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Symbolab works best as a supplement to classroom materials and helps students -- and teachers -- step through solutions to various equations (from simple to complex). Students can practice various skills, especially with a paid account (the free account is limited to only a few practice topics and questions). With a paid account, students can also access pre-made or custom quizzes, giving teachers the ability to create content specific to what their class is currently learning or to allow students to practice supplemental materials (either filling in gaps or extending their skills to topics not being covered).
The hints provided by Symbolab are good at guiding students who may be stuck but don't take the place of instruction in the classroom. It also provides a very handy "cheat sheet" that covers a large number of math concepts.Continue reading Show less
Symbolab is a website and app that gives teachers and students a powerful tool for exploring math equations and seeing, step by step, how they're solved. The interface is fairly intuitive and plain, and the tool provides a number of tutorial videos. A free account (with ads) gives basic solutions to almost any math problem, including showing graphical representations to allow students to see how the equations, and proofs, are worked out in a clear set of steps. To get into some of the more useful parts of Symbolab (practice questions, quizzes, an unlimited notebook) a paid subscription is required.
Symbolab provides a number of examples that can be viewed to get an idea of how to approach a solution without solving the exact questions being asked. However, those examples can be easily altered to reflect the questions being asked.
Symbolab feels like it was developed by mathematicians for mathematicians. The interface is very plain and the focus is really just on showing solutions to math equations. It's a great tool for allowing students to explore complex equations and to help teachers build very clear explanations. However, in order for Symbolab to be effective, teachers need to consider how students are using it. Symbolab makes it very easy for kids to simply copy step-by-step solutions from the tool into any assignment without gaining the knowledge behind why they're writing each step. For the practice questions, hints are provided, but if enough hints are clicked, the final answer is simply given.
In this way, Symbolab can be both good and bad for learning. For students who really study each step and try to understand where each part comes from, it can be a great visual tool to help them understand how to solve an equation, graph a function, or work through a proof. For other students, it may be a quick way to just get the answer without developing an understanding of how or why. Another drawback to Symbolab is that it asks for a final answer but doesn't provide space for students to work through their solutions using the system. Therefore, another method (such as pen and paper) is required for students to work out their solutions before entering their final answer.
Key Standards Supported
Arithmetic With Polynomials And Rational Expressions
Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2 can be used to generate Pythagorean triples.
(+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.1
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
Write a function that describes a relationship between two quantities.
Determine an explicit expression, a recursive process, or steps for calculation from a context.
Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
(+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
Find inverse functions.
Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x ≠ 1.
(+) Verify by composition that one function is the inverse of another.
(+) Read values of an inverse function from a graph or a table, given that the function has an inverse.
(+) Produce an invertible function from a non-invertible function by restricting the domain.
(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
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