There’s one skill that most elementary teachers agree must be mastered in order for students to “go deeper” or work at a higher level and that’s fact fluency. The memorization of multiplication facts has become a prime example of why math standards in the U.S. have grown very wide and not so deep. Third grade teachers have for years asked 4th grade teachers to continue the work on mastering multiplication facts knowing that students need even more help mastering basic addition and subtraction facts!

When students cannot recall the answer to a math fact with speed and accuracy, they run into challenges processing multi-step problems because their working memory is bogged down trying to recall 6 x 9.

Kathering Garnett gives a hierarchy to number sense, which leads eventually to automatic recall (Garnett, 1992). She explains, “As with swift word recognition and fluency in reading text, developing number-fact fluency normally occurs with sufficient practice over a considerable time period.”

In a Singapore math classroom, students learn WHY addition, subtraction, multiplication and division work using visual models, pattern reasoning, multiple methods and mental math strategies. From there, they follow an intentional and systematic sequence of learning and mastering basic facts. Embedded within a sequence of practice activities including hands-on exercises, guided practice questions, games, math journaling and exploration-based problems, are numerous opportunities for students to practice fact recall and apply at a gradually increasing level. So, when taught with fidelity, Singapore math lessons involving the introduction, practice and mastery of math facts can and do show that students can gain fluency without supplemental programs.

**Math Facts and Math in Focus (My Pals Are Here! Maths)
**The expectation in

*Math in Focus*is that students will eventually develop fact fluency with basic facts, but they must first learn the math, understand the relationships between facts and have strategies to calculate a new fact based on a known one. Students learn to verbalize their thinking and become confident in their strategies.

“If I know that 10 x 5 is 50, then 9 x 5 is 5 less than 50.”

“8 + 2 is 10, so 8 + 4 is two more, or 12.”

Direct instruction on “why” math works and explanation of patterns in math calculation is modeled throughout the Student Books using metacognitive thinking bubbles (shown below).

**Grade 1** introduces addition and subtraction facts. Facts to 10 are covered in Chapters 3 and 4, including fact families. Number Bonds and Ten Frames are used as visual models for developing fluency.

“Show all the ways to make 6.”

Vocabulary for part-part-whole relationships is used consistently and picks up from **Grade K** use in addition and subtraction lessons. Later in the year, students apply the strategy of “making a ten” to learn addition and subtraction facts to 20.

**Grade 2** teaches multiplication using an array model for 2′s, 3′s , 5′s and 10′s then 4′s. Like addition and subtraction fact lessons in Grade 1, students are taught to think about a known fact to learn a new one.

“6 x 2 is the same as adding 1 group of 2 to 5 x 2.”

**Grade 3**, continues teaching multiplication facts for 6′s, 7′s, 8′s and 9′s using the same dot arrays. Students continue to practice these in context and later apply for solving operations using larger numbers (106 x 6).

The time invested in the thorough teaching of the concepts of addition, subtraction, multiplication and division is what allows for mastery. Note that facts are not introduced repeatedly in multiple grade levels, a signature component of a mastery program. Teachers spend a day helping students “recall prior knowledge” to abate a natural lack in recall from spending the summer away from school. But after this day of preparation, students should be ready to learn new concepts and apply previously mastered concepts at a higher level. Students who are confident and fluent in fact recall are able to work on higher-order thinking problems.

As with any goal set within the academic, athletic or professional world, more practice equals better results. So consider candid conversation with your students and their families regarding the concept of fact practice at home. Share the approach to learning math facts in Singapore math. Most adults can recall the task of memorizing multiplication facts as a young student and will relate to the importance of mastery in order to move on.

**Common Core State Standards Initiative and Math Facts**

In a nation-wide transition to more advanced math standards in primary grades, a call for math fact mastery is acknowledged as an identifiable area for needed improvement. Newer standards call for students to demonstrate fluency in math fact recall according to the table below.

Grade Level | Demonstrate fluency in… | …facts to… |

1 | addition & subtraction | 10 |

2 | addition & subtraction | 20 |

3 | multiplication & division | 100 |

**Recommended Reading**

Trends in Math Achievements: The Importance of Basic Skills

Common Core State Standards Initiative Grade 1 Operations and Algebraic Thinking (navigate for other grades)

## 12 comments

## Cathy Tebo says:

December 27, 2010 at 7:53 pm (UTC -7)

Hi Kelly,

Well, this is the second article I’ve read authored by you; must’ve hit the bull’s eye finding you!!! I appreciate this article, just as it is always a topic of contention among elementary teachers, and up into 5th and even 6th grades.

Just a bit more about me. I teach 4th grade at a private Episcopal school (St. Andrew’s) in Jackson, MS. We are (cross fingers and toes) hoping, and it is looking good – to adopt Math in Focus for the fall of next year. I am also hoping to become a trainer with MIF, and will be joining in on the webinars to begin in the new year. I would imagine you are either hostessing them or aware of them.

Although I’m ‘just’ a teacher, I am a huge advocate of the Singapore methods, as much as I know about it… and admittedly, I am no expert. I am here to learn more, spread the good word, and with passionate helpers like yourself, hopefully be effective in teaching to students as well as other educators.

Once again, thanks for the article. I will forward to some other on-boarders at our school.

Cathy Tebo

## kellitrainer says:

January 2, 2011 at 9:22 am (UTC -7)

Cathy…so glad to see you found this post helpful. As more teachers subscribe to the blog, you will see more feature posts with professional development resources for educators, administrators and parents.

Many educators consider themselves “just a teacher” when gauging whether they are an influencer in adopting a better program such as Singapore math (Math in Focus). However, our biggest success stories came from a groundswell of teachers within a school or district who wanted to see improvement in their math classrooms and shared what they saw in it. Catch you via email or facebook soon!

## Phyllis Yucatonis says:

January 2, 2011 at 3:36 pm (UTC -7)

Imagine my delight to discover my colleague also participating in the training via MIF website! I look forward to the training and conversations. Phyllis, third grade (S.A. Episcopal, Jackson, MS)

## kellitrainer says:

January 3, 2011 at 5:52 pm (UTC -7)

Great to see you found each other. Sounds like you two are off to a great start!

## Lee says:

January 6, 2011 at 5:36 pm (UTC -7)

An interesting post! I use a lot of math games in my 2nd grade classroom to develop fact fluency and mental strategies such as doubles, near doubles, plus ten facts etc. We also do a lot of work with dot cards and ten frames. This year I discovered a great website that offers a wealth of free printable games and resources aligned with the Common Core State Standards and I have been making good use of 1st and 2nd Grade Number pages and the page titled ECAM (Early Childhood Assessment in Math) which provides a continuum of the different stages children go through in developing addition and subtraction fluency with resources for each stage. The site is:

http://www.k-5mathteachingresources.com/index.html

## Dan Erholtz says:

March 31, 2011 at 12:14 pm (UTC -7)

kelli, have you been a part of an entire school developing a plan to work towards multiplication facts mastery. We adopted MIF this year and next year we wanted to add a math fact mastery “time”/compnent and I wanted to pick someone’s brain before we jumped in. Dan

## kellitrainer says:

April 2, 2011 at 10:37 pm (UTC -7)

Dan… we have worked with many schools and districts that recognize the importance of fact mastery and look for feedback on how to integrate additional math practice while implementing Singapore Math (Math in Focus) with fidelity. There are a few generic suggestions I can offer, then follow up via email to answer specific questions. Remember that students need to first learn how to add or subtract, multiply or divide before moving to memorization of facts. Set a timeline for introducing fact mastery components to your math program based on when students develop that conceptual knowledge. Another critical analysis is to study subsequent chapters in each Grade level to identify embedded practice and the growing importance of mental math skills.

To honor the philosophy of Singapore Math (and Common Core State Standards), maintain a focused and coherent sequence of fact practice and assessment for mastery. For example, you would set students up for success by asking for mastery of basic addition and subtraction facts before moving to multiplication and division. Don’t stretch “fact mastery” across too many grades, which can be interpreted as non-essential. Conduct an inventory. In Grade 3, teachers can take a multiplication chart for facts through 12 and work with the teacher to cross out (or bingo marker blot) the facts they know with speed and accuracy. Usually multiples of 0, 1, 2, 5, 10 are checked off first. Next, set a short-term goal, individualized to the student and assign it as weekly homework. “Let’s work on mastering 3 x 9, 6 x 8, 3 x 8 and 9 x 12 this week. You’ll notice something interesting about the product of 6 x 8 and 3 x 8…I think. Your family might ask you to spontaneously answer one of these problems (send inventory home) and I know my teacher friends will ask if they see you in the hallway!” Conduct inventory, motivate, point out psychology behind practice & improvement, repeat.

You might find that the students who are not naturally math/logic-minded, find great ownership in tasks where repeated practice reaps rewards. Students who have become too comfortable with knowing the right answer…and first…without having to think too hard may not find value in committing information to memory. They may identify with being gifted and not receive messages regarding necessary improvement. Implementing a school-wide program allows for accountability for students, teachers and parents.

To avoid losing instructional time during math class, you can conduct fact mastery practice & assessment at a later time. Traditionally, adults have mis-interpreted fact mastery for achievement in math. Though students who memorize multiplication facts can show success on some standardized tests, this will cease as 2014 approaches. Students will need to apply that conceptual understanding of number and computation at a much higher level. Your teachers will find great benefits if a focus is put on the transition to Singapore Math. So any fact mastery program added to the day should be… brief, gradeless, simple, individualized and well-defined. The inventory as recommended is so that students don’t sit with a worksheet for 9 minutes completing the few problems they already know.

Everyday Counts Calendar Math has fact fluency throughout.

## Peggy Broadbent says:

April 26, 2011 at 1:54 pm (UTC -7)

I agree that memorizing is just as important as understanding all of it. Understanding alone will not reap very good results. Hooray for Singapore!

I am retired now but taught for many years. I have some multiplication models I used in my combined first and second grades, but they could be for any age. Each blog gives a way to fully understand the processes:

http://peggybroadbent.com/blog/index.php?s=Models+of+Multiplication

Read more about my math program, including models of addition and subtraction in my book, Early Childhood Programs: Opportunities for Academic, Cognitive, and Personal Success. Included is a web site where programs and activities can be downloaded for use in a classroom. Also, see 7 reviews on http://www.amazon.com

## Judy says:

January 28, 2012 at 5:20 pm (UTC -7)

I have been studying the Singapore methods for some time. I made a lot of effort focusing learning Singapore strategies while obtaining my master’s degree. I found the strategies to be useful and implemented as much as possible in my 2nd grade classroom. The reason I now write is that our 2nd grade was asked to pilot the Math in Focus program this year. Our 1st grade did likewise last year. What we found was actually disturbing. While the students were much better at dealing with word problems in general…. they were far, far less prepared with their basic facts than we had EVER seen before in other years. Unfortunately the 2A books start immediately with place value through the hundreds place and very quickly move to 3 digit addition with carrying (regrouping) to the hundreds….. and then immediately in chapter 3 move to subtraction of the same. The children were counting on fingers and could not do basic sums – even with amounts less than ten. It is very troublesome. They explored number bonds and the relationships between addition and subtraction- as we used to call math fact families- and they used many, many hands on concrete activities…. but the movement from the exploration to the speed and accuracy of fact fluency did not happen. We have a whole 2nd grade of children who struggle greatly with their basic facts….. Let me tell you, it is terrifically hard to teach the more difficult concepts when the students cannot do the basic.

The concept that I learned about Singapore was that moving slowly and with depth, teaching to mastery- was not what I found in Math in Focus. It is terribly hard and moves too fast without attention to the speed and accuracy of fact knowledge.

It makes me sad. I wanted it to work.

## Kathy says:

April 1, 2012 at 7:32 am (UTC -7)

Were the teachers using the Every Day Counts Calendar Math program, which is referenced at the beginning of each chapter in Math in Focus? There is visualization using the tens frames for addition and subtraction facts daily which helps build fact fluency.

## kellitrainer says:

April 2, 2012 at 9:35 am (UTC -7)

Judy, it sounds as if your teachers, who have implemented Math in Focus, did not transition students into the program, which is a prescribed method for honoring the Singapore math philosophies using content from the Math in Focus series, often previous grades. The example Kathy gives regarding the tens frame is a perfect example.

It is rare that a second grade can pick up a textbook and learn at the recommended pacing (as used in Singapore) without transitioning students by building key concepts and ideas from Kindergarten and Grade 1. It is common that teachers report that the program “expects” students to know things. It does not. It is authored as a complete program for grades K through 8.

There is not an alternate version of Math in Focus for schools that are implementing in Grade 1, then 2. Through professional development, an in-depth analysis of where your students are and where they need to be, you can create an implementation plan including recommended pacing during this period of time. Eventually, you will find that your students have a strong number sense, fact fluency and are closer to the recommended pacing.

## kerrie says:

March 29, 2012 at 10:50 am (UTC -7)

Judy-

In Singapore, they believe that if they spend their time teaching students math facts just by memorization, then they are not teaching them to “think”. They feel that spending time on memorizing basic computations that a calculator can do, is putting their children in direct competition with “machines”. And “machines” (calculators, computers, etc) are relatively cheap compared to the cost of hiring a person. However, they do feel that children will eventually “remember” their facts not “memorize” them. And…at the end of the day…they’ve also mastered the concept as well.

I know it seems difficult to believe in something that is different than the way we were taught…but Singapore ranks in the top 3 in Math, while the US ranks the lowest of all industrialized nations. They know what they are talking about.