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

Language Comprehension Skills: Bump Out Puzzles for Vocabulary Enrichment

All students need experiences with categorizing. In the classroom, this can look like sorting spelling words, organizing class materials, and grouping like things together. 

As an enrichment teacher, I love categorizing activities as ways to help students think more deeply about how different objects, words, and concepts relate. One of my favorite activities for this is a tried and true technique called "bump out".

The concept is easy. Present students with a list of four words, three of which go together. Students have to figure out which word doesn't belong and then "bump" it to the next box, making a new set of four words.

For example, in the set

chair

pencil

marker

eraser

the word "chair" is bumped out, because it is not a school supply like the others. 

While the concept is simple, putting together the activities can be tricky. I used to try to make one for each science unit, struggling to make the word boxes behave in Microsoft Word until I gave up and started hand drawing my sets. I still have some (bad) scans of these early bump out activities that I made!

This year, I started making new sets of bump out puzzles for my first and second grade enrichment students. Instead of hand drawing, though, I used Google Slides to get the text boxes right! Students enjoyed the challenge, and I enjoyed the rich discussions that followed as we talked about why some words didn't belong. On each puzzle, I include some that are very easy and others that require a little bit more background knowledge.  

If you'd like to pick up a set for your classroom, you can find the finished set here: Vocabulary Enrichment Bump Out Puzzles.

Main Ideas for Middle School Readers

 Helping readers to find main ideas is important work. It's also complicated, messy, and challenging enough to make me want to tear out my hair! Those of us who remember working through the colors of the SRA reading kits as students were never really taught how to find a main idea. (Here's an interesting blog post about the history of the color-coded kits!)  Instead, we just read the paragraphs and guessed until we figured out the pattern on our own! As a teacher I wanted to do a little bit more than just have a set of materials in the corner.

What is a main idea?

Too many students and teachers confuse topic and main idea. As I wrote in my book Summarizing, Paraphrasing, and Retelling, a topic is the superordinate word or phrase to which all of the ideas in a passage refer (Aulls 1975). On the other hand, a main idea is best expressed in a complete sentence. Sometimes an author states the main idea; sometimes an author leaves the main idea implicit. The old Write Source 2000 books called this "a topic + an attitude or statement about the topic" which is a good definition to use with students.

Why is this so hard?

Skilled readers create mental models of a text as they read, building a hierarchy of ideas. You may be doing this right now with this text! However, less skilled readers often connect one sentence only to the one before or after. They are reading at a very local level, and rarely see the big picture (Kintsch 1990). To teach main idea, then, is to help students see nested hierarchy of ideas in a text--paragraphs have main ideas, but so do sections, and so does the text as a whole.

It sounds so simple to talk about it, but if you've ever looked at a roomful of sixth graders you know that saying, "Let's look for a nested hierarchy of ideas in the text!" is not likely to bring you much success as a teacher. Part of the difficulty is rooted in the fact that authors express main ideas in a variety of ways. Sometimes they are at the beginning of the text, sometimes they are at the. end, and sometimes they are not stated at all. Distressingly, some texts written for students seem not to have a main idea at all!

Working with middle school readers

My favorite order for teaching main idea is to follow these steps:

• Single paragraphs with explicit main idea at the beginning
• Single paragraphs with explicit main idea in another location
• Multi-paragraph pieces with an explicit main idea
• Poorly written pieces

With sixth and seventh grade readers, I am often tempted to go directly to the third step and jump right into multi-paragraph pieces. Year after year, though, I have learned that skipping main ideas at the paragraph level can lead to big problems later on! I generally like to start with one of the single paragraph activities from my text set Main Ideas and Details in Expository Text or my old standby Finding Topics and Main Ideas (free PowerPoint). Depending on how these go, I can move directly on to multi-paragraph pieces or stick around in single paragraph land for awhile.

New Resource

When I can't find a text, I write my own! This resource was written to accompany the Wonders Unit 1, Week 3, but it can be used for most sixth and seventh grade readers. It includes a single text about extremophiles, along with a tree map graphic organizer that shows the hierarchy of ideas in the text. In addition, comprehension questions refer to the individual paragraphs and sections as well as to the article as a whole, leading students to consider how the ideas fit together. You can find it here: Middle School Main Ideas: Article and Activities for Grades 6-7.

References

Aulls, M.W. 1975. "Expository Paragraph Properties that Influence Literal Recall." Journal of Reading Behavior 7: 391-400.

Kintsch, E. 1990. "Macroprocesses and Microprocesses in the Development of Summarization Skill." Cognition and Instruction 7: 161-95.

Kissner, E. 2006. Summarizing, Paraphrasing, and Retelling: Skills for Better Reading, Writing, and Test-Taking. Portsmouth, NH: Heinemann.

Sixth Grade Wonders: Secret Life of Caves, Unit 1 Week 3

 This is my favorite week of the first unit of Wonders in sixth grade! Of course, if you know me and my interests, you will understand why. Caves, animal adaptations, deep sea exploration--this week has it all.

Which is why, in my classroom, it was never a single week of instruction. I think that the pacing of Wonders is far too fast, especially for complex texts and complex ideas. "Okay, kids, we're going to introduce the idea of chemosynthesis in a single day of reading. Don't understand the ideas in this text? No worries, we're already done and on to the next thing!" This doesn't really lead to the kind of thoughtful, reflective reading I hope to develop. So, for Unit 1 Week 3, I usually took 2-3 weeks.

Additions to the Wonders resources

In addition to the texts and activities provided in the weekly instruction, I supplemented with these resources.

Caverns Informational Text: This text, written by me for Reading Intervention, became a homework text to go along with the unit. I added a comprehension quiz and a note-taking sheet to reinforce the concepts of main idea.

Speed Drill and Questions for "The Secret Life of Caves"

Speed drills are a great way to increase fluency and help students to notice semantic elements. When I noticed that many of my students were skipping over the tougher words instead of breaking them apart, I added syllable practice to the page. This set also has some practice multiple choice questions and an open-ended response that mirrors the question for the Weekly Assessment.

Yeti Crab Subject and Predicate

My students loved reading about the yeti crab in "Journey Into the Deep," so I made them an additional grammar practice page starring this creature.

Troglobites Clip from BBC Earth

My students loved this clip and begged to watch it again during dismissal time!

I hope that you enjoy teaching this week of instruction as much as I did!

Sixth Grade Wonders: Drumbeat of Freedom, Unit 1 Week 2

 This Reading-Writing Workshop selection in Unit 1, Week 2 is a strong story. When I used it in a co-taught setting, though, I needed to add some more activities to allow for differentiation and some small group meetings. Over several years I added and refined these activities. Here they are, ready for you to use in your own classroom this year!

Speed Drill, Multiple Choice Questions, and Story Map

I still like using speed drills to increase student automaticity and fluency. Not only do speed drills help students to recognize words, but they also give us a chance to talk about word meanings that might be new for them.

I also wrote some multiple choice questions in the style of the questions used on the Weekly Assessments. These questions proved useful for small group work, as we could talk together about the questions and possible answers. Students are much more willing to share their thinking when talking to five others as opposed to talking with the entire class! For the Part A and Part B questions, I learned that some of my students really didn't know what to look for, and this allowed me to target instruction to help them with this.

Finally, I added a story map and list of events for students to work on. I really like giving students lists of events from a story to read and sequence. No matter what the age, this activity helps students to think about how a story unfolds. Students can also use the given events to help them write a short summary of the story, or create an illustrated plot diagram.

If you try these out, be sure to write a note and let me know!