Is my child proficient enough?

After reading our articles and understanding the importance of arithmetic proficiency, you may wonder if your child is proficient enough for the basic arithmetic. We encourage you try the following worksheets even your child is 5th grade.

In this article, we share two key worksheets within more than 100 worksheets that we developed and are using and how to use them with the progress tracking sheet. We also share the statistics so that you can get a rough idea of your child proficiency at the first test.

We have developed many questions and worksheets with a target time to ensure proficiency of each student from Kindergartner to 5th-grade covering number sense, addition, subtraction, multiplication, division, decimal, fraction, prime numbers including GCF and LCM, reading time and units. We use the worksheet in the tutoring sessions and Critical Thinking/Math classes.

We use the following 45 patterns of addition with carryover in the later stage of 1st-grade addition to ensure the students’ proficiency in carryover and strongly encourage them to memorize the pattern.  We expect all our students to finish this worksheet at least in 2 minutes 30 seconds, preferably in 2 minutes with 100% accuracy.

(Afterschool search got permition from STEAM Dojo to use the worksheets)

The worksheet below is the last worksheet for the single-digit addition. We expect all first graders finish this worksheet in 3 minutes with 100% accuracy. The average time of the first attempt is 6 minutes 23 seconds with a standard deviation of 2 minutes 5 seconds. It means that about 2/3 of students are between 4 minutes 18 seconds and 8 minutes 28 seconds. An average number of mistakes in the first attempt is 0.97.

Random addition matrix

If your child is in 2nd grade or above and takes more than 6 minutes 23 seconds, you better worry about the proficiency of your child and take additional efforts to improve your child’s proficiency quickly. If you see your child is filling this worksheet, you can immediately tell which combinations are his/her weaknesses.

Also, if your child made more than two mistakes, a red light starts flashing — no excuse for the number of mistakes.


The great things of these worksheets are; 1) clarifying your child’s weakness, 2) allowing you to measure the progress, 3) improving your child’s focus, 4) not taking a long time, and 5) you can use the same worksheet again and again.

Majority of students achieve the target time with 100% accuracy in two weeks and love the challenge. You may surprise how children enjoy the worksheets. Many of them resist the first time. However, once they see the progress, they love it. Even after they reach the goal, they eager to try time attack and measure the improvement.

Please try above worksheets with your child to ensure his/her proficiency.

Please promise that you never say a negative word to your child even he/she could not reach the target, instead, please praise him/her for their efforts, and encourage him/her to try again later, hopefully, every day.

Please take time and score the worksheet since both speed and accuracy are equally important and plot the time and number of mistakes to the following “Progress tracking sheet.” This Progress tracking sheet visualizes the progress and motivates your child to reach the goal.

Progress Tracking Sheet

We hope that these worksheets help you to assess your child to improve proficiency and that you get the idea of how to manage the process.

Again, the key points for the successful experiment are

1) being patient

2) praise him/her for his/her efforts no matter how long he/she takes

3) use positive expression when you communicate

4) take time for the scoring and review together with a positive attitude.

If you have difficulty to keep above four key points, ask a tutor or third party to take care of it. We know that teaching our own child is very stressful and challenging for the parents.

August 24, 20192 CommentsUncategorized
Unfortunate Truth of Math

Math has unique characteristics that other subjects such as language art, social study, and the majority of science do not have. If you do not understand the characteristics well and treat Math and your child as other subjects, it causes a huge problem later.

1. Layered skills and concepts

Math requires a solid understanding of previously learned skills and concepts to learn a new concept. To understand addition, solid understanding of number sense is required. Understanding subtraction requires an understanding of addition. Multiplication involves addition. Division requires multiplication and subtraction. Fraction involves addition, subtraction, multiplication, and division. Understanding of division is crucial for a fraction.  In Geometry, arithmetic skills are required to calculate angles, areas, and volumes. Many geometry questions require ratio to solve it.

Both time and measurement also require all arithmetic skills.


So, if your child does not have a solid number sense, all other concepts never become solid than the number sense. If your child does not have a solid addition skill, then he/she is not able to get better scores in all other areas that he/she learns later either.

On the other hand, other subjects such as language art and social study have no or less dependency on the previous concepts or area of study.

In other words, Math is a vertical subject, while other subjects are more horizontal and require no or small vertical dependency.

The layered structure of Math concepts

You may not concern so much if your child takes 70 points on one subject in Social Study or language art. But if you have the same level of concern on Math with other subjects, it is a huge mistake. As discussed above, math is a vertical subject. So, if you allow your child to keep taking 70 points, your child is almost guaranteed to have a tough time to keep up with Math around 4th to 6th grade.

Conceptually, 70% in number sense x 70% in addition x 70% in subtraction x 70% in multiplication x 70% in division x 70% fraction = 11.8%

How can he/she understand the ratio that comes next on top of just 11.8% of understanding?

You may think that this is too simplified. It could be. But watching many students struggled with Math starting fraction and ratio, and the majority of them do not have a solid understanding of the arithmetic, the above number aligns our experience.

2. Proficiency

Another unusual characteristic of Math is that it strongly requires proficiency and the proficiency of one area affects the following subjects. I see a significant discrepancy on the degree of emphasis on proficiency between Asian families and families in other races. Many Asian families put great focus on the proficiency of arithmetic.

Reality is that proficiency is crucial in the basic arithmetic, especially addition, subtraction, and multiplication. Knowing how to calculate is not enough at all, if it takes time to calculate, it is the same as not able to calculate in the real world even in elementary school. Many parents seem not to push their child enough to practice the calculation if they understand how to calculate even it takes time. It’s a huge mistake.

Unfortunately, if it takes a too long time to calculate an arithmetic problem, it is the same as not to able to solve it since all tests have a time limitation. So, you need to fully grasp that understanding the concept and being able to use it is completely different. For instance, many students understand how to calculate carryover, regrouping, and multiplication but take a too long time to calculate problems. So, they can not solve questions in time.

The worse is that the lack of proficiency hinders to learn the next concept. In the process of mastering multiplication, students use addition a lot to fill the gap of imperfect memorization of the multiplication table. For instance, to calculate 8 x 7, many students calculate 8 x 5 + 8 + 8 when they are not able to remember the answer of 8 x 7. The lack of proficiency of addition slows down the mastering multiplication.

Children need to remember combinations of two numbers that make 10, and 45 carryover patterns, and multiplication table and need to be able to answer all of them instantly.  Memorizing these patterns is simple and requires limited efforts, usually two weeks or so for 45 carryover patterns and another two to three weeks for multiplication table. But becoming proficient to these calculation generates an unbelievable difference and confidence.

Many students who understand concepts but could not get good scores are due to lack of proficiency. Also, proficiency affects directly to the child’s confidence in Math.

If your child seems to understand how to calculate addition with carryover and subtraction with regrouping, but still struggling to get a good score, check the proficiency. Lack of proficiency hinders to learn new concepts such as multiplication, division, fraction. So, make sure that your child does not only understand the key concepts such as carryover and regrouping but also the proficiency enough on these.

3. Concept and technique

Another challenge that math has is difficult to distinguish whether your child understands a concept or the technique. Your child can remember combinations of addition and multiplication and how to calculate carryover and regrouping. They can remember tables and techniques without an understanding of the concepts. They can get a full score without understanding the concept with techniques. High dependency on techniques could be a downside of putting too much emphasis on proficiency.

These students who are great students following parents’ order, practicing a lot, and getting great scores and mastering the techniques. But these students tend to start struggling late in elementary school in 4th grade or so.

It is a kind of sad story, but not uncommon.

Students who do not understand the number sense fully, start struggling in decimal and large numbers.

A similar thing happens to the students who master multiplication and division technically but not conceptually, struggle with word problems since they do not understand how to apply them.

Children who did not play with actual objects and count them tend to have this number sense problem. But this widely varies by individual. Some children get the idea instantly, and some students need a much longer time.

Fraction and ratio are not an exception. Students also need to understand the concepts to be able to apply them to word problems.

Please make sure that your child fully understands the concept then teach related techniques and have him/her practice for proficiency.

Take outs

  1. Math test score should be 100 points always as Math is a vertically integrated subject.
  2. Proficiency of arithmetic is crucial.
  3. Ensure that your child understands the concept fully.



Based on the research done by UC Irvine, The relative importance of adolescent skills and behaviors for adult earnings: A cross-national study, Math has the highest correlation with the completion of school and earnings among major subjects. Be sure that your child is good at math.

July 4, 2019No commentsArticles, Mathearnings | improve score | layered | Math | proficiency | Unfortunate truth
Kumon vs. Mathnasium vs. RISU

I have been asked similar questions many times after we launched RISU Math that is a tablet-based, self-directed learning service. So, we would like to provide a comparison with our best knowledge. I would appreciate your feedback as our knowledge of Kumon and Mathnasium is limited.


1. Summary

    Kumon and Mathnasium are excellent services with different focuses. The table below will give you the positioning of each service.

Study location
Center only Center and Home Home only
Focus area Arithmetic  — Kumon  —
All math Mathnasium RISU Tutoring RISU Math
Critical Thinking, Competitive math  — RISU Critical Thinking


2. Service Overview

 1) Kumon

Kumon started more than 60 years ago in Japan where RISU began in 2014. There was no electronic calculator at the time. So, Kumon has put its emphasis on arithmetic and developed the program that uses the worksheet extensively to meet the personalization needs. The instructors do not teach but provide worksheets that meet their personal needs. The students need to finish the worksheets at home usually one sheet per day. The students come to the class twice a week and spend about 30 minutes at the class solving the worksheets. Kumon is a great system and the largest educational franchise in the world with nearly 3 million subscribers worldwide.

The students can establish an everyday study habit and build solid arithmetic skills. Though some parents point out the inefficiency and arithmetic focus as the negative side of the service. Mr.  Kumon developed the program before the computer era, designed to maximize the number of students that one instructor can handle and provide standardized quality by eliminating the teaching part. To achieve the goal, he developed great number of worksheets with gradual difficulty level difference so that students can solve them by themselves and learn new subjects.

2) Mathnasium

The students of Mathnasium study at the center and do not bring back the homework. It uses worksheets arranged based on the assessment test. One instructor takes care of a few students to provide better personal attention and teach math if necessary. It covers all math curriculum, not only arithmetic but also geometry and word problems.

No homework, students/instructor ratio, and the full coverage give a clear contrast from Kumon. The price is higher than Kumon to offer lower student/instructor ratio.


RISU provides two types of services.

i) RISU Math and RISU Critical Thinking

  Both programs are tablet-based programs run only on the designated tablet which runs only the RISU application and can be subscribed at home. RISU Math covers all the Common Core State Standards area, and RISU Critical Thinking covers competitive math and five key reasoning areas (figurative (2D), spatial (3D), verbal, numerical and logical reasoning). These programs utilize tablets, AI, videos, parent portal site, emails to provide the family with the most efficient, self-directed and personalized learning experience.

  The Math program fits well with families that the parents can take care of the child’s study or to the child who can manages the practice by him/herself with the most affordable cost.

  The Critical Thinking program is the perfect choice for students who would like to expand their strength to the competitive math and reasoning areas or families that the parents would like to help the child building a further advantage in math. Critical Thinking has a great fit with former Kumon students who have solid arithmetic skills.

ii) RISU Tutoring

  The students study at the center and at home. RISU Tutoring utilizes both tablet and paper worksheets, covers all math curriculum, and assigns homework to establish daily learning habit.  It has a similar student/instructor ratio with Mathnasium to provide personalized teaching. RISU Tutoring utilizes RISU Math and RISU Critical Thinking program to provide efficient, personalized self-directed learning, and uses the paper worksheet to ensure proficiency in the necessary calculation skills.


3. How to select the best fit program

 Assuming someone can take your child to the center twice a week, the first two questions are “are you ok with the daily homework?” in another word, “are you willing to establish daily learning habit?”, and the second question is “are you willing to afford the cost?”. As mentioned above, Kumon and RISU require homework, while Mathnasium does not provide it. Since both Kumon and Mathnasium are franchise, the prices vary by the center and greatly different by area. Kumon usually charges around $100 to $130 per subject per month in the San Francisco Bay area, (Silicon Valley). RISU charges $120 per month. Mathnasium is a few times higher to afford the lower student/teacher ratio.

If you are not able to take your child to the center twice a week in various reasons, RISU Math could be one of the alternatives and RISU Critical Thinking could be the supplement.

The focus area could be the another considering point. If you would like your child to learn all subjects, Mathnasium or RISU would be the choice. If you are fine with focusing on arithmetic, Kumon could be the choice.


4. Comparison

1) Initial Assessment

Kumon Mathnasium RISU Tutoring RISU Math


   Kumon, Mathnasium and RISU provide the initial assessment to identify the level of understanding of your child. This is a major difference from personal tutors who usually do not have the structured and well-tuned assessment method. RISU uses the proprietary tablet-based assessment that dynamically changing the questions based on the accuracy of the answers to more accurately assess the level of understanding.

  All services set the starting point based on the assessment result.

2) On going personalization

Kumon Mathnasium RISU Tutoring RISU Math


   Kumon, Mathnasium and RISU have their own proprietary methods and the curriculum. Kumon instructors select worksheets based on the progress of your child every time. Mathnasium instructors follow the set of worksheets assigned based on the assessment, but the speed will be adjusted based on the understanding of your child. RISU instructors assign target stage in the tablet software or paper worksheets based on understanding and proficiency of your child. All three services follow the own curriculum with some flexibility.

3) Autonomy

Kumon Mathnasium RISU Tutoring RISU Math


   Students of Kumon and Mathnasium need to follow the curriculum and assigned worksheets. RISU students have a wider autonomy and can pick the maximum seven subjects concurrently based on their interest and progress such as number sense, addition, subtraction, multiplication, division, geometry, measurement.

4) Teaching

Kumon Mathnasium RISU Tutoring RISU Math


  Kumon does not allow the instructors to teach and have them force the students to work on the worksheets by themselves. This may sound weird. But Kumon believes that each student can learn new skills by him/herself through the worksheets and designed the worksheets to enable it. This is true to many students but not all. RISU shares the same philosophy and RISU Math was designed to enable it with recent technologies such as videos to provide the better support, and proved that this method works for many students but not all like Kumon.

  Mathnasium and RISU Tutoring instructors teach if necessary, to improve the learning efficiency and ensuring the understanding.

5) Center Visit Frequency

Kumon Mathnasium RISU Tutoring RISU Math
Center Visit per week 2 2 2 0


This will affect your daily life the most. Three services require you or someone bring you child to the center twice a week and pick them again after 30 to 60 minutes. The number is the most generic frequency and may be adjusted to accommodate each family’s needs.  In case of 30 minutes, many parents stay at the center since it is too short to go back home or go somewhere and come back again. If both parents work, it could be a huge challenge.

6) Tuition per subject

Kumon Mathnasium RISU Tutoring RISU Math
Approximate Tuition $100 – $150 A few times of Kumon $120 $38 – $80


The above tuition is based on our own research in the San Francisco Bay Area in later 2018 and subject change. Since Kumon and Mathnasium are franchise, the amount depends on the center and widely vary based on the geography. So, please visit or contact the center where you may take your child and ask for the amount, refund policy, minimum commitment and other restrictions.

The amount of RISU Math is based on the progress speed. If your child progress more than twice faster than the school curriculum, it will go up to $80.

7) Learning location

Kumon Mathnasium RISU Tutoring RISU Math
Learning location Center & Home Center only Center & Home Home only


Mathnasium does not provide homework and has the student study only at the center. So, you do not need to worry about ensuring your child finishing the homework on top of school homework at the same time may think that only twice a week may not enough.

Both Kumon and RISU believe daily study is important. RISU’s research with more than 5,000 students shows the students who study almost every for 15 to 20 minutes achieved the best result compare to the students who studied longer time less frequently and proved our belief.  Therefore, RISU assigns the homework.

In anyway, studying math periodically is very important to better understand it and improve the proficiency.

5. Conclusion

Schools never go back to the subject taught once. So, if your child is not able to keep up with the school’s pace, these services or private tutor are the alternative and only way to prevent your child from drop out except you can do it by yourself. Also, if your child is gifted and talented and the math class at the school is painfully boring, these services also help your child moving forward without school grade boundary and enabling exploring their interest much faster. One of RISU students finished three years portion of math, (4th, 5th and 6th) in six months.

Also, proficiency that is almost ignored in the US is very important especially lower grade. Understanding how to calculate is not enough. Your child needs to be able to calculate accurately and fast enough to succeed in Math. These services help ensuring the proficiency too.

I hope that this article can help you to make the selection decision.

   Hiroji Fukui

May 17, 2019No commentsArticles, MathComparison | Kumon | Math | Mathnasium
How to improve Math score

1. Not good at math?

There are many reasons that a child is not able to get a good score in Math.

So, our first work as tutors is identifying the causes that prevent the child from getting a perfect score every time and prioritize them.  If your child is in the first or second grade, it is easier to figure it out as the subjects they have learned are limited. As the grade of the child goes up, it gets more complicated and time-consuming, even identifying the causes.

2. Three major reasons.

Even though there are many reasons that your child is not able to get the perfect score every time, the following three types of reasons cover the majority of them. We break down each reason further to more specific ones that directly associate with the action items.

However, understanding these three types is very important since the types of countermeasures are entirely different.

1) Not proficient enough

    This reason applies to addition, subtraction, multiplication, division, fraction so on. If a child tends to get 40 to 70 points in tests, this may be the primary cause. In the US, the lack of emphasis on proficiency causes a huge problem for years. Asian families tend to put the emphasis on the proficiency of basic arithmetic culturally and pave the way for the child to succeed in the STEM area.

     Knowing how to calculate and calculating accurately at a reasonable time are entirely different. Even your child knows how to add 8 + 9; if he/she uses his/her finger or calculating carry over by dividing 9 to 2 + 7 and takes more than 1 seconds, your child is not proficient enough.

  Many parents did not understand the importance of proficiency fully and leave their child at risk. Of cause, your child needs to know how to calculate. In addition to that, your child needs to memorize the combinations even in addition and subtraction like you memorized a multiplication table.

2) Lack of conceptual understanding

    If the child is not able to answer some patterns of questions at all such as carry over, regrouping, rounding, decimals, or fraction, this could be the reason.

3) Comprehension

    There are a group of students who are very good at calculation but not at all on word problems.  Many students who attended Kumon are in this group.

3. Typical symptoms

1) Proficiency

If the child can get 60 to 70 points in the majority of math tests, but not a perfect score, we check his/her proficiency. Since the child could get 60 or 70 points in the many tests, he/she usually understands the key concepts but was not able to solve all questions in time or made many mistakes.

2) Missing concept

If the child got a significantly lower score in a particular subject comparing other subjects, it suggests he/she could not get the key concept of the subject. Usually, he/she feels uncomfortable on the subject and self-recognize that he/she does not fully understand the concept.

This happens a lot in fraction, reading time and approximation. Some students do not have a good understanding of number sense and struggle with math after 4th grade when they start using large numbers and decimals. They know how to calculate technically or mechanically but do not know fully what each digit means. So, once the numbers get larger or have a decimal, then they easily confuse.

3) Comprehension

The child who is good at math and gets a good score in general especially calculation. However, he/she made mistakes frequently on word problems or is not able to understand the meaning of questions.

4. Assessment

1) Do not ignore proficiency

If your child is categorized in case 2, missing concept, or case 3, comprehension, usually the problem is clear, and the child recognizes the weakness. The challenge is case 1 and the combination of case 1 and case 2 and/or case 3.

2) 80 points is not enough

If your child is not able to get more than 90 points on the math tests, I would strongly suggest checking the proficiency of basic calculation. In general, the proficiency requirement in the US is too low unless ignored. There is misunderstanding or confusion on proficiency requirement. Again, knowing how to calculate is not enough and often useless in the real world.

3) Avalanche effect

Your child needs to be able to calculate addition, subtraction, and multiplication fast and accurate to go to the next step. These are fundamentals. Without using addition, you are not able to calculate multi-digit multiplication. Without using multiplication and subtraction, you are not able to calculate division. Without understating division, you are not able to calculate fraction and ratio. Without using addition and subtraction, you are not able to calculate time and angle. Without using multiplication, you are not able to calculate area and volume.

So, all Math and STEM subjects entirely rely on these fundamental arithmetic skills. So, these skills should be proficient and accurate.

4) Addition and subtraction need memorization

The basic pattern of addition, subtraction and multiplication require memorization of patterns. Knowing how to calculate is crucial but not enough. To be proficient, your child needs to memorize the patterns. Here is a gap. Majority of parents do not understand the need for memorization and as a result, leave their child behind.


Let’s change the viewing point. Do you build a multi-story building on top of foundation half done?

5) Sad but common drop off pattern

If you accept 70 point test score when your child is/was in 1st and 2nd grade and have/had your child go on, this is what you do or did.  You can easily predict what happens near future. Right?


70% (addition) x 70% (subtraction) x 70% (multiplication) x 70% (division) x 70% (fraction) = 17%

Reality is worse. Since multi-digit multiplication requires addition, if your child got 70 points in addition and learning multiplication, conceptually 70% (multiplication proficiency) x 70% (addition proficiency) = 49%. Since division requires multiplication and subtraction, it is worse. So, some students give up math around division and fraction.


5. Countermeasures

1) Proficiency

If your child has proficiency issues, you need to forget his or her grade and go back to the crucial point and have him/her practice it. It may be annoying for your child or you may face resistance to practice simple addition or multiplication. Some parents complained to us that their child is 5th grade and why their child needed to go back to addition or multiplication too. You need to understand the necessity and explain to your child that knowing how to calculate is not enough, and the speed and accuracy requirement to your child.

You also need to understand that your child needs to memorize the patterns, not calculate fast and accurate, just memorize them.

I have many experiences that the test scores of my students jumped up after improving the proficiency and boost up the confidence of the students.

From our experience, almost all students reached the goal of proficiency in less than two weeks per subject if they practice 15 minutes a day.  Please consider, 15 minutes x 14 = 3.5 hours makes life-changing effects and diverts the course from drop out to an A student. Does it worth to spend?

The practice may sound tedious. But what I found was the opposite. If we share a clear goal, the majority of students enjoy the exercise and tracking the progress. As he/she gets closer to the target time, they are more willing to practice to beat the goal. Once they hit the target time, it gives them satisfaction and confidence. Repeating these practices build their confidence and teach them how to overcome challenges.

2) Missing concept

Concept-related problem is relatively easy to fix. Just revisit the concept. The point is taking enough time and ensure that your child fully understands the concept.  Since school teachers have very limited time per subject, the teachers are not able to wait for all student getting it. If you can sit with your child and spend enough quality time, it would be the best scenario. However, we are all busy, and teaching our child is emotionally challenging for many parents. So, asking a tutor or using other services may be the better choice for you and your child.

Since schools are not able to come back for the follow-up, it is essential to detect this issue as early as possible before the problem causes the ripple effects.

After your child gets the concept, please confirm it by having him/her solving several questions. Understanding concept and being able to use it properly are entirely separate issues.

3) Comprehension

Improving comprehension is challenging and requires mindset change of your child. There are some techniques, but they are not perfect.

i) Change the gear

Your child has trained to solve simple calculation fast and accurate as we discussed at proficiency. Children who attended Kumon have a strong tendency as they have trained to be an excellent human calculator, which is not a bad thing as we discussed in proficiency issue. So, many children try to solve word problem with the same approach, as fast as possible without thinking, which does not work at all.

ii) Three-step approach

They need to change the gear and understand that they need to perform three different steps to solve the word questions. The first step is information extraction. All word problems contain all the necessary information to solve them. In this first step, they need to perform two sub-steps. First of all, they need to understand what they need to answer. Then they need to extract information from a word problem to solve it. Reading a word problem aloud a few times helps a lot to change the gear and understand what they need to answer.

The second step is constructing the equation with the extracted information. This step is far tricky than many adults think for children and requires practice. Many children can perform step 1 but not this step. Some techniques may help in this area. For instance, if the question asks a difference, the equation uses subtraction.

The third step is an easy step and requires just calculating the equation. It is better to explain to your child the needed actions. If you can solve several questions with your child strictly following the steps. Your child will understand the steps and be able to use it. Please note that step 2 requires practices.

6. Additional consideration

If your child struggles printed questions but not much when you ask the question, please check if he/she may have dyslexia. Some researches show about 8% of children have some level of dyslexia.

7. Actions

So, if your child struggles a bit or a lot in Math, please check 1) if he/she is proficient enough. If not, please have them practice as soon as possible. 2) if he/she understands all key concepts. If not, take time and ensure that he/she understands it correctly and can use it properly. 3) if he/she are not good at word problems, share the steps, and practice the steps, especially step-2.

Hiroji Fukui

May 16, 20191 CommentArticles, Mathimprove score | Math | Math score