# MathFactLab in the Classroom

### Key Principles for Successfully Implementing MathFactLab

Students practice the basic math facts with a multitude of models: number lines, ten frames, rekenreks, bar diagrams, dice, dominoes, dots, area models and arrays of objects.

Through repeated application of a variety of strategies, students develop fluency and (in most cases) automaticity with all the basic math facts.

In addition, for example, students learn the 'Sums of 10' facts by completing tens frames, by estimation using double-bar diagrams, and by discovering the variety of sums of ten on a rekenrek.

In multiplication, for example, students learn the x5 facts by dividing the x10 facts in half, by using their knowledge of clocks, by making jumps of five on a number line, and by pairing fives to make tens.

According to Baroody (2006), there are three stages of development in math fact acquisition:

- Phase 1: Counting strategies [and constructing meaning]
- Phase 2: Reasoning strategies - using known information (e.g., known facts and relationships) to logically determine (deduce) the answer of an unknown combination
- Phase 3: Mastery - efficient (fast and accurate) production of answers

Phase 1 is what happens in good classrooms: providing students with an understanding of numbers, operations, and a means of solving the basic math facts.

- It is expected that students have completed Phase I before beginning MathFactlab.

Unlike most math fact websites, MathFactLab, with its multiple-model approach, is a powerful tool for Phase 2’s development of reasoning strategies.

With sufficient practice using a broad variety of strategies, our students develop the mastery of Phase 3 without need for memorization.

MathFactLab student sessions are from 5 to 20 minutes long. The default is 12.5 minutes.

- Teachers can determine the length of student sessions in the teacher dashboard.

For greatest success, we recommend that students complete at least three sessions per week.

- While multiple sessions can be completed in a single day, distributed (or spaced) practice has been shown to be a more effective method of learning.

The many small steps that the program is divided into allows for ample opportunity for students to recognize their growth and to feel proud of it.

Although MathFactLab goes well beyond the basics, only the basic facts are essential for your students to master.

While certainly worthwhile, consider the advanced stages to be enrichment, not essential.

- The advanced stages enhance mental math skills while providing a means for all students - not just those working on the basic facts - to be engaged in math fact study.
- Note: Students should have mastery of the advanced +/- stages before tackling the advanced x/÷ stages

The addition/subtraction program consists of 17 levels, broken into 4 stages:

- Basic Facts Part 1 (Levels A - F)

- Level A: +1
- Level B: +2
- Level C: +0
- Level D: Doubles
- Level E: +3 or +4
- Level F: +10

- Basic Facts Part 2 (Levels G - K)

- Level G: Near doubles
- Level H: +9
- Level J: +8
- Level K: +7

- Advanced Facts (Levels L - M)

- Level L: +11 to 20
- Level M: +21 to 90

- Super-Advanced Facts (Levels N - R)

- Level N: 2-digit + multiple of 10 (sums less than 100)
- Level O: 2-digit + 2-digit (sums less than 100)
- Level P: 2-digit + 2-digit ending in 9 (sums less than 100)
- Level Q: 2-digit + multiple of 10 (sums greater than 100)
- Level R: 2-digit + 2-digit (sums greater than 100)

The multiplication/division program consists of 25 levels, broken into 4 stages:

- Basic Facts Part 1 (Levels A - E)

- Level A: x2
- Level B: x10
- Level C: x5
- Level D: x1
- Level E: x0

- Basic Facts Part 2 (Levels F - L)

- Level F: x4
- Level G: x3
- Level H: x6
- Level J: x9
*Note: While students are introduced to a new nine fact at each level (for example, 4 x 9 at Level F), mastery of most nine facts is not expected until this level.* - Level K: x8
- Level L: x7

- Advanced Facts (Levels M - N)

- Level M: x11
- Level N: x12

- Super-Advanced Facts (Levels O - T)

- Level O: x11 (advanced)
- Level P: x12 (advanced)
- Level Q: x50
- Level R: x15
- Level S: x25
- Level T: x20

- Super-Duper-Advanced Facts (Levels U - Z)

- Level U: x19
- Level V: x18
- Level W: x14
- Level X: x16
- Level Y: x13
- Level Z: x17

This assessment mirrors the levels of the programs, first starting with questions from Level A and progressing level-by-level towards the final level.

- Depending on their assigned learning mode, students begin with either addition or multiplication.
- After the student has responded inaccurately and/or non-fluently five times, that operation’s assessment ends.
- The student then begins the 2nd operation’s assessment (either subtraction or division), which will also end after the fifth inaccurate and/or non-fluent response

Before beginning the placement assessment, students are asked to type in a variety of two-digit numbers. The average response time can help teachers best determine an appropriate required fluency rate for each student.

- Students who have slower than typical response times may need to be assigned a slower required fluency rate.

We know that students make typos or, at times, respond incorrectly to facts that they may know well.

- With this in mind, at each level in the placement assessment, students are given a second try for up to two incorrect or slow responses.
- This helps us make sure that students are being accurately placed within the program.

Students are assigned to begin MathFactLab at the level where they have made their third inaccurate and/or non-fluent response.

We know that If a teacher feels a student’s results on a placement assessment is not reflective of the student’s ability, the teacher has two choices.

- One, the student can be given the opportunity to take the placement assessment again. (The teacher selects ‘Reassess’ under ‘Actions’ on the student’s row in the teacher dashboard.)
- Two, the teacher can place the student in the program at the level determined most appropriate by the teacher. (Select ‘Edit’ on the student’s row in the teacher dashboard.)

MathFactLab is not game-based, nor are there reward tokens,games, etc. Instead, we find that our students are generally intrinsically motivated by the growth that they see in their own performance as they move through the levels of the program.

You will find that making progress in the program is a source of pride for your students, especially for those who have struggled with math facts in the past.

Implementing small celebrations in your classroom, like clapping for those each day who move up a level, can add to student pride in their successes.

By default, MathFactLab students are expected to respond accurately to a given prompt in under four seconds, but you will find that this pace is unrealistic for some students.

Teachers are able to change the required response time in the teacher console. This can be set from 2 up to 120 seconds.

A longer response time will be helpful for a good percentage of special education students.

We know that some general education students may also need a longer response time.

- While typically teachers may choose a slower pace for those with a learning disability in math, keep in mind that you may also have general education students working at grade level or above who - because of their processing speed - simply are not capable of responding consistently in less than four seconds.
- To keep MathFactLab a positive, pleasant experience, adjust the required fluency rate for students who need it to one that is appropriately challenging while also achievable.

For students working on addition/subtraction - in order to break dependencies on counting fingers - it is important that their required response time be no longer than necessary.

- This time restraint will help to encourage the student to use more efficient strategies.