# FAQs

### Why MathFactLab?

Our founder developed MathFactLab because he could not find a true math fact fluency program on the internet. While the others may claim to develop fluency, they are, at best, only drilling for automaticity through memorization.

Automaticity is just automatic recall, like knowing your phone number; it requires no understanding. Fluency, on the other hand, is flexible, efficient and based on a foundation of reasoning and understanding.

Fluency can’t be developed through rote memorization and drill, which is the approach used by our competitors. Students develop true math fact fluency when they explore the basic math facts through a variety of strategies, continuously being challenged to find the interconnections and relationship between the various facts and their inverse operations. MathFactLab was built to do just this.

MathFactLab was created by Mike Kenny, a working fifth-grade math, science and social studies teacher. The idea for MathFactLab sprang from a master’s project completed when he was a student in the Vermont Mathematics Initiative.

He had been frustrated by the absence of any commercially-available math fact program that actually aligned with the research, so, for his project, he developed a large set of strategy-based flashcards for his students to use as they practiced their math facts.

As there were so many flashcards, the students struggled to keep the sets organized in a way that was effective, so Mike eventually moved the program online using Google Slideshows. This made a huge improvement and Mike began to truly see the effectiveness of providing a range of strategies for students to develop true math fact fluency.

Google Slides, however, lacked the interactivity and memory of a true webapp, so after seeing first hand the potential of this strategy-based approach, Mike began the long process of building a website, with the hope that this approach could be used not only by his students and those in his school, but by students around the world.

Yes, Mike Kenny, MathFactLab’s creator, is happy to meet with teachers via Zoom to help them get the most out of MathFactLab.

### Cost

Please see our pricing page for details.

### General Questions about MathFactLab’s Approach

Yes, because accommodation is necessary to meet the variety of needs within any class, we have included multiple means of accommodation within MathFactLab.

For example, the fluency rate setting, by default, is set at 4 seconds per problem. That, however, can be adjusted down to 2 seconds or up to 120 seconds (essentially untimed).

Additionally, teachers can adjust the pass rate on the Level Lifter, our assessment tool. Also, teachers can give interview-style assessments to those who may find traditional computer-based assessments a struggle.

First, let’s define ‘math fact fluency’. Fact fluency is not automatic recall, although students who are fluent with the basic facts will most likely have automatic recall for most or all facts, but not necessarily.

If you ask a student who is fluent with the multiplication facts what is ‘6 x 8’, she might not be able to say, ‘48’ instantly, without thought. However, she will be able to figure it out within a couple seconds and tell you multiple ways she could have solved it: double 3 x 8, double 4 x 6, add one more eight to five eights, etc.

Likewise, she could tell you that 7 + 8 is one more than double 7, one less than double 8, or 7 + 3 + 5.

Automaticity through memorization has no depth of understanding to it; like learning to identify words without knowing letter sounds. Nor is long-lasting. If math fact knowledge is based on memorization, it’s likely to fade over time.

We believe that rote memorization through drill encourages students to think of math as a mess of discrete factoids. In our view, it’s one reason why there is so much adult mathematics illiteracy.

All the strategies and models used by MathFactLab students can be accessed by teachers through the teacher dashboard. We call this feature ‘Teaching Tools’.

In Teaching Tools, teachers can click on any level in either learning mode to see all of the strategy options available to students. Teachers first choose whether to present questions from that level in numerical order or randomly or to present a typical student which includes previous-level problems as well. They then simply choose the strategy they wish to introduce or practice with their class or small group.

Yes, at the beginning of each session, students are shown their ‘progress table’ which maps out the stages and levels of the program. At each level, students can see the exact fact triangles that they are focusing on at their particular level. This way students are fully aware of the day’s learning targets, and can see by the generally small amount of fact triangles at any given level, that the task before them is manageable.

Each year, Mike has new fifth-grade students who tell him that they can’t divide. He explains that if they can multiply, they can divide. They just haven’t realized how to harness one to do the other.

MathFactLab has multiple strategies particularly designed to help students see the relationships of the inverse operations. On some strategies, students are simultaneously adding and subtracting. While on others they are dividing and multiplying at the same time. Mathematics is the art of pattern hunting. The more patterns our students see the less complicated and the more comprehensible the world of mathematics becomes. When students see the relationship of the inverse operations, they realize that there is so much less to learn.

No, through practice with the large variety of strategies that we offer, we believe our students will, in general, have so many means of solving a given fact and so much practice doing so that, for the most part, automaticity will be the natural result. Or, another way to put it, they will be able to solve any given math fact problem so easily that it will be as fast as (or nearly) as an automatic response.

Will all students know all the basic facts by heart, with instant recall? No, but most students who work through the basic fact program will most likely be able to do so for the vast majority of facts. And essentially all will be able to respond to any basic fact prompt fluently.

Memorization is not necessary for fluency. Fluency (and in most cases automaticity) will develop simply through the strategic practice we offer.

Yes, multiplication fact fluency is taught alongside division fact fluency. We, of course, also teach addition and subtraction fact fluency.

No, MathFactLab goes well beyond the basics. In fact, we offer two advanced addition/subtract stages and three advanced multiplication/division stages.

In advanced addition/subtraction, students learn to apply their basic fact knowledge in situations where a one-digit number is added or subtracted from a two digit number or when the difference between two two-digit numbers is ten or less.

In super-advanced addition/subtraction, students learn to use their fact knowledge to add and subtract two-digit numbers mentally.

In advanced multiplication/division, students learn the elevens and twelves facts, up to 12x12, a traditional expectation of math fact knowledge.

In super-advanced multiplication, students step out of tradition by extending their knowledge of eleven and twelves up 12 x 20. They also learn to do the same with fifties, fifteens, twenty-fives, and twenties, again up to __ x 20.

Super-duper-advanced multiplication challenges even the most capable by helping them learn to efficiently solve nineteens, eighteens, fourteens, sixteens, thirteens and seventeens all the way up to __ x 20. A graduate of these three advanced multiplication programs should be able to quickly, accurately and flexibly respond to any multiplication problem up to 20 x 20!

We do provide hints, not always, but often. You will see, as your students use MathFactLab, a hint button in the top left corner. This typically appears two seconds after the problem is revealed. Students can hit this button to reveal a hint. Some problems offer a second hint. Sometimes hints are automatically given.

Yes, we’re proud to say that MathFactLab goes well beyond the basics. In fact, we offer two advanced addition stages and three advanced multiplication stages.

In advanced addition/subtraction, students learn to apply their basic fact knowledge in situations where a one-digit number is added or subtracted from a two digit number or when the difference between two two-digit numbers is ten or less.

In super-advanced addition/subtraction, students learn to use their fact knowledge to add and subtract two-digit numbers mentally.

In advanced multiplication/division, students learn the elevens and twelves facts, up to 12x12, as is traditionally taught.

In super-advanced multiplication, students step out of tradition by extending their knowledge of eleven and twelves up 12 x 20. They also learn to do the same with fifties, fifteens, twenty-fives, and twenties, again up to __ x 20.

Super-duper-advanced multiplication challenges even the most capable by helping them learn to efficiently solve nineteens, eighteens, fourteens, sixteens, thirteens and seventeens all the way up to __ x 20. A graduate of these three advanced multiplication programs should be able to quickly and accurately respond to any multiplication problem up to 20 x 20!

Yes, absolutely. As MathFactLab was founded by a public-school teacher, we know the importance of student privacy. Please see our Privacy Policy for details.

### General Questions about Math Fact Instruction

In simplest terms, fluency has depth of understanding. Automaticity is simply easy recall.

The three elements of fluency are flexibility, accuracy and efficiency.

A student could be fluent, but might not have automaticity - meaning they can respond accurately and efficiently, but there might be some mental effort involved.

Likewise, a student can have automaticity without being fluent - meaning they can respond effortlessly, because they have memorized a set of facts, but their understanding is shallow, inflexible and prone to being forgotten.

At MathFactLab, our primary goal is to help students develop a deep, fluent understanding of all the basic math facts.

Most of the math fact websites you will find on the internet quiz students on the basic facts in one way or another without providing them a strategic means to solving the basic facts. This is drill.

If a student cannot respond accurately to a fact prompt, such as 6x7, these websites will not suggest that the student uses their knowledge of 3x7 and double it or add another seven to 5x7. Rather, it will just tell the student that the product is 42, and encourage them to memorize this fact. Drill only makes sense if students already have a very solid foundation with the facts and are simply working to increase their response time. Even then, it’s not a particularly good choice.

A strategy-based program helps students - through the use of a variety of models - to find multiple ways to solve a math fact prompt. A strategy-based approach encourages the flexible thinking that is a hallmark of good mathematicians.

Yes, multiplication table practice is the same as multiplication facts practice. They are really two names for the same thing.

### Our Addition/Subtraction Program

MathFactLab harnesses the power of five and ten to help students master the basic addition and subtraction facts. We do this by using ten frames and rekenrek-like beads and number lines. These are not new inventions; they are the basic tools of any well-run primary-grade math class. We use them for the same reason good teachers across the world use them: they are effective.

We also introduce facts in a research-based sequence allowing students to construct new facts using previously mastered facts.

One of the best ways to quickly familiarize yourself with the strategies we offer is to use our ‘Teaching Tools’, which you will find in the teacher dashboard. In Teaching Tools, teachers can click on any level in either learning mode to see all of the strategy options available to students.

Students work on the addition and subtraction facts simultaneously; thus, taking advantage of addition and subtraction fact families and the relationships between these inverse operations.

Our basic addition and subtraction program has ten levels, which proceed according to the research. Students begin with the foundational facts in the following order: +1 facts, +2 facts, facts with 0, and doubles. From there, students cover the within 10 facts, sums of 10, and the near-doubles. These are followed by three levels of the remaining beyond-ten facts: +9, +8 and lastly +7.

The primary models used in the basic addition and subtraction program are ten frames, number lines, double-bar diagrams and rekenrek-like beads. More models are on the way.

MathFactLab also offers advanced and super-advanced addition and subtraction programs. Students completing the basic addition and subtraction program progress directly into the advanced addition and subtraction program.

In MathFactLab, the subtraction facts are learned alongside the addition facts; thus, taking advantage of addition and subtraction fact families and the relationships between these inverse operations.

Our basic addition and subtraction program has ten levels, which proceed in a research-based order. Students begin with the foundational facts in the following order: +1 facts, +2 facts, facts with 0, and doubles. From there, students cover the within 10 facts, sums of 10, and the near-doubles. These are followed by three levels of the remaining beyond-ten facts: +9, +8 and lastly +7.

The primary models used in the basic addition and subtraction program are ten frames, number lines, double-bar diagrams and rekenrek-like beads. More models are on the way.

MathFactLab also offers advanced and super-advanced addition and subtraction programs.

Students completing the basic addition and subtraction program progress directly into our advanced and super-advanced addition and subtraction programs.

The doubles facts are taught in Level D of the addition/subtraction program. Students use ten frames, rekenrek beads, number lines and double-bar diagrams to develop fluency with these foundational facts.

The double-plus-one facts (or near-doubles) are taught in Level G (the seventh level) of our addition/subtraction program. The idea of one more than a known fact is particularly emphasized with the use of ten frames using three different color chips: the traditional yellow and red plus one purple chip to represent the one extra.

### Our Multiplication/Division Program

Each level in our multiplication/division learning mode has its own unique strategies. For example, in Level A (x2), the doubling strategy is the primary one. This doubling strategy is modeled using both ten frames and dice. In this level, we also represent the x2 facts on number lines, open arrays, area models and bar diagrams.

One of the best ways to quickly familiarize yourself with the strategies we offer is to use our ‘Teaching Tools’, which you will find in the teacher dashboard. In Teaching Tools, teachers can click on any level in either learning mode to see all of the strategy options available to students.

Students work on multiplication and division facts simultaneously; thus, taking advantage of multiplication and division fact families and the relationships between these inverse operations.

Our basic multiplication and division program has eleven levels, which proceed in a research-based order. Students begin with the foundational facts: x2, x10, x5, x1, x0. With that solid foundation, students are then ready to construct the derived facts, which students proceed through in the following order: x4, x3, x6, x9, x8, and x7.

The primary models used in the basic multiplication and division program are dice, number lines, area models, and bar diagrams. Other models are used only for particular levels: ten frames (for x2, x3 & x4), place-value charts (x10), clock faces (x5), number patterns (x9). More models are on the way.

MathFactLab also offers advanced, super-advanced, and super-duper-advanced multiplication and division programs, which teach strategies for multiplication up to 20 x 20.

Students work on the division as they learn the multiplication facts; thus, taking advantage of multiplication and division fact families and the relationships between these inverse operations.

Our basic multiplication and division program has eleven levels, which proceed in a research-based order. Students begin with the foundational facts: x2, x10, x5, x1, x0. With that solid foundation, students are then ready to construct the derived facts, which students proceed through in the following order: x4, x3, x6, x9, x8, and x7.

The primary models used with division are number lines, area models, and bar diagrams.

Yes, Level A of our multiplication/division learning mode teaches the x2 facts. We harness student prior knowledge of doubling to make for an easy start to our multiplication program.

In Level A (x2) students practice x2 facts using ten frames, dice, number lines, and bar diagrams.