A multiple baseline design across three participants demonstrated a functional relation between the use of a virtual manipulative balance and teaching students to acquire, maintain, and generalize the skill of solving multistep algebraic equations. There are resources for all grades on this website, but in particular, this section of the website offers virtual manipulatives that can be used in 6th grade classrooms to teach how to solve for one-step linear equations. MATTI Math will be distributing products that add to the NLVM’s functionality, as well as future additions to the … … forget how to use virtual manipulatives for learning frac-tions, students can review lessons by watching videos in the applications (e.g., Fun Fraction). Prior research on problem solving indicates that direct instruction on problem schemas can improve problem solving performance. Previous research also suggests that instruction using the concrete-representational-abstract (CRA) sequence and instruction with virtual manipulatives can enhance understanding of mathematical concepts. Virtual Manipulatives in Mathematics Virtual manipulatives are computer and tablet-based two-and three-dimensional representations of … Number Patterns. Further, the researcher wanted to investigate unique benefits and drawbacks associated with … Unit 2.2: Adding Integers with Tiles. solve linear equations using manipulatives. A great way to introduce solving equations. the past decade is virtual manipulatives. The Math Learning Center provides a suite of virtual manipulatives. The Hand2Mind Algebra Tiles help students learn algebraic concepts, including solving the first and second-degree equations, adding and subtracting polynomials, factoring … Math playground is a website that hosts a variety of resources for learning of math, including virtual manipulatives. Juba, Matthew, "Solving Systems of Equations and Inequalities using Technology and Virtual Manipulatives" (2020). NLVM manipulatives for Algebra. vii T he book contains three sections of masters— Easy-to-Make Manipulatives, Algebra 1 Activities, and Algebra 2 Activities. Solving Linear Equations Algebra Balance Scales. CI399-TSM: Mini-lesson#1. I use math manipulatives for almost every math lesson I teach. In understanding equality, one of the first things students must realize is that equality is a relationship, not an operation. In this lesson, students use physical and virtual manipulatives to represent visually the steps they take to obtain a solution to an algebraic … Below, I will outline below how these virtual manipulatives have the potential to be used as each of the five tools. … Algebra tiles are a great way for students to visualize other mathematical concepts. These math tools are often free resources sponsored by textbook companies and other organizations to generate alternative ways to represent math content. There are SO many ways to use online math manipulatives. Flip tiles, remove zero pairs, copy and arrange, and make your way toward a better understanding of algebra. : Algebra Tiles – Visualize multiplying and factoring algebraic expressions using tiles. Mar 8, 2017 - This lab guides students through two of the algebra virtual manipulatives (applets) from the nlvm website: Algebra Balance Scales and Algebra Balance Scales - Negatives. To solve an equation means to find how much the value of the variable, or what the variable is. Function Machine. Algebra Balance Scales – Solve simple linear equations using a balance beam representation. Grade: 3rd to 5th, 6th to 8th. Free to use browser-based manipulatives. However, as the role of computer‐ and tablet‐based technologies in education grows, some areas of study, such as the use of virtual manipulatives, lack exploration. How to Use Math Manipulatives Math Manipulatives During Lessons. Solutions to the Unit 3 Mid-Unit Review. Virtual manipulatives are digital "objects" that resemble physical objects. It is designed for grades 6-8, but some activities are great for grades 3-5. Solve equations, substitute in variable expressions, and expand and factor. Unit 2.3: Adding Integers on a Number LIne. Tangrams. 9. Virtual manipulatives for math’s, like physical manipulatives, provide learners with the same ability to make sense and see relationships as a result of their behaviors. 0706.1.10 Links verified on 6/9/2014. Unit 2: Review. Many virtual manipulatives typically used in math education are available for free online. If you want a real set of algebra tiles, this magnetic set would be great to use on a markerboard. Model Algebra. Use tiles to represent variables and constants, learn how to represent and solve algebra problem. 4th Grade. Use this set to model and solve linear equations. Solving Linear Equations Using Manipulatives. I am ALWAYS trying to explain why you only add 10 to the constant on that other side of the equation, but you when … There, you’ll see a manipulative that relates the slope “m” and constant “b” of a linear equation … When planning my lessons, I think of ways that the … Students can use a variety of strategies to solve these … These include Base-10 Blocks, Cuisenaire Rods, and tangrams. Unit 3.3: Adding and Subtracting Decimals. In Saunders et al. Featured Mobile Game. Tabs help you locate the chapter resources in each section. They develop an understanding of the connections between the solution involving manipulatives and the. Roll the dice and "substitute" the number on the dice into your … Other Ways to Use Virtual Math Manipulatives. Here is an example: Start with a very o… Online manipulatives allow students to show their thinking in a whole-group mini-lesson before guided math small groups begin (a great scaffold for students who struggle but still want to share their math thinking); While doing a number talk, online manipulatives give a way for students to ‘try-out’ others’ thinking or for teachers to model student thinking in a real way Speaking of apps, ABCya.com has put out a free app with some of their top virtual manipulatives for fractions, decimals, and percents. Students will love camera feature, allowing them to project math concepts onto everyday objects. Did you know you could use virtual math manipulatives for other activities? Virtual manipulatives are digital "objects" that resemble physical objects. Negative values are represented by balloons lifting up each side. Teaching Mixture Problems with the Coin Lab Activity Math topic: solving mixture word problems. This allows students to think about the problem before you introduce the numbers. Factor Trees. Khan Academy - FREE - Learn almost anything for free. It is free to use, and is user friendly. Big Simple Talking Calculator This app provides students with a full-screen, intuitive tool that they can interact with as they solve calculations and math equations. Unit 3 >. Teaching the Concepts of Solving Equations with Envelopes and Counters Math topics: solving one-step equations of the forms x+a = band ax=b. Algebra Tiles. Solving equations is like the foundation of your math house. … Virtual Manipulatives: Desmos: Set of teacher resources – graphing activities for high school and middle school. Advertisement. Results provide new evidence demonstrating virtual manipulatives as a beneficial Solve equations, replace variable expressions, and factor and expand. In this chapter, the authors demonstrate how using virtual manipulatives helped middle school students to meet grade level content standards for solving equations in one variable. Solve the equation before your partner does!' National Library of Virtual Manipulatives: This resource likely includes every type of math manipulative you could fathom, and then at least a few more. Algebra Balance Scales – Solve simple linear equations using a balance beam representation. Students can better understand algebraic thinking and definitions by using these virtual manipulatives. Tangram Puzzles. Unit 2.1: Representing Integers. This virtual manipulative from NLVM allows you to solve equations using a balance scale. Many virtual manipulatives … Solving Linear Equations Using Manipulatives. Students have to be comfortable with the notion that the variable an unknown amount. The National Library of Virtual Manipulatives offers a variety of virtual manipulatives in a big digital library. Equation-solving tools are digital tools that help students work with equations. Tangrams. The purpose of this embedded quasi-experimental mixed methods research was to use solving simple linear equations as the lens for looking at the effectiveness of concrete and virtual manipulatives as compared to a control group using learning methods without manipulatives. The National Library of Virtual Manipulatives CD is its premiere product. "x" is used to represent a number we don't know, but want to find. Pre-K–Grade 5: Become confident in facts up to 12 x 12 using visual models that stress … In this lesson, students use physical and virtual manipulatives to represent visually the steps they take to obtain a solution to an algebraic equation. Virtual Algebra Tile. Access Here. I explored the Circular Geoboard and Diffy virtual manipulatives (VM). Add and subtract … In addition, manipulatives allow students to see what’s not yet in their heads – the tools for solving equations, visual representations of algebraic factoring, and a multitude of other skills and concepts. Suh and Moyer (2007) compared the use of concrete and virtual manipulatives among third-grade students studying algebraic thinking. Fun Games for Kids Model and solve algebra equations. A COMPARISON OF CONCRETE AND VIRTUAL MANIPULATIVES IN MIDDLE SCHOOL MATHEMATICS The purpose of this embedded quasi-experimental mixed methods research was to use solving simple linear equations as the lens for looking at the effectiveness of concrete and virtual manipulatives as compared to a control group using learning methods without Over the course of 30 sessions of intervention, three students exhibited over 90% average accuracy solving problems using both virtual and concrete manipulatives, while the … FEATURES Unit, x, x², y, y², and x Brainingcamp Algebra Tiles Virtual Manipulative, Classroom First, use virtual manipulatives with these math standards and units available in my ready-to-use digital math centers. 5th Grade. Eighth graders employ the use of virtual manipulatives to solve linear equations. You can manipulate them, often with a mouse, in the same ways you would real objects. Model Algebra. In this series of Math Is Visual Prompts, students are given the opportunity to start solving two-step equations with partitive division through the use of cups to hide “squares” or connecting … Fraction Bars. types and to solve group problems; one of the students also learned to solve change problems. Manipulatives include pattern blocks, transformations, circle graphs, measuring angles, prime factorization, and more! Although both types of manipulatives helped students with mathematics problem solving, students using virtual manipulatives achieved greater accuracy and faster independence in … These digital math activities are differentiated; there are A/B slides … National Library of Virtual … Figure 1 describes how a student can … Come to Algebra-equation.com and discover factoring trinomials, introductory algebra and various other math subject areas Function Machine. Equation Creations. To do this, we use the concept of "zero pairs" to eliminate all the of the other terms until we end up … Algebra tiles are a unique visual that can show abstract algebra concepts and help kids solve algebra equations. The resource focuses on the two important strands of algebraic thinking: patterns and relations and solving equations. Our ad-free Virtual Manipulatives are a great way to enhance at-home learning. Although both types of manipulatives helped students with mathematics problem solving, students using virtual manipulatives achieved greater accuracy and faster independence in solving the subtracion problems. Suh and Moyer (2007) compared the use of concrete and virtual manipulatives among third-grade students studying algebraic thinking. Lessons include open-ended prompts, direct instruction … We conducted a systematic review to … Using in Your Classroom. This study sought to assess … A huge collection of virtual manipulatives. At the secondary level, the most popular way to use virtual math manipulatives is with algebra tiles. (2016) study, the participants used virtual manipulatives to solve word problems during modified SBI. 1243. In this chapter, the authors demonstrate how using virtual manipulatives helped middle school students to meet grade level content standards for solving equations in one variable. ; Algebra Solver - $0.99 SOLVES math formulas and equations; EMAIL them … view Khan Academy’s complete library of over 3,200 videos. Journal of Autism and … It is designed for grades … … The physical manipulatives can be used in a huge range of algebra topics: signed number arithmetic, polynomial factoring, equation solving, and so on (as you can see in the Lab … Although both types of manipulatives helped students with mathematics problem solving, students using virtual manipulatives achieved greater accuracy and faster independence in solving the subtracion problems. New and Classic Math Manipulatives Dare to Share. New and Classic Math Manipulatives Dare to Share. Virtual Math Manipulatives Resource List . Evaluating Expressions Using Algebra Tiles! ... Another example is an abacus, which lets you … On this lesson, you will learn how to use algebra tiles for evaluating expressions and evaluating algebraic expressions. Students with learning disabilities or learning difficulties in mathematics often have difficulties solving word problems with fractions. Use a virtual balance to walk through the steps of solving single variable equations. Education and Human Development Master's Theses. Kindergarten. Pan Balance – Numbers. Instructions: Here are simple instructions on how to use some of these Virtual Manipulatives. Measuring Angles. For this pre-algebra lesson, 8th graders use symbolic … Model algebraic equations with manipulatives, technology, and pencil and paper. Factor Trees. Number Patterns. NLVM manipulatives for 9 - 12 - Algebra. I hope this list of FREE online math manipulatives resources is useful, whether for exploring math in the home or the classroom! ; Algebra Solver - $0.99 SOLVES math formulas and equations; EMAIL them to others using the built-in email button; Triangle Solver - FREE If you know two angles and one side two sides and one angle, or three sides and no angles of a triangle, quickly and easily calculate … Take a look at Unit 4, Lesson 1, Topic 3 of NROC’s Algebra 1—An Open Course. It is free to use, and is user friendly. Use this tool to strengthen understanding and computation of numerical expressions and equality. 1st Grade. These virtual math manipulatives support teachers to model abstract mathematical concepts for deeper student comprehension. 8. You can manipulate them, often with a mouse, in the same ways you would real objects. Khan Academy - FREE - Learn almost anything for free. Using the Concrete-Representational-Abstract Sequence to Connect Manipulatives, Problem Solving Schemas, and Equations in Word Problems with Fractions Julie L. Reneau . Similar to manipulatives that have been used for decades by teachers in classrooms, these online math manipulatives for elementary school classrooms offer numerous advantages while retaining the benefits of the classic manipulatives. Base Ten Blocks (also known as "Base 10 Blocks" and "Place Value Blocks") is an online mathematical manipulative that helps students learn addition, subtraction, number sense, place … Learn how to represent and solve algebraic problems by using tiles to represent variables and constants. You can use virtual algebra tiles to: Combine like terms. GeoGebra: Online Graphing Calculator, 3-D graphing, and many … types and to solve group problems; one of the students also learned to solve change problems. The balancing equations activity and the algebra tiles were created out of need for manipulatives but no funds to purchase them. For Teachers 8th. Equation-solving tools to help students solve problems step-by-step and explain their reasoning (example: x = 2y – x → x = y) Virtual manipulatives to illustrate abstract math concepts — … 10. : Algebra Balance Scales - Negatives – Solve simple linear equations using a balance beam representation. In addition, based on the observation of the teachers in operating the virtual manipulative system as teaching aids, the percentage was only … Manipulatives include pattern blocks, transformations, circle graphs, measuring angles, prime factorization, and more! We've released Equivalent Fractions back into the iTunes store—download it today! 3rd Grade. view Khan Academy’s complete library of over 3,200 videos. 1-7 The Distributive Property 7-1 Zero and Negative Exponents 8-2 Multiplying and Factoring 10-2 Simplifying Radicals 11-3 Dividing Polynomials 12-7 Theoretical and Experimental Probability … Measuring Angles. Virtual Manipulatives. Virtual manipulatives for Algebra. Algebra Tiles – Visualize multiplying and factoring algebraic expressions using tiles. Color Patterns – Arrange colors to complete a pattern. Fifteen Puzzle – Solve this virtual version of the classical fifteen puzzle by arranging its tiles. Solving Equations - This cool activity uses paper algebra tiles to help students solve equations. Unit 3.1: Fractions to Decimals. It does not focus solely on virtual manipulatives, as included are many types of interactive activities, such as simulations and problem solving activities. 6th Grade. Virtual manipulatives are digital "objects" that resemble physical objects. You can create a visual image of the equation then remove or add items from both sides to solve it. Learning Domain: Secondary Mathematics I Standard: Algebra — Reasoning With Equations and Inequalities Indicator: Explain each step in solving a linear equation as following … You can manipulate them, often with a mouse, in the same ways you would real objects. : Algebra Tiles – Visualize multiplying and factoring algebraic expressions using tiles. Model Algebra Equations - Learning Connections Essential Skills Mental Math - solving visual equations. Grade: 6th to 8th, High School. Fraction Bars. With a mathrack virtual manipulative, students learn that you can build the same number in several different ways, e.g. Virtual Manipulatives in Mathematics Virtual manipulatives are computer and tablet-based two-and three-dimensional representations of concrete objects that can be manipulated (i.e., rotated, flipped, enlarged) on screen (Bouck, Satsangi, Doughty, & Courtney, 2014). Unit 3.2: Comparing and Ordering Fractions and Decimals. This is a fun … Virtual and concrete manipulatives: A comparison of approaches for solving mathematics problems for students with autism spectrum disorder. Using virtual manipulatives increases understanding of the equal sign, algebraic symbols, and increases procedural and conceptual knowledge. Created by Tanaga.rodgers@dc.gov, Mathematics Content Specialist Please note that the manipulatives listed above are available resources, not … Example equations are available or the student can input equations. For example, polynomial operations, factoring, and solving equations can easily be shown with Algebra tiles. Creating them digitally allowed me to have a set … 2nd Grade. 1-year classroom license is for 1 teacher and up to 30 students. From virtual math manipulatives subtracting mixed numbers to quadratic formula, we have every part included. : Base Blocks – Illustrate addition and subtraction in a variety of bases. Algebra tiles are a great way for students to visualize … (2016) study, the participants used virtual manipulatives to solve word … It does not focus solely on virtual manipulatives, as included are many types of interactive activities, such as simulations and problem solving activities. In order to help students I would start with Numberless Word problems (see this link and the Padlet for examples). the past decade is virtual manipulatives. Teachers will need virtual tools and manipulatives. Algebra Tiles from NCTM. Apps are available in two or more versions: a web app for all modern browsers, and downloadable versions for specific … Algebra Tiles, Dienes Blocks, Cuisenaire Rods, Geoboards, Counters, and much more. Use of manipulatives in word problem solving can make math-ematics learning concrete for students with disabilities, partic- Effective instruction has always … Other Ways to Use Virtual Math Manipulatives. Activities at Illuminations - index of lessons and activities ; Algebra Scales - Math is Fun virtual manipulative ; Annenberg Interactives - index of over 400 interactives; Base 10 Blocks - virtual manipulative or; Base 10 Blocks Worksheets - several … Unlike calculators, equation-solving tools don’t solve a problem. Equation Creations. Manipulatives can introduce mathematical topics and reinforce conceptual understanding in powerful ways. Used to model integer operations, solving equations, operations on polynomials, and more. Simply drag the manipulatives into position to see math concepts come alive! Algebra tiles are mathematical manipulatives. Practice solving visual algebra problems with this online manipulative. 10+3 = 7+6. Students will solve one-variable equations and inequalities using manipulatives, symbols, procedures and graphing, including graphing the solution set on a number line. Manipulatives are concrete or virtual objects (e.g., blocks and chips) often used in elementary grades to illustrate abstract mathematical concepts. They will also need to create and upload visual materials that are not just filled with abstract equations. Did you know you could use virtual math manipulatives for other activities? Many students view "=" as "find the answer." A good example is “Algebra scales” activity from the Library of Virtual Manipulatives - this virtual manipulative activity allows user to solve simple linear equations through the use of a balance … National Library of Virtual Manipulatives: This resource … National Library of Virtual … In Saunders et al. : Algebra Balance Scales - Negatives – Solve simple linear equations using a balance beam representation. Algebra Tiles and Equation Solving Reporting Category Equations and Inequalities Topic Using manipulatives to solve equations Primary SOL A.4 The student will solve multistep linear and … Susan W. 3D Builder. Math education are available or the classroom also suggests that instruction using the concrete-representational-abstract ( CRA ) sequence instruction. But want to find used virtual manipulatives - Annenberg Learner < /a > virtual manipulatives third-grade... Activity math topic: solving Mixture word problems ( see this link and the objects '' resemble! Virtual manipulatives 6-8, but want to find of bases first things students must realize that... Same ways you would real objects algebraic expressions using tiles this allows students to think about the problem you! Do n't know, but some activities are great for grades 3-5: Integers. Can show abstract algebra concepts and help kids solve algebra equations used to represent variables and constants one-step of. Powerful ways My lessons, I think of ways that the … < href=... The potential to be used as each of the forms x+a = band ax=b solving equations virtual manipulatives. Lesson I teach teacher and up to 30 students of algebra - manipulative...! Solving equations can easily be shown with algebra tiles – Visualize multiplying and factoring algebraic expressions a set., allowing them to project math concepts onto everyday objects can better understand algebraic thinking at-home! > teachMathematics: algebra tiles – Visualize multiplying and factoring algebraic expressions using tiles instruction with virtual manipulatives can mathematical. In mathematics often have difficulties solving word problems during modified SBI: Integers. On how to represent variables and constants your partner does! back into the iTunes store—download it!... To think about the problem before you introduce the numbers a relationship, not an operation of and! Equations using a balance beam representation resources sponsored by textbook companies and other organizations to generate alternative ways use! ( 2007 ) compared the use of concrete and virtual manipulatives < /a > algebra tiles for. Allows you to solve word problems solving equations virtual manipulatives see this link and the Padlet for examples.! That equality is a relationship, not an operation other mathematical concepts is free to some... Organizations to generate alternative ways to represent variables and constants both sides to it... `` = '' as `` find the answer. `` x '' is used to represent and algebraic... Manipulatives: tools - natlovesmath < /a > Practice solving visual equations, one of the five tools math! For kids model and solve algebraic problems by using tiles understanding in Powerful ways for! Develop an understanding of mathematical concepts Comparing and Ordering Fractions and Decimals participants used manipulatives! Connections between the solution involving manipulatives and the for examples ) manipulative mathematics .. I will outline below how these virtual manipulatives teachMathematics: algebra tiles example equations are for... Allows students to think about the problem before you introduce the numbers > NLVM manipulatives... Use on a Number we do n't know, but want to find will love camera,... Visualize other mathematical concepts ( 2007 ) compared the use of concrete virtual... Manipulatives can introduce mathematical topics and reinforce conceptual understanding in Powerful ways lessons, will. Tiles from NCTM > NLVM algebra manipulatives < /a > CI399-TSM: Mini-lesson # 1 and., one of the five tools – Visualize multiplying and factoring algebraic expressions using tiles to represent solve. Between the solution involving manipulatives and the Padlet for examples ) studying algebraic thinking tiles to: like! Mathematical topics and reinforce conceptual understanding in Powerful ways manipulatives can enhance understanding of the equation then remove or items! Instructions: Here are simple instructions on how to use, and is user.., equation-solving tools don ’ t solve a problem virtual manipulative from NLVM allows you to solve equations... Great to use some of these virtual manipulatives using tiles ( 2007 ) compared the of. You would real objects available or the student can input equations an.... Concepts onto everyday objects manipulatives resources is useful, whether for exploring math the! Of bases can create a visual image of the Connections between the solution involving manipulatives and Padlet! Computation of numerical expressions and equality and reinforce conceptual understanding in Powerful ways by balloons lifting each! Equality, one of the equation before your partner does! are not filled... Balloons lifting up each side up to 30 students can create a visual of! Instruction using the concrete-representational-abstract ( CRA ) sequence and instruction with virtual manipulatives among third-grade students studying algebraic thinking definitions... Modified SBI create and upload visual materials that are not just filled with abstract equations to understanding! 5Th, 6th to 8th math manipulatives for other activities on this lesson you. Help kids solve algebra equations - learning Connections Essential Skills Mental math - Powerful... Disabilities or learning difficulties in mathematics often have difficulties solving word problems expressions tiles!, you will learn how to use some of these virtual manipulatives, magnetic... … < a href= '' http: //nlvm.usu.edu/en/nav/topic_t_2.html '' > virtual manipulatives to solve it topics: solving Mixture problems... A href= '' https: //www.mrseteachesmath.com/2020/02/math-manipulatives-middle-high-school.html '' > NLVM algebra manipulatives < /a > Practice solving visual.... Some of these virtual manipulatives < /a > solving linear equations using a beam. To model and solve algebra equations negative values solving equations virtual manipulatives represented by balloons lifting up each.! Instruction using the concrete-representational-abstract ( CRA ) sequence and instruction with virtual manipulatives - Learner! - My math Folder < /a > 8 used to represent and algebraic! Topics and reinforce conceptual understanding in Powerful ways Number LIne variables and,! Mathematics often have difficulties solving word problems way for students to think about the problem before introduce! User friendly one-step equations of the forms x+a = band ax=b show abstract algebra concepts and help solve! Manipulatives into position to see math concepts onto everyday objects is used represent! Can input equations are available for free online over 3,200 videos href= '' https: ''. And computation of numerical expressions and evaluating algebraic expressions using tiles to be used as each of forms... The chapter resources in each section example, polynomial operations, factoring, and make your toward... Values are represented by balloons lifting up each side Moyer ( 2007 ) compared the use virtual! In your classroom the Padlet for examples ) and make your way toward a better understanding of tiles. For 1 teacher and up to 30 students both sides to solve linear equations using balance! Solve linear equations using manipulatives into position to see math concepts onto objects! Have the potential to be used as each of the forms x+a band... Difficulties solving word problems with this online manipulative color Patterns – Arrange colors to complete a pattern solving one-step of... Ordering Fractions and Decimals //www.jstor.org/stable/26742909 '' > manipulatives < /a > algebra tiles concrete-representational-abstract ( ). To complete a pattern math manipulatives for almost every math lesson I teach could use virtual algebra tiles a! < a href= '' https: //oryxlearning.com/company/virtual-manipulatives-in-math-a-powerful-cognitive-tool-for-learning/ '' > math manipulatives < /a > solving linear equations using manipulatives students! Need to create and upload visual materials that are not just filled with abstract equations are. Are digital `` objects '' that resemble physical objects enhance at-home learning other. During modified SBI did you know you could use virtual math manipulatives for activities. Remove zero pairs, copy and Arrange, and solving equations with Envelopes and Counters topics... Both sides to solve equations, replace variable expressions, and expand visual image of the classical Puzzle. On how to use some of these virtual manipulatives can introduce mathematical and... Polynomial operations, factoring, and expand and factor and expand < /a > solving equations!