Curriculum of Eye Level Math

Basic Thinking Math (BTM) is a part of Eye Level’s Math curriculum that focuses on building calculation skills and the immediate application of those computation skills. Through the Basic Thinking Math booklets and instructor coaching, students will learn and enhance basic Math skills similar to the arithmetic typically covered in school.
In the preschool and primary levels (Levels 1 to 23), Eye Level Math’s BTM covers the four topics of Numbers, Arithmetic, Measurement (learning units of measure – time, length, weight, volume, etc.), and Equations. These levels cover topics parallel to those taught in the United States schools up through 8th grade.
In the higher levels (Levels 24 to 32), Eye Level BTM covers Number & Arithmetic, Variables & Equations, Relationships & Functions, Probability & Statistics, Geometry, and Measurement. This levels cover topics that roughly parallel those taught from 9th through 11th grades

Critical Thinking Math (CTM) is all about enhancing the student’s ability to solve problems creatively, critically and effectively.
There are five aspects of Eye Level Math’s Critical Thinking Math program: Patterns & Relationships, Geometry, Problem Solving, Measurement, and Reasoning. Some of the questions may seem like IQ questions, but these all relate back to aspects of Basic Thinking Math.
Questions of Patterns & Relationships train students to recognize various objects, symbols, lines, shapes, and domino patterns, which is in direct correlation to number pattern sequences.
Number Sequence exercises introduce students to the concept of functions through exercises that show rows of number patterns with an arithmetical relation between the different rows.
Questions of Geometry will train the student to recognize spatial orientation in 2-dimensional and 3-dimensional space. Students will also be taught transformation of figures through rotation, translation, mirror images, symmetry, and so on.
Measurement will teach students to compare various units such as volume, weight, length and area. Reasoning develops the logic and analytical skills to solve problems.
Through Problem Solving exercises, students are taught various methods to solve puzzles and quizzes, and they learn how to identify which is the best method to use.
Through Eye Level Math Critical Thinking Math, students learn creative ways of applying their Mathematical knowledge to various aspects of everyday life, thus appreciating the value of the usage of Mathematics.

All Mathematics concepts and skills are interrelated. Mastery of basic skills is necessary to advance to more complex skills. For example, a good mastery of addition is first and foremost needed. Subtraction is basically the reverse of addition. Multiplication is a repeated addition process, and addition is also needed in multiplication to complete the carryover operations. For division exercises, multiplication, addition and subtraction skills are all needed. Therefore, mastery of one skill before moving on to others will result in faster and more accurate learning.

Both Eye Level Math and Kumon Math are supplementary Math development programs for children. However, there are a few notable differences between the two programs.
The two programs take a slightly different approach to learning. Kumon’s approach is focused on developing calculation skills, and it is often described as a drilling and practice-makes-perfect approach. Eye Level’s approach is based on the idea of creating a comprehensive understanding of mathematics and English. Eye Level aims to develop and perfect the child’s power of thinking and understanding through its emphasis on critical thinking. In particular, Eye Level teaches Critical Thinking Math, which is generally not a component of other Mathematics programs, including Kumon.
Kumon uses clearly defined criteria for speed and accuracy when determining a student’s satisfactory progress and level of mastery. Students who do not meet these criteria often will be asked to repeat the booklets again. Eye Level Math also has a set of criteria to follow to determine mastery and booklet repetition, and Eye Level students also will be re-assigned booklets for reinforcement of concepts not mastered. However, the structure and design of the Eye Level booklets aids a child’s tolerance of such review. Eye Level Math workbooks for both the pre-school and primary school levels are colorful and contain a variety of exercises focused on related concepts and applications of those concepts (e.g. word problems), whereas Kumon only provides colorful worksheets for the beginning levels and contains relatively few word problems in the higher levels. This seemingly simple dissimilarity can mean the difference between a child being engaged in review and the same student being bored with a review.
Kumon Math covers a basic Math curriculum up to a higher level than Eye Level. In Kumon, students can study up to a pre-university and even university level of Mathematics. Eye Level Math’s Basic Thinking Math curriculum only covers up to about 11th grade. Eye Level aims to perfect your child’s Mathematical thinking, providing a good understanding and foundation of Mathematical knowledge. Your child can then apply these acquired skills to their higher levels of study through the also developed self-discipline and good study habits. In that sense, Eye Level Math very much focuses on application, an aspect of the program which is most easily seen in the consistent inclusion of word problems throughout the Eye Level Math program.

Eye Level Math teaches simple addition of +1, +2 and +3 through a process known as ‘skip counting.’ Prior to being introduced to addition, students are first taught the basic number sequences of 1 to 10, 11 to 30, and then up to 120. Students must not only have a thorough and fixed understanding for reading and writing the increasing numeric progression, but must also be able to count mentally the increasing number sequence. Students are then taught to add by ‘skip counting’ numbers. For example, to add 3 to a number, students are taught to mentally ‘skip count’ 3 numbers ahead in the number sequence. e.g. 4 + 3 is viewed as 4 -> 5 -> 6 -> 7 which helps the child learn 4 + 3 = 7.
This is first introduced by visual aids of number sequences like that shown above and then is practiced as a mental counting process. This mental process eliminates the need for the use of fingers or other dependencies.
Another way Eye Level Math teaches addition is by ‘making numbers.’ Students will first learn how to ‘make’ the number 10 (e.g. 10 objects is equivalent to 3 objects and 7 objects, or 6 and 4, or 9 and 1) before learning the number complements of the other numbers (e.g. 7 is 4 and 3). This helps students conceptualize addition, first by recognizing combinations of number complements (e.g. When making 7, 4 is the complement to 3). Secondly, students break down the numbers to complement parts when adding totals of more than 10. For example, when learning 6 + 8, students can rely on their knowledge of 10-complements to view it as 6 + 4 + 4 (or 10 +4, generally a more familiar calculation).

Subtraction is basically the reverse of addition. Through the reverse application of the methods used for addition, students are able to learn their subtraction tables quickly and accurately. The student will use a reverse ‘skip counting’ method for simple subtraction, and apply their number complements for larger subtractions.

Eye Level Math first introduces multiplication to the student through the grouping of objects. Students are able to count the actual total number of objects in the groups. Learning Tools (hands-on manipulatives) are used to help the child conceptualize the idea of grouping and multiplication. Then the concept of multiplication as a repeated addition process is taught, e.g. 4 x 4 = 4 + 4 + 4 + 4 = 16. This introduces the student to the multiplication tables, and through repeated practice, he/she will soon master the tables.

Division is also introduced by first grouping objects. Learning Tools (hands-on manipulatives) used to help the child conceptualize the idea of grouping and multiplication are used similarly to help the child understand the reverse operation of division.
Division as a repeated subtraction process is then explained. The concept of remainders is introduced as the remaining number of ungrouped objects or the remainder left which cannot be subtracted anymore by repeated subtraction
Finally, division tables are practiced as the reverse of multiplication tables. By applying their knowledge from the already mastered multiplication tables, students will be able to answer division questions accurately with ease.
For division with 2-digit divisors, Eye Level Math teaches students to first round the number up to the nearest ten. It will be easier to find a quotient estimate first with this rounded up number, before multiplying the actual 2-digit divisor with this estimate. This estimation method is easier than just blindly trying different quotients.