Algebra by Hand completes needed calculations to ensure students can focus on algebraic problem-solving. Teachers, however, don't have to let good calculation practice slide. A student can be assigned to complete the work on the site and then describe how to solve an identical problem to their partner, who must correctly work the equation with accurate calculations.
Once basic algebraic concepts have been learned, teachers can introduce a more complex equation for teams of students to tackle. Students can set upon an algebraic "adventure," as the program allows students to attempt several different approaches to the equation (as long as steps are taken using the tools provided and the steps are mathematically sound). The result of these adventures can be several methods, which can then be displayed to encourage class analysis and mathematical discourse.
If your class loves games, why not use Algebra by Hand for a little competition? Split the class into teams and assign the same worksheet. Teams can earn points for solving complex equations using the fewest moves or can challenge other teams to complete equations in a fewer number of steps.Continue reading Show less
Algebra by Hand is an interactive tool designed to improve algebraic proficiency. Account setup is intuitive and students are easily added -- one at a time -- using each student's email, first name, and last name. Teachers can manage student accounts, assign worksheets, and view progress. Although there are a few public worksheets ready to be assigned, teachers have the option of creating their own. To create a worksheet, teachers can employ a menu of options such as "cut and paste" as well as features to insert common mathematical notation (like quotients and exponents). Once the worksheet has been created, teachers can also include an answer key where, using a drag-and-drop movement, a step-by-step process is laid out. The drag-and-drop movements are unique to the program and, even after watching the tutorial provided, may take some time to master. The tutorial includes a list of five operations with up to six movements each, videos, and examples that users can practice with to be sure they're ready to move on.
With their free accounts, students have access to assignments and can perform the drag-and-drop moves to solve algebraic expressions and equations in a step-by-step format. Several help options are available if a student is stumped. Help ranges from "Tell me what to do," which names the step to take; "Show me what to do," which highlights the drag-and-drop motion needed to perform the operation; and "I give up, do it for me," which completes a single step to help the student along. Notations of the used help options are made visible to both teachers and students.
Once worksheets have been assigned and completed, the program scores the work. If desired, a teacher can view specific worksheets with a class score sheet or view questions completed by individual students. Student work is displayed with each step taken, and teachers can measure proficiency with Common Core State Standards. A Basic Skill Report for each student outlines algebraic standards by grade level and displays a proficiency score.
Teachers should assign work in Algebra by Hand only after concepts have been taught; it doesn't teach algebraic concepts but allows students the focused practice that solidifies those skills. Each problem begins with the answer displayed, so the focus isn't on the answer, but instead on the process. Taking the calculations out of the equation allows students to focus on the properties and procedures needed to solve complex problems. Because the program allows only accurate mathematical steps, students cannot make a wrong move that would complicate the solution. With this freedom, they can see how an equation would change using various properties and feel confident they can always "undo" a step if they've reached a dead end. If a student has a creative solution and requests a hint, the program will take them back to the first step that diverged from the listed steps provided in the answer key. This may cause students to feel they have been inaccurate in their work and may discourage creative problem-solving.
Drag-and-drop features are touchy on both desktop and touchscreen devices. Students may get frustrated easily, especially if they're just learning to use the program. Although it's helpful for teachers to make their own worksheets, creating them takes a bit of time. More adaptable, premade worksheets would be helpful.
Key Standards Supported
Expressions And Equations
Write and evaluate numerical expressions involving whole-number exponents.
Write, read, and evaluate expressions in which letters stand for numbers.
Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.
Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole- number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.
Apply the properties of operations to generate equivalent expressions.
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Solve linear equations in one variable.
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
Reasoning With Equations And Inequalities
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
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