parallel-lines-definition
2) How Do You Know If Lines are Parallel
http://www.virtualnerd.com/algebra-1/linear-equation-analysis/parallel-line-slope-test.php
3) Finding Perpendicular Lines
http://www.virtualnerd.com/algebra-1/linear-equation-analysis/parallel-perpendicular-lines/perpendicular-lines/line-slope-from-perpendicular

Assignments
1)  Functions and Function Notation Worksheet
Download Worksheet here.
2) Page 426 #'s 15-29 odd, 30.

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
We have finally moved on from solving simple and complex equations to the concept of graphing.  We did a very quick overview of graphing equations and inequalities on the number line, reviewed the coordinate plane, discussed ordered pairs and plotting coordinate points, and finally moved on to finding solutions for equations that have two variables.

Sections Covered in Textbook
1) 8-1: Equations and the Number Line (pages 284-285)
2) 8-2: Inequalities and the Number Line (pages 286-288)
3) 8-3: Ordered Pairs (pages 290-292)
4) 8-4: The Coordinate System (pages 293-295)
5) 8-5: Equations with Two Variables (pages 296-298)

Video Tutorials
1) How Do You Graph a Set of Numbers on a Number Line
http://www.virtualnerd.com/algebra-1/algebra-foundations/real-number-represent-compare/sets-number-lines/number-line-graph-a-set
2) How Do You Graph an Inequality on a Number Line
http://www.virtualnerd.com/pre-algebra/inequalities-multi-step-equations/inequalities-graphs/graphs/number-line-graph-inequality
3) What is an Ordered Pair?
http://www.virtualnerd.com/algebra-1/relations-functions/coordinate-plane/coordinate-plane-graphing/ordered-pair-definition
4) How do you plot points in the Coordinate Plane?
http://www.virtualnerd.com/algebra-1/relations-functions/coordinate-plane/coordinate-plane-graphing/ordered-pair-definition

Assignments
1) Coordinate Graphing Worksheet
Download Coordinate Worksheet here.  You can also always find graph paper on my graph paper page of this blog!
2)  Page 297 #'s 8-23 first column only

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

Topics for March 23rd

Algebra I

Today we discussed
We are working steadily on the concept of linear equations and their various forms.  Today we discussed the slope-intercept form of a line, and determined the x-intercepts and y-intercepts of a line.  We also summarized all we know about lines so far:

Sections Covered in Textbook
1) 10-3: Slope-Intercept Form of Linear Equations (pages 410-414)

Video Tutorials
1)  Slope-Intercept Form of a Line
http://www.virtualnerd.com/algebra-1/linear-equation-analysis/slope-intercept-form/slope-intercept-form-examples/slope-intercept-form-definition
2)  A whole bunch of videos on Slope-Intercept form can be found here....
http://www.virtualnerd.com/pre-algebra/linear-functions-graphing/slope-intercept-form/slope-intercept-form-examples

Assignments
1)  Pages 413-414 #'s 21-53 odd

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
We reviewed multi-step equations including those that contain fractions.  We discussed two different methods for solving these, with the second method involving multiplying every piece of an equation to eliminate the fractional pieces.  From there, we moved on to solving multi-step inequalities.  We also worked on translating sentences into equations and inequalities.

Recall:

When multiplying or dividing by a negative number,
you must flip/change/reverse the inequality sign
to keep the truth of the inequality!  

Sections Covered in Textbook
1) 7-6: Solving Multi-Step Inequalities (pages 270-271)

Video Tutorials
1) Solving Multi-step Inequalities

• http://www.virtualnerd.com/pre-algebra/inequalities-multi-step-equations/inequalities-multiple-steps/solve-multiple-step-inequalities/multi-step-reverse-order-of-operations
• https://www.khanacademy.org/math/algebra/one-variable-linear-inequalities/multi-step-inequalities/v/multi-step-inequalities

2)  Translating Sentences into Multi-Step Inequalities
https://www.educreations.com/lesson/view/translating-sentence-to-multi-step-inequality/14680201/

Assignments
1) Page 271 #'s 9-33 odd

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

Concepts for March 21st

Algebra I

Today we discussed
First we reviewed slope as rise over run and used our slope formula to find missing coordinates when given an incomplete point, a second point, and the value for the slope.  Then our discussion about graphing and functions moved into the various forms that represent lines.  We discussed the point-slope form and the standard form of a line.  When given a point and the slope, we plugged those values into the point-slope formula and then solved to put the line in its standard form.

Recall:

Standard form of a line is:

Ax + By = C

Point-slope Form of a line is

y - y₁ = m(x - x₁) where m=slope and (x₁,y₁) is a given point.

Sections Covered in Textbook
1) 10-1: Slope of a Line (Page 402 - Example 5)

2) 10-2:  Point-Slope and Standard Forms of Linear Equations (pages 405-409)

Video Tutorials
1)  Writing Equations in Point-Slope form
http://www.virtualnerd.com/algebra-1/linear-equation-analysis/point-slope-standard-form/point-slope-examples/point-slope-line-direct-example
2)  Writing an Equation of a Line in Standard Form when given a point and the slope
http://www.virtualnerd.com/algebra-1/linear-equation-analysis/point-slope-standard-form/standard-form-examples/write-linear-equation-standard-form-slope-point

Assignments
1) Page 404 #'s 32, 34, 36-39, 40, 41
2) Page 408 #'s 15-35 odd

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
We are getting really competent at solving more and more complex equations.  We reviewed the different types of equations and the distributive property, and moved into multi-step equations and the steps needed to solve those.  We also reviewed basic solving of inequalities and then began our exploration of solving multi-step inequalities.

Sections Covered in Textbook
1)  7-5:  Solving Multi-Step Equations (pages 267-269)

2)  7-6:  Solving Multi-Step Inequalities (pages 270-271)

Video Tutorials
1) Solving Multi-Step equations using the Distributive Property
http://www.virtualnerd.com/pre-algebra/inequalities-multi-step-equations/equations/solve-multiple-step-equations/distributive-propertiy-multi-step-example
2) How to Solve Multi-Step Equations
https://www.youtube.com/watch?v=ahtHbGYSZ-4

Assignments
1) Page 55268 #'s 11-16 all, 17-23 odd

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

Algebra I

Today we discussed
We continue to explore functions and graphing.  Today we discussed how to graph 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

From here, we moved to to a discussion about slope with slope being defined as rise over run.  Another way to express slope is

change in y

change in x

Sections Covered in Textbook
1) 9-6:  Graphing Inequalities in Two Variables (pages 379-383)
2) 10-1: Slope of a Line (pages 400-404)

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

2) What is the Slope of a Line?

http://www.virtualnerd.com/algebra-1/linear-equation-analysis/slope-rate-of-change/understanding-slope/slope-definition

3)  Slope Formula

http://www.virtualnerd.com/algebra-1/linear-equation-analysis/slope-rate-of-change/understanding-slope/slope-formula-definition

4)  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 382#'s 19-47 odd, 48
2) Page 403 #'s 15-31 odd

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Class did not meet today.  Please review the lesson we completed in September that covered the distributive property.  A link to the blog entry can be found by clicking here. 

Assignments
1)  Worksheet on the Distributive Property
Download Worksheet and Answers Here!

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

Faux Snow. . . Happy Pi Day & Topics for 3.14

Algebra I

Today we discussed
Our discussion moved into defining what a function is, how to use the vertical line test to determine if a graph is a function, and also how to evaluate functions for given values of the domain (x) values.

Remember!  We can now use two different methods to write an equation that is a function:

y = 3x -4

is the same thing as

f(x) = 3x - 4

When you are asked to evaluate a function for a given value of x, simply substitute that value for x:

f(x) = 3x - 4

f(5) = 3(5) - 4

f(5) = 11 

Sections Covered in Textbook
1) 9-5: Function s(pages 374-378)

Video Tutorials
1) What is a function?

• http://www.virtualnerd.com/algebra-1/relations-functions/functions/function-notation/standard-form-definition
• https://www.khanacademy.org/math/algebra/algebra-functions/evaluating-functions/v/what-is-a-function

2) What is the vertical line test?
http://www.virtualnerd.com/algebra-1/relations-functions/functions/functions-examples/vertical-line-test-definition

3)  Evaluating Functions for given values of x.
http://www.virtualnerd.com/algebra-1/relations-functions/functions/function-notation/f-of-x-evaluation

Assignments
1)  Pages 377-378 #'s 17-47 odd; 49, 50, 51 & 52

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
Class did not meet today; please review solving equations with variables on both sides.

Assignments
1)  Complete solving equations worksheet.
Download worksheet and answers here.

Moving on . . . March 9th

Algebra I

Today we discussed
We are getting more in depth on the concepts of relations.  We discussed the requirements for linear equations - that is, any equation that can be written in the form of Ax + By = C is a linear equation.  Today, we worked on graphing linear equations and talked about intelligent selection of our domain (x) values.  Remember this discussion when you are dealing with fractions!  We then briefly touched on functions, and will revisit this topic during our next class.

Sections Covered in Textbook
1)  9-4: Graphing Linear Relations (pages 369-373)

Video Tutorials
1) Graphing Linear Equations Using a Table
http://www.virtualnerd.com/algebra-1/relations-functions/graphing-linear-equations/graphs-examples/linear-equation-graphing-method

Assignments
1) Page 372 #'s 17-43 odd, 47
2) Page 661 #'s 35-45 odd (This should be review....)

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

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Pre-Algebra

Today we discussed
We reviewed two-step equations and equations with variables on both sides.  A review of solving two-step equations can be found on the Pre-Algebra section of the blog by clicking here.  A review of solving equations with variables on both sides can be found on the Pre-Algebra section of the blog by clicking here!

Sections Covered in Textbook
1)  7-4: Variables on Each Side (pages 263-266)  (*This was review work.*)

Video Tutorials
1) Variables on both sides of equation
https://www.youtube.com/watch?v=fDMxOiS5g7k

Assignments
1) Page 266 #'s 14-36 even

Concepts for February 23rd

Algebra I

Today we discussed
Our discussion about relations moved into equations as relations.  A solution of a relation that has two variables is any ordered pair that makes the equation true.  We reviewed solving literal equations, and solving for a particular variable.  A review of literal equations can be found here.

Sections Covered in Textbook
1) 9-3: Equations as Relations (pages 364-368)

Video Tutorials
1)  Equations as Relations
https://www.youtube.com/watch?v=hQerO3N2zEE

Assignments
1)  Worksheet 8-9 #'s 1-14 all
Download Worsheet and Answers Here!
2)  Graphing Picture.
Download Coordinates Here!
Download Graph Paper Here!

3) Pages 367-368 #'s 13-41 odd; 42, 43, 44

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

OPTIONAL!

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Pre-Algebra

Today we discussed
Our discussion about solving equations moved to working with variables on both sides.  We discussed strategies for moving the variable first, and which one to pick to start the process.  Remember, there are now three possibilities for solutions: you may have one solution, you may have an infinite number of solutions (all real numbers work), or you may have no solution at all.

Sections Covered in Textbook
1) 7-4: Variables on Each Side (pages 263-266)

Video Tutorials
1) Variables on both sides of equation
https://www.youtube.com/watch?v=fDMxOiS5g7k

Assignments
1) Worksheet on Two Step Equations

Download Worksheet and Answers here!

2) Page 266 #'s 13-35 odd; 42

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

OPTIONAL!

Back To Work on February 21st!

Algebra I

Today we discussed
We moved on to begin a discussion about coordinate graphing, ordered pairs, and relations. We discussed what a relation is and how domain and range are defined.  We also discussed what the inverse of a relation is, and how to represent relations in four different ways:  ordered pairs, table, mapping and coordinate graphing.

Sections Covered in Textbook
1)  9-1; Ordered Pairs (pages 354-358)
2)  9-2: Relations (pages 359-363)

Video Tutorials
1) What is the Coordinate Plane?
http://www.virtualnerd.com/middle-math/integers-coordinate-plane/coordinate-plane/coordinate-plane-definition
How do you plot coordinates in the coordinate plane?
http://www.virtualnerd.com/algebra-1/relations-functions/coordinate-plane/coordinate-plane-graphing/coordinate-plane-graph-points-example
3) What is a relation?
http://www.virtualnerd.com/middle-math/integers-coordinate-plane/coordinate-plane/coordinate-plane-definition
4) Finding the Domain and Range of a Relation
http://www.virtualnerd.com/algebra-1/relations-functions/relations/relations-examples/find-domain-range-example
5) Finding the Inverse of a Relation
http://www.virtualnerd.com/algebra-1/relations-functions/relations/definitions/inverse-definition

Assignments
1) Pages 362-363 #'s 13-41 odd; 42

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK

OPTIONAL!
If you need practice on coordinates and graphing, compete Page 257 #'s 17-53 odd.

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Pre-Algebra

Today we discussed
Today we moved into solving two-step equations.  These equations have two operations going on.  We discussed solving using inverse operations, and using the reverse order of operations to figure out where to start solving.  Also, keep in mind that when you have a fraction that has an operation in the numerator, there is an understood set of parentheses there.  That operation will need to be "undone" last.

Sections Covered in Textbook
1) 7-2:  Solving Two Step Equations (pages 255-258)

Video Tutorials
1)  Solving Two-Step Equations

• http://www.virtualnerd.com/pre-algebra/one-two-step-equations/two-step/two-step-solution/two-step-example
• https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq/alg-two-steps-equations-intro/v/solving-equations-1

Assignments
1)  Page 257 #'s 17-47 odd

**PLEASE CHECK ODD ANSWER IN BACK OF TEXTBOOK