Saturday, May 24, 2014

Parallel & Perpendicular Art

When I noticed that quite a few of my students were confused by the terms "parallel" and "perpendicular," I decided it was time for an end-of-year art activity. I visited my Math - Art Pinterest page and discovered a sweet little project at Math Activities*. Students worked on this during free moments at home and at school.

*You'll notice that we purposely did the lesson a bit different than originally described.

I love the way this turned out. And, yes...they now can tell me what parallel and perpendicular are! ;)

Monday, May 19, 2014

Fraction Arrays: What Do You Notice?

Students made a series of arrays demonstrating fraction multiplication. As a group, they studied the arrays and put them in sequential order by area. This activity alone provided incredible growth opportunity as students discovered mistakes (hey...why is that array bigger than the one next to it but the product is smaller?) and had to occasionally reformulate so that the pattern made sense.

In a subsequent discussion, we shared more observations and looked for additional patterns. We considered similarities and differences in:
  • fraction x fraction multiplication
  • fraction x whole number multiplication
  • whole number x whole number multiplication
Afterwards, students wrote reflections. I posted a sample with our display. I'm so impressed by their insights and understandings. (Click on individual photos for magnification to read student comments.)

Lesson Credit: Bridges in Mathematics, Second Edition, grade 5

Left side.

Tuesday, May 13, 2014

Number Frames App is Here (Free!)

The Math Learning Center just released another free math app: Number Frames. It's currently available on iTunes and will soon be released in an online version. Can't wait to use this one! Enjoy. :)

Tuesday, May 6, 2014

TPT Sale May 6-7 - extended!

Update: the sale has been extended to the 8th on TPT. Enjoy!

In honor of Teacher Appreciation Week, the sale begins on Tuesday with all of my products offered at reduced prices. Add the TPT promo code for even deeper discounts. Here are a few suggestions for end-of-the-year fun:

Design a Cube City - Students use isometric dot paper to draw 3-D buildings and design their own cube cities.
Poetry & 3-D Art for Every Season - write diamante poems--reviewing nouns, verbs, and adjectives--and create 3-D art displays to brighten any season or holiday.

Skittle Fractions, Estimation & Graphing

Vacation Workstation

Descriptive Poetry & Tissue Painting

Thursday, April 24, 2014

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!

Tuesday, April 22, 2014

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

Friday, April 18, 2014

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.

Tuesday, April 15, 2014

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

    Friday, April 11, 2014

    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

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