Illustrative Mathematics
The Circle and The Line
Here is a resource where algebra learners show their understanding of a system of equations involving a circle and a line. Once graphed, learners see two points of intersection, one where the ordered pair is read, and a second where...
Illustrative Mathematics
Dimes and Quarters
Here is a coin problem where the algebra learner determines the pair of linear equations needed to solve the system. Whether the equations are taken from a table, or your scholars recognize the format of a coin problem, it is an...
PBL Pathways
Gas Prices
How can math help your vehicle run better? Complete an interesting project-based learning task with your classes to determine the cheapest approach to mixing the ideal octane level of gasoline. Scholars create and solve a system of...
Illustrative Mathematics
Two Lines
Here is a resource that helps your algebra learners understand the connection between the graph of two lines, the equations of lines, and the solutions and intersecting points of lines. It would make a great assessment question, but can...
5280 Math
Go with the Flow
Round and round they go ... where they stop, only scholars will know. By writing systems of equations, classes determine the number of cars a roundabout can handle given specific constraints. Systems use up to six variables and become...
Curated OER
Linear and Quadratic System
Learners find the common point of a linear and quadratic system given a graph of the system. Then they find a specific point located only on the parabola.
Curated OER
Accurately Weighing Pennies II
Drawing from a scenario of the history of the penny, learners write and solve a system of linear equations from a context.
Illustrative Mathematics
Summer Swimming
Here is a real-world application for systems of equations. When is it better to pay an enrollment fee and lower daily rate, and when is it better to pay the regular price? The local swim center is having a special offer, reductions in...
Illustrative Mathematics
Sammy's Chipmunk and Squirrel Observations
Here is a fun project. Sammy observes a chipmunk and a squirrel to see how many holes each needs in order to stash the same number of acorns. Scholars could find the answer algebraically or create a table to analyze the problem in...
Curated OER
Find A System
Learners must think critically about the graphical and algebraic forms of a system of linear equations in order to come up with their own system when given a point that is the solution to the system.
5280 Math
More or Less the Same
Tell the story of the math. Given a graph of a linear system, learners write a story that models the graph before crafting the corresponding functions. Graphs intersect at an estimated point, allowing for different variations in the...
Curated OER
Pairs of Whole Numbers
Mathematical reasoning and linear systems are two of the strategies used to solve this number puzzle. Your learners will enjoy the challenge and the variety of ways to approach this challenge.
Curated OER
Accurately Weighing Pennies I
Drawing from a scenario of the history of the penny, learners write and solve a system of linear equations from a context.
Illustrative Mathematics
Fixing the Furnace
This comprehensive resource applies simultaneous equations to a real-life problem. Though the commentary starts with a graph, some home consumers may choose to begin with a table. A graph does aid learners to visualize the shift of one...
Curated OER
Solution Sets
Here is a task that gives the graph of the solutions of a system of linear inequalities and asks learners to analyze and write the algebraic form of the systems. By turning the problem around, learners make the connections between...
Curated OER
Sum of Even and Odd
Your algebra learners will make use of structure and manipulate expressions involving function notation using the definition of odd and even functions. They then advance even further to analyze the structure in a system of two equations.
Curated OER
What Functions do Two Graph Points Determine?
Your algebra learners write linear, exponential, and quadratic equations containing the same two graph points in this collaborative task.
5280 Math
Pythagorean Triples
From Pythagorean triples to the unit circle. Learners use the Pythagorean Theorem to find Pythagorean triples and then relate their work to the unit circle in a fun algebra project. Their discovery that x^2+y^2 is always equal to one on...
Illustrative Mathematics
How Many Solutions?
Determining the number of solutions is an important stepping stone to higher math. For this case, the resource asks algebra pupils to find a second linear equation for a certain solution of a system. When one is asked for a linear...
Illustrative Mathematics
Growing Coffee
Ask your algebra learners to write an equation that has unit constraints. This commentary talks about the constraints, but does not show them in the equation. It is important that your mathematicians understand that the units apply to...