Mathematics Tip - Levels 5 - 7


Here are some topics of concern that may arise as you are working with students in Level 5 through Level 7.

How do the ‘Making Numbers’ exercises in Level 5 help our students?

‘Making Numbers’ helps students visualize the part/whole relationship and understand how numbers work together. Therefore, students can understand the basis of the inverse relationship between addition and subtraction. The concept of ‘Making Numbers’ plays a big part in school math textbooks; therefore, it is a good idea to explain to parents in advance how these exercises help students for their future learning.

Should Instructors coach ‘Adding 4’ differently from ‘Adding 1 through 3’?

Yes, these topics should indeed be approached in a different manner. At this point, students should start memorizing addition facts. Some instructors ask students to find the number that is 4 more, by asking the student to count the next, then the next, then the next, and then the next number. With this approach instructors will find that it results in finger counting and relying on drawings. By using flashcards and EMO, students can practice adding and develop their mental calculation skills while building up their confidence all at the same time.

Why is it important to observe how students answer addition problems?

Without keen observation, instructors may not be able to grasp precisely each students’ mastery level since it’s hard to recognize finger counting, murmuring, drawing marks, and other habits which should be corrected right away. Consequently, instructors should observe students carefully during 1:1 coaching or feedback sessions and give the right coaching to help students proceed in their learning without these habits.

What should I do when a student is struggling with adding one-digit numbers to 10-19 in Level 7?

If a student is struggling a lot, the Instructor needs to find the root cause as opposed to simply repeating booklets. The student may not have all his facts memorized. One good way to check this is by using a verbal test. If it turns out that the intuition hasn’t been developed fully yet, it is recommended to reinforce the addition facts that students haven’t fully mastered through Key & Note or flashcards This also means that previous progress was not determined properly. Instructors and Center Directors should be aware that it could give students the feeling of frustration later when trying to rush through levels. Therefore, always keep in mind that offering the Level Test should be done very thoughtfully and after plenty of observation.

Please refer to the ELU for more guidance on successfully instructing for students that are in Level 5 through Level 7.

Reference: Key & Instructors. May-July 2019.

Mathematics Tip - SCT

  In Eye Level Math, there are three components of mastery, simple and clear directions, accuracy, and speed. The booklets take a small step-by-step approach with explicit instruction so that students know what they are doing every step of the way. The second component of mastery, accuracy, was the focus of the July 2019 Key and News math article. The third component of mastery is speed. Speed is extremely important for math, especially when learning the basic operations in Levels 1 to 16. Each booklet in the mathematics program from Levels 1 to 23 has a Standard Completion Time (SCT) per page.  The SCT requirement can be found on the cover of each booklet, but a summary of the SCT requirements for the entire math program can be found on the ORL, under Math resources. There are two versions, one in color, as shown below, and one in black and white. Each color represents a different time range. Ideally, a student will be closer to the smaller end of the range, but if the student is the range it is acceptable.


The SCT should be found on the review page, page 2 and recorded in Key & Manager. On this page, there is a specific spot on the top right corner to record the time. At least one BTM booklet should be recorded per student per class session. If all the review pages can be timed, that is even better. Any SAR page can be timed in the booklet to continue to work on the student’s speed, and the time used should always be within the time range on the cover the booklet. If you want to time additional pages in the booklet, it is recommended to use non-target pages such as 11 or 12.  Now through Key & Manager, a Record Sheet is produced which clearly tracks the SCT found for the booklet. This will help you see clearly track how fast the student can complete a page in the booklet over time and decide if repetition is needed.

Mathematics Tip - Levels 1 to 4


Here are some topics of concern that may arise as you are working with students in Level 1 through Level 4.

What should I do when a student writes a number backwards?

This is a common mistake that young students make. When a young student learns numbers for the first time, the student captures and remembers the number as a shape or an image, such as a circle or a triangle. When students write numbers while thinking about the shape, they tend to write them backwards. This tendency naturally disappears for most students as they continue to practice writing numbers. Use the Key & Note, or reassign booklets 1-01 through 1-04, to continue to practice correct stroke order.

 Why are students counting objects for such a long time?

The purpose of ‘Practicing Numbers’ in Levels 1 and 2 is not just counting numbers accurately. Through the concept of ‘Practicing Numbers’ students will understand the concept of complements. Complements are pairs of numbers that add up to a particular sum, most often 5 or 10. By understanding complements, students will more easily learn the concepts of carrying and borrowing in Levels 10 and 11.  

 How can I help a student that having trouble with two-digit numbers?

Young learners sometimes write two-digit numbers in reverse. For example, they write 03 for 30 and 02 for 20. In this case, it is advisable to practice writing multiples of 10 such as 10, 20, 30, 40, and so on to help students accurately understand the number writing pattern. Furthermore, it is valuable to complete number recitation practices. Reciting numbers is the most effective way for young students to learn the number sequence. There are 3 ways of reciting numbers: 1) in increasing order, 2) in decreasing order, and 3) taking turns. Reciting numbers helps the students learn number sequences in a fun way and they will be able to progress smoothly through booklets 3-01 through 3-04.

 How can I consult with parents who insist that ‘Adding 1’ is too easy for their child?

‘Adding 1’ often looks easy to parents. It’s not difficult to find the answers as long as the child has learned to read and write numbers in sequence. However, ‘Adding 1’ is the stage where the mathematical symbol called ‘plus’ appears for the first time and the visualized concept changes into an abstract concept. Explain the importance of adding 1 as the completion of the number sequence as well as the basis of adding larger numbers.

 What do I do if a student is using fingers or drawing marks for addition?

Young learners try to find visual aids to do addition and counting on their fingers or drawing marks are two of the most used methods. However, these methods can cause students difficulties when they learn addition with larger addends. There are more places to make mistakes and it can take students a long time to complete exercises if they continue to use visual aids. Introduce ‘Adding 1’ through next-number exercises. This process will eliminate the need for the use of fingers or other dependencies. Once the student masters ‘Adding 1, 2, and 3’, it will be easy to advance to adding with large addends.

Please refer to the ELU for more guidance on successfully instructing and consulting for students that are in Level 1 through Level 4 in Eye Level Math.


Reference: Key & Instructors. January-April 2019.





Mathematics Tip - SAR

  In Eye Level Math, we do not focus on accuracy of the entire BTM booklet, but instead we focus on SAR. SAR stands for Study Achievement Rate, which is the number of perfect pages in the main section of the BTM booklets. The main section consists of pages 3-7 and 9-13. These pages are the practice pages of the booklet concept. Through Key & Manager, the SAR is automatically found. The SAR requirement can be found on the cover of each booklet, but a summary of the SAR requirements for the entire math program can be found on the ORL, under Math resources. There are two versions, one in color, as shown below, and one in black and white.


Why is SAR important? The other pages of the math booklet are not practice pages of the concept itself, therefore we should not consider those mistakes when deciding if the booklet should be repeated or not. Page 2 is a review page of the previous booklet, Page 8 is a fun activity, Page 14 is word problems, Page 15 is usually a challenging puzzle, and Page 16 is an assessment. If there are five mistakes on five different main section pages, the SAR would be 50%. This shows that there is a knowledge gap that needs to be addressed. If there are five mistakes on one practice page, the SAR would be a 90%. This happens more often because the student did not read the directions or skipped a question. It is important to examine the mistakes when deciding if a booklet should be repeated. Now through Key & Manager, a Record Sheet is produced. This will help you see clearly where the student is making mistakes and decide if repetition is needed.

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Mathematics Tip - Teaching Tools Games

One of the more under-utilized teaching tools is Numerical Figures. In the Eye Level program, Numerical Figures are used in BTM booklets in Levels 1-4. However, Numerical Figures can also be used for games in the higher levels as well. Using games in the classroom is a fun way to engage students and to break up the class session. On the ORL, there is a guide that explains some games that can be used with the student and what tools you will need. Below is an example of one the games. To find the other games be sure to visit the ORL.

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Mathematics Tip - Test with Key & Manager

Another way to use Key & Manager in the classroom is during a Level Test. Students that are in lower grades should take their Level Test at the instructor desk. The instructor can grade the Level Test at the same time the students are completing the paper test. Students in upper levels will need a longer time to complete the test and therefore can complete the test at their SDL Desk. Students can complete CTM tests at their desk as well since time is not factor in achieving mastery. First, find the student that is taking the Level Test. Under the Schedule, you will only see the students that are currently in class. Click on the three yellow dots next to the student’s name to see the different options. Click on Level Test.

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Select the Level Test subject and booklet that is being administered. Be sure to choose the correct booklet and examine closely whether you are choosing BTM or CTM. We will examine a BTM test first. If you are watching the student complete the test, you can use the timer that is provided. Like the DT, if a student makes a mistake you can check the box. If the student skips a question, swipe to the left and the question will turn pink. At the end of the test, click the blue arrow to see the results.

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At the end of the test, there is a result page. In this example the student passed the test because she achieved 88% accuracy and completed the test within the time limit. The student can advance to level 6.

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Below is an example of CTM. There is no timer because time is not a factor in CTM mastery. This student got many questions wrong at the end of test. The note explains that the student should repeat the booklets related to the missed concepts. Once the necessary repetitions are completed, the student will retake the Level Test.

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The Level Test should only be given as a confirmation of mastery. An instructor should be confident a student is going to pass the test before the Level Test is assigned. If there are any other questions, please reach out to your Field Consultant.