Getting Started with Fluency Practice

Fluency Practice, made in collaboration with Math for Love, provides students daily, personalized fluency practice on math facts. Based on the theory of spaced repetition, students more frequently practice the facts they are most likely to forget. When students correctly answer a fact, they won’t see that same fact again for some time - anywhere from 1-2 days to a few weeks, depending upon how many times they have already correctly answered that fact. However, if they answer the fact incorrectly, they will see that fact again the next time they practice. Read below for more specifics about Fluency Practice.

Glossary of Terms

• Flashcard Set: the operation-based collection of cards. We currently have three flashcards sets, but more are coming soon:
  • Addition and Subtraction by Heart I
  • Addition and Subtraction by Heart II
  • Multiplication by Heart
• Decks: Each flashcard set is split up into a certain number of decks. Each deck has a different visual representation, different number facts, and/or different fluency strategies.
• Boxes: The boxes refer to where a specific card lives along the journey of spaced repetition.
• Card: The individual flashcard that moves from box to box.
• Fact: The actual math fact, like 3 x 4, which appears on multiple different cards.

How often should students practice?

We recommend that students use Fluency Practice daily. The program will automatically select up to 40 flashcards for students each day. This daily practice should take most students 5 – 10 minutes.

How do the flashcard sets align to grade level expectations?

These grade-level recommendations are based on the fluency Common Core Math Standards.

• Kindergarten: Numbers by Heart (Coming Soon!)
• 1st Grade: Addition and Subtraction by Heart I
• 2nd Grade: Addition and Subtraction by Heart II
• 3rd Grade: Multiplication by Heart
• 3rd Grade: Division by Heart (Coming Soon!)

How do students access Fluency Practice?

Amplify Desmos Math Students: Students using Amplify Desmos Math can access Fluency Practice from Student Home.

Other Students: All other students can go to fluency.amplify.com and sign in. Read this page for information about creating free teacher and student accounts inside Desmos Classroom.

How does the program decide what cards students see each day?

Using the spaced repetition theory as described above, the program automatically selects up to 40 cards each day, personalized for every student. These will be a combination of new cards they haven’t seen yet and/or various cards students are still working on. To keep track of where specific cards are in the journey towards memorization, we organize the cards into 6 boxes - A, B, C, D, E, and Memory. Cards start in Box A. Facts answered correctly move up a box and facts answered incorrectly move back to Box A (or stay in Box A).

The program selects cards based on how long they have been in their current box. As students answer questions correctly and the cards move through the boxes, more days will pass until students see that card again:

For example, if a card has been in Box C for about 5 days, that card will likely be amongst the 40 cards to appear on that day. Teachers are not able to change the order of how the cards appear. The box letter of each card appears in the upper right hand corner of that card.

What happens when a student has finished their assigned cards for the day?

Students will see an “All done for today!” screen and the option to continue practicing. If students click the “Continue practicing” button, the program will give them more practice of a random set of cards from all the cards in any of their boxes right now - from Box A through Memory. The only way students can get to Practice Mode is by completing their cards for the day. If students complete one round of Practice Mode, they’ll see the same message again and can repeat if they want. Work done in Practice Mode does not impact cards moving boxes - answering them correctly won’t move them up a box and answering them incorrectly won’t move them to Box A. Accordingly, none of the work done in this mode will impact progress shown on the student grid.

What happens when all the cards reach the memory box?

If a student gets all the cards from each deck of the practice set into their memory box, congratulate them – they have successfully memorized all the facts! However, to ensure long-term retention of the cards in the memory box, the program will continue to show these cards to students in a variety of ways:

• On any day in which students are scheduled to see less than 40 cards due to the spaced repetition algorithm, the program will randomly add cards from the memory box into the assigned cards for the day so students see a total of 40 cards.
• Any cards in the memory box will be randomly shown to students in the practice mode as described above.

Cards in the memory box will appear mixed in with cards from the other boxes. However, rather than listing the box letter in the upper right hand corner of the card, cards in the memory box will show a 🧠 in the upper right hand corner.

If a student answers a card in the memory box incorrectly after both attempts, the card will move back to Box A and begin the spaced repetition process from the beginning. Teachers can override this on the teacher dashboard by moving all the cards in a given deck to the memory box. If teachers don’t want students ever seeing cards from their memory boxes, they can un-assign the entire practice set on the teacher dashboard.

How can teachers and students view progress?

All student progress is tracked on the Teacher Dashboard. Teachers using Amplify Desmos Math will find a link to the dashboard on Teacher Home and the dashboard will automatically be synced with their classes.

For all other teachers, if your students are not already part of a rostered class inside of Desmos Classroom, you’ll need to first create a free Desmos Classroom teacher account and then create classes of students. Read this page for information about creating free teacher and student accounts inside Desmos Classroom.

On the dashboard, teachers can see a record of daily completion, a summary progress grid for the class for each flashcard set, and an individual progress grid for each student for each practice set.

Students are able to view their progress by clicking on the Progress button.

What information is shown on the student and class progress grids?

On the individual progress grids, you can see what box the given fact is in at that moment in time by looking at the letter.

• Gray: student hasn’t seen the fact yet
• A: That fact is currently in box A
• B: That fact is currently in box B
• C: That fact is currently in box C
• D: That fact is currently in box D
• E: That fact is currently in box E
• No letter, just green: That fact is in the Memory box

Some facts appear on multiple cards. For example, in Multiplication by Heart, 6 x 8 appears in Deck 2 as an array and in Deck 3 shown in prime factor circles. For these cards, the letter shown in the grid is the lowest location of all the cards with that fact.

The class summary grid works a bit differently than the individual progress grids. The letters in the grid reflect the average location of the fact for the whole class.

Both the class summary and the individual student grid can be downloaded as a CSV file.

How do teachers assign flashcard sets and decks to students?

Student assignments can be controlled on the teacher dashboard by selecting the flashcard sets and specific sets available to students. Teachers can make changes that apply to the entire class or to specific students in the class.

Can students make changes to what they are working on?

Students that are rostered in a class with a teacher, either through Amplify Desmos Math or Desmos Classroom class, do not have the ability to make any changes to their assignment. Student users that are NOT part of a rostered class do have the ability to make changes.

My students already know some of the more simple facts. Can they skip these?

Yes! Teachers can decide which decks in a practice set they want to assign to each student. If a teacher knows that a student has already memorized the simpler facts, the teacher can simply click a button to move all the cards in that deck into the Memory Box. As described above, students will still occasionally see some of the cards in their Memory Boxes.

Can students work on multiple flashcard sets at once?

Yes! Teachers can assign multiple flashcard sets to students. The program will combine all of the cards to create a cohesive experience for students. All student progress on the cards is saved, even if the teacher unassigns some of the flashcard sets or decks from an individual student.

Can I purchase a physical set of the cards?

Yes! Fluency Practice is made in partnership Math for Love. Multiplication by Heart, Addition by Heart, and many more wonderful games are available at Math for Love. Physical versions of the other Fluency Practice sets are planned as well.

Video Overview

Below is a video that covers much of the content above. Note that this video was made prior to Multiplication by Heart moving from Mathigon to Amplify. So, rather than making a Mathigon account as mentioned in the video, students will need to make accounts in Desmos Classroom or use their Amplify Desmos Math accounts.

https://www.youtube.com/watch?v=gsexZ1I30xE&t=1s