Virtual math

Objective: This virtual activity is designed to be used in the math lessons in the next chapter: Theoretical part 1. Definition and representation Examples: 2. Comparing positive and negative numbers on the number axis 3. Operations on positive and negative numbers Addition: Subtraction: 4. Modulus of a number The modulus of a number is its absolute value, i.e., its distance from zero. The modulus of a number is always a non-negative number. Notation: The modulus of a is written as |a|. Examples: |5| = 5, |-3| = 3, |0| = 0. Virtual Experiment The “Number Line: Operations” simulator is based on integers, which allows you to perform operations on integers.  Workflow: Step 1. Start the simulation: you will be offered 4 different modes: “Chips”, “Net Worth”, “Operations” and “Generic”. Open the “Chips” section.  Section 1. Calculating Coins Students can play by adding and subtracting integers using the coin pattern. Step 2. In the work area, you will find Step 3. Put the coins into the bag with the green strap. You can put in up to 15 coins. Calculate your income by adding the coins. Step 4. Put the coins into the bag with the red ribbon. You can put up to 15 kopecks. Calculate your expenses by adding the coins. If your income is equal to your expenses, your score is 0. Show negative numbers by coordinates if you have more expenses. Shows positive numbers by coordinates if your income is higher.  Part 2. Status Screen Students can use real-world examples to reinforce their understanding of integer operations. Step 5. Open the Net Worth section. In the workspace, you will see: Step 6.Here you can perform various operations and calculations on your assets and liabilities. Section 3. Operations Screen  Students can set an initial net worth and then perform operations on it. In this section, you will only work with hundredths of a percent. For example, 100 200 300. Step 7. Open the Operations Section. In the work area you will find Step 8. Set the initial net cost. Step 9. Select any hundred on the hundredths board and add it. Step 10. Go to the second hundred board and mark and subtract some hundreds. In this way, try different operations and make calculations. Section 4. Generic Screen The Generic screen provides flexibility in modeling operations with integers, working with numbers up to 100, and using the number line to reinforce abstract understanding of operations. Step 11. Open the Generic Section. The work area provides you with Step 12. Mark the initial number by moving the blue point.  Step 13. Mark and add any number in the number field. Step 14. Go to the second number board and mark and subtract any number. In this way, try different operations and perform calculations. Step 15. Mark two coordinate axes for the work area. Perform two separate calculations on each axis. Compare the axes. Conclusion On the horizontal number line, the addition and subtraction of whole numbers has been pictorially calculated in terms of the order of the numbers. Recognized and created equivalence classes of whole number sums and differences. Verified that the sum of a number and its additive inverse is 0.

Objective: This virtual activity is designed to be used in the math lessons in the next chapter: Theoretical part 1. Definition and representation Examples: 2. Comparing positive and negative numbers on the number axis 3. Modulus of a number The modulus of a number is its absolute value, i.e., its distance from zero. The modulus of a number is always a non-negative number. Notation: The modulus of a is written as |a|. Examples: |5| = 5, |-3| = 3, |0| = 0. Virtual Experiment In the “number line: integers” simulation, students can explore the many contexts in which integers can be compared to integers on a number line. After students explore height, bank accounts, and temperature, they can make generalizations about comparing integers and determine absolute value.  On the Explore screen, students can compare integers in different contexts.  On the Generic screen, students can compare whole numbers on different scales and begin to define absolute value in a general way. Workflow: Step 1. Start the simulation: You will be given 2 different modes, “Explore” and “Generic”. Open the “Explore” section.  Step 2. In the work area you are given: Step 3. Position the person on the plane. Start the absolute value button. Explore the data from the coordinate axis associated with altitude, moving the person across the water, sky, and mountains.  Step 4. Place the bird and fish on the plane. Explore data from the comparison panel by moving 3 objects to different locations on the plane.  Step 5.Open the section with the piggy bank image. You are given: Step 6. Click the absolute value. Do some operations and make a comparison by picking up and licking a coin on the piggy bank. Step 7. Add 2 piggy banks to the coordinate axis that shows the balance. Do a comparison by counting the coins in these 2 piggy banks.  Step 8. Open the section showing the thermometer. You are given: Step 9. Change the unit of temperature measurement to degrees Celsius. Place the thermometer on the map and measure temperatures in different parts of the Earth.  Step 10. Place the remaining 2 thermometers on the map and make a comparison by examining the temperature changes in each part of the world.  Step 11. Change the month from January to another month and examine and compare the temperature changes.  Step 12. Open the Generic section. In the workspace you are provided with: Step 13. Activate the data display buttons on the coordinate axis. Explore the data by moving the point on the coordinate axis.  Step 14. Add 2 more points to the coordinate axis and make a comparison by moving them. Step 15. Change the length and position of the coordinate axis and make some more comparisons.  Conclusion The simulator can be an aid in mastering the concept of absolute value so that students can familiarize themselves with negative numbers. Describing the position of a point in a number line with respect to another number, describing the position of a number line with respect to the opposite side of a point, they made sure that the negative number was smaller than the positive number each time. 

Objective: This virtual activity is designed to be used in the math lessons in the next chapter: Theoretical part 1. Definition and representation Examples: 2. Comparing positive and negative numbers on the number axis 3. Operations on positive and negative numbers Addition: Subtraction: Multiplication: Division: 4. Modulus of a number The modulus of a number is its absolute value, i.e., its distance from zero. The modulus of a number is always a non-negative number. Notation: The modulus of a is written as |a|. Examples: |5| = 5, |-3| = 3, |0| = 0. Virtual Experiment The Number Line: Modeling Distance simulation teaches students to subtract in different contexts, identify patterns, and generalize about how to interpret subtraction as distance. The Explore screen allows students to explore subtraction with two objects and determine whether the distance between them is taken into account in subtraction. The Generic screen provides flexibility to reason about subtraction in any context or out of context, and generalizes the concept of subtraction as the distance between two integers on a number line.  Workflow: Step 1. Start the simulation: You will be given 2 different modes, “Explore” and “Generic”. Open the “Explore” section.  Step 2. In the workspace you are provided with Step 3. Position the house and person on the plane. Examine the coordinate axis data. What is the absolute value?  Step 4. Click the Simple Value button. How has the data changed in the Calculation Panel?  Step 5. Click the Move Bodies button. Examine the data on the coordinate axis and in the Calculation Panel.  Step 6. Click the Absolute Value button. Examine the changes in the calculations again.  Step 7. Change the distance between the house and the person. Perform the study by repeating the above steps. Step 8. Open the second case of the calculation. Here you will study the temperature difference.  Step 9. Place the thermometers on a plane representing the seasons. Just as you would study the distance between a house and a person, you will study between temperatures.  Step 10. Open a third case. Here you are investigating the vertical distance between a bird and a fish. Step 11. Place the bird in the sky and the fish in the water. Research between them as you would research the distance between a house and a person.  Step 12. open the Generic section. In the workspace you are provided with: Step 13. Place two points on the coordinate axis. Examine the data on the Coordinate Axis and on the Calculation Panel. Step 14. Explore the distances between the bodies by performing different point calculations.  Conclusion Students have explored the relationship between horizontal and vertical number lines and the coordinate plane. This simulation provides real-life situations that set the stage for applying the knowledge in real life. Absolute value, application of operations to rational numbers can serve as a tool for mastering the topics.

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 offered 3 different modes: “Multiply”, “Factor” and “Divide”. Open the “Multiply” section.  Part 1. “Multiply”. Step 2. You are given 3 levels: Level 1 performs multiplication of numbers 1-6, Level 2 1-9, and Level 3 1-12. Choose Level 1. In the workspace, you are given: Step 3. The Pythagoras table displays an expression that is colored and multiplied below the table. Write the value of the multiplication in the box where you write the result of the multiplication. Step 4. Click the “Check” button. If the result is correct, the expression of the next product is given. If there is an error, the “try again” button will appear. If there is an error, click the same button and write the result of the product from the beginning. Step 5. You can complete all the level 1 productions and go to the next level, or you can complete some more level 1 productions from the beginning.  Part 2. “Factor”. Step 6. Open the “Factor” section. There are 3 levels: Level 1 does multiplication of numbers 1-6, Level 2 does multiplication of numbers 1-9, and Level 3 does multiplication of numbers 1-12. Step 7. You are given in the work area: Step 8. The expression below the table gives the result of the product. In the Pythagoras table, mark the two numbers you need to multiply. Step 9. If the result is correct, the expression for the next product is given. If there is an error, a “try again” button appears. If there is an error, press the same button and write the result of the product from the beginning.  Step 10. You can complete all level 1 pieces and go to the next step, or you can complete some more level 1 pieces from the beginning. Part 3. “Divide”.  Step 11. Open the “Divide” section. There are 3 levels: Level 1 does multiplication of numbers 1-6, Level 2 does multiplication of numbers 1-9, and Level 3 does multiplication of numbers 1-12. The work area is similar to the “Multiply” section. Step 12. The expression below the table gives one of the multiplication numbers and the result of the product. Find the second number to multiply. Check the second number by marking it on the Calculator bar. Step 13. If the result is correct, the expression of the next product is given. In case of an error, the “Try again” button will appear. If there is an error, press the same button and write the result of the product from the beginning.   Step 14. You can finish all level 1 productions and go to the next step, or you can do some more level 1 productions from the beginning. Conclusion Students will learn how to multiply using the Pythagorean table through this virtual activity. This is interesting for students because they work with the multiplication operation visually and it makes it easier to memorize the multiplication table.

Objective: This virtual activity is designed to be used in the math lessons in the next chapter: Theory A derivative is a mathematical function that shows the rate of change of another function. Studying the graph of the derivative provides valuable information about the behavior of the original function. 1. The relationship between the graphs of f(x) and f'(x) The points of intersection with the x-axis: The x-coordinates of the points of intersection of the graph of the derivative with the x-axis are the points of extremum (maximum or minimum) of the original function. Intervals of monotonicity: If f'(x) > 0 on the interval (a, b), then f(x) is increasing on this interval. If f'(x) < 0 on the interval (a, b), then f(x) is decreasing on that interval. Local maxima and minima: A point x0 is a maximum point of f(x) if f'(x0) > 0 and then f'(x) < 0. A point x0 is the point of minimum of f(x) if f'(x0) < 0 and then f'(x) > 0. Asymptotes: The horizontal asymptote y = L if limx → ±∞ f(x) = L. The vertical asymptote x = a if limx → a f(x) = ±∞. 2. Algorithm to study the graph of the derivative Virtual Experiment The Exploring the Graph of a Function Using the Derivative virtual activity allows students to explore and determine relationships between the graphs of a function and its derivative. On the derivative screen, students can change the function and view the graph of its derivative. Course of work: Step 1. Start the simulation: You will be presented with 4 different modes: “Derivative”, “Integral”, “Advanced” and “Lab”. In this work, you will be working in the “Derivative” section. Open the “Derivative” section. Step 2. In the workspace provided to you: Step 3. Click the Planes grid display button. Step 4. Draw the graph of the function f(x). Draw the graph by raising or lowering the blue line along the OX axis. If you raise the line, it is the function – cos(x), if you lower it, it is sin(x). You will automatically have a graph of the derivative in the lower plane. If f(x)=cos(x), then f'(x)=sin(x). If f(x)=sin(x), then f'(x)=cos(x). Step 5. Click view Tangent graph. A discontinuous line with a red straight line and a round head appears on the screen. Explore the movement of the tangent graph by moving the wheel over the graph of the function. You can also see that the tangent has a different value in each part of the graph in the panel that appears on the left.  Step 6. Delete the graph on the plane by clicking the eraser. Change the volume of the wave.  Step 7. Draw the graph by raising or lowering the blue line along the OX axis. Examine the graphs of the functions f(x) and f'(x) and the movement of the tangent along the graph. If the graph of the derivative is not displayed completely in the plane, you can click the “-” button and zoom out. Step 8. Delete the graph on the plane by clicking on the eraser. Select the second type of graph. The function f(x) is a complex function. Draw the graph by moving the blue line up or down.  Step 9. Examine the graphs of the functions f(x) and f'(x) and the movement of the tangent on the graph. Step 10. Delete the graph in the plane by clicking on the eraser. Select the third type of graph. Here f(x)=±kx. Draw the graph by raising or lowering the blue line along the OX axis.  Step 11. You have f'(x) = ±k. Study the graphs of the functions f(x) and f'(x) and the movement of the tangent along the graph.  Step 12. Delete the graph in the plane by clicking on the eraser. Select the type of the fourth graph. Here f(x)=±k. Draw the graph by raising or lowering the blue line along the OX axis.  Step 13. You have f'(x)=0. Study the graphs of the functions f(x) and f'(x) and the movement of the tangent along the graph.  Conclusion Through this virtual activity, students have studied the graphs of derivative functions using graphs of given functions. They have also studied the tangent, one of the most important elements of the graph of a function. Since the use of the derivative is an early, important topic in mathematical analysis, this simulation can be very useful for students.

Objective: This virtual activity is designed for use in mathematics lessons on the following topics Theoretical part Ordinary fractions are numbers represented as fractions where the numerator and denominator are integers and the denominator is not zero. Writing a fraction: Example: Meaning of the fraction: Example: Types of fractions: Example of a mixed number: Writing a mixed number: Converting fractions to mixed numbers: Virtual experiment “Fraction Matcher” virtual activity teaches students to find and match matching fractions using numbers and pictures. Performs fraction calculations in a fun way to easily master the topic of simple fractions. Match the same fractions using different numbers and fraction representations. Course of work: Section 1: Play with correct and incorrect simple fractions Step 1. Start the simulation: You will be presented with 2 different modes: “Fraction” and “Mixed Numbers”. Open the “Fraction” section. Step 2. In the work area you will be presented with 8 different levels of problems. Levels 1-2 use only fractions smaller than 1. Levels 3-6 use fractions smaller than 2. Levels 7-8 use only fractions greater than 1 and less than 2. Step 3. Open the first level. In the work area, you will see  Step 4. Bring any fraction to the scales by left-clicking and dragging it. Step 5. Among the remaining fractions, find a fraction that is equal or proportional to the fraction on the scale. Place it on the second weight.  Step 6. Check for correctness by clicking on the “Check” button. If the fractions are equal, click “OK” and perform the next alignment. If there is an error, click “Try Again” and compare the fractions from the beginning.  Step 7. Complete the tasks in a level and move on to the next level. Section 2: Mixed Numbers Game Step 8. Open the “Mixed Numbers” Section. In the workspace, you will see 8 different levels of problems. Levels 1-6 use less than 2 mixed number fractions. Levels 7-8 use more than 1 and less than 2 fractions. Step 9. Open the first level. This section also introduces the work area as in the first section. Here you will do problems with mixed numbers. Step 10. Move any fraction to the scales by left-clicking and dragging. From the remaining fractions, find one that is equal to or proportional to the fraction on the scale. Place it on the second scale. Step 11. Check your work by clicking on the “Check” button.  Step 12. Complete the tasks of one level and move on to the next levels.  Conclusion  In this simulation, students worked on fraction-related game tasks to further explore the topic of fractions. They used the basic property of fractions to reduce fractions, compare fractions, and make fractions equal to each other.

Objective: This virtual activity is designed to be used in 1st grade math lessons on numbers, counting objects. Theoretical part What are numbers? Numbers are special symbols that we use to indicate the number of objects. There are 10 numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. How do you learn to count? To learn to count, you must Memorize the names of the numbers: 0 (zero), 1 (one), 2 (two), 3 (three), 4 (four), 5 (five), 6 (six), 7 (seven), 8 (eight), 9 (nine). Know how to show numbers with your fingers: Practice counting: Virtual experiment The “Counting Objects” Simulator allows students to become familiar with and explore numbers. By displaying numbers and pictures on the screen, students can easily learn to count objects visually.  Course of work: Part 1. Working with numbers 1-10 Step 1. Start the simulation: You will be presented with 4 different modes: “Ten”, “Twenty”, “Game” and “Lab”. Open the “Ten” section. Step 2. You will see the following in the work area: Step 3. Place the number “1” on board 1 to place the items by holding down the left side of the mouse. Automatically, 1 puppy will appear on board 2. The number “1” will appear in the number box. Step 4. Place another number “1” on board 1. There will be 2 puppies on the 2nd board. The number box will show “2”. Step 5. Count the puppies in the same way, making numbers up to 10.  Step 6. Click the “reload” button and clear the boards. Replace the puppy with another object. For example, an apple. Step 7. Place the object (apple) on the 2nd board. The number 1 will automatically appear on the 1st board.  Step 8. You can draw some objects on the board and see the numbers on the 1st board. And the window will show the number of the object. Try this several times. Part 2. Working with Numbers 1-20 Step 9. Open the Twenty Section. In this section you will also work with numbers up to 20 as in Part 1. Step 10. Repeat the above steps (steps 3-8) for numbers 1-20 as you worked with numbers 1-10.  Part 3. The Game Step 11. Open the “Game” section. You will be given 4 different levels of the game. The first level will have tasks related to numbers 1-10, the second level will have tasks related to numbers 11-20, the third level will have tasks related to numbers 1-5, and the fourth level will have tasks related to numbers 6-10. Step 12. Open the first level. Some number of substances are represented in the workspace.  Step 13. Count these substances and mark the number corresponding to the quantity of the substance from the numbers below. Step 14. A button will appear on the screen to go to the next task, click it and go to the next task.  Step 15. There are 10 problems per level. You can go to the next level by completing the same tasks. Or you can replay the level with new tasks. Conclusion In this virtual activity, students have learned how to count objects. Learning numbers and counting is an important stage in a child’s development. The ability to count will be useful to children in everyday life and will also help them in their further study of mathematics.

Objective: This virtual activity is designed to be used in the geometry lessons in the next chapter: Theoretical part Area is a quantitative measure of a two-dimensional surface. It represents the space occupied by a flat figure. Knowing the area of figures is important in several fields, including math, physics, engineering, architecture, and design. Formulas for calculating area: Each of the basic geometric figures has a formula for calculating its area: Ways to calculate area: Virtual Experiment The Area of Figures simulation teaches students how to find the area of a figure by counting unit squares. Describes the relationship between area and perimeter. Constructs figures with a given area and perimeter. Workflow: Step 1. Start the simulation: you will be offered 2 different modes, “Explore” and “Play”. Open the “Explore” section. Step 2. In the workspace you will find Step 3. Build the figure by drawing a row of unit squares on the board. Activate the button “Show shape size” on the board. Step 4. Look at the data on the board that shows area and perimeter. Examine how the area and perimeter of the figure are calculated. Step 5. Erase the board by clicking the eraser.  Step 6. Create a new figure on the board. Examine its area and perimeter. Step 7. Click the button to divide the workspace in half.  Step 8. Create two different shapes on two boards. Study their area and perimeter. Step 9. Try to create and study several figures in this way. Step 10. Open the “Game” section. You will be given tasks in the form of a game on 6 different levels. Open the first level. Step 11. In the workspace you will find: Step 12. The area of the figure to be built is set. Build the figure on its base. If necessary, you can add the buttons for displaying the grid and the size of the figure.  Step 13. Click on the Verify button to check that the figure is correct.  Step 14. Complete the tasks of the first level and move on to the next levels.  Conclusion Students have learned how to find the areas of figures of different irregular shapes. Made the connection between area and perimeter. Explored the topic of neighborhood by making shapes with a given area and perimeter.

Objective: This virtual activity is designed for use in math 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 Area Model simulator helps students learn how to find the area of a rectangle. Gives the rectangle different dimensions and creates problems. Checks their understanding of the area model by finding the missing dimensions or total area in the game section. 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 Generic and Game sections. Open the Generic section. Step 2. You are presented with a workspace: Step 3. Click on one of the spaces next to the rectangle. A calculator will appear on the screen. Enter the length of the rectangle. Step 4. Enter the dimensions of the rectangle in the other 3 spaces. Step 5. Click on “a*b” to see the expression of the length and width of the rectangle.  Step 6. You can see the result of the area for each rectangle by clicking the “A” button.  Step 7. There are 2 views of the calculation panel. They show the calculation of the area.  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 length and width of the rectangle and calculate the area again. Construct several expressions in this way. Step 9. Change the type of subdivision of the rectangle. 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 workspace you will see Step 12. The game requires you to find the unknown number associated with the rectangle. Do the calculation and find the number. 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 By creating this virtual activity, students can further develop their knowledge of the area. They perform different investigations on the area of a rectangle and create problems in a game-like way. This makes the lesson more fun and easier to learn.

Objective: This virtual activity is designed for use in math lessons on the following topics Theoretical Part The rule for multiplying decimal fractions To multiply two decimal fractions, you must: Multiplying a decimal fraction by a whole number To multiply a decimal fraction by 10, 100, 1000, and so on. To multiply a decimal fraction by 10, 100, 1000, and so on, you must: Virtual Experiment The “Area Model: Decimals” simulation is designed to help students learn how to multiply decimals. Multiplication is learned by finding the area of a rectangle in the form of a Pythagorean table.  Workflow: Step 1. Start the simulation: in the workspace provided to you: Step 2. The table is divided into 10 parts. Each part represents 0.1, which is an integer of 1. The table represents a square of size 0.5*0.5. Divided horizontally into sections (0.2;0.3). The Multiplier Numbers panel and the Multiplication Results panel display the data. Click the button to color the square. Step 3. Click the “a*b” button from the square information in the table. The expressions 0.2*0.5 and 0.3*0.5 appear in the parts of the square.   Step 4. 2 views of the Calculation Panel are given. They 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 square information in the table. The value of the expressions on the “a*b” button appears in the parts of the square.  Step 6. Explore the changes in the product by moving the divider up and down the square. Step 7. Move the horizontal divider up the square so that it does not divide the square. Move the vertical divider to the right. Examine the data. Observe the changes as you move the divider right and left. Step 8. Explore dividing the square into rectangles of different sizes by alternating the vertical and horizontal dividing lines in the square. Step 9. Create a new rectangle size by clicking on the green button next to the square. Explore the product of decimals. Step 10. Try to change the information about the quadrilateral in the table, the dividing lines. Step 11. You can change the size of the table to 2*2 and 3*3. Make the calculations by repeating the above steps. Change the dimensions of the rectangle and calculate the products. Conclusion In this virtual activity, students solve multiplication problems with decimal fractions using the area model. Multiplication in the Pythagorean table provides a visual way to learn the subject. This makes it easier to learn a new lesson.