This site teaches High Schoolers how to create equations through a series of 298 questions and interactive activities aligned to 5 Common Core mathematics skills.
CK-12 Algebra Explorations is a hands-on series of activities that guides students from Pre-K to Grade 7 through algebraic concepts.
CK-12 Algebra Explorations is a hands-on series of activities that guides students from Pre-K to Grade 7 through algebraic concepts.
CK-12 Foundation's Algebra FlexBook is an introduction to algebraic concepts for the high school student. Topics include: Equations & Functions, Real Numbers, Equations of Lines, Solving Systems of Equations & Quadratic Equations.
Students connect polynomial arithmetic to computations with whole numbers and integers. Students learn that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers. This unit helps students see connections between solutions to polynomial equations, zeros of polynomials, and graphs of polynomial functions. Polynomial equations are solved over the set of complex numbers, leading to a beginning understanding of the fundamental theorem of algebra. Application and modeling problems connect multiple representations and include both real world and purely mathematical situations.
Module 2 builds on students previous work with units and with functions from Algebra I, and with trigonometric ratios and circles from high school Geometry. The heart of the module is the study of precise definitions of sine and cosine (as well as tangent and the co-functions) using transformational geometry from high school Geometry. This precision leads to a discussion of a mathematically natural unit of rotational measure, a radian, and students begin to build fluency with the values of the trigonometric functions in terms of radians. Students graph sinusoidal and other trigonometric functions, and use the graphs to help in modeling and discovering properties of trigonometric functions. The study of the properties culminates in the proof of the Pythagorean identity and other trigonometric identities.
In this module, students synthesize and generalize what they have learned about a variety of function families. They extend the domain of exponential functions to the entire real line (N-RN.A.1) and then extend their work with these functions to include solving exponential equations with logarithms (F-LE.A.4). They explore (with appropriate tools) the effects of transformations on graphs of exponential and logarithmic functions. They notice that the transformations on a graph of a logarithmic function relate to the logarithmic properties (F-BF.B.3). Students identify appropriate types of functions to model a situation. They adjust parameters to improve the model, and they compare models by analyzing appropriateness of fit and making judgments about the domain over which a model is a good fit. The description of modeling as, the process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions, is at the heart of this module. In particular, through repeated opportunities in working through the modeling cycle (see page 61 of the CCLS), students acquire the insight that the same mathematical or statistical structure can sometimes model seemingly different situations.
Students build a formal understanding of probability, considering complex events such as unions, intersections, and complements as well as the concept of independence and conditional probability. The idea of using a smooth curve to model a data distribution is introduced along with using tables and techonolgy to find areas under a normal curve. Students make inferences and justify conclusions from sample surveys, experiments, and observational studies. Data is used from random samples to estimate a population mean or proportion. Students calculate margin of error and interpret it in context. Given data from a statistical experiment, students use simulation to create a randomization distribution and use it to determine if there is a significant difference between two treatments.
In this module, students reconnect with and deepen their understanding of statistics and probability concepts first introduced in Grades 6, 7, and 8. Students develop a set of tools for understanding and interpreting variability in data, and begin to make more informed decisions from data. They work with data distributions of various shapes, centers, and spreads. Students build on their experience with bivariate quantitative data from Grade 8. This module sets the stage for more extensive work with sampling and inference in later grades.
In earlier grades, students define, evaluate, and compare functions and use them to model relationships between quantities. In this module, students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally; translate between representations; and understand the limitations of various representations.
In earlier modules, students analyze the process of solving equations and developing fluency in writing, interpreting, and translating between various forms of linear equations (Module 1) and linear and exponential functions (Module 3). These experiences combined with modeling with data (Module 2), set the stage for Module 4. Here students continue to interpret expressions, create equations, rewrite equations and functions in different but equivalent forms, and graph and interpret functions, but this time using polynomial functions, and more specifically quadratic functions, as well as square root and cube root functions.
This site teaches Reasoning with Equations and Inequalities to High Schoolers through a series of 5909 questions and interactive activities aligned to 36 Common Core mathematics skills.
This site teaches Structure in Algebraic Expressions to High Schoolers through a series of 3482 questions and interactive activities aligned to 26 Common Core mathematics skills.
Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensures that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.
This lesson centers around the How AI Works: Equal Access and Algorithmic Bias video from the How AI Works video series. Watch this video first before exploring the lesson plan.
In this lesson, students will practice cropping images to uncover the bias underlying the Twitter cropping algorithm. Then, students will read and watch a video about the discovery of this biased algorithm. Finally, students will discuss ways to recognize and reduce bias along with analyzing Twitter's response to the allegations of bias in their cropping algorithm.
This lesson can be taught on its own, or as part of a 7-lesson sequence on How AI Works. Duration: 45 minutes
In this game activity students practice comparing shapes and naming something that is alike or different about them.
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.
Acting as engineering teams, students take measurements and make calculations to determine the specific strength of various alloys and then report their data to the rest of the class. Using this class data, students write data-based recommendations to NASA regarding the best alloy to use in the construction of the engine and engine turbines for the Space Launch System that will eventually be used to transport astronauts to Mars.
This short video and interactive assessment activity is designed to teach second graders an overview of am and pm.
In this task, the students are not asked to find an answer, but are asked to analyze word problems and explain their thinking. In the process, they are faced with varying ways of thinking about multiplication.