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Teaching algebraic reasoning, graphing, and making connections with geometry can be confusing. The map is packed with tools to help a teacher. It includes games, videos, lesson plans, and tools to help your students succeed. The outline is provides the major topics about how to teach alegebraic reasoning, graphing, and make connections with geometry.
The map can also refresh those skills that may have been forgotten. The mind map will keep you organized and shows you how key concepts can be chunked together.
References:
Alex Lesson Plans. Alabama Learning Exchange. Retrieved from
http://alex.state.al.us/lesson_view.php?id=26338
https://www.youtube.com/watch?v=k4KdGiJPbN8
Basics About a Circle.
http://www.areacircle.com/basics-about-area-of-a-circle.html
Basic Algebra. Basic Mathematics. Retrieved from
http://www.basic-mathematics.com/what-is-slope.html
Better Explained Math Insights with a Click. Retrieved from
http://betterexplained.com/articles/techniques-for-adding-the-numbers-1-to-100/
Bing Image. The Cartesian Coordinate Plane. Carhttp://www.plane-land.net/wp-content/uploads/2012/01/Cartesian-Coordinate-Plane.jpg
Bing Image. Fibonacci Sequence. Retrieved from https://nakawligaw.files.wordpress.com/2014/02/fibonacci-sequence.png
Bing Image. Pie. Retrieved from http://3.bp.blogspot.com/_a1VB-fjgHlQ/TLXptDsnlYI/AAAAAAAAAFY/EHoN5473VVU/s1600/diameter,+radius,+circumference.jpg
Bing Image. Plotting Points. Retrieved from http://stufiles.sanjac.edu/THEA/THEA_Math_Review/Graphs_of_Number_Relationships/930.png
Brain Pop. Gopher Game. Retrieved from https://www.brainpop.com/games/gameovergopher/
Ehow. Game for Parallel and Perpendicular lines. Retrieved from https://www.youtube.com/watch?t=17&v=hQ64ZoDvN_k
Khan Academy. Coordinate Plane. Retrieved from
https://www.khanacademy.org/math/algebra-basics/core-algebra-graphing-lines-slope/core-algebra-graphing-coordinate-plan/v/plot-ordered-pairs
Math Worksheets 4 Kids. Retrieved from http://www.mathworksheets4kids.com/function/graphing-linear1.pdfPromethean Planet. Teaching Resources.
Prometheplanet. Retrieved from http://www.prometheanplanet.com/en/Search/resources/language/english/?Keywords=function+tables
PBS. Using Two Variables to Express Algebraic Equations. Retrieved from http://www.pbslearningmedia.org/resource/vtl07.math.algebra.var.lptwovaria/using-two-variables-to-express-algebraic-relationships/Purple Math. The Quadrants o the Cartesian Plane.
http://www.purplemath.com/modules/plane3.htm
Teaching Channel. Chessboard Algebra Function Machine. Retrieved from
https://www.teachingchannel.org/videos/algebra-lesson-planning
Writing Equations of a Line. Algebra Lab. Retrieved from http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_LinearEqEquationsOfLines.xml
Additional website resources for teaching algebraic reasoning, graphing, along with connections in geometry.
1. Alex Learning Lessons (Investigating and Discovering Input & Output Patterns).
http://alex.state.al.us/lesson_view.php?id=26338
2. Function Tables
http://www.prometheanplanet.com/en/Search/resources/language/english/?Keywords=function+tables
3. Teacher Channel Video (learn how Ms. Bottomley uses a function machine to have students predict the rule).
https://www.teachingchannel.org/videos/algebra-lesson-planning
4. Graphing Linear Functions Worksheet
http://www.mathworksheets4kids.com/function/graphing-linear1.pdf
5. Graphing Two Variables to Express Algebraic Relationship
http://www.pbslearningmedia.org/resource/vtl07.math.algebra.var.lptwovaria/using-two-variables-to-express-algebraic-relationships/
6. Modeling with Mathematics (Keys to Modeling with Mathematics in the K-8 Classroom).
https://www.teachingchannel.org/blog/2013/05/29/3-keys-to-modeling-with-mathematics/
7. Variables
http://www.pbslearningmedia.org/resource/vtl07.math.algebra.var.lptwovaria/using-two-variables-to-express-algebraic-relationships/
- A non-linear function is not a linear function.
- A quadratic function is
f (x) = ax 2 + bx + c , where a, b, c if a≠ 0 .
-Exponential function (see video)
We need to study the problem to have a better understanding of what we are being asked. We need to decide how to solve it. Then it is important to being to solve it. Then reflect and look back at the solution.
What Theorem needs to be used.
1. The point-slope form is will be used when we are given a point (x1, y1) and a slope m. Then the numbers are plugged into the formula:
y – y1 = m(x – x1)
2. The slope-intercept form is used where m is the slope and b is the y-intercept.
y=mx+b
3 For the two-point form of the equation of a line we would use the formula
y – y1 = m(x – x1)
The slope and (x1, y1) is a point on the line. Point-slope is the form used most often when finding the equation of a line.
Functions:
-A linear function is a straight-line graph.
What is the slope? A real world example is walking up or down a flight of stairs.
The slope of a line defines the steepness of the line. It allows us to know if the line is rising or falling.
Slope = Rise/Run
We can use this formula to determine the distance between the two points (4,5) and (1,2).
Quadrant I both coordinates are positive.
Quadrant II first coordinate is negative and second coordinate is positive.
Quadrant III both coordinates are negative.
Quadrant IV first coordinate is positive and second coordinate is negative.
Plotting Points
References:
Ehow. How to Use Functions to Teach Algebra. Retrieved from http://www.bing.com/videos/search?q=how+to+use+functions+tables+youtube&FORM=VIRE7#view=detail&mid=D23955324C10AFD5B81ED23955324C10AFD5B81E
Graph Game. Retrieved from
http://www.mathxl.com/Student/MediaPopup.aspx?type=assignedmedia&assignmentId=283516755&loc=3&flush=yes&record=1&OnOpenerViewed=doMedia_onViewed
Graphic. Retrieved from
http://www.jackanderica.com/math/images/plot007.jpg
IXL. Retreived from http://www.ixl.com/math/grade-3/solve-for-the-variable-addition-and-subtraction-only
Long, C. et al. (2015). Mathematics Reasoning for Elementary Teachers. Boston, MA. Pearson
Math Antics. Circles, Circumference And Area. Retrieved from https://www.youtube.com/watch?v=O-cawByg2aA
Math Help. Mapping Diagrams. Retrieved from
http://www.bing.com/videos/search?q=functions+as+arrow+diagrams+video+algebra&FORM=VIRE5#view=detail&mid=49B4EB35DDBD9F4C138949B4EB35DDBD9F4C1389
Math Plant. Retrieved from
http://www.mathplanet.com/education/algebra-1/discovering-expressions,-equations-and-functions/expressions-and-variables
Math XL. Retrieved from
http://www.mathxl.com/Student/MediaPopup.aspx?type=assignedmedia&assignmentId=283516755&loc=4&flush=yes&record=1&OnOpenerViewed=doMedia_onViewed
Solving Equations. Retrieved from
http://www.sosmath.com/algebra/solve/solve0/solve0.html
Think Math. Retrieved from
http://thinkmath.edc.org/resource/guess-my-rule
Who Wants to a Hundredaire. (n.d). Retrieved from
http://www.math-play.com/Algebraic-Expressions-Millionaire/algebraic-expressions-game.html
Math is integrated into many different areas such as geometry, probability, and algebra. They will continue to keep building on one another.
Picture a circle and you are standing in the center of it. If you were to run from the center to the outside edge in a straight line that distance is the radius.
Using the circle analogy again, if you were to run in a straight line, starting on one side through the center of the circle and end on the other side, this would be the diameter.
If you were to run in a perfect circle, the distance that you covered would be the circumference of that circle.
Parallel lines are parallel if they are always the same distance apart and will never meet. Therefore, their slopes are always the same.
Perpendicular lines meet at a right angle (90°).
We can solve equations by using visual functions such as "What's my rule, function tables, arrow diagrams, machines, and graphs."
Example of the Fibonacci sequence and the doubling function
A math function table is a table used to plot possible outcomes.
The definition of function requires that a single value y be assigned to each x-value in the domain.
Example,
We are at the gas station, filling the vehicle with gas which is priced at $3.95 per gallon. "How much does 15 gallons cost?"
The answer is $59.25. This is the only cost of the gas because there is only one value for y for each x.
Machines were invented to make these calucations fast and error free for us.
An equation is a mathematical expression, stating that two algebraic expressions have the same value.
Algebraic expression is a representation that involves variables, numbers, and operations symbols.
Lets start with algebraic reasoning. Here are some topics we will cover.
• What are variables?
• How to form algebraic expressions involving variables, numbers, and operation symbols?
• What is the definition and visualization of functions?
Variables used in algebra are letters such as x, y, f, or any letter to represent unknown numbers.
Variables express formulas
Commonly used formulas
Variables serve as unknowns in equations
Find a number to place in the blank that makes the sentence true.
__ + 7 = 9
or
(3x-6)(x-2)=0
Variables express relationships
Variables express relationships, here are some examples.
J=K-6 ("Addy is six years younger than Kendra")
K=J+6 ("Sara is six years older than Addy.")
K-J=6 ("The difference in age between Sara and her younger sister Addy is six years.")
Variables describe generalized properties
Example
Example:
a(b+C) = ab+ac
A constant is a non-changing value that represents a fixed number.
Here are several examples of a constant
3, 10, π, 1/2.
Examples
One dozen eggs equals 12.
There are four sides to a rectangle
and
2 + 5 = 7
Why is it important to teach students algebraic reasoning, and graphing? Why do student's need to make connections with geometry? Forty years from now, four plus four will still equal eight. Students need critical thinking skills so they can think through an issue, and reason logically to solve problems outside the classroom in real world.
