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