Beyond Basic Facts: Math Fluency for Advanced Students

 

As an enrichment teacher, I work in two different schools. Both of these schools have school-wide fact fluency initiatives in which students in every classroom work toward fluency in addition, subtraction, multiplication, and division facts.

While basic facts are important, there are other aspects of mathematical fluency that I want to address as well. When students have some values committed to memory, higher level problems become faster and more efficient. Understanding number relationships helps students to move quickly between fractions, decimals, and percents. As problems get harder, they can quickly decide when to keep numbers as fractions or when to change them to percents.

I have realized that working toward mathematical fluency has a place in the enrichment classroom. We can go beyond the basic facts to work on topics that have some mathematical richness and room for discussion.

For fourth graders, these topics include:

• addition and subtraction within 100
• extended multiplication and division facts
• simplifying fractions

Fifth graders benefit from fluency practice with:

• multiplication and division by powers of 10
• comparing decimal and fraction values
• fractions to decimals

For sixth graders, fluency practice can explore:

• percents
• exponents and square roots
• integer operations
• using area and perimeter formulas

 Creating fluency practice for students isn't difficult! Choose a topic, then create sets of problems within that topic. Students enjoy competing against themselves week after week, aiming for improvement. With my enrichment students, I made improvement the goal instead of a set number of problems. This makes success within everyone's grasp.

If you would like the sets that I created, they are available below.

Beyond Basic Facts: Fourth Grade

Beyond Basic Facts: Fifth Grade

Beyond Basic Facts: Sixth Grade

Reading Intervention for Fluency, Academic Vocabulary, and Nonfiction Text Structure

      This product has been a labor of love. Back in 2010, I wanted to put together a research-based set of activities for classroom teachers working with intermediate level readers. I wanted materials that would focus on academic vocabulary and nonfiction text structure, with lessons that were easy enough to add to an already full schedule and materials that were ready to be copied. Most importantly, I wanted to create something that would be inexpensive for classroom teachers. After months of work, I created this:

Reading Intervention for Fluency, Academic Vocabulary, and Nonfiction Text Structure.

     I worked this summer to freshen up the materials to make them even easier for classroom teachers, adding answer keys, PDFs, and better formatting. More than ten years after I wrote it, I'm still proud of the features!

The texts

    In this set, the texts are science-based, with topics ranging from poison ivy to bluebirds to caverns. I worked with topics that are adjacent to key science topics, often inspired by my visits to area museums, science centers, and parks. 

Academic Vocabulary

     Academic vocabulary is essential for unlocking the meanings and nuances of nonfiction texts. In certain reading series, I've noticed that the vocabulary words are jammed into texts, resulting in some odd usages and questionable sentences. Instead of doing this, I wrote the texts, and then searched them for academic words from Averil Coxhead's Academic Word List and other academic word list sources. 

     Engaging students in learning academic vocabulary is important. In my experience, building playful experiences in which students use the words to answer questions works well! I created a PowerPoint presentation for each text in which the words are introduced. These presentations include photos and questions to help students interact with the words, see them repeatedly in print, and use them in sentences. 

Fluency

     Is fluency broken? I kind of think so. I'm not sure that it has the prediction power that it once held. (Read more here.) Nevertheless, I still value time spent in helping students to read aloud with accuracy and expression. Each text in this intervention set includes a phrase-cued text for students to read and a fluency progress monitoring page.

     I love phrase-cued texts because they help students to see how sentences can be chunked for easier reading. Phrase-cued texts also support students in understanding sentence chunks for my favorite grammar activity, sentence unscrambling! 

     Fluency readings are a great way to talk one-on-one with a student and get a better idea of how they are word-solving. When I do fluency readings with students, I emphasize that the timing is just one part of the reading, and that I also want to hear what they can do with expression and word-solving. At the end of the reading, I give the student a compliment ("I notice that you took the time to figure out the word vanished.") and choose a quick teaching point to discuss with the student. Sometimes we look at the pronunciation of a word, and sometimes we focus on expression within a sentence. The next time that I work with the student, we review what we talked about previously.

    I created fluency passages for each of the texts in this intervention. Fluency passages are also a great way to involve parent volunteers or instructional assistants in your reading intervention. Most adults enjoy the opportunity to work individually with students.

Nonfiction text structure

     Many readers in grades 4-6 are still reading at the "local level"--that is, they're focusing on individual words and sentences within a passage without building a model of the passage as a whole. Understanding text structure and using graphic organizers to represent details can help students to move beyond the local level and develop a global model of the text.

     Each text in this series includes a graphic organizer to represent the big ideas and important details in the text. Students can then use these graphic organizers to help them write a summary of the passage as a whole.

Multiple choice questions

      While these were not part of the original program, I decided to add them as I was using the program with my own students. Each passage has 4-5 questions, along with an open-ended response prompt. 

Working on this intervention has been a bit of a passion project for me, and it's been gratifying to see so many positive reviews. Here's to another 10 years of academic vocabulary, fluency, and text structure!

Goldilocks Speed Drills

When I work with readers who are having trouble with word recognition and fluency, I like to preview words with a speed drill before they read a text. (This article from ldonline is a nice introduction to speed drills. ) 

To make a speed drill, I simply take a selection of words from a text and put them into a table. "But which words do you choose?" some teachers ask. My choices are partly intuitive, but I do use a rough formula:

• Words that need to be pronounced correctly
• Visually similar words
• Words with inflected endings
• Words which carry significant meaning in the text
• Words that are easy to say, but harder to define

Here is a speed drill that I made for a set of texts about landforms of the Northeast. I included the names of the states because, if nothing else, I want kids to be able to pronounce Connecticut!

The second speed drill, which I made for "Groundhog Day" by Lillian Moore, includes some words that are not in the original text. The group that I was working with was having trouble with visually similar words, and I wanted them to practice reading words with different endings.

Goldilocks Reading

Just reading the speed drill can be kind of monotonous. Luckily, my husband (who teaches third grade) taught me Goldilocks Readings. 

First read: Too slow
Second read: Too fast
Third read: Just right

It is so much fun, and so helpful for intermediate readers. Of course, during our slow reading of the words, I exaggerate the syllabication and the emphasis. It only takes one read-through for kids to pick up on this process and they enjoy slowing down their reading as well. 

After the Speed Drill

On some speed drills, I add questions to encourage students to make predictions. On others, I include questions about word awareness and vocabulary use (find the compound words, look for synonyms, etc.) But the speed drill doesn't become a long vocabulary task. Instead, we keep the focus on read the words with accuracy and getting ready for the real reading task--because that is where we are always, always going!

Roman Readers Theater

About ten years ago I realized that I could write my own resources to use in the classroom. The process at first was grueling--it would take me weeks to plan, write, and format one informational article.

I'd like to think that I can now move through the process a little more quickly, but it still requires a particular mindset to accomplish.

Luckily my husband has been one of my best critics and my best advocate. Last week, he asked if I could write some materials for his enrichment group. They are a lively, intelligent bunch (and my son happens to be in the group!) Knowing about my son's current love for mythology and ancient history, I wrote a series of readers theater scripts about ancient Rome.

I was excited for my son to read them. "What did you think of the scripts?"I asked on our way home.

"Mm. They were fun. I wanted to be the smallest part, so I chose the notary. Could you put the bit about the fluffy bunnies in all of the scripts?'

"You wanted the smallest part?" I asked, a bit surprised.

"Of course. I always want the smallest part," he answered. "But you need to put fluffy bunnies in all of the scripts. It would be so easy."

I pressed him a bit more to see if he had learned anything from the scripts (which was after all the point), and he rattled off details about the different jobs of ancient Rome. "But they all need fluffy bunnies," he persisted.

So I added the fluffy bunnies detail to all of the scripts and resolved that next year, when he was in fourth grade, I'd have to make sure that he didn't always get the smallest part.

News and Notes
-Roman Readers Theater is available if you are interested.
-I've added a new text (Water Pollution) to the Cause and Effect unit. If you've already purchased it, you can re-download it for free, with the latest updates.

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Story Elements Readers Theatre

I love using Readers Theatre in my classroom. It's so much fun to watch the students show off their dramatic talents with zany, information-filled plays.

Unfortunately, I've become very picky about scripts. I don't want scripts that are more than 3 pages long, because no fourth grade audience has they attention span to watch the performance. I don't like scripts with more than 6 characters, because the groups often start fighting.

One of my long-time favorite set of scripts has been Read-Aloud Mini Plays with Leveled Parts. (Follow the link to read the Amazon review that I wrote of it back in 2008.) I like how the scripts include parts with different reading levels. These scripts also have the right level of silliness for my fourth graders. (Unfortunately, the follow-up book only has 12 scripts, and has some uneven parts that has led to great angst in the classroom.)

I go through all of the scripts in this book in about two months. To build my script base, I have written several sets of scripts to go along with what I am teaching. These scripts are all roughly the same length, with about the same number of parts. Once we perform a set, extra scripts are kept in one spot in the classroom for students to use during free time and indoor recess. 

These scripts do not come easily. Coming up with a situation, explaining a topic, and making sure that each character has a decent set of lines is hard to manage. Making it all fit on 2-3 pages is even harder! I can usually only manage it every few months or so. Interestingly, it's not something I spread out, like the text structure packets; instead, I write these in an intensely concentrated period of time.

Story Elements Readers Theatre
Five scripts (character, setting, plot, theme, conflict) review the key story elements, with varying degrees of silliness.

Text Structure Readers Theatre
Four scripts (chronological order, compare and contrast, problem/solution, and cause/effect) explain text structures.

Purpose for Reading
Three scripts explain why readers choose books. I have always meant to add a fourth script to this set, but every time I sit down to do it my brain just--refuses.

Animal Classification Readers Theatre
Five scripts explain the differences between mammals, reptiles, amphibians, fish, and birds.

Scientific Method Readers Theatre (whole class): This one isn't my favorite, but it makes for a fabulous substitute lesson.