Variables and Patterns: Focus on Algebra
Learning Targets
- I can explain the concept of a variable.
- I can make a graph from a given data table.
- I can explain advantages and disadvantages of using a table or a graph to represent data.
- I can explain how average speed is shown on a distance-time graph.
- I can label independent variables on the axes of a graph.
- I can plot ordered pairs in all four quadrants of a coordinate plane.
- I can describe how a graph increases, decreases, or stays constant using words.
- I can explain the concept of an equation.
- I can write a one-step equation from a given situation.
- I can write a two-step equation from a given situation.
- I can evaluate algebraic expressions with variables.
- I can combine like terms to simplify expressions.
- I can determine whether two algebraic expressions are equivalent.
- I can write equivalent algebraic expressions using the distributive property.
- I can solve one-step equations involving addition and subtraction.
- I can solve one-step equations involving multiplication and division.
- I can explain the concept of an inequality.
- I can solve one-step inequalities.
- I can graph inequalities on a number line.
Video Notes Links and Additional Resources/Practice
What is a Variable?
I can explain the concept of a variable.
Constructing Graphs from Tables
I can make a graph from a given data table.
Average Speed on a Graph
I can explain how average speed is shown on a distance-time graph.
Independent and Dependent Variables
I can label independent and dependent variables on the axes of a graph.
I can plot ordered pairs in all four quadrants of a coordinate plane.
Describing Graphs in Words
I can describe how a graph increases, decreases, or stays constant using words.
What is an Equation?
I can explain the concept of an equation.
Writing One-Step Equations
I can write a one-step equation from a given situation.
Writing Two-Step Equations
I can write a two-step equation from a given situation.
Evaluating Algebraic Expressions
I can evaluate algebraic expressions with variables.
I can combine like terms to simplify expressions.
Equivalent Algebraic Expressions
I can determine whether two algebraic expressions are equivalent.
Solving One Step Equations - Addition and Subtraction
I can solve one-step equations involving addition and subtraction.
Solving One Step Equations - Multiplication and Division
I can solve one-step equations involving multiplication and division.
What is an Inequality?
I can explain the concept of an inequality.
Solving Inequalities
I can solve one-step inequalities.
Graphing Inequalities
I can graph inequalities on a number line.
I can explain the concept of a variable.
- Video tutorial #1: https://www.youtube.com/watch?v=JZ9jacCqss4
- Video tutorial #2: https://www.youtube.com/watch?v=pARqOO5GOl0
- Video tutorial #3: https://www.youtube.com/watch?v=tHYis-DP0oU
Constructing Graphs from Tables
I can make a graph from a given data table.
- Video tutorial #1: https://www.youtube.com/watch?v=XDm0CjHlhpY
- Video tutorial #2: https://www.youtube.com/watch?v=FLF7wllkiVM
- Video tutorial #3: https://www.youtube.com/watch?v=cNDd8QqZUcA
- Constructing graphs practice: https://www.mathgames.com/skill/6.99-create-line-graphs
- Video tutorial #1: https://www.youtube.com/watch?v=rheOa2Y9UfQ
- Visual Battle: Table vs. Graph article: http://www.storytellingwithdata.com/blog/2011/11/visual-battle-table-vs-graph
- Keep in mind that the video and article above are just two opinions. When do you prefer to use tables? When do you prefer to use graphs? Why?
Average Speed on a Graph
I can explain how average speed is shown on a distance-time graph.
- Video tutorial #1: https://www.youtube.com/watch?v=w7Oj2-Z8avE
- Video tutorial #2: https://www.youtube.com/watch?v=l93-BkAJ3UY
- Video tutorial #3: https://www.youtube.com/watch?v=9LQdLDDEJ1g
- Constructing a distance-time graph:
https://www.thephysicsaviary.com/Physics/Programs/Games/MotionGraphMatching/index.html - Calculating average speed practice: https://www.khanacademy.org/science/ap-physics-1/ap-one-dimensional-motion/instantaneous-velocity-and-speed/e/average-velocity-and-average-speed-exercise
Independent and Dependent Variables
I can label independent and dependent variables on the axes of a graph.
- Video tutorial #1: https://www.youtube.com/watch?v=rU7l5FkIHus
- Video tutorial #2: https://www.youtube.com/watch?v=H3vZ8wIQ4kI
- DRY MIX is a very helpful way to remember that the independent variable goes on the x-axis and the dependent variable goes on the y-axis.
- Video tutorial #3: https://www.youtube.com/watch?v=-9ikuu997LY
- Identifying variables practice:
I can plot ordered pairs in all four quadrants of a coordinate plane.
- Video tutorial #1: https://www.youtube.com/watch?v=1O12C9EcdFo&t=18s
- Video tutorial #2: https://www.youtube.com/watch?v=r16I6LB2YbQ
- Video tutorial #3: https://www.youtube.com/watch?v=cze5B-AiV88
- Plotting points practice:
- https://www.geogebra.org/m/A5rSmb3Z
- Be sure to click on the "Next Point" button so that you can plot more points!
- https://www.geogebra.org/m/kVkHsYfp#material/xPFzv5FW
- https://www.geogebra.org/m/kVkHsYfp#material/RCA9CT3s
- https://www.geogebra.org/m/A5rSmb3Z
- Locate the alien game: http://www.mathplayground.com/locate_aliens.html
- Bonk the mole game: http://funbasedlearning.com/algebra/graphing/points3/
- Word problems practice: https://www.khanacademy.org/math/on-sixth-grade-math/on-geometry-spatial-sense/on-coordinate-plane/e/coordinate-plane-word-problems
Describing Graphs in Words
I can describe how a graph increases, decreases, or stays constant using words.
- Video tutorial #1 (vocabulary): https://www.youtube.com/watch?v=xqgZN54ai_Q
- Video tutorial #2: https://www.youtube.com/watch?v=Ux1w_1whjH8&t=9s
- Video tutorial #3: https://www.youtube.com/watch?v=eul9UlmPSJ8&t=217s
What is an Equation?
I can explain the concept of an equation.
- Video tutorial #1: https://www.youtube.com/watch?v=DO-hzLh79uw
- Video tutorial #2: https://www.youtube.com/watch?v=Ot-KSERw8Gc
- Modeling equations game: http://www.hoodamath.com/mobile/games/algebrabalanceequations.html
- In this game, focus on making the two sides of the scale equal based on the problem provided. Then, click "new problem." You do not have to solve the equations at this time...although you are certainly welcome to!
Writing One-Step Equations
I can write a one-step equation from a given situation.
- Video tutorial #1: https://www.youtube.com/watch?v=yUOn9o8SOT4
- Focus on learning how to write an equation. We'll solve one-step equations in a couple of weeks!
- Video tutorial #2: https://www.youtube.com/watch?v=2REbsY4-S70
- Writing equations practice:
- https://www.khanacademy.org/math/pre-algebra/pre-algebra-equations-expressions/pre-algebra-equation-word-problems/e/equations-in-one-variable-1
- https://www.mathgames.com/skill/5.98-write-variable-equations-to-represent
- https://www.mathgames.com/skill/6.148-write-variable-equations-to-represent
- When writing equations, we do not use a multiplication sign between the variable and coefficient (number in front of the variable). For example, instead of 117 x n, we write 117n.
Writing Two-Step Equations
I can write a two-step equation from a given situation.
- Video tutorial #1: https://www.youtube.com/watch?v=VB_G6Gotpp0
- Video tutorial #2: https://www.youtube.com/watch?v=Qs5mCkkjdTY
- Writing equations practice: https://braingenie.ck12.org/skills/105348
Evaluating Algebraic Expressions
I can evaluate algebraic expressions with variables.
- Video tutorial #1 (definition of expression): https://www.youtube.com/watch?v=D2vDY4hX_PI
- Video tutorial #2: https://www.youtube.com/watch?v=4oyYyqcfWu4
- Video tutorial #3: https://www.youtube.com/watch?v=S_OX3ByvBSc
- Evaluating expressions practice (one variable):
- Evaluating expressions practice (two variables):
- Jeopardy game: https://www.superteachertools.us/jeopardyx/jeopardy-review-game.php?gamefile=357262#.V7y96pgrLIU
- Who wants to be a millionaire game: https://www.quia.com/rr/195129.html?AP_rand=61657093
I can combine like terms to simplify expressions.
- Video tutorial #1: https://www.youtube.com/watch?v=gOChLkYvTjE&t=338s
- Video tutorial #2: https://www.youtube.com/watch?v=RFfeEp5JmUs
- Combining like terms practice:
- Identifying like terms games:
- Who wants to be a millionaire? game: https://www.quia.com/rr/195128.html?AP_rand=1413834248
Equivalent Algebraic Expressions
I can determine whether two algebraic expressions are equivalent.
- Video tutorial #1: https://www.youtube.com/watch?v=Cfl6juyoZBQ
- Video tutorial #2: https://www.youtube.com/watch?v=rHNY01R2VSQ&disable_polymer=true
- Identifying equivalent expressions practice: https://www.khanacademy.org/math/algebra/introduction-to-algebra/alg1-equivalent-expressions/e/equivalent-forms-of-expressions-1
- Video tutorial #1: https://www.youtube.com/watch?v=DTS_5AStqwo&t=297s
- Video tutorial #2 (area model): https://www.youtube.com/watch?v=WSEpAKvE2Z4
- Video tutorial #3 (numbers only): https://www.youtube.com/watch?v=udm1E-gNU6M
- Writing equivalent expressions practice:
- https://www.khanacademy.org/math/algebra-basics/alg-basics-algebraic-expressions/alg-basics-distributive-property/e/distributive-property-with-variables
- http://studyjams.scholastic.com/studyjams/jams/math/multiplication-division/distrib-property.htm
- Click on "Test Yourself" to access the practice problems. Make sure that you review your answers and click on the "Feedback" button for any answers that were incorrect.
- Exploring the area model for the distributive property: https://www.geogebra.org/m/cHCpcEEW
- Battleship game: https://www.quia.com/ba/15357.html
Solving One Step Equations - Addition and Subtraction
I can solve one-step equations involving addition and subtraction.
- Video tutorial #1: https://www.youtube.com/watch?v=sP_lJyo1U00
- Video tutorial #2: https://www.youtube.com/watch?v=l3XzepN03KQ
- Interactive practice: https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebra-solving-basic-equations/e/one_step_equations
- Soccer game: http://www.math-play.com/soccer-math-one-step-equations-game/one-step-equations-game.html
- Jeopardy games:
Solving One Step Equations - Multiplication and Division
I can solve one-step equations involving multiplication and division.
- Video tutorial #1: https://www.youtube.com/watch?v=NJoUIId_bRM
- Video tutorial #2: https://www.youtube.com/watch?v=Qyd_v3DGzTM
- Interactive practice: https://www.khanacademy.org/math/in-eighth-grade-math/linear-equations-one-variable/equations-linear-expressions-one-side-numbers-other/e/linear_equations_1
- Jeopardy games:
What is an Inequality?
I can explain the concept of an inequality.
- Video tutorial #1: https://www.youtube.com/watch?v=g0CWB3CshFY
- Video tutorial #2: https://www.youtube.com/watch?v=G0b7VtWDQ8Y
Solving Inequalities
I can solve one-step inequalities.
- Video tutorial #1 (adding and subtracting): https://www.youtube.com/watch?v=smX2wkIUPvQ
- Video tutorial #2 (multiplying and dividing): https://www.youtube.com/watch?v=QLMlYoXz2Zg&t=219s
- Solving inequalities practice:
- Adding and subtracting: http://www.math-aids.com/cgi/pdf_viewer_2.cgi?script_name=pre-algebra_inequality_add_sub.pl>=1<=1>e=1<e=1&language=0&memo=&answer=1&x=153&y=17
- Multiplying and dividing: http://www.math-aids.com/cgi/pdf_viewer_2.cgi?script_name=pre-algebra_inequality_multi_divide.pl>=1<=1>e=1<e=1&language=0&memo=&answer=1&x=72&y=38
Graphing Inequalities
I can graph inequalities on a number line.
- Video tutorial #1: https://www.youtube.com/watch?v=jrWmqEJjhLY
- Video tutorial #2: https://www.youtube.com/watch?v=IDG20QMlcm8
- You will not be assessed on any inequalities with "and" or "or."
- Video tutorial #3: https://www.youtube.com/watch?v=nif2PKA9bXA
- Graphing inequalities practice:
- Car race game: http://www.xpmath.com/forums/arcade.php?do=play&gameid=102
- Earn points by driving over the red part of the number line. Visualize the inequality in your head first