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E.nopi program
> E.nopi MATH-Tutorial samples |
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| Level 1 |
Learning and practicing numbers up to 10
Level 1 focuses on learning, practicing, and ordering numbers from 1 through 10. Students progress to the next level only after they are able to count intuitively.
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| Level 2 |
Making 10; practicing numbers up to 30
This level focuses on learning, practicing, ordering numbers from 11 through 30, and number pairs which make 10. Students will group by 10's to understand numbers up through 30.
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| Level 3 |
Learning numbers to 120; adding 1, 2, and 3; practicing adding 1,2 and 3
Children learn numbers through 120 by grouping and place values. They also practice adding 1, 2, and 3. By linking adding with the number sequence and counting, students will have a deeper conceptual understanding of the processes of addition.
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| Level 4 |
Practicing adding and subtracting 1,2 and 3
Children practice addition and subtraction of 1 through 3. Oral tests are administered to ensure students' complete competency with all skills.
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| Level 5 |
Making numbers; practicing addition up to 10; adding two single-digit numbers (1)
Children further develop their mental arithmetic skills by creating numbers and using addition tables.
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| Level 6 |
Developing mental addition and practicing addition of two single-digit numbers and three single-digit numbers
Students practice the process of carrying (regrouping) until it becomes an automatic mental operation.
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| Level 7 |
Practicing (2-digit) + (1-digit); addition of three single-digit numbers; reviewing students' progress in addition
Students are provided with a variety of problems designed to help them sharpen their mental computational skills in the addition of multiple-digit numbers. The aim of the lesson is to help children reach a level where they are able to answer questions intuitively.
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| Level 8 |
Simple subtraction; practicing subtraction; studying subtraction tables
Level 8 introduces subtraction and brings children to understand addition and subtraction as inverse arithmetic, thus, deepening their mathematical understanding and developing the mental arithmetic of subtraction.
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| Level 9 |
Practicing (2-digit) - (1-digit); (2-digit) - (2-digit); subtraction with three numbers
This level builds on basic subtraction skills by bringing the student to a full understanding of subtraction of one-digit numbers from two-digit numbers [(2-digit) - (1-digit)]. By developing mental computational skills, students will be able to master the basic subtraction processes.
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| Level 10 |
Adding with numbers up to 99 and practicing adding 2-digit numbers and 3-digit numbers
This lesson focuses on regrouping (carrying) with multiple-digit numbers. Students are provided with a variety of problems designed to help them sharpen their computational skills with addition and enhance their understanding of place value.
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| Level 11 |
Practicing subtraction with 2-digit and 3-digit numbers and addition and subtraction with three numbers
This level focuses on the skills of subtraction and addition with and without regrouping (carrying or borrowing). Students apply their mental knowledge of differences to more complex subtraction problems, which are designed to help them sharpen addition and subtraction skills with multi-digit numbers.
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| Level 12 |
Learning multiplication and practicing multiplication of (1-digit) x (1-digit) and (2-digit) x (1-digit)
Multiplication is introduced along with multiplication tables. Children learn the relationship between addition and multiplication, broaden their understanding and skills in multiplication, and prepare themselves to study the process of division.
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| Level 13 |
Practicing basic multiplication up through 3-digit numbers
This level provides students with practice using mathematical facts (times tables) to complete (2-digit) x (1-digit) problems. Students gain experience with a wide range of multiplication problems that use regrouping, including (2-digit) x (2-digit) problems, (3-digit) x (2-digit) problems, and (3-digit) x (3-digit) problems.
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| Level 14 |
Introduction to division, with and without remainders
Students learn two methods of division and study the concept that remainders are always smaller than the divisor. After learning division facts by using the numbers 1 through 9 as divisors, students gain experience with progressively larger divisors.
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| Level 15 |
Practicing division with progressively larger divisors and dividends, beginning with 3-digit dividends and 1-digit divisors and progressing to 5-digit dividends and 3-digit divisors.
Students also review place values for large numbers and gain practice in estimating quotients. While a quick speed in calculating quotients is promoted, accuracy and self-checking of quotients are emphasized.
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| Level 16 |
Learning metric units of measurement and the order of operations in problems having a mixture of arithmetic operations
Students practice solving problems having a mixture of the four operations, with and without parentheses. Units of measurement are introduced, and students gain experience in converting units and labeling answers.
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| Level 17 |
Comparing fractions; addition and subtraction of fractions with the same denominators; learning units of measurement
Students learn about fractions and practice adding and subtracting fractions with the same denominators.
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| Level 18 |
Adding and subtracting decimals, multiples and factors; simplifying fractions
This level allows students to become familiar with decimals and fractions through five study topics: understanding decimals, adding and subtracting decimals, multiples and factors, equivalent fractions, and simplifying fractions. Students study simplifying fractions to lowest terms.
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| Level 19 |
Simplifying fractions; addition and subtraction of fractions with different denominators; addition and subtraction of fractions with different denominators
In this level, students practice simplifying fractions and adding and subtracting fractions with different denominators. Students will also practice finding common denominators by using their knowledge about the greatest common factor and the least common multiple.
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| Level 20 |
Addition and subtraction of three fractions; multiplying fractions; dividing fractions
Students will practice converting fractions to decimals, decimals to fractions, and mixed numbers to improper fractions. This level also involves the skills of finding equivalent fractions and simplifying fractions.
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| Level 21 |
Multiplying decimals; dividing decimals; ratios
In this level, students will become familiar with the basic operations involving fractions, multiplying decimals, dividing decimals, basic operations using decimals, and ratios. Students will practice operations with fractions and decimals. In addition, the concept of ratios will be introduced.
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| Level 22 |
Equations; equivalent ratios; proportions; circular geometry
This level provides a comprehensive foundation in equations, proportions, and continued proportions.
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| Level 23 |
Basic operations with whole numbers; fractions and decimals; converting units of measurement; surface area and volume of 3D objects
Students develop the ability to calculate fractions and complete the compound calculations of four arithmetic operations.
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| Level 24 |
Prime factorization; sets; multiplication and division with rational numbers
Students learn about divisors, multiples, decimal fractions and composite numbers. They will also become familiar with division of prime factors through studying the theory of sets and operations. In this level, students broaden their knowledge about numbers from whole numbers to integers.
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| Level 25 |
Evaluating expressions; equations; functions and their graphs
This level shows students how to apply the four arithmetic operations to rational numbers. They will practice solving linear equations based on an understanding of the properties of equalities. Graphs are also introduced and students learn to plot points on the coordinate plane.
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| Level 26 |
Functions and their graphs; polygons; surface area; volume of solid figures
In this level, students learn how to find the relationships of directly proportional and inversely proportional functions and draw graphs. They will learn about domains and co-domains. In addition to studying relative frequencies and cumulative frequencies, they will also become familiar with the positional relationships between lines and planes on a flat plane and in space. Triangles, circles, sectors, the congruence conditions of two triangles, and how to find the surface area and volume of solid figures are also covered in this level. |
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| Level 27 |
Multiplication and division of monomials; linear equations with two variables; system of equations
This level covers approximate values, the law of exponents, and addition, subtraction, multiplication and division of monomials and polynomials. Students learn how to solve linear equations and systems of equations containing two variables.
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| Level 28 |
Systems of equations; linear inequalities; linear functions and their graphs
Students learn about systems of equations in which coefficients are decimals or fractions, as well as the other forms of systems of equations. Students gain an understanding of the properties of inequalities, including how to solve various forms of linear inequalities. This level also covers the concepts of linear functions, graphs, slopes, and intercepts.
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| Level 29 |
Properties of isosceles triangles; the circumcenter and incenter of a triangle; application of similarity
This level provides instruction on probabilities and statements. By learning about the properties of various triangles and squares, students practice solving a variety of figure-related problems. Students learn how to draw similar figures by understanding conditions related to the similarity of triangles, as well as learning about midpoints of a triangle.
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| Level 30 |
Irrational numbers; multiplying polynomials; factorization
Based on an understanding of square roots, students learn the concept of irrational and real numbers. They learn how to expand polynomials using the distributive law and product rule. By understanding factoring and perfect-square expressions, students learn how to factor various equations. Finally, this level introduces new forms of quadratic equations and the different methods to solve them.
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| Level 31 |
Systems of equations; linear inequalities; linear functions and their graphs
This level covers systems of equations in which coefficients are decimal or fractional, as well as the other forms of systems of equations. Students will learn the concept of properties of inequalities and how to solve various forms of linear inequalities. This level also reinforces understanding of linear functions, graphs, slopes and intercepts, as well as probabilities.
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| Level 32 |
Generalization of the Pythagorean theorem; circles; trigonometric ratios
In this final level of Basic Thinking Math, students learn how to solve various problems with planes and solid figures by utilizing the Pythagorean theorem. They learn about arcs, chords and the positional relationship between two circles, as well as concepts involving inscribed angles, central angles, tangent lines, and chords. This level also covers the meaning of trigonometric ratios, including those of complementary angles and the relationship between three trigonometric ratios.
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