This is a project that generally follows the PBL framework that can be used to help students master the concept of qudratics in their study of intermediate algebra. Specifically, it was designed to help students master the concept of quadratic functions, equations, and inequalities, including the parts of both standard & vertex equations, as well as how to identify the domain & range of a quadratic function; how to apply quadratics as the square of binomials; how to make decisions about a specific quadratic problem or application relative to the significance of the vertex and roots; and how to transform a quadratic by manipulating its parent equation. Note that the project was designed and delivered per the North Carolina Math 2 curriculum and it can be customized to meet your own specific curriculum needs and resources.

This question provides students with an opportunity to see expressions as constructed out of a sequence of operations: first taking the square root of n, then dividing the result of that operation into s. Students studying statistics encounter the expression in this question as the standard deviation of a sampling distribution with samples of size n when the distribution from which the sample is taken has standard deviation s.

This task has some aspects of a mathematical modeling problem (SMP 4) and it also illustrates SMP 1 (Making sense of a problem). Students are given all the relevant information on the nutritional labels, but they have to figure out how to use this information. They have to come up with the idea that they can set up two equations in two unknowns to solve the problem.

This tasks is an example of a mathematical modeling problem (SMP 4) and it also illustrates SMP 1 (Making sense of a problem). Students are only told that there are two ingredients in the pasta and they have a picture of the box. It might even be better to just show the picture of the box, or to bring in the box and ask the students to pose the question themselves.

The purpose of the task is to show students a situation where squaring both sides of an equation can result in an equation with more solutions than the original one. The reason for this is that it is possible to have two unequal numbers whose squares are equal.

Explore forces, energy and work as you push household objects up and down a ramp. Lower and raise the ramp to see how the angle of inclination affects the parallel forces acting on the file cabinet. Graphs show forces, energy and work.

Explore forces, energy and work as you push household objects up and down a ramp. Lower and raise the ramp to see how the angle of inclination affects the parallel forces acting on the file cabinet. Graphs show forces, energy and work.

Ratey pops up when you least expect him. And he can't resist pointing out the rates and "purrportions" in daily life. It turns out that everyday decisions rely on mathematical reasoning about rates.

The battle is on in this game where you build your own potions! Check your ratios to win this mixture mix-off. Ratio Rumble guides students in: identifying ratios when used in a variety of contextual situations; providing visual representations of ratios; solving common problems or communicating by using rate, particularly unit rates; and explaining why ratios and rates naturally relate to fractions and decimals.

In this video segment from Cyberchase, the CyberSquad learns how to read a thermometer as they try to keep their chocolate sculpture from melting.

It is important to expose students to the beauty and usefulness of mathematics. Since computer graphics are familiar to most students due to video games and movies, they make a great source for motivating topics in mathematics. This activity shows students an application of solving quadratic equations to computing the line of sight to spherical objects in computer graphics.

Critical Thinking is important in all areas of life. Math is not an exception. I believe that it is important to teach students to think “outside the box” in mathematics.

In this series of lessons:
Students will learn to observe and note details of sequential patterns and then a math problem.

Students will begin to think critically as they approach a math word problem.

Prior Knowledge:
Students should have a knowledge of basic mathematics: fractions through percents.
Students should be familiar with algebraic equations.

This is an interactive, technology-based course, which investigates the connections and interplay among various mathematical topics for both the baccalaureate-prep and technical-prep student. The function concept is introduced informally. Linear and quadratic functions and their graphs are covered in-depth. Other topics include rational exponents, radical and rational equations, linear and non-linear systems and right triangle trigonometry. A heuristic approach to problem-solving is emphasized with problem situations modeled numerically, algebraically and graphically.

This Remote Learning Plan was created by Elizabeth Hock in collaboration with Craig Hicks and Tyler Cronin as part of the 2020 ESU-NDE Remote Learning Plan Project. Educators worked with coaches to create Remote Learning Plans as a result of the COVID-19 pandemic.The attached Remote Learning Plan is designed for 9-12 mathematics students. Students will use technology to graph and describe functions. This Remote Learning Plan addresses the following NDE Standard: MA 11.2.1 Algebraic Relationships: Students will demonstrate, represent, and show relationships with functions. It is expected that this Remote Learning Plan will take students 100 minutes to complete. Here is the direct link to the Google Doc: https://docs.google.com/presentation/d/1DsoE018GEbWmtkv2GaeH6WCvdnx_LpxfQ7t0xxnbBtU/view

This lesson unit is intended to help teachers assess how well students are able to: translate between decimal and fraction notation, particularly when the decimals are repeating; create and solve simple linear equations to find the fractional equivalent of a repeating decimal; and understand the effect of multiplying a decimal by a power of 10.

In eighth grade, students studied how linear functions represented by equations, tables, and graphs can be used to model and solve real world situations. Particular attention was given to using the rate of change and initial value from multiple representations to model the relationship between two values with the generalizable function, y=mx+b. In Algebra 1, students continue using and making connections between representations of linear functions. A common misconception when making connections between representations is that constant rate of change and slope can be used interchangeably when “a linear function does not have slope, but the graph of a non-vertical line has a slope.” (High School Functions progression document, page 6) Unit 2 establishes a deep understanding of the characteristics of linear functions. This understanding includes exploring linear functions geometrically by analyzing the effects of transformations on the graph by replacing f(x) by f(x) + k, kf(x), f(kx) and f(x + k) for specific values of k. These understandings allow students to compare linearity to function families studied in future units (e.g., exponential, quadratic).

In this unit, students will extend their focus from slope intercept form to reasoning about standard form and point slope form. Students begin to make distinctions about which of these forms are most beneficial when modeling a real world situation. Different contexts lend themselves to different forms of linear equations. Students may build a function to model a situation, using parameters from that situation (e.g., rate of change, start value, ordered pair). Other situations are more efficiently modeled with standard form (e.g., Dana purchased 3 brauts and 4 drinks for $8.50). Symbolic manipulation from one form to another can reveal new characteristics of the function or assist in solving systems of equations.

In 6th and 7th grade students solved one and two step equations and inequalities algebraically. In 8th grade students solved linear equations using graphs, tables, and algebraic manipulation. In this unit, students will apply what they know about solving equations and inequalities to solving multi-step inequalities which include variables on both sides. Students will make sense of what a solution means for an equation compared to an inequality. Students will extend their understanding of solving linear equations with two variables. First, they will manipulate equations to solve for specific variables. Second, students will justify their reasoning by supplying mathematical properties to explain each step in solving an equation. This work will help set the groundwork for mathematical proofs in tenth grade.

In addition, students will extend their 8th grade understanding of solving systems of linear equations to include systems of linear inequalities as representations of real world situations. Students will solve systems of linear equations exactly (e.g. with substitution principle, combination/elimination), and approximately (e.g., with graphs) with a new emphasis on the conceptual understanding and justification of why these strategies work. Students will compare and contrast the benefit of using each of these strategies in different situations.

In this unit students are using what they know about linear functions to build new understandings of piecewise linear functions including absolute value functions. In addition, students will use tables and graphs to solve absolute value equations as described in HSA.REI.D.11. The Michigan State Standards no longer require students to be able to algebraically solve piecewise and absolute value functions.

Learn about the physics of resistance in a wire. Change its resistivity, length, and area to see how they affect the wire's resistance. The sizes of the symbols in the equation change along with the diagram of a wire.

Learn about the physics of resistance in a wire. Change its resistivity, length, and area to see how they affect the wire's resistance. The sizes of the symbols in the equation change along with the diagram of a wire.

These worksheets, provided by Barbara Gilbert, review mathematics concepts that are necessary in physics, including linear equations, quadratic equations, unit conversion, significant figures, and trigonometry.

RocketModeler was developed at the NASA Glenn Research Center in an effort to foster hands-on, inquiry-based learning in science and math. RocketModeler is a simulator that models the design and flight of a model rocket. The program works in two modes: Design Mode or Flight Mode. In the Design Mode, you can change design variables including the size of the rocket body, the fins, and the nose cone. You can also select different materials for each component. You can select from a variety of standard solid rocket engines. The program computes the center of gravity and pressure for your rocket and determines the stability. When you have a design that you like, you can switch to the Flight Mode (shown below), where you can launch your rocket and observe its flight trajectory. You can pause at any time to record data and then continue the flight through parachute deploy and recovery. This program has recently (Oct 8, 2004) been upgraded to support stomp rockets, bottle rockets, and ballistic shells in addition to solid model rockets. It also supports both English and metric units.