Milk Cap Magic Squares

Ready for some fun? Grab a copy of Ben Franklin and His Magic Squares to read aloud. Stop reading after it says, "Now Ben wondered if he could make the numbers [1-9, in a square] add up to 15..."

Give each student a set of 9 milk caps (I don't EVER throw them away!) to number, 1-9.

Challenge them to make a 3 x 3 array in which every row, column, and diagonal totals 15.

If they think they've found the answer, have them scurry off to write it down! (And hide it from everyone else!)

Stop periodically to talk about strategies. Today we discussed ideas like:

1. Not having all of the biggest numbers--or the smallest numbers--in the same row, column, or diagonal.

2. Setting some of the combinations in #1 and then working around those numbers.

3. Only moving a few caps at a time, especially if you're getting close.

You can also give the online version a try!

Student Video Tutorials: Multi-Digit Multiplication

We're excited to share student-produced video tutorials on the multi-digit multiplication strategies that we've been learning. The tutorials were recorded using a free app, Educreations.

As we began, I asked if any of them had ever seen a video tutorial. Grinning, they all said that they had. They were thrilled with the idea of making their own!

After randomly selecting a multi-digit multiplication strategy, they planned presentations, including visuals and text/dialog. This organizer helped guide the process. (Click on the sheet for a free copy.)

Take a peek...
Students plan and write the visuals and the dialogue...

 

...and practice presentations on mini whiteboards...

This was a powerful way for them to demonstrate what they've learned. As students planned, I heard incredible mathematical conversations.  In one example, while working on the ratio table presentation, a student experimented with several sets of numbers--conversing with classmates about choices--before he came up with an example that demonstrated optimal efficiency.

Enjoy their videos. If you'd care to share, they would love to read your comments!




















The articles in this 3-part series on Teaching Multi-Digit Multiplication include:
1. Multiple Strategies for Multi-Digit Multiplication (introduction)
2. Choosing the BEST Strategy
3. Student Video Tutorials

Explore Volume with Mini Cube Cities

It's April. Time for a little "art break" in math class. In this case, I wanted students to apply what they've learned about volume. I pulled out the isometric drawing paper and we got busy, each student designing a "Mini Metropolis."

I led them through step-by-step practice sheets to learn how to draw cubes and rectangular prisms. Almost immediately I heard, "...this is cool!" followed by "...this is like Minecraft [video game]!"

To make the drawings just a wee bit more 3-D, we learned to do a little shading.

After practice, I gave each City Planner a "Design a Mini Metropolis" sheet and related table. The assignment required them to:

1. draw some buildings with given dimensions, calculating volume
2. draw some buildings with a given volume, calculating dimensions
3. invent some buildings, calculating dimensions & volume

Rulers kept our lines straight.

If we needed help making rectangular prisms with a given volume, centimeter cubes helped.

Aren't the buildings lovely?

We planned for roads, parks, foliage and other metropolis necessities!

Students loved this lesson. Some of them have continued drawing ever since we began this assignment, printing out more isometric dot paper at home.

If you are interested in purchasing the lesson, you'll find it here.

Multi-Digit Multiplication: Choosing the BEST Strategy

Warning: this is a ginormous post, filled with student work. I am feeling just math-teacher-pride-nerdy enough to post it. You've been warned.

I mentioned how my students have learned many strategies for multi-digit multiplication this year. That, in itself, is terrific. But even better? They understand what types of numbers work best with certain strategies. This ability--to determine which strategy is most efficient in a given situation--shows that have an incredible array of mathematical knowledge in their tool boxes.

In the first several examples, students could choose from 20 multiplication expressions, selecting the problem that they thought was a good match for each of the strategies they've learned. They had to:

1. choose an appropriate problem for the strategy
2. solve the problem using that strategy
3. explain why that strategy fit the problem
4. double check their answer using a second strategy. 

It's important to note that when the year began, some students had zero strategies for multi-digit multiplication. We've come a LOOONNNGGGG way!!

I've added captions to a few examples near the end...stuff you mustn't miss. And then read on...there's more below!

Strategy: Doubling & Halving

 Strategy: Over Strategy

 Strategy: Using Quarters

 

Strategy: Four Partial Products

Strategy: Ratio Table

Strategy: Standard Algorithm

Notice that this student deliberately chose more challenging numbers to use on this strategy.

Cracks me up...I told them that the standard algorithm is the only strategy I was taught. Notice what this kiddo wrote in his explanation...

After completing the strategy sheets, I compiled a list of the strategies and the problems chosen by students for each one. Students selected the identical expression on some problems (like 99x73 for the over strategy) and had different expressions for others. This led to a great discussion about which strategy was chosen for each, and why.

Tips for Multi-Digit Multiplication Strategies
After my students finished the strategy sheets, they made posters--TIPS--for using each strategy...

I wish you could have heard the discussions that went with both the development and the presentation of these tip sheets. I couldn't believe the amount of higher-level thinking involved.

Do these students "get" multi-digit multiplication, or what??? A parent told me that her student was about ready to bust a button when he proudly said, "I know TEN ways to solve problems."

Awesome, awesome work!!!!!! (And thank you to Math Learning Center, Bridges Second Edition, Grade 5, for the strategies and core lessons.)


The articles in this 3-part series on Teaching Multi-Digit Multiplication include:
1. Multiple Strategies for Multi-Digit Multiplication (introduction)
2. Choosing the BEST Strategy
3. Student Video Tutorials

Multiple Strategies for Multi-Digit Multiplication

For the record, I was cheated. As a child, I learned ONE WAY to calculate multi-digit multiplication: the "standard" or "traditional" algorithm. As an adult, I was shocked to learn that the "standard" method is NOT standard in all parts the world, and neither is it always the easiest or most efficient way to solve a problem.

This past school year, my students have learned many strategies for multi-digit multiplication. I am astounded by their ability to think flexibly and find the best strategy to fit a particular problem. They can compute so much faster and with greater ease and efficiency than I was ever able to do with only one multi-digit multiplication tool. Many times, they can compute mentally because the right strategy makes multiplication easy. This week, we reviewed using 25 x 96. Take a look.

(The sheet below comes from Bridges Grade 5 Second Edition and is used by permission.)

Doubling & Halving

Ratio Table

 Over Strategy

Using Quarters

Partial Products

Standard Algorithm

After the review, I gave them a sheet of multi-digit multiplication expressions and let them choose a different problem to illustrate each of the six strategies. They organized their work on these Strategy Support Sheets (questions/ideas modified from Bridges Second Edition) where they had to:

1. show their work using the strategy
2. explain why that strategy was well-suited for that particular problem
3. prove their answer correct by solving with a second strategy.

I heard kids exclaim, "this is FUN!" and saw example after example of high-level mathematical thinking. They GET which strategies are the most efficient for different types of problems. The sheets will be used as reference pages in their math notebooks.

I can't begin to describe how proud I am!

The articles in this 3-part series on Teaching Multi-Digit Multiplication include:
1. Multiple Strategies for Multi-Digit Multiplication (introduction)
2. Choosing the BEST Strategy
3. Student Video Tutorials

Making & Keeping Friends: Helping Kids to Find Success

During my sophomore year in high school I went to my mom with a bout of teen angst saying, "I want to be popular." I had plenty of friends. Enjoyed a variety of activities. But I felt like I was missing something. I've never been voted to a high school court or been nominated for a class office. It seemed like there was a magical "something" out there that others had figured out, leaving me in the dark.

So my mom made me a bet: if I read How to Win Friends and Influence People, she'd pay me a nickel for every instance that I used one of the techniques in the book. I focused on finding ways to give people GENUINE COMPLIMENTS. In order to do this, I had to constantly be on the lookout for things that I liked in other people.

I started doing it. I don't think the nickel thing lasted more than a few weeks, because the immediate results were far more beneficial. Within a matter of months, I'd been elected to represent my class on a royal court and was eventually chosen as Student Body President.

Now, granted, this began with somewhat questionable motives. But I doubt that my mom did it because she wanted me to be "popular." She did it because she knew it would teach me an incredible life lesson. And it did. I learned a TON about what makes people tick. What began as a solution for self-centered teen angst became a set of life skills that have served me ever since, even helping me to become more altruistic.

As an adult, I've turned to the book again to help several students, including my own children. Lately, I've begun reading sections of it aloud to one of my children who sometimes struggles in social situations. After each chapter, he makes a poster to summarize the big ideas. I can tell the lessons are sticking as he has started to apply the knowledge to daily life situations.

I hope to someday see the book rewritten for kids. But until then, filtered and condensed, it can still serve as an amazing resource for kids who struggle to make and keep friends. Try it. I bet ya a nickel that it'll work! :)

Math Vocabulary Fun (free new resource!)

This morning, one of my math students reflected on a comment heard at home. "My mom doesn't get why we say 'product' instead of just saying 'the answer.'"

This led to a fabulous conversation in which students explained how specific vocabulary leads you to understand what operation is being performed. They listed and defined vocabulary for different "answers":

• Sum
• Difference
• Product
• Quotient

Math Vocabulary Cards
I then introduced a free new app (also available as an online tool) that provides ample opportunity to explore mathematical vocabulary. Each Math Vocabulary Card includes:

1. the word
2. the definition
3. a visual

Any of these components can be hidden. This morning I chose a smattering of vocabulary that complemented our discussion (sum, difference, etc.) and also included some concepts that we've been recently studying. I set the program to flip through that limited set of cards and covered the upper left section, masking the vocabulary word. So, for example, I showed them this card:

After most of them had a word in mind, I revealed the answer:

I sent the link home in an email, encouraging students to use the vocabulary cards at home with their parents. I suggested they mask different portions of the screen; they loved the idea of quizzing their parents!

The vocab cards include sets for grades K-2 or 3-5 and can be explored by specific math category. One click takes you from English to Spanish definitions/vocabulary.

This free app (also available as an online resource) from The Math Learning Center can be accessed at Math Vocabulary Cards.

Celebrate Poetry Month: April (Ideas Galore!!)

As an English major, I often found poetry a bit dry. In many of my classes--Brit Lit, American Lit, International Lit, etc--we analyzed each stanza, line and verse. It was intense. After the methodical analysis, on the rare occasion I was asked to actually write poetry, I felt intimidated.

It was only after I began teaching that I learned to love poetry. Why?

• At its heart, poetry is about playing...with words. 
• Students who are overwhelmed by longer pieces of writing may find it easier to tackle a short poem. 
• Poetry encourages creativity.
• Poetry can match any mood. Humorous poems quickly capture student interest.
• Poetry can enhance any subject. How? Here are some ideas...

Poetry and Math

While it might seem like an unusual combination, poetry can add a fun twist to math. We've written word equations using Amy Krouse Rosenthal's 2011 book, This Plus That: Life's Little Equations. The related blog entry includes a free handout to get students started on their own life equations.

Poems can describe mathematical concepts, like temperature, described in this blog post.

Books like  One, Two, Skip a Few! capture more math ideas in rhyme form. (See this blog post.) These poems can be enjoyed by young children or used as models for writing with older students.

More mathematical models for poetry are located in the book Mathematickles, and discussed here. And don't miss this multitude of resources for combining math and poetry.

Poetry and Drama 
Kids love to act. You can provide opportunities by acting out poems...especially those with humor. (Think Shel Silverstein.) My students enjoyed dramatizing "Smart" from Where the Sidewalk Ends.

Poetry and Art

Diamante poems are a perfect match for the 3-D art activity pictured at left. Spring and Mother's Day are great topics, but they can also be used for other seasons and holidays: fall, Christmas, winter, Valentine's Day, Easter, etc.

But my all-time favorite poetry lesson (pictured right) is one in which students use their 5-senses to write descriptive poetry, that they then mount on tissue painting backgrounds. 

Still stumped for poetry ideas? My friend Sherri at By Degrees has more fabulous ideas to make poetry come alive. (She sat by me during all those poetry analysis sessions in college. The woman knows her stuff!) ;)

How are you celebrating poetry this month? Comment below. ;)