An elementary math curriculum for supplementary or home school should teach much more than the “how to” of simple arithmetic. A good math curriculum should have elementary math activities that build a solid foundation which is both deep and broad, conceptual and “how to”.
Time4Learning teaches a comprehensive math curriculum that correlates to state standards. Using a combination of multimedia lessons, printable worksheets, and assessments, the elementary math activities are designed to build a solid math foundation. It can be used as a , an , or as a for enrichment.
Time4Learning has no hidden fees, offers a 14-day money-back guarantee for brand new members, and allows members to start, stop, or pause at anytime. Try the interactive or view our to see what’s available.
Teaching Elementary Math Strategies
Children should acquire math skills using elementary math activities that teach a curriculum in a proper sequence designed to build a solid foundation for success. Let’s start with what appears to be a simple math fact: 3 + 5 = 8
This fact seems like a good math lesson to teach, once a child can count. But the ability to appreciate the concept “3 + 5 = 8” requires an understanding of these elementary math concepts:
- Quantity– realizing that numbers of items can be counted. Quantity is a common concept whether we are counting fingers, dogs or trees.
- Number recognition– knowing numbers by name, numeral, pictorial representation, or a quantity of the items.
- Number meaning– resolving the confusion between numbers referring to a quantity or to the position in a sequence (cardinal vs. ordinal numbers.
- Operations– Understanding that quantities can be added and that this process can be depicted with pictures, words, or numerals.
To paint a more extreme picture, trying to teach addition with “carrying over” prior to having a solid understanding of place value is a recipe for confusion. Only after mastering basic math concepts should a child try more advanced elementary math activities, like addition. Trying to teach elementary math strategies prior to mastering basic math concepts cause confusion, creating a sense of being lost or of being weak at math. A child can end up developing a poor self image or a negative view of math all because of a poor math curriculum.
It’s important to implement an elementary math curriculum that teaches math in a sequence, using elementary math activities that allow children to progressively build understanding, skills, and confidence. Quality teaching and curriculum follows a quality sequence.
Time4Learning teaches a personalized elementary math curriculum geared to your child’s current skill level. This helps to ensure that your child has a solid math foundation before introducing harder, more complex elementary math strategies. , included in the curriculum, provides practice in foundation skill areas that is necessary for success during elementary school. Get your child on the right path, about Time4Learning’s strategies for teaching elementary math.
Time4Learning's Elementary Math Curriculum
Time4Learning’s math curriculum contains a wide range of elementary math activities, which cover more than just arithmetic, math facts, and operations. Our elementary math curriculum teaches these five math strands.*
- Number Sense and Operations– Knowing how to represent numbers, recognizing ‘how many’ are in a group, and using numbers to compare and represent paves the way for grasping number theory, place value and the meaning of operations and how they relate to one another.
- Algebra– The ability to sort and order objects or numbers and recognizing and building on simple patterns are examples of ways children begin to experience algebra. This elementary math concept sets the groundwork for working with algebraic variables as a child’s math experience grows.
- Geometry and Spatial Sense– Children build on their knowledge of basic shapes to identify more complex 2-D and 3-D shapes by drawing and sorting. They then learn to reason spatially, read maps, visualize objects in space, and use geometric modeling to solve problems. children will be able to use coordinate geometry to eventually specify locations, give directions and describe spatial relationships.
- Measurement– Learning how to measure and compare involves concepts of length, weight, temperature, capacity and money. Telling the time and using money links to an understanding of the number system and represents an important life skill.
- Data Analysis and Probability– As children collect information about the world around them, they will find it useful to display and represent their knowledge. Using charts, tables, graphs will help them learn to share and organize data.
Elementary math curriculums that cover just one or two of these five math strands are narrow and lead to a weak understanding of math. Help your child build a strong, broad math foundation.
The SAT Math Test covers a range of mathematical methods, with an emphasis on problem solving, mathematical models, and the strategic use of mathematical knowledge.
SAT Math Test: just like in the real world
Instead of testing you on every math topic, the new SAT tests your ability to use the math you'll rely on most times and in many different situations. Math test questions are designed to reflect problem solving and models that you will be dealing with in
University studies, directly studying mathematics, as well as natural and social sciences;
- Your daily professional activities;
- Your daily life.
For example, to answer some questions, you will need to use several steps - because in the real world, situations where one simple step is enough to find a solution are extremely rare.
SAT Math Format
SAT Math Test: Basic Facts
The SAT Math section focuses on three areas of mathematics that play a leading role in most academic subjects in higher education and professional careers:
- Heart of Algebra: Fundamentals of algebra, which focuses on solving linear equations and systems;
- Problem Solving and Data Analysis: Problem solving and data analysis essential to general mathematical literacy;
- Passport to Advanced Math: Fundamentals of advanced mathematics, which asks questions that require manipulating complex equations.
The math test also draws on additional topics in mathematics, including geometry and trigonometry, which are most important for university studies and professional careers.
SAT Math Test: video
Basics of algebra
Heart of Algebra
This section of SAT Math focuses on algebra and the key concepts that are most important for success in college and career. It assesses students' ability to analyze, solve and construct linear equations and inequalities freely. Students will also be required to analyze and fluently solve equations and systems of equations using multiple methods. To fully assess knowledge of this material, problems will vary significantly in type and content. They can be quite simple or require strategic thinking and understanding, such as interpreting the interaction between graphical and algebraic expressions or presenting a solution as a reasoning process. Test takers must demonstrate not only knowledge of solution techniques, but also a deeper understanding of the concepts that underlie linear equations and functions. SAT Math Fundamentals of Algebra is scored on a scale of 1 to 15.
This section will contain tasks for which the answer is presented in multiple choice or independently calculated by the student. The use of a calculator is sometimes permitted, but not always necessary or recommended.
1. Construct, solve or interpret a linear expression or equation with one variable, in the context of some specific conditions. An expression or equation may have rational coefficients, and several steps may be required to simplify the expression or solve the equation.
2. Construct, solve or interpret linear inequalities with one variable, in the context of some specific conditions. An inequality may have rational coefficients and may require several steps to simplify or solve.
3. Construct a linear function that models a linear relationship between two quantities. The test taker must describe a linear relationship that expresses certain conditions using either an equation with two variables or a function. The equation or function will have rational coefficients, and several steps may be required to construct and simplify the equation or function.
4. Construct, solve and interpret systems of linear inequalities with two variables. The examinee will analyze one or more conditions existing between two variables by constructing, solving, or interpreting a two-variable inequality or system of two-variable inequalities, within certain specified conditions. Constructing an inequality or system of inequalities may require several steps or definitions.
5. Construct, solve and interpret systems of two linear equations in two variables. The examinee will analyze one or more conditions that exist between two variables by constructing, solving, or analyzing a system of linear equations, within certain specified conditions. The equations will have rational coefficients, and several steps may be required to simplify or solve the system.
6. Solve linear equations (or inequalities) with one variable. The equation (or inequality) will have rational coefficients and may require several steps to solve. Equations may have no solution, one solution, or an infinite number of solutions. The examinee may also be asked to determine the value or coefficient of an equation that has no solution or has an infinite number of solutions.
7. Solve systems of two linear equations with two variables. The equations will have rational coefficients, and the system may have no solution, one solution, or an infinite number of solutions. The examinee may also be asked to determine the value or coefficient of an equation in which the system may have no solution, one solution, or an infinite number of solutions.
8. Explain the relationship between algebraic and graphical expressions. Identify the graph described by a given linear equation or the linear equation that describes a given graph, determine the equation of a line given by verbally describing its graph, identify key features of the graph of a linear function from its equation, determine how a graph might be affected by changing its equation.
Problem solving and data analysis
Problem Solving and Data Analysis
This section of SAT Math reflects research that has identified what is important for success in college or university. Tests require problem solving and data analysis: the ability to mathematically describe a certain situation, taking into account the elements involved, to know and use various properties of mathematical operations and numbers. Problems in this category will require significant experience in logical reasoning.
Examinees will be required to know the calculation of average values of indicators, general patterns and deviations from the general picture and distribution in sets.
All problem solving and data analysis questions test examinees' ability to use their mathematical understanding and skills to solve problems they might encounter in the real world. Many of these issues are asked in academic and professional contexts and are likely to be related to science and sociology.
Problem Solving and Data Analysis is one of three subsections of SAT Math that are scored from 1 to 15.
This section will contain questions with multiple choice or self-calculated answers. Using a calculator here is always permitted, but not always necessary or recommended.
In this part of SAT Math, you may encounter the following questions:
1. Use ratios, rates, proportions, and scale drawings to solve single- and multi-step problems. Test takers will use a proportional relationship between two variables to solve a multi-step problem to determine a ratio or rate; Calculate the ratio or rate and then solve the multi-step problem using the given ratio or ratio to solve the multi-step problem.
2. Solve single and multi-step problems with percentages. The examinee will solve a multi-level problem to determine percentage. Calculate the percentage of a number and then solve a multi-level problem. Using a given percentage, solve a multi-level problem.
3. Solve single- and multi-step calculation problems. The examinee will solve a multi-level problem to determine the rate unit; Calculate a unit of measurement and then solve a multi-step problem; Solve a multi-level problem to complete the unit conversion; Solve a multi-stage density calculation problem; Or use the concept of density to solve a multi-step problem.
4. Using scatter diagrams, solve linear, quadratic, or exponential models to describe how variables are related. Given the scatterplot, select the equation of the line or curve of fit; Interpret the line in the context of the situation; Or use the line or curve that best suits the prediction.
5. Using the relationship between two variables, explore the key functions of the graph. The examinee will make connections between the graphical expression of data and the properties of the graph by selecting a graph that represents the described properties or using a graph to determine values or sets of values.
6. Compare linear growth with exponential growth. The examinee will need to match two variables to determine which type of model is optimal.
7. Using tables, calculate data for various categories of quantities, relative frequencies and conditional probabilities. The examinee uses data from various categories to calculate conditional frequencies, conditional probabilities, association of variables, or independence of events.
8. Draw conclusions about population parameters based on sample data. The examinee estimates the population parameter, taking into account the results of a random sample of the population. Sample statistics can provide confidence intervals and measurement error that the student must understand and use without having to calculate them.
9. Use statistical methods to calculate averages and distributions. Test takers will calculate the mean and/or distribution for a given set of data or use statistics to compare two separate sets of data.
10. Evaluate reports, draw conclusions, justify conclusions, and determine the appropriateness of data collection methods. Reports can consist of tables, graphs, or text summaries.
Fundamentals of Higher Mathematics
Passport to Advanced Math
This section of SAT Math includes topics that are particularly important for students to master before moving on to advanced math. The key here is understanding the structure of expressions and the ability to analyze, manipulate and simplify those expressions. This also includes the ability to analyze more complex equations and functions.
Like the previous two sections of SAT Math, questions here are scored from 1 to 15.
This section will contain questions with multiple choice or self-calculated answers. The use of a calculator is sometimes permitted, but is not always necessary or recommended.
In this part of SAT Math, you may encounter the following questions:
1. Create a quadratic or exponential function or equation that models the given conditions. The equation will have rational coefficients and may require several steps to simplify or solve.
2. Determine the most appropriate form of expression or equation to identify a particular attribute, given the given conditions.
3. Construct equivalent expressions involving rational exponents and radicals, including simplification or conversion to another form.
4. Construct an equivalent form of the algebraic expression.
5. Solve a quadratic equation that has rational coefficients. The equation can be represented in a wide range of forms.
6. Add, subtract and multiply polynomials and simplify the result. The expressions will have rational coefficients.
7. Solve an equation in one variable that contains radicals or contains a variable in the denominator of the fraction. The equation will have rational coefficients.
8. Solve a system of linear or quadratic equations. The equations will have rational coefficients.
9. Simplify simple rational expressions. Test takers will add, subtract, multiply or divide two rational expressions or divide two polynomials and simplify them. The expressions will have rational coefficients.
10. Interpret parts of nonlinear expressions in terms of their terms. Test takers must relate given conditions to a nonlinear equation that models those conditions.
11. Understand the relationship between zeros and factors in polynomials and use this knowledge to construct graphs. Test takers will use the properties of polynomials to solve problems involving zeros, such as determining whether an expression is a factor of a polynomial, given the information provided.
12. Understand the relationship between two variables by establishing connections between their algebraic and graphical expressions. The examinee must be able to select a graph corresponding to a given nonlinear equation; interpret graphs in the context of solving systems of equations; select a nonlinear equation corresponding to the given graph; determine the equation of the curve taking into account the verbal description of the graph; identify key features of the graph of a linear function from its equation; determine the effect on the graph of changing the governing equation.
What does the SAT math section test?
General mastery of discipline
A math test is a chance to show that you:
Perform mathematical tasks flexibly, accurately, efficiently and using solution strategies;
- Solve problems quickly by identifying and using the most effective approaches to solution. This may involve solving problems by
performing substitutions, shortcuts, or reorganization of information you provide;
Conceptual understanding
You will demonstrate your understanding of mathematical concepts, operations, and relationships. For example, you may be asked to make connections between the properties of linear equations, their graphs, and the terms they express.
Application of subject knowledge
Many SAT Math questions are taken from real-life problems and ask you to analyze the problem, identify the basic elements needed to solve it, express the problem mathematically, and find a solution.
Using the calculator
Calculators are important tools for performing mathematical calculations. To successfully study at a university, you need to know how and when to use them. In the Math Test-Calculator part of the test, you will be able to focus on finding the solution and analysis itself, because your calculator will help save your time.
However, a calculator, like any tool, is only as smart as the person using it. There are some questions on the Math Test where it is best not to use a calculator, even if you are allowed to do so. In these situations, test takers who can think and reason are likely to arrive at the answer before those who blindly use a calculator.
The Math Test-No Calculator portion makes it easy to evaluate your general knowledge of the subject and your understanding of certain math concepts. It also tests familiarity with computational techniques and understanding of number concepts.
Questions with answers entered into a table
Although most questions on the math test are multiple choice, 22 percent are questions where the answers are the result of the test taker's calculations - called grid-ins. Instead of choosing the correct answer from a list, you need to solve the problems and enter your answers into the grids provided on the answer sheet.
Answers entered into a table
Mark no more than one circle in any column;
- Only answers indicated by completing the circle will be counted (You will not receive points for everything written in the fields located above
circles).
- It doesn't matter in which column you start entering your answers; It is important that the answers are written inside the grid, then you will receive points;
- The grid can only contain four decimal places and can only accept positive numbers and zero.
- Unless otherwise specified in the task, answers can be entered into the grid as decimal or fractional;
- Fractions such as 3/24 do not need to be reduced to minimum values;
- All mixed numbers must be converted to improper fractions before being written into the grid;
- If the answer is a repeating decimal number, students must determine the most accurate values that will
consider.
Below is a sample of the instructions test takers will see on the SAT Math exam:
The following are also used with this calculator:
Graphical method for solving ZLP
Simplex method for solving ZLP
Solving a matrix game
Using the online service, you can determine the price of a matrix game (lower and upper bounds), check for the presence of a saddle point, find a solution to a mixed strategy using the following methods: minimax, simplex method, graphical (geometric) method, Brown's method.
Extremum of a function of two variables
Dynamic programming problems
The first stage of solving the transport problem is to determine its type (open or closed, or otherwise balanced or unbalanced). Approximate methods ( methods for finding a reference plan) allow for second stage of solution in a small number of steps obtain an acceptable, but not always optimal, solution to the problem. This group of methods includes the following methods:
- deletion (double preference method);
- northwest corner;
- minimum element;
- Vogel approximations.
Reference solution to the transport problem
The reference solution to the transport problem is any feasible solution for which the condition vectors corresponding to the positive coordinates are linearly independent. To check the linear independence of the vectors of conditions corresponding to the coordinates of an admissible solution, cycles are used.Cycle A sequence of cells in a transport task table is called in which two and only adjacent cells are located in the same row or column, and the first and last are also in the same row or column. A system of vectors of transport problem conditions is linearly independent if and only if no cycle can be formed from the corresponding cells of the table. Therefore, an admissible solution to the transport problem, i=1,2,...,m; j=1,2,...,n is a reference only if no cycle can be formed from the table cells occupied by it.
Approximate methods for solving the transport problem.
Cross-out method (double preference method). If there is one occupied cell in a row or column of a table, then it cannot be included in any cycle, since a cycle has two and only two cells in each column. Therefore, you can cross out all the rows of the table that contain one occupied cell, then cross out all the columns that contain one occupied cell, then return to the rows and continue crossing out rows and columns. If, as a result of deleting, all rows and columns are crossed out, it means that from the occupied cells of the table it is impossible to select a part that forms a cycle, and the system of corresponding vectors of conditions is linearly independent, and the solution is a reference one. If, after deleting, some cells remain, then these cells form a cycle, the system of corresponding vectors of conditions is linearly dependent, and the solution is not a reference one.
Northwest Angle Method consists of sequentially going through the rows and columns of the transport table, starting from the left column and the top line, and writing out the maximum possible shipments in the corresponding cells of the table so that the supplier’s capabilities or the consumer’s needs stated in the task are not exceeded. In this method, no attention is paid to delivery prices, since further optimization of shipments is assumed.
Minimal Element Method. Despite its simplicity, this method is still more effective than, for example, the North-West Angle method. Moreover, the minimum element method is clear and logical. Its essence is that in the transport table, the cells with the lowest tariffs are filled first, and then the cells with high tariffs. That is, we choose transportation with the minimum cost of cargo delivery. This is an obvious and logical move. True, it does not always lead to the optimal plan.
Vogel approximation method. With the Vogel approximation method, at each iteration, the difference between the two minimum tariffs written in them is found for all columns and all rows. These differences are recorded in a specially designated row and column in the table of problem conditions. Among the indicated differences, the minimum is chosen. In the row (or column) to which this difference corresponds, the minimum tariff is determined. The cell in which it is written is filled in at this iteration.
Example No. 1. Tariff matrix (here the number of suppliers is 4, the number of stores is 6):
| 1 | 2 | 3 | 4 | 5 | 6 | Reserves | |
| 1 | 3 | 20 | 8 | 13 | 4 | 100 | 80 |
| 2 | 4 | 4 | 18 | 14 | 3 | 0 | 60 |
| 3 | 10 | 4 | 18 | 8 | 6 | 0 | 30 |
| 4 | 7 | 19 | 17 | 10 | 1 | 100 | 60 |
| Needs | 10 | 30 | 40 | 50 | 70 | 30 |
∑a = 80 + 60 + 30 + 60 = 230
∑b = 10 + 30 + 40 + 50 + 70 + 30 = 230
The balance condition is met. Supplies equal needs. So, the model of the transport problem is closed. If the model were open, it would be necessary to introduce additional suppliers or consumers.
On second stage The reference plan is searched using the methods given above (the most common is the least cost method).
To demonstrate the algorithm, we present only a few iterations.
Iteration No. 1. The minimum matrix element is zero. For this element, inventories are 60 and requirements are 30. We select the minimum number 30 from them and subtract it (see table). At the same time, we cross out the sixth column from the table (its needs are equal to 0).
| 3 | 20 | 8 | 13 | 4 | x | 80 |
| 4 | 4 | 18 | 14 | 3 | 0 | 60 - 30 = 30 |
| 10 | 4 | 18 | 8 | 6 | x | 30 |
| 7 | 19 | 17 | 0 | 1 | x | 60 |
| 10 | 30 | 40 | 50 | 70 | 30 - 30 = 0 | 0 |
Iteration No. 2. Again we are looking for the minimum (0). From the pair (60;50) we select the minimum number 50. Cross out the fifth column.
| 3 | 20 | 8 | x | 4 | x | 80 |
| 4 | 4 | 18 | x | 3 | 0 | 30 |
| 10 | 4 | 18 | x | 6 | x | 30 |
| 7 | 19 | 17 | 0 | 1 | x | 60 - 50 = 10 |
| 10 | 30 | 40 | 50 - 50 = 0 | 70 | 0 | 0 |
Iteration No. 3. We continue the process until we have selected all the needs and supplies.
Iteration No. N. The element you are looking for is 8. For this element, supplies are equal to requirements (40).
| 3 | x | 8 | x | 4 | x | 40 - 40 = 0 |
| x | x | x | x | 3 | 0 | 0 |
| x | 4 | x | x | x | x | 0 |
| x | x | x | 0 | 1 | x | 0 |
| 0 | 0 | 40 - 40 = 0 | 0 | 0 | 0 | 0 |
| 1 | 2 | 3 | 4 | 5 | 6 | Reserves | |
| 1 | 3 | 20 | 8 | 13 | 4 | 100 | 80 |
| 2 | 4 | 4 | 18 | 14 | 3 | 0 | 60 |
| 3 | 10 | 4 | 18 | 8 | 6 | 0 | 30 |
| 4 | 7 | 19 | 17 | 0 | 1 | 100 | 60 |
| Needs | 10 | 30 | 40 | 50 | 70 | 30 |
Let's count the number of occupied cells of the table, there are 8 of them, but it should be m + n - 1 = 9. Therefore, the support plan is degenerate. We are making a new plan. Sometimes you have to build several reference plans before finding a non-degenerate one.
| 1 | 2 | 3 | 4 | 5 | 6 | Reserves | |
| 1 | 3 | 20 | 8 | 13 | 4 | 100 | 80 |
| 2 | 4 | 4 | 18 | 14 | 3 | 0 | 60 |
| 3 | 10 | 4 | 18 | 8 | 6 | 0 | 30 |
| 4 | 7 | 19 | 17 | 0 | 1 | 100 | 60 |
| Needs | 10 | 30 | 40 | 50 | 70 | 30 |
As a result, the first support plan is obtained, which is valid, since the number of occupied cells of the table is 9 and corresponds to the formula m + n - 1 = 6 + 4 - 1 = 9, i.e. the reference plan is non-degenerate.
Third stage consists in improving the found reference plan. Here they use the potential method or distribution method. At this stage, the correctness of the solution can be monitored through the cost function F(x) . If it decreases (subject to minimizing costs), then the solution is correct.
Example No. 2. Using the minimum tariff method, present an initial plan for solving a transportation problem. Check for optimality using the potential method.
| 30 | 50 | 70 | 10 | 30 | 10 | |
| 40 | 2 | 4 | 6 | 1 | 1 | 2 |
| 80 | 3 | 4 | 5 | 9 | 9 | 6 |
| 60 | 4 | 3 | 2 | 7 | 8 | 7 |
| 20 | 5 | 1 | 3 | 5 | 7 | 9 |
Example No. 3. Four confectionery factories can produce three types of confectionery products. The production costs of one quintal (quintal) of confectionery products by each factory, the production capacity of the factories (quintal per month) and the daily requirements for confectionery products (quintal per month) are indicated in the table. Draw up a confectionery production plan that minimizes total production costs.
Note. Here, you can first transpose the cost table, since for the classical formulation of the transport problem, capacities (production) come first, and then consumers.
Example No. 4. For the construction of facilities, bricks are supplied from three (I, II, III) factories. Factories have 50, 100 and 50 thousand units in warehouses, respectively. bricks Objects require 50, 70, 40 and 40 thousand pieces, respectively. bricks Tariffs (den. units/thousand units) are shown in the table. Create a transportation plan that minimizes total transportation costs.
will be closed if:A) a=40, b=45
B) a=45, b=40
B) a=11, b=12
Condition of the closed transport problem: ∑a = ∑b
We find, ∑a = 35+20+b = 55+b; ∑b = 60+a
We get: 55+b = 60+a
Equality will be observed only when a=40, b=45
Lesia M. Ohnivchuk
Abstract
The article considers way to extend the functionality of LMS Moodle when creating e-learning courses for the mathematical sciences, in particular e-learning courses "Elementary Mathematics" by using flash technology and Java-applets. There are examples of the use of flash-applications and Java-applets in the course "Elementary Mathematics".
Keywords
LMS Moodle; e-learning courses; technology flash; Java applet, GeoGebra
References
Brandão, L. O., "iGeom: a free software for dynamic geometry into the web", International Conference on Sciences and Mathematics Education, Rio de Janeiro, Brazil, 2002.
Brandão, L. O. and Eisnmann, A. L. K. “Work in Progress: iComb Project - a mathematical widget for teaching and learning combinatorics through exercises” Proceedings of the 39th ASEE/IEEE Frontiers in Education Conference, 2009, T4G_1–2
Kamiya, R. H and Brandão, L. O. “iVProg – a system for introductory programming through a Visual Model on the Internet. Proceedings of the XX Simpósio Brasileiro de Informática na Educação, 2009 (in Portuguese).
Moodle.org: open-source community-based tools for learning [Electronic resource]. – Access mode: http://www.moodle.org.
MoodleDocs [Electronic resource]. – Access mode: http://docs.moodle.org.
Interactive technologies: theory, practice, evidence: methodical guide to auto-installation: O. Pometun, L. Pirozhenko. – K.: APN; 2004. – 136 p.
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GeoGebra. Materials [Electronic resource]. – Access mode: http://tube.geogebra.org.
Hohenvator M. Introduction to GeoGebra / M. Hohenvator / trans. T. S. Ryabova. – 2012. – 153 p.
REFERENCES (TRANSLATED AND TRANSLITERATED)
Brandão, L. O. "iGeom: a free software for dynamic geometry into the web", International Conference on Sciences and Mathematics Education, Rio de Janeiro, Brazil, 2002 (in English).
Brandão, L. O. and Eisnmann, A. L. K. “Work in Progress: iComb Project - a mathematical widget for teaching and learning combinatorics through exercises” Proceedings of the 39th ASEE/IEEE Frontiers in Education Conference, 2009, T4G_1–2 (in English).
Kamiya, R. H and Brandão, L. O. “iVProg – a system for introductory programming through a Visual Model on the Internet. Proceedings of the XX Simpósio Brasileiro de Informática na Educação, 2009 (in English)..
Moodle.org: open-source community-based tools for learning. – Available from: http://www.moodle.org (in English).
MoodleDocs. – Available from: http://docs.moodle.org (in English).
Pometun O. I., Pirozhenko L. V. Modern lesson, Kiev, ASK Publ., 2004, 192 p. (in Ukrainian).
Dmitry Pupinin. Question Type: Flash . – Available from: https://moodle.org/mod/data/view.php?d=13&rid=2493&filter=1 – 02.26.14 (in English).
Andreev A., Gerasimenko R. Using Flash and SCORM to create tasks final control. – Available from: http://cdp.tti.sfedu.ru/index.php?option=com_content&task=view&id=1071&Itemid=363 – 02.26.14 (in Russian).
GeoGebra Wiki. – Available from: http://www.geogebra.org (in English).
Hohenwarter M. Introduction to GeoGebra / M. Hohenwarter. – 2012. – 153 s. (in English).
DOI: https://doi.org/10.33407/itlt.v48i4.1249
Copyright (c) 2015 Lesia M. Ohnivchuk