Virtual math

Objective: This virtual activity is designed for use in mathematics lessons on the following topics Theoretical Part A polynomial is an algebraic expression consisting of one or more non-inomials connected by “+” or “-” signs. A polynomial is the product of a numerical coefficient, letter variables, and their degrees. The degree of a polynomial is the largest of the degrees of the variables that make up the polynomial. The terms of a polynomial are called its singletons. Similar terms of a polynomial are terms that have the same letter parts (i.e., the same variables in the same degrees). Example: -4x^2y^2 + a – 3: This is a 2nd degree polynomial with 3 terms. Standard form of a polynomial: Example: Write the polynomial: 3x^2 – 5x + 2 – x^2 + 4x – 1 into standard form. Solution:  Virtual Experiment The “Algebra with Area Model” simulation is designed for students to work on the topic of polynomials in algebra. For given dimensions of a rectangle, students specify individual terms and calculate the resulting polynomial.   Course of Work: Step 1. Start the simulation: You will be presented with 4 different modes, “Explore”, “Generic”, “Variables” and “Game”. You will work on this experiment in the “Variables” and “Game” sections. Open the “Variables” section. Step 2. You are given in the work area: Step 3. Click on one of the fields next to the square. A calculator will appear on the screen. Enter the uninomial.  Step 4. Type different uninomials in the other 3 spaces. Step 5. Click on “a*b” to see the expression for multiplying uninomials.  Step 6. You can see the result of multiplication of uninomials for each rectangle by clicking on “A”.  Step 7. 2 kinds of calculation tables are given. This shows the calculation of polynomials. If in one of them you will see the expression step by step by clicking the “Next” button, and in the other you will see the complete calculation at once.  Step 8. Change the values of the polynomial squared and calculate the polynomial again. Create several expressions in this way. Step 9. Change the way the square is divided. Repeat the above steps. Step 10. Open the “Game” section. You will be presented with games on 6 different levels. Select the first level. Step 11. In the work area you will be presented with Step 12. The game requires you to find the appropriate expression for the space inside the square. View the polynomial, perform the calculation, and find the expression. Step 13. Check if the expression is correct by clicking the Check button. Step 14. Continue playing the game. After completing one level, you can solve the problems in the next levels. Conclusion Students go deeper into the topic of polynomials by doing this virtual activity. It makes it easier to understand calculations by visualizing them on the screen. They can learn calculations in a fun and playful way.

Objective: This virtual activity is designed for use in math lessons on the following topics: Theoretical part Area is a measure of how big a plane figure is. Simply put, it is how much space it takes up on the plane. How do we measure area? To measure area, we use special units of measurement called area units. The most common units of area are in square centimeters (cm²) and square meters (m²). Area of a square: To find the area of a square, you need to square its side. For example, if the side of a square is 4 cm, its area would be: 4 cm * 4 cm = 16 cm² Area of a rectangle: To find the area of a rectangle, you need to multiply its length by its width. For example, if the length of the rectangle is 5 cm and the width is 3 cm, then its area will be: 5 cm * 3 cm = 15 cm² Virtual experiment The simulation “Area. Unit of Area” will help students learn how to find the area of a rectangle. On the screen, they are introduced to the operation of multiplication in the form of a table. Manipulating the numbers, they get the results of multiplication. Course of Work: Step 1. Start the simulation: you will be presented with 2 different modes, “Multiply” and “Partition”. You will work on this experiment in the “Partition” section. Open the “Partition” section. Step 2. Given to you in the workspace: Step 3. The table presents a square of size 5*5. It is vertically divided into (2; 3) parts. The multiplier and multiplicand number board and the multiplication result board show the data. Click “a*b” from the rectangle information in the table. The expressions 5*2 and 5*3 appear on the parts of the square.  Step 4. Open the calculation panel. This shows the calculation of the area of the square. Because of the division by the vertical (2;3) part, the calculation is expressed as on the screen. Step 5. Click the “A” button from the rectangle information in the table. In the 10 and 15 parts of the square – the values of the expressions 5*2 and 5*3 appear.  Step 6. Swipe the divider you are dividing right, left across the square and examine the changes in the data. Step 7. Change the dividing line vertically to horizontal. Examine the data. Monitor the changes by moving the divider up and down. Step 8. Create a new rectangle size by clicking the green button next to the square. Examine the changes in the workspace.  Step 9. Try changing the rectangle information in the table, and the separator line. Step 10. You can change the size of the table to 12*12. Change the dimensions of the rectangle and calculate the squares. Conclusion In this virtual activity, students performed calculations related to area. Changing the size of the rectangle, dividing it into parts gave a deeper understanding of the subject.

Objective: This virtual activity is designed for use in mathematics lessons on the following topics Theoretical part Area is a measure of the size of a plane figure. It is measured in square units, such as square centimeters (sq cm) or square meters (sq m). The area of a rectangle A rectangle is a quadrilateral whose angles are all right angles (equal to 90°) and whose opposite sides are equal in pairs. To find the area of a rectangle, multiply the length of its base (a) by its width (b). The formula is S = a * b Where: Example: Find the area of a rectangle with sides 5 cm and 3 cm: S = 5 cm * 3 cm = 15 square cm Area of a square A square is a rectangle with equal sides. To find the area of a square, you need to square its side (a). The formula is S = a² Where: Example: Find the area of a square with side 4 cm: S = 4 cm² = 16 square cm Virtual Experiment The “Finding the area of a rectangle and a square” simulation helps students learn how to find the area of a rectangle. They learn how to use the area model to reason about the product of two numbers, that the product/area can be divided by smaller products/areas, and that the total area is equal to the sum of the partial areas. Course of Work: Step 1. Start the simulation: You will be presented with 3 different modes: “Explore”, “Generic” and “Game”. You will work on this experiment in the “Explore” section. Open the “Explore” section. Step 2. You are given a workspace: Step 3. The table displays a square of the size 10*10. Horizontally divided into sections (5;5). The Multiplier and Multiplier Numbers panels and the Multiplication Results panel show the data. Click the square coloring button. Click “a*b” from the square information in the table. The 5*10 expressions appear on the parts of the square. Step 4. There are 2 views of the calculation panels. These show the calculation of the area of the square. In one of them you will see the expression step by step by clicking the “Next” button, and in the other you will see the complete calculation at once.  Step 5. Click on the “A” button of the rectangle information in the table. The 50 – values of the 5*10 expressions appear in the parts of the square.  Step 6. Draw the divider you are dividing up and down the square and examine the changes in the data. Step 7. Move the horizontal dividing line up the square so that it does not divide the square. Move the vertical dividing line to the right. Examine the data. Trace the changes as you move the divider right, left. Step 8. Explore dividing the square into rectangles of different sizes by alternately moving the vertical and horizontal dividers in the square. Step 9. Create a new rectangle size by clicking the green button next to the square. Examine the changes in the work area.  Step 10. Try to change the information about the rectangle in the grid. Step 11. You can change the size of the table to 100*100. Change the dimensions of the rectangle and calculate the areas. Conclusion In this virtual activity, students performed calculations related to area. Changing the size of the rectangle and dividing it into parts gave them a deeper understanding of the topic.

Objective: This virtual activity is designed to be used in math lessons in the next chapter: Theoretical part Multiplication Operation Imagine you are a baker and you want to bake lots of delicious pies. How many pies will you get if you use 2 cups of flour for each pie? That’s where multiplication comes to our rescue! Multiplication is the addition of identical groups. In our case: 1 pie = 2 cups of flour 2 pies = 2 cups of flour + 2 cups of flour = 4 cups of flour. 3 pies = 2 cups flour + 2 cups flour + 2 cups flour + 2 cups flour = 6 cups flour Let’s write it down like this: 2 x 3 = 6, where: 2 is the multiplier (what we are multiplying) – the amount of flour for 1 pie 3 is the multiplier (how many times we multiply) – the number of pies 6 is the product (the result of multiplication) – the total amount of flour. Division operation The more pies we bake, the more flour we use! Now let’s imagine that you have 8 delicious apples and you want to put them equally into 2 baskets. How many apples will be in each basket? Division will help us with that. Division is dividing a number into equal groups. In our case: 8 apples / 2 = 4 apples in each basket We write it like this: 8 : 2 = 4, where: 8 is the divisor (what we are dividing) – the total number of apples 2 is the divisor (how many groups we divide into) – the number of baskets 4 is the quotient (the result of division) – the number of apples in each basket. Let’s write it like this: 8 : 2 = 4, where: 8 is the divisor (what we are dividing) – the total number of apples 2 is the divisor (how many groups we divide into) – the number of baskets 4 is the quotient (the result of division) – the number of apples in each basket. The more apples, the more baskets with the same number of apples you get! Multiplication and division are like two sides of the same coin: Virtual experiment The “multiplication” simulation is an aid for students to familiarize themselves with the multiplication table. The screen introduces the multiplication operation in the form of the Pythagoras table. By manipulating the numbers, he gets the results of multiplication. Course of Work: Step 1. Start the simulation: you will be presented with 2 different modes, “Multiply” and “Partition”. You will work on this experiment in the “Multiply” section. Open the “Multiply” section. Step 2. Given to you in the work area: Step 3. The Pythagoras table shows the expression 1*1: 1*1=1. You can see the result of numbers up to 10 multiplied by 1 by left-clicking and moving to the right. For example, 1*5=5.  Step 4. You can see the expressions 1*9=9 in the multiplication and multiplication numbers pane and in the multiplication results pane. Step 5. Clean the table with an eraser. Step 6. Move the table down one unit. You have the expression 2*1: 2*1=2. You can see the result of numbers up to 10 multiplied by 2 by left clicking and moving to the right. For example, 2*7=14. You can see the expression information on the right side of the screen. Step 7. Clear the table with an eraser and move the table down two units. You have the expression 3*1: 3*1=3. Here you can see the result of numbers up to 10 multiplied by 3. For example, 3*4=12. On the right side of the screen, there are more details. Step 8. Thus, familiarize yourself with the multiplication table by moving the table down and to the right. The table shows the multiplier and the multiplier up to 10. So you can see the product 10*10=100. Step 9. If you change the size of Pythagoras table to 12*12, you can learn the product 12*12=144.  Step 10. You can learn the multiplication table by changing the numbers in the multiplier and multiplier number panel. The table automatically changes according to the multiplier and multiplicand. You can see the result of multiplication on the board. You can click show and hide the numbers in the table and not show the numbers.  Conclusion Students learn how to multiply using the Pythagoras table by doing this virtual activity. It will be interesting for students as they will work with the multiplication operation visually and make it easier to memorize the multiplication table.

Objective: This virtual activity is designed to be used in math lessons in the next chapter: Theoretical part Addition and Subtraction: Identical symbols: Addition: When adding rational numbers with the same signs (e.g., + and +), add their numerators, keeping the sign. For example: 23+13=2+13=33=1 Subtraction: When subtracting rational numbers with the same signs (e.g., – and -), subtract their numerators, keeping the sign. For example: 54-24=5-24=34 Different Symbols: Addition: When adding rational numbers with different signs (e.g., + and – or – and +), subtract their numerators and keep the sign of the number that has the larger numerator. For example: 45+-25=4-25=25 Subtraction: When subtracting rational numbers with different signs (e.g., + and – or – and +), subtract their numerators and keep the sign of the first number. For example: 37–17=3+17=47 Multiplication and division: Same symbols: Multiplication: When multiplying rational numbers with the same signs (e.g., + and + or – and – and -), multiply their numerators and denominators. The sign of the result will be positive. For example: 23*45=2*43*5=815 Division: When dividing rational numbers with the same signs (e.g., + and + or – and – and -), divide the numerator of the first number by the numerator of the second number, and the denominator of the first number by the denominator of the second number. The sign of the result will be positive. For example: 5623=5*36*2=1512 Different Symbols: Multiplication: When multiplying rational numbers with different signs (for example, + and – or – and +), multiply their numerators and denominators. The sign of the result will be negative. For example: 34*-56=3*(-5)4*6=-1524 Division: When dividing rational numbers with different signs (for example, + and – or – and +), divide the numerator of the first number by the numerator of the second, and the denominator of the first by the denominator of the second. The sign of the result will be negative. For example: 79-23=7*(-2)9*3=-1427 Virtual experiment On the numbers screen, students perform arithmetic operations on rational numbers. This allows them to understand arithmetic functions by comparing them in different representations. Course of Work: Step 1. Start the simulation: you will be presented with 4 different modes: “Patterns”, “Numbers”, “Equations” and “Mystery”. You will work on this experiment in the “Numbers” section. Open the “Numbers” section. Step 2. You are given:  Step 3. Open the tables in the function machine. Step 4. Place an arithmetic operation on the function machine. You can add and subtract numbers 1-3, multiply by numbers 0-2, and divide by numbers 1-3. Step 5. Enter the incoming number into the function machine. The input panel shows the numbers (-4; 7). Step 6. You can see the number of inputs, function value and expression in the tables. The function value panel shows the value of the expression.  Step 7. Place another arithmetic operation on the function machine.  Step 8. Put an input number into the function machine. Examine the function data.  Step 9. Activate the button showing the value of the expression after each operation. Enter the number. After the first operation, the value of the expression is displayed.  Step 10. To perform the next operation, you pass the expression value to the next operation by holding down the left side of the mouse. Step 11. Change the data as you see fit and create different expressions. You can use the input numbers panel, operations. Conclusion This simulation allows students to interactively learn arithmetic operations with rational numbers. That is, students can create expressions on their own, modify them, and track changes in the results. Presenting numbers and techniques on the screen makes learning to read understandable and engaging. Overall, this simulation is a valuable tool for learning arithmetic operations with rational numbers. It can be used both as a supplement to traditional teaching methods and for independent research work.

Objective: This virtual activity is designed to be used in math lessons in the next chapter: Theoretical part 1. Definition: A linear equation with one variable is an equation of the formaah+b=0, where: a and b are arbitrary numbers (coefficients of the equation), wherea0. x is the unknown variable. 2. Examples: 3. Solving a linear equation: Goal: To find all values of the variable x at which the equation becomes true. Algorithm: Example: 3x – 5 = 0 3x = 5 x = 5/3 Answer: x = 5/3. Virtual Experiment On the equation screen, students can interpret, compare, and translate multiple representations of an algebraic function. It can predict the output of a function on given inputs and create a new function. Workflow: Step 1. Start the simulation: you will be presented with 4 different modes: “Patterns”, “Numbers”, “Equations” and “Mystery”. You will work on this experiment in the “Equations” section. Open the “Equations” section. Step 2 You are given:  Step 3. Open the tables on the function machine. Step 4. Place an arithmetic operation on the function machine. You can change the numbers with an interval from -3 to +3. You can use addition, subtraction, multiplication and division operations.  Step 5. Enter the incoming number into the function machine. The input panel shows the numbers (-5; 7) and the variable x. Step 6. You can see the number of inputs, function value, graph and equation in the tables. The function value panel shows the value of the expression. Step 7. Place more different arithmetic operations on the function machine. You can place up to three techniques there. Step 8. Put the input number into the function machine. Examine the function data.  Step 9. Activate the button indicating the value of the expression.  Enter the input number into the machine. After the first operation, the value of the expression is displayed.  Step 10. To perform the next operation, you pass the expression value to the next operation by holding down the left side of the mouse. Step 11. Change the data as you see fit and create different expressions. You can use the input numbers panel, operations. Conclusion For students, working with a given function machine in virtual work is an easy way to explore functions and their effect on input data. Following the steps in sequence allowed them to experiment with different arithmetic operations and input numbers, and to observe changes in function values and equations.

Objective: This virtual activity is designed to be used in math lessons in the next chapter: Theoretical part A linear equation with two variables x and y (with two unknowns x and y) is an equation of the form a*x+b+y+c=0, where a,b,c are numbers, and a and b are not equal to 0 at the same time. For example, -2x+7y=0; 12x-11y+5=0 are linear equations with two variables. Since in such equations there are two variables, so the solution to equations with two variables is not one but two numbers, which are usually written in parentheses, and the number that we substitute into the equation instead of x, we write in the first place, and y – in the second place: (x, y). The solution of an equation with two variables a*x+b+y+c=0 is such a pair of numbers, when substituting which instead of x and y in the equation, the correct numerical equality is obtained. For example, the pair of numbers (0,5;1) is a solution to the equation with two variables 12x-11y+5=0. To solve a linear equation with two variables is to find the set of solutions.  If a pair of numbers is a solution to an equation with two variables, the pair is also said to satisfy the equation. Equations with two variables are called equivalent if all the solutions of one equation are equal to the solutions of the other equation. Virtual experiment The “Equality Explorer: Two Variables” simulation allows students to explore the conditions that result in equality and inequality when there are two variables present. Students can build a system of equations and develop a meaningful understanding of a system of equations. Workflow: Step 1. You are given:  Step 2. Generate an equation in x =1, y=1 values. You can use the button that adjusts the expressions over the weights. Step 3. Click the camera button and save to the image panel. Step 4. Change the value of x and make the equation. If necessary, you can use the eraser and button to adjust the expressions over the weights. Save to the image panel. Step 5. Change the x and y values and make the equation. You can click the lock button and express both sides of the equation with the same numbers. Save in the image panel. Step 6. Compose the equations by assigning different values to the x and y variables. Fill in the image panel. Conclusion Performing the virtual work “Equality Explorer: Two Variables” allowed students to deepen their knowledge of linear equations with two variables and learn how to use them to solve practical problems. The fact that the variable has a different value by balancing it on weights makes it easier for students to visualize and learn how to make different equations.

Objective: This virtual activity is designed for use in math lessons on the following topics: Theoretical part Complex equations are equations that contain two or more arithmetic operations. The number that converts it to a correct equality when you put a letter in an equation is called the solution to the equation or the root. A variable is a quantity that can take on different values. Expressions with several variables can also be simplified and then find the values at given letter values. Transformations of expressions that result in a simpler expression are called simplifying expressions. For example:  x + x + x + x + x  “4 times x” can be written shorter (simplify): 4 ∙ x or 4x.  The multiplication sign is often not written in such cases. x + x + x + x + x = 4x If a transformation can be performed on the left or right side of an equation, simplify the expression first and then solve the equation. Consider how you solved the equation.  5x + 2x = 49  The left side of the equation can be simplified. Let’s do this.  7x = 49  Now let’s solve the simple equation by the rule of finding the unknown multiplier. x = 49:7  x = 7  Verification.  5 ∙ 7 + 2 ∙ 7 = 49  35 + 14 = 49  49 = 49 Virtual experiment The “Equation” simulation allows students to explore the concept of equation, inequalities, and variables. On the “Variables” screen, students explore how different values of a variable affect the state of equality. On the “Calculations” screen, students can construct an inequality or equation and apply universal operations to find out what happens to each term and learn how to undo the operation. Progression: Part 1. Variables Step 1: Start the simulation: you will be presented with 5 different modes: ‘Basics’, ‘Numbers’, ‘Variables’, ‘Operations’ and ‘Solve it’. You will work on this experiment in the “Variables”, “Operations” sections. Open the “Variables” section. Step 2. You are given:  Step 3. Generate the equation in the value of x =1. If necessary, you can use the eraser and button to adjust the items above the scales. Step 4. Click the camera button and save the equation in the image panel. Step 5. Change the value of x and make the equation. You can press the lock button and express both sides of the equation with the same numbers. Save in the image panel. Step 6. Compose the equations by assigning a different value to the variable x. Complete the image panel. Part 2. Calculations  Step 7. Open the “operations” section. You are given:  Step 8. Construct the first equation: x =1. You can construct the equation using the variables and numbers located at the bottom. You can use the operations panel above. In the operations panel, you can create expressions with numbers from 1 to 10 in the operations ( + ), ( – ), variables 1x-10x, numbers from 1 to 10 in the operations ( * ), ( / ). Click the camera button and save in the image panel. Step 9. Change the value of x and make an equation. Save to the image panel. Step 10. Compose equations by assigning a different value to the variable x. You can use all of the tools in the workspace when composing an equation. Fill in the image panel. Section 3. Solving an equation Step 11. Open the “Solve it” section. You are given levels of the equation:  Step 12. Level 1: Discover one-step equations. In the work area you are provided with: Step 13. Equation to be solved solve the equation using the operations board with the given board. As you solve the equation, the value of x should remain on one side of the scale and the value of x should remain on the other side of the scale. If the equation is solved correctly, the “next” button will appear.  Step 14. Click “next” and move on to the next equation. Solve the given equation. Try solving more than one equation. Step 15. Go to other levels. Solve the equations. Conclusion The virtual “equation” simulator allowed students to gain a deeper understanding of the topic of equations. The equations that the students have learned to solve so far entered a complex form in this activity and helped them to sharpen their knowledge. The fact that the variable has a different value by balancing it on a scale makes it easier for students to visualize and learn how to make different equations.

Objective: This virtual activity is designed to be used in math lessons on the following topics: Theoretical part Compound equations are equations that contain two or more arithmetic operations. A variable is a quantity that can take on different values. Expressions with several variables can also be simplified and then find the values at given letter values. Transformations of expressions that result in a simpler expression are called simplifying expressions. For example:  x + x + x + x + x  “4 times x” can be written shorter (simplify): 4 ∙ x or 4x.  The multiplication sign is often not written in such cases. x + x + x + x + x = 4x If a transformation can be performed on the left or right side of an equation, simplify the expression first and then solve the equation. Consider how you solved the equation.  5x + 2x = 49  The left side of the equation can be simplified. Let’s do this.  7x = 49  Now let’s solve the simple equation by the rule of finding the unknown multiplier. x = 49:7  x = 7  Verification.  5 ∙ 7 + 2 ∙ 7 = 49  35 + 14 = 49  49 = 49 Virtual experiment The “Equation” simulation allows students to explore the concept of equation, inequalities, and variables. On the “Variables” screen, students explore how different values of a variable affect the state of equality. On the “Calculations” screen, students can construct an inequality or equation and apply universal operations to find out what happens to each term and learn how to undo the operation. Progression: Part 1. Variables Step 1: Start the simulation: you will be presented with 5 different modes: ‘Basics’, ‘Numbers’, ‘Variables’, ‘Operations’ and ‘Solve it’. You will work on this experiment in the “Variables”, “Operations” sections. Open the “Variables” section. Step 2. You are given:  Step 3. Generate the equation in the value of x =1. If necessary, you can use the eraser and button to adjust the items above the scales. Step 4. Click the camera button and save the equation in the image panel. Step 5. Change the value of x and make the equation. You can press the lock button and express both sides of the equation with the same numbers. Save in the image panel. Step 6. Compose the equations by assigning a different value to the variable x. Complete the image panel. Part 2. Calculations  Step 7. Open the “operations” section. You are given:  Step 8. Construct the first equation: x =1. You can construct the equation using the variables and numbers located at the bottom. You can use the operations panel above. In the operations panel, you can create expressions with numbers from 1 to 10 in the operations ( + ), ( – ), variables 1x-10x, numbers from 1 to 10 in the operations ( * ), ( / ). Step 9. Click the camera button and save in the image panel. Step 10. Change the value of x and make an equation. Save to the image panel. Step 11. Compose equations by assigning a different value to the variable x. You can use all of the tools in the workspace when composing an equation. Fill in the image panel. Conclusion The virtual “equation” simulator allowed students to gain a deeper understanding of the topic of equations. The equations that the students have learned to solve so far entered a complex form in this activity and helped them to sharpen their knowledge. The fact that the variable has a different value by balancing it on a scale makes it easier for students to visualize and learn how to make different equations.

Objective: This virtual activity is designed for use in math lessons on the following topics: Theoretical part Equation is an equality with an unknown. To find the unknown is to solve the equation. The unknown is labeled with a letter. The goal of solving an equation: to find the unknown number when solving an equation. For example: x+3=7 x=4 4 is the root of the equation. You can find the root of the equation, or you can use knowledge about the relationship between addition and subtraction. The solution of the equation must be checked. Virtual experiment The simulation “Equation” allows students to explore the concept of equations, inequalities, and variables. On the “basics” screen, students can compose equations and create functional definitions of equality and inequality. Numbers on the screen students can work with numbers and create unique equations. Progression: Section 1: Basics Step 1. Start the simulation: you will be offered 4 different modes: “Basics”, “Numbers”, “Variables”, “Operations” and “Solve it”. You will work on this experiment in the “Basics”, “Numbers” sections. Open the “Basics” section. Step 2. You are given:  Step 3. Perform a reciprocal comparison by placing items one on either side of the scales.  Step 4. Construct the first equation. Step 5. Click the camera button and save to the image panel. Step 6. Make the next equation. If necessary, you can use the eraser and button to position the items on the scales correctly.  Step 7. Create multiple equations and fill the image panel. Step 8. You can create and experiment with different equations by alternating the types of sets of items. Section 2: Numbers Step 9. Open the “Numbers” section. You are given:  Step 10. Make the first equation from the numbers. You can express the number 1 by adding and taking it several times. Step 11. Click the camera button and save to the image panel. Step 12. Make the following equation. Click the lock button and try to express both sides of the equation with the same numbers. If necessary, you can use the eraser and button to adjust the items above the Scales.  Step 13. Create multiple equations and fill in the image panel. Conclusion The virtual “Equation” simulation allowed students to gain a deeper understanding of the topic of equations. The objects had different meanings and balanced them on the scales, students were comfortable with visual perception and learned how to make different equations.