CK-12 Algebra Explorations is a hands-on series of activities that guides students from Pre-K to Grade 7 through algebraic concepts.

Students learn about linear programming (also called linear optimization) to solve engineering design problems. As they work through a word problem as a class, they learn about the ideas of constraints, feasibility and optimization related to graphing linear equalities. Then they apply this information to solve two practice engineering design problems related to optimizing materials and cost by graphing inequalities, determining coordinates and equations from their graphs, and solving their equations. It is suggested that students conduct the associated activity, Optimizing Pencils in a Tray, before this lesson, although either order is acceptable.

Analyzing probability of events through Venn diagramsMathematics Instructional Plans (MIPs) help teachers align instruction with the 2016 Mathematics Standards of Learning (SOL) by providing examples of how the knowledge, skills and processes found in the SOL and curriculum framework can be presented to students in the classroom.

In the Ball Bounce task, teams of three students collect real-time ball bounce data for two minutes to organize, display and use to form predictions. After collecting and organizing their data, students first observe how the data behave. Then they make predictions using data, scatterplots, or the equation of the curve of best fit to solve a
practical problem. This task offers students collaborative experience in using mathematical models of linear functions.

Normal Distribution Mathematics Instructional Plans (MIPs) help teachers align instruction with the 2016 Mathematics Standards of Learning (SOL) by providing examples of how the knowledge, skills and processes found in the SOL and curriculum framework can be presented to students in the classroom.

This task provides an exploration of a quadratic equation by descriptive, numerical, graphical, and algebraic techniques. Based on its real-world applicability, teachers could use the task as a way to introduce and motivate algebraic techniques like completing the square, en route to a derivation of the quadratic formula.

Students research two variables about the car model they intend to purchase. They use Desmos to compare these same variables across five different car models. Students use analysis of bivariate data in order to decide which car makes sense to buy. Students prepare and share a summary statement and include desmos screen shots in order to justify their purchase. This task offers students experiences in making predictions, using data, scatterplots, or the equation of the curve of best fit for decision-making in a practical problem.

How are grocery shelf location and sugar content of cereals related? In this task, students visit two grocery stores to compare the amount of sugar in boxes of cereal that are displayed on the top shelf to the amount of sugar in boxes of cereal that are displayed on the second to the bottom shelf. They design and conduct a survey to compare their findings from two stores. In doing so, they encounter sample size, sampling technique, data collection, and
data analysis and reporting. Students compare their data in summary plots using two box and whisker plots. Students create a written report to share and relate findings to marketing decision making.

With your mouse, drag data points and their error bars, and watch the best-fit polynomial curve update instantly. You choose the type of fit: linear, quadratic, cubic, or quartic. The reduced chi-square statistic shows you when the fit is good. Or you can try to find the best fit by manually adjusting fit parameters.

With your mouse, drag data points and their error bars, and watch the best-fit polynomial curve update instantly. You choose the type of fit: linear, quadratic, cubic, or quartic. The reduced chi-square statistic shows you when the fit is good. Or you can try to find the best fit by manually adjusting fit parameters.

Modeling Data Using an Appropriate FunctionMathematics Instructional Plans (MIPs) help teachers align instruction with the 2016 Mathematics Standards of Learning (SOL) by providing examples of how the knowledge, skills and processes found in the SOL and curriculum framework can be presented to students in the classroom.

In this task, students decide which team wins the egg-launching contest by analyzing data from a table, graph and a verbal representation with a quadratic equation. In doing so, students analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems using models of quadratic functions.

Exploring Exponential ModelsMathematics Instructional Plans (MIPs) help teachers align instruction with the 2016 Mathematics Standards of Learning (SOL) by providing examples of how the knowledge, skills and processes found in the SOL and curriculum framework can be presented to students in the classroom.

Reflecting, Dilating and Translating FunctionsMathematics Instructional Plans (MIPs) help teachers align instruction with the Mathematics Standards of Learning (SOL) by providing examples of how the knowledge, skills and processes found in the SOL and curriculum framework can be presented to students in the classroom.

In this performance task, students consider two scenarios in a card game and conduct an experiment to analyze and compare experimental to theoretical probabilities with different game rules. In doing so, students will calculate probabilities to explore the effect of independent vs. dependent events on the outcomes in the card game.

Key concepts include:
a) conditional probability;
b) dependent and independent events;
c) mutually exclusive events;
d) counting techniques (permutations and combinations); and
e) Law of Large Numbers.

Students will use linear programming techniques to create a plan for a 4H Club to maximize profits selling fir trees. In doing so, learners will Identify the feasible region of a system of linear inequalities, identify the coordinates of the vertices of a feasible region and determine and describe the maximum or minimum value for the function defined over a feasible region.

In this activity, students use the graphs of quadratic functions and equations to find the zeros or solutions, y-intercepts, and factors. There are 10 equations or functions for the students to match-up.

An introduction to logarithmic functions as the inverse of an exponential. Mathematics Instructional Plans (MIPs) help teachers align instruction with the Mathematics Standards of Learning (SOL) by providing examples of how the knowledge, skills and processes found in the SOL and curriculum framework can be presented to students in the classroom.

Probability Mathematics Instructional Plans (MIPs) help teachers align instruction with the Mathematics Standards of Learning (SOL) by providing examples of how the knowledge, skills and processes found in the SOL and curriculum framework can be presented to students in the classroom.

Linear ProgrammingMathematics Instructional Plans (MIPs) help teachers align instruction with the Mathematics Standards of Learning (SOL) by providing examples of how the knowledge, skills and processes found in the SOL and curriculum framework can be presented to students in the classroom.