Category Archives: Resources

Trying Out Quizlet to Practice Deriving and Recalling Multiplication Facts

[Update – I’ve added a four more Quizlet study sets to my Multiplication Facts Practice folder. The three “Practice Doubling” study sets are designed to provide students practice doubling a number, a necessary skill to be able to efficiently use the Doubling Multiplication Fact Strategy The “Practice Halving” study set is designed to provide students practice halving a multiple of ten, a necessary skill to be able to efficiently use the Use-Ten Multiplication Fact Strategy.]

As a member of NCSM, I get a weekly email called the Marshall Memo that shares summaries of a variety of education-themed articles. What I like about the Marshall Memo is that I get exposed to articles I may never have encountered on my own. Even better, while many articles are on topics that aren’t math-specific, I’m still often able to able to make connections to my own work.

Take this recent article from The Reading Teacher, for example, called “More Than Just Word of the Day: Vocabulary Apps for English Learners.” I don’t have access to the full article, but in this summary, Marshall notes that the authors reviewed 53 free vocabulary-teaching apps for grades 3-8. Out of all these apps, Quizlet was the only app they endorsed. That piqued my interest!

It also connected to something I’ve been thinking a lot about lately, which is the strong research evidence that retrieval practice promotes learning:

“Retrieval practice” is a learning strategy where we focus on getting information out. Through the act of retrieval, or calling information to mind, our memory for that information is strengthened and forgetting is less likely to occur.”

https://www.retrievalpractice.org/

If you’re unfamiliar with the IES Practice Guides, they provide research-based recommendations on a variety of educational topics. In their guide Organizing Instruction and Study to Improve Student Learning, Recommendation 5b is Use quizzes to re-expose students to information. The level of research evidence for this recommendation is strong, according to the guide. It goes on to say,

“…quizzes or tests that require students to actively recall specific information (e.g., questions that use fill-in-the-blank or short-answer formats, as opposed to multiple-choice items) directly promote learning and help students remember information longer.”

IES Practice Guide, Organizing Instruction and Study to Improve Student Learning, page 21

This also brings to mind “Rachel,” a thought-provoking blog post from Michael Pershan that has had me thinking about the interrelationships between deriving and recalling facts.

Suppose a student has just derived 9 x 4. If they’re confident and successful, they might have an opportunity to share that solution with the class — I might ask them to share their solution, and they might have a moment where they ask themselves, “wait, what was 9 x 4 again?” This is recall practice. Or, maybe, they are working on a larger problem in which 9 x 4 is merely a step, and their later work calls on them to remember the product of 9 x 4. They derive it, and then turn back to the problem and ask themselves, “what was 9 x 4?” Or perhaps, while working on a large set of multiplication problems, a student derives 9 x 4 and is then asked to derive 90 x 4. They ask themselves: what is 9 x 4?

Rachel by Michael Pershan

All of this thinking got me inspired to give Quizlet a try for creating study sets that provide students practice both deriving and recalling multiplication facts. I organized my study sets around the thinking strategies shared in The Book of Facts: Multiplication, published by ORIGO Education.

“Research show that the most effective way for students to learn the basic facts is to arrange the facts into clusters. Each cluster is based on a thinking strategy that students use to help them learn all of the facts in that cluster.”

The Book of Facts: Multiplication, ORIGO Education

If you’re unfamiliar with these thinking strategies, ORIGO has kindly created a one-minute overview video of each one:

For each strategy I created three levels of study sets in Quizlet. Level 1 focuses on reinforcing the thinking strategy. As students practice the flashcards, they are presented a pictorial representation of the multiplication fact that reinforces the thinking strategy. For example, if students are solving 8 × 5, the reverse side of the flashcard shows the product as well as a visual that reinforces the idea that each fives fact is half of the related tens fact. In this case, the array model shows that 8 × 5 is half of 8 × 10.

Front
Back (Level 1)

Level 2 focuses on a verbal reminder of the related thinking strategy. The front of the card remains the same, but the back of the card includes a reminder of what students can think about to help them derive the fact. Here’s the back of the 8 × 5 card in Level 2:

Back (Level 2)

Finally, in Level 3, the focus is on recalling the multiplication facts. The back of the card does not include any reminders; it just shows the product. If students get stuck, the teacher can ask the student to recall the thinking strategy they’ve learned, otherwise students should focus on recalling the facts.

In addition to the strategy-focuses study sets, I’ve also included three study sets that practice a variety of multiplication facts when students are ready to focus on recalling across all of the facts. Version 1 focuses on the x0, x1, x2, x3, x4, and x5 facts. Version 2 includes a wide variety of all facts. Version 3 focuses on the x6, x7, x8, and x9 facts.

You can access all 21 study sets on Quizlet. If you’re not familiar with Quizlet, there is a free version and a paid version. I’d recommend starting with a free account. If you’re a teacher, be sure to indicate it when creating your account because teachers get extra features.

Some words of advice, Quizlet offers a wide variety of modes for practicing study sets.

I’ve noticed that many of these activities show the product and students are supposed to answer with the multiplication expression. If you want to start by presenting the multiplication fact to the students, all you have to do is click the Options button and then change “Answer with” to “Definition” instead of “Term.” I recommend doing this because generally we want students to recall the product not the multiplication expression.

In the Flashcards activity, I recommend turning on Shuffle. If students are at a point of focusing on recall rather than deriving each fact, then I also recommend turning on Play. This will make the flashcard automatically turn over after a few seconds. This prevents students from falling back on counting strategies.

In the Learn activity, I recommend going into the options and deselecting “Multiple choice questions.” For retrieval practice, research does not recommend multiple choice questions. Rather, the “Flashcards” and “Written questions” are preferable Question Types for this activity.

In the Test activity, I recommend only the “Written” and “True/False” question types. Again, in all of these activities, don’t forget to change the “Answer With” option from Term to Definition.

And finally, if your students are not familiar with the thinking strategies in these study sets, then they may be very confusing and unhelpful to students. In The Book of Facts series, ORIGO recommends four teaching stages:

  • Introduce the strategy – Hands-on materials, stories, discussion, and familiar visual aids to introduce the strategy or sub-strategy
  • Reinforce the strategy – This stage make links between concrete and symbolic representations of the facts being examined. Students also reflect on how the strategy or sub-strategy works and the numbers to which it applies.
  • Practice the strategy – This stage aims to develop accuracy and increase ‘speed’ of recall. In this stage, a range of different types of written and oral activities is used.
  • Extend the strategy (to greater numbers) – Students are encouraged to apply the strategy to numbers beyond the range of the basic number facts. The activities in this stage are designed to further strengthen students’ number sense, or “feel” for numbers.

The Quizlet study sets I created fall within the Practice stage. If you’d like to teach these strategies to your students, I do recommend checking out The Book of Facts: Multiplication because it provides several activities at each of the four stages for each strategy.

If you try out these study sets with your students, let me know how it goes! I’m excited to be able to share this resource for retrieval practice to the teachers in my district. If I hear feedback from them, I’ll be sure to let you all know how it goes.

Crystal Capture

This weekend I made something fun and wanted to share it in case it provides fun for anyone else.

My daughter has a board game called Unicorn Glitterluck.

It’s super cute, but not the most engrossing game. She and I especially like the purple cloud crystals, so this weekend I started brainstorming a math game I could make for us to play together. I know number combinations is an important idea she’ll be working on in 1st grade, so I thought about how to build a game around that while also incorporating the crystals.

Introducing…Crystal Capture!

Knowing that certain totals have greater probabilities of appearing than others, I created a game board that takes advantage of this. Totals like 6, 7, and 8 get rolled fairly frequently, so those spaces only get 1 crystal each. Totals like 2, 3, 11, and 12, on the other hand, have less chance of being rolled, so I only put 1 space above each of these numbers, but that space has 3 crystals.

I mocked up a game board and we did a little play testing. I quickly learned a few things:

Play-Test

I originally thought we would play until the board was cleared. Everything was going so well until all we had left was the one space above 12. We spent a good 15 minutes rolling and re-rolling. We just couldn’t roll a 12!! That was getting boring fast which led me to introduce a special move when you roll a double. That at least gave us something to do while we waited to finally roll a 12.

That evening I made a fancier game board in Powerpoint and we played the game again this morning:

Since clearing the board can potentially take a long time, which sucks the life out of the game, I changed the end condition. Now, if all nine of the spaces above 6, 7, and 8 are empty, the game ends. Since these numbers get rolled more frequently, the game has a much greater chance of ending without dragging on too long.

I did keep the special move when you roll doubles though. This adds a little strategic element. When you roll a double, you can replenish the crystals in any one space on the board. Will you refill a space above 6, 7, or 8 to keep the game going just a little bit longer? Or will you replenish one of the three-crystal spaces in hopes of rolling that number and claiming the crystals for yourself?

All in all, my daughter and I had a good time playing the game, and I learned a lot about where she’s at in her thinking about number combinations. Some observations:

  • She is very comfortable using her fingers to find totals.
  • Even though she knows each hand has 5 fingers, she’ll still count all 5 fingers one-at-a-time about 75% of the time.
  • She is pretty comfortable with most of her doubles. She knows double 5 is 10, for example. She gets confused whether double 3 or double 4 is 8. We rarely rolled double 6, so I have no idea what she knows about that one.
  • In the context of this game at least, she is not thinking about counting on from the larger number…yet. She doesn’t have a repertoire of strategies to help her even if she did stop and analyze the two dice. If she sees 1 and 5, she’ll put 1 finger up on one hand and 5 on the other, then she’ll count all.
  • I did see hints of some combinations slowly sinking in. That’s one benefit to dice games like this. As students continue to roll the same combinations over and over, they’ll start to internalize them.

Several folks on Twitter expressed interest in the game, so I wanted to write up this post and share the materials in case anyone out there wants to play it with their own children or students.

You’ll have to scrounge up your own crystals to put in the spaces, but even if you don’t have fancy purple ones like we do, small objects like buttons, along with a little imagination, work just as well. Oh, and if you can get your hands on sparkly dice, that helps, too. My daughter loves the sparkly dice I found in a bag of dice I had lying around.

Have fun!

A Little Preview

Next week I have the privilege of presenting a session about numberless word problems at the 2018 NCTM Annual conference. Even if you don’t teach in grades 3-5, I still invite you to join us because there will be lots of ideas shared of interest to multiple grade levels.

2018-NCTM-Program-Bushart

During the session, I’ll be referencing a few numberless word problems used over the course of several months in a 3rd grade classroom in my district. I thought it might be fun to share them before my session so folks could take a peak (and possibly even try one or two of them out before my session!).

The Collie and Chihuahua Problem – This is a comparison problem where the difference is unknown.

The Ancient Penguin Problem – This is another comparison problem. This time the larger quantity is unknown.

The Sand Castle Problem – This is an equal groups problem with an unknown product.

The Minecraft Problem – This is a multi-step problem involving multiplication and addition.

The Piano Practice Problem – This is a multi-step problem involving addition and subtraction.

The Pie Problem – This is a multi-step problem involving multiplication.

Enjoy! And if you’ll be joining me next week at NCTM, I look forward to seeing you in Washington, D.C.!

Rethinking Test Prep

I don’t know about you, but here in Texas we’ve got a state math test in grades 3, 4, and 5 coming up soon. The 5th grade test is taking place in mid-April followed by the 3rd and 4th grade tests in mid-May. In my school district, we used to stop instruction for one to two weeks prior to the test to focus on review. It’s always rubbed me the wrong way, and this year we changed that. If you want to read more about our rationale for doing that, I recommend reading Playing the Long Game, a post I wrote on my district blog. I also recommend checking out my Ignite talk from NCSM 2017. The work I’m sharing here has been a chance for me to put into practice the principles I shared in that talk.

If you don’t have time for all that right now and you’d rather check out the review activities I’ve created and get access to them for yourself, read on!

This year, with the help of our district instructional coaches, I put together collections of 15-20 minute spiral review activities that can be used daily for a month or so before the state test to review critical standards and prepare students without interrupting the momentum of regular math instruction. Here they are:

(Note: If you want to modify an activity, you are free to do so. Either make a copy of the file in your Google drive or download a copy to your computer. You will have full editing rights of your copy.)

When you look at an activity, it might look short. You might ask yourself, “How could this possibly take 15-20 minutes?” Good question! These activities are designed for student discourse. Students can and should be talking regularly during these activities. The goal is for students to be noticing, wondering, questioning, analyzing, sharing, and convincing  each other out loud. These discussions create opportunities to revisit concepts, clear up misconceptions, and raise awareness of the idiosyncrasies of the test questions, especially with regards to language.

Most of the activities are low or no prep, though here and there a few activities need some pages printed ahead of time. Be sure to read through an activity before facilitating it in your class so you don’t catch yourself unprepared.

Each collection of activities is organized around the Texas state standards (also known as TEKS). If you don’t live in Texas, you still might find these activities useful since there’s so much overlap between our standards and others. To help non-Texans navigate, I’ve added a column that (very) briefly describes the concept associated with each activity. If you’re interested in reading the actual TEKS each activity is aligned to, check out these documents:

If you try any of these activities out with your students, let me know how it goes in the comments. Enjoy!