| Code |
Description |
| MA.912.A.3.1: | Solve linear equations in one variable that include simplifying algebraic expressions. |
| MA.912.A.3.2: | Identify and apply the distributive, associative, and commutative properties of real numbers and the properties of equality. |
| MA.912.A.3.3: | Solve literal equations for a specified variable. |
| MA.912.A.3.4: | Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution. |
| MA.912.A.3.5: | Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities. |
| MA.912.A.3.6: | Solve and graph the solutions of absolute value equations and inequalities with one variable. |
| MA.912.A.3.7: | Rewrite equations of a line into slope-intercept form and standard form. |
| MA.912.A.3.8: | Graph a line given any of the following information: a table of values, the x- and y-intercepts, two points, the slope and a point, the equation of the line in slope-intercept form, standard form, or point-slope form . |
| MA.912.A.3.9: | Determine the slope, x-intercept, and y-intercept of a line given its graph, its equation, or two points on the line. |
| MA.912.A.3.10: | Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line. |
| MA.912.A.3.11: | Write an equation of a line that models a data set, and use the equation or the graph to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change. |
| MA.912.A.3.12: | Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph. |
| MA.912.A.3.13: | Use a graph to approximate the solution of a system of linear equations or inequalities in two variables with and without technology. |
| MA.912.A.3.14: | Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods. |
| MA.912.A.3.15: | Solve real-world problems involving systems of linear equations and inequalities in two and three variables. |
This cluster includes the following access points.
| Access Point Number |
Access Point Title |
| MA.912.A.3.In.a: | Solve equations with one unknown (variable) involving addition, multiplication, subtraction, and division of whole numbers representing problems in real-world situations. |
| MA.912.A.3.In.b: | Use the commutative, associative, and equality properties of addition as strategies to solve equations involving real-world situations. |
| MA.912.A.3.In.c: | Use the commutative and associative property of multiplication and the properties of one and zero for multiplication as strategies to solve equations involving real-world situations. |
| MA.912.A.3.In.d: | Solve equations involving common literal formulas related to real-world situations. |
| MA.912.A.3.In.e: | Solve real-world equations and inequalities with one unknown (variable) using visual models to represent the procedure. |
| MA.912.A.3.In.g: | Create function tables and simple graphs that show the mathematical relationship between number pairs. |
| MA.912.A.3.In.h: | Use function tables and simple graphs representing equations to make predictions for real-world situations. |
Vetted resources educators can use to teach the concepts and skills in this topic.
| Name |
Description |
| MIT BLOSSOMS - The Broken Stick Experiment: Triangles, Random Numbers and Probability: | This learning video is designed to develop critical thinking in students by encouraging them to work from basic principals to solve a puzzling mathematics problem that contains uncertainty. One class session of approximately 55 minutes is necessary for lesson completion. First-year simple algebra is all that is required for the lesson, and any high school student in a college-preparatory math class should be able to participate in this exercise. Materials for in-class activities include: a yard stick, a meter stick or a straight branch of a tree; a saw or equivalent to cut the stick; and a blackboard or equivalent. In this video lesson, during in-class sessions between video segments, students will learn among other things: 1) how to generate random numbers; 2) how to deal with probability; and 3) how to construct and draw portions of the X-Y plane that satisfy linear inequalities. |
| Get a Half-life!: | In this activity students are challenged to model a decay function by collecting data from a few trials, graphing the data, and then drawing a curve of best fit. The student must decide which of the equations best fits his/her data. |
| Drip, Drop, Drip, Drop: | Students design an experiment to model a leaky faucet and determine the amount of water wasted due to the leak. Using the data they gather in a table, students graph and write an equation for a line of best fit. Students then use their derived equation to make predictions about the amount of water that would be wasted from one leak over a long period of time or the amount wasted by several leaks during a specific time period.
|
| Name |
Description |
| Solving Systems by Substitution 1: No Solution: | This video demonstrates the substitution method to solve a system of equations, that there is no solution, and that the graphs of the equations are parallel. |
| Parallel Lines 2: | This video shows how to determine which lines are parallel from a set of three different equations. |
| Parallel Lines: | This video illustrates how to determine if the graphs of a given set of equations are parallel. |
| Perpendicular Lines 2: | This video describes how to determine the equation of a line that is perpendicular to another line. All that is given initially the equation of a line and an ordered pair from the other line. |
| Example of Solving for a Variable - Khan Academy: | This video takes a look at rearranging a formula to highlight a quantity of interest. |
| Basic Linear Function: | This video demonstrates writing a function that represents a real-life scenario. |
| Graphing Lines 1: | Khan Academy video tutorial on graphing linear equations: "Algebra: Graphing Lines 1" |
| Fitting a Line to Data: | Khan Academy tutorial video that demonstrates with real-world data the use of Excel spreadsheet to fit a line to data and make predictions using that line. |
| Soybean growth rate response to touch: | A time-lapse video showing differential growth rates for touch-treated seedlings and control seedlings. This would be appropriate for lessons about plant growth responses to environmental stress and graphing growth rate. Plants were grown in a vermiculite soilless medium with calcium-enhanced water. No other minerals or nutrients were used. Plants were grown in a dark room with specially-filtered green light. The plants did not grow by cellular reproduction but only by expansion of existing cells in the hypocotyl region below the 'hook'.
Video contains three plants in total. The first two plants to emerge from the vermiculite medium are the control (right) and treatment (left) plants. A third plant emerges in front of these two but is removed at the time of treatment and is not relevant except to help indicate when treatment was applied (watch for when it disappears). When that plant disappears, the slowed growth rate of the treatment plant is apparent.
Treatment included a gentle flexing of the hypocotyl region of the treatment seedling for approximately 5 seconds. A rubber glove was used at this time to avoid an contamination of the plant tissue.
Some video players allow users to 'scrub' the playback back and forth. This would help teachers or students isolate particular times (as indicated by the watch) and particular measurements (as indicated by the cm scale). A graph could be constructed by first creating a data table and then plotting the data points from the table. Multiple measurements from the video could be taken to create an accurate graph of the plants' growth rates (treatment vs control).
Instructions for graphing usage:
The scale in the video is in centimeters (one cm increments). Students could observe the initial time on the watch in the video and use that observation to represent time (t) = 0. For that value, a mark could be made to indicate the height of the seedlings. As they advance and pause the video repeatedly, the students would mark the time (+2.5 hours for example) and mark the related seedling heights. It is not necessary to advance the video at any regular interval but is necessary to mark the time and related heights as accurately as possible. Students may use different time values and would thus have different data sets but should find that their graphs are very similar. (Good opportunity to collect data from real research and create their own data sets) It is advised that the students collect multiple data points around the time where the seedling growth slows in response to touch to more accurately collect information around that growth rate slowing event. The resulting graph should have an initial growth rate slope, a flatter slope after stress treatment, and a return to approximately the same slope as seen pre-treatment. More data points should yield a more thorough view of this. This would be a good point to discuss. Students can use some of their data points to calculate approximate pre-treatment, immediate post-treatment, and late post-treatment slopes for both the control and treatment seedlings.
This video was created by the submitter and is original content.
Full screen playback should be an option for most video players. Video quality may appear degraded with a larger image but this may aid viewing the watch and scale for data collection. |
Vetted resources students can use to learn the concepts and skills in this topic.
| Title |
Description |
| Parallel Lines 2: | This video shows how to determine which lines are parallel from a set of three different equations. |
| Parallel Lines: | This video illustrates how to determine if the graphs of a given set of equations are parallel. |
| Perpendicular Lines 2: | This video describes how to determine the equation of a line that is perpendicular to another line. All that is given initially the equation of a line and an ordered pair from the other line. |
| Example of Solving for a Variable - Khan Academy: | This video takes a look at rearranging a formula to highlight a quantity of interest. |
| Basic Linear Function: | This video demonstrates writing a function that represents a real-life scenario. |
| Graphing Lines 1: | Khan Academy video tutorial on graphing linear equations: "Algebra: Graphing Lines 1" |
| Fitting a Line to Data: | Khan Academy tutorial video that demonstrates with real-world data the use of Excel spreadsheet to fit a line to data and make predictions using that line. |
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
