Systems of Equations
1 Hook/Attention Getter
Teacher will create 3 substitution questions on the Kahoot template to assess students prior knowledge of solving systems of equations with substitution (survey mode).
Questions will be listed under student instructions.
Students will respond to the following questions utilizing the Kahoot template.
1. x- 2y = 27
y = 5x
a. (-3, -15) b. (-3, -16) c. (-4, -20) d. (3, 15)
2. x + 3y = 1
5x + 2y = -21
a. (-6, 3) b. (-5, 2) c. all ordered pairs along x + 3y = 1
d. no solution
3. y = 13 - 3x
9y + 2x = -8
a. (-5, -2) b. (5, 2) c. (-5, 2) d. (5, -2)
2 Direct Instruction
Teacher will show a video from Khan Academy on the topic of solving systems of equations with substitution.
Teacher will expand upon the video by teaching three more examples on the board.
*Same questions from Hook/Attention Getter
Students will be instructed to watch the short video clip from Khan Academy and take notes on the problem/s being taught.
Students will ask questions/worth through the hook/attention getter questions with teacher. Students may volunteer to participate interactively at the board.
3 Guided Instruction
Teacher will give pairs of students a system of equations to solve with substitution. Students will be instructed to collaborate with each other to solve their system and demonstrate to classmates how to solve.
Teacher will observe the classroom to classify the students that need more assistance with their system of equations.
1. y = 5x -4
y = 5x - 5
2. 2x - 3y = -1
y = x - 1
3. y = 5x - 7
-3x - 2y = -12
4. -4x + y = 6
-5x - y = 21
5. -3x + 3y = 4
-x + y = 3
Students will be given instructions to work with their partner to solve the system of equations given. They will be prompted to ask questions if needed.
Students will present their solution to the class, demonstrating mastery to their classmates.
4 Independent Practice
Teacher will notify a select group of about the use of Khan Academy on the computers. These students are the "middle of the road" performers.
*Refer to the link from direct instruction.
The below-average performers will work in a small group setting with the teacher while the "high flyers" will work independently on a worksheet. High flyers may also explore the option of completing a scavenger hunt.
Students will be given specific instructions from the teacher about their placement within the classroom.
5 Wrap Up
Teacher will set up two questions on Kahoot in order to assess student learning.
The two systems are as follows:
1. y = 6x + 11
2y - 4x = 14
2. 2x - 3y = -4
x + 3y = 7
Students will be instructed to enter their response on the kahoot template.
Key Standards Supported
Expressions And Equations
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.
Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
Solve linear equations in one variable.
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
Analyze and solve pairs of simultaneous linear equations.
Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.