Spontaneity Brings Math to Life!

By Nyla Phillips-Martin, Guest Blogger

Last week, while in the midst of teaching a lesson on cuboids, I quickly realised that I had to do something drastic to get the attention of my most easily distracted student. I mean, there I was feeling all proud of myself for having everything I needed, I had my examples and non-examples for the students to handle, observe and compare attributes. My classroom was buzzing with excitement; hands were fervently flying up during Q & A time as I selected students to answer questions.

But the hand that I was looking for at the front corner of the class never went up. Justin (let’s call him Justin) just sat there looking away from me, tapping his ruler on the desk. Then he poked another student with his pencil. Now, it is not uncommon for him to be like this because he sometimes gets into trouble in order to avoid class work. What I needed to do was to get his attention without halting the momentum that the other students were having. At that moment, an idea popped into my head.

I walked out of the room, spun around and returned with a silly grin and a cuboid net in my hand. I didn't say a word. I just slowly folded the net into a talking cuboid (like a puppet). Think of a box with the top lid open – that flap became the puppet’s mouth. Anyway, I used the silliest voice I could muster and made the puppet talk.

He introduced himself as Corey the Cuboid and went on to talk about his other siblings and the fact that he feels like the odd one out because he cannot roll like the cylinder or sphere and he’s not as cute as his brother the cube. My fourth grade students were wide eyed and everybody was paying attention – not to me the teacher, but to the cuboid on show.

They all wanted to have their turn with handling Corey the Cuboid and making him talk (including Justin). In fact, they had so much fun making him talk that I videotaped one of my students as she brought Corey to life!

I really enjoyed that cuboid net lesson and it taught me that even with a lot of planning, a touch of spontaneity keeps things interesting. The lesson gave me an idea for their math project – to have them put on their own puppet show featuring different talking 3D Shapes.

If you like the idea of having students create puppets from 3D shapes, feel free to use the patterns from this free assortment of 3D shape nets that I created to save yourself some time! And don’t forget to flip out and be just a tad spontaneous!

Nyla Phillips-Martin, is a young wife, mother, and teacher in the Caribbean. She has a B. Ed Degree in Primary Education and is in her seventh year of teaching. She hopes to show other teachers in her country the power of using technology for use in records, planning and especially in the classroom. To her, education is all about fostering creativity and facilitating hands-on learning. Visit Nyla's blog, Nyla's Crafty Teaching, for more engaging lesson ideas!

Winning a Million - Math Lessons and More!

What would you do if you won a million dollars? The NC Education Lottery offers winners a choice between the entire amount paid over 20 years, or a lump sum payout of a smaller amount. What are the implications of each choice?

Today I saw a news article about a local man, James Anderson, who won $1 million in the Holiday Millions lottery game. One part of the story in particular really captured my interest:

"Top prize winners in the Holiday Millions game have the option of claiming their prize as a 20-year annuity or a lump sum. Anderson chose the $600,000 lump sum, which left him with $408,006 after taxes."

When I read this part of the article, my teacher brain went into overdrive! Do you realize that by accepting $600,000, Mr. Anderson gave up $400,000 of his payout just so he could get the money now instead of spreading it over 20 years? Furthermore, the government took such a big chunk that he now has less than half of that million dollars.

Million Dollar Lottery Lessons
As I read this, I immediately saw all kinds of possibilities for lessons about winning a million dollars. There are loads of obvious math lesson ideas, but I can also think of many literacy lessons as well. Here are a few quick thoughts about where you could go with this topic. Please share your ideas, too!

• Read informational text.  Begin by having students read the article. You can find the article online here on the Fayetteville Observer website.  Then ask them to complete a "What's the Scoop?" graphic organizer to uncover the important facts and details in the news story. You could also use the Current Event Report form in my Social Studies file cabinet to have students write a summary of the important information. 
• Analyze the math involved in Mr. Anderson's decision. What exactly did it mean in financial terms to take $600,000 now instead of a million paid over 20 years? I called the lottery hotline to make sure I understood how the 20-year annuity worked, and it's basically an option for taking out 1/20th of the money each year for 20 years. So how much money did Mr. Anderson give up? If you received a million dollars in annual payments over 20 years, how much would you get each year? What would that be on a monthly basis? What is the average salary in America? Would you be rich, living comfortably, or just getting by?  
• Debate the pros and cons of the two payout options. Even though he gave up $400,000 to take out the immediate lump sum of $600,000, it might actually not be such a bad deal if he invests the money wisely. Disregard taxes because taxes will have to be paid on the money either way, and consider what would happen if he invested the full $600,000. What interest rate would be needed to make that money grow to $1 million in 20 years? As a side note, the person I spoke with on the lottery hotline said that the last 5 jackpot winners all took the lump sum payout. I'm assuming they contacted a financial adviser before making that decision, so it may be that taking the lump sum is a better option. But what if you took the money and just spent it? Would you be able to invest it?
• Explore probability - Discuss the probability of winning money in the Holiday Millions game. You can read more about this particular game on the Holiday Millions page of the NC Education Lottery website. Players can win different amounts; what is the probability of winning each amount? (Click here to download a chart showing the approximate odds of winning.)
  
  
  
  A lottery ticket costs $20. Look at the odds of winning a million dollars. What if you bought a ticket every day for a year? How much would you spend? How much would you improve your chances of winning?  
• Research possible purchases. What can you buy with $408,000 (the amount after taxes)? Research the cost of a home in your area, the cost of a new car, a dream vacation, etc. 

• Discuss the concept of a million. Read the book How Much is a Million or If You Made a Million written by David Schwartz and illustrated by Steven Kellogg. Use the ideas in these books as a springboard for discussing just how big a million really is. 
• Discuss impact of winning a $1 million. How would your life change? Are people with more money happier? What problems might be caused by winning a lot of money? Would people treat you differently? (I've heard that many people who win large sums of money end up broke and unhappy in a few years. It would be interesting to research the facts on this and discuss your findings with your students.)
• Write an expository paragraph or paper - What would you do if you won a $1 million and had a choice between taking a lump sum of $600,000 or the whole amount over 20 years? How might your life change based on your decision?

These are just a few lesson ideas that came to mind as I thought about the implications of winning $1 million dollars. How would you teach a million dollar lottery lesson? I think we can agree that this topic is a goldmine of rich learning opportunities, no pun intended!

Weathering, Erosion, or Deposition? Sorting Out the Processes

Science is one of my favorite subjects, and I've always been interested in geology and landforms. I remember hiking through the White Mountains of New Hampshire as a child, listening to my father explain the geology of the area. He showed me evidence of glaciers that once covered the area, interesting caves and rock formations, and fossils of sea animals that somehow ended up high in the mountains! I still enjoy hiking and other outdoor activities, and I often wonder how certain features of the earth were formed.

I guess those early experiences are why I enjoy teaching students about landforms of the Earth. Hands-on activities and opportunities to explore nature are especially important in this area of study. One of my favorite projects is to have students work in teams to create islands from salt dough, and each island has to include specific landforms. When students share about their islands with the class, they have to explain how those landforms might have been formed. We read books about weathering, erosion, and deposition, and even take walks outside to observe evidence of these three processes in nature. I show photos of pictures I have taken myself and other pictures I've found on the internet to explain how weathering, erosion, and deposition shaped Earth's surface.

Sorting Out the Processes (and a Freebie!)
Yet even with all of those activities, my students still had trouble remembering the difference between weathering, erosion, and deposition. These concepts are very confusing. To help them practice, I created a sorting activity with examples that students could read and classify into one of the three categories.

They worked in teams because having time to discuss and debate the placement of the cards was really helpful as they grappled with the concepts. When they discussed a card, they had to talk over the action taking place and decide if it was most likely weathering, erosion, or deposition. They took turns so all students had the opportunity to participate equally.

If you'd like to use this sorting activity with your students, you can download it for free from my TeachersPayTeachers store.

Illustrated Task Cards and Self-Grading Google Quizzes
If you believe that a picture is worth 1000 words, you'll love my resource for teaching this topic. Weathering, Erosion, and Deposition Task Cards and Google Quizzes includes 24 printable task cards in both black & white and color, as well as 24 task card images that can be used with the free Plickers program or with Google Classroom. You can even use the images to create digital decks of task cards for cooperative learning activities like Showdown! Weathering, Erosion, and Deposition also includes two self-grading Google quizzes that can be assigned with Google Classroom or administered as online formative assessments. 

The illustrations on these Weathering, Erosion, and Deposition task cards are what make them really unique. Most of drawings were created by my daughter Wendy Candler of Digital Classroom Clipart on TpT, and I love the simplicity of her artwork. Somehow Wendy was able to capture the essence of how weathering, erosion, or deposition contributed to each situation being depicted without adding unnecessary details.

I hope these activities and resources help your students develop a deeper understanding of the difference between weathering, erosion, and deposition.

Common Core Math Problem Solving

I'm a big believer in the importance of daily math problem solving. It's far more effective to integrate problem solving into other instruction than it is to teach problem solving in isolation. For years, I struggled with how to include problem solving lessons in my regular math instruction, and I finally developed an easy plan that takes just ten or fifteen minutes a day. This was the start of my Daily Math Puzzler program, a series of four ebooks with problems on different instructional levels. Recently, several people have asked me if my Daily Math Puzzler program is aligned with the Common Core. The answer is not as simple as it might seem because of the design of the Common Core Math Standards.

Two Types of Math Standards
The Math Standards are divided into two major categories. The mathematical practice standards describe the "how" and the content standards describe the "what" in math instruction. Much attention has been given to the content standards, but it's easy to overlook those all-important mathematical practices. Yet those practices are at the heart of good mathematics instruction. Because it's easy to forget about the practices, I created this Standards for Mathematical Practices chart to use as a checklist to be sure that you are addressing these important areas throughout the week. Print it out and keep it in your lesson plan book. As you plan each math lesson, review the eight Standards for Mathematical Practice to determine which standards you can incorporate into each lesson.

Daily Math Puzzler Program and the Common Core
Each book in the Daily Math Puzzler program includes a variety of word problems integrating different content areas across the various mathematical domains. Because these books are not specific to a particular grade level, it would be impossible to align them with the Common Core Math Content Standards. When students solve problems, they need to integrate content from previous grade levels, so it wouldn't really make sense to align the books with one grade.

However, the entire Daily Math Puzzler program IS compatible with the Standards for Mathematical Practice, the "how" of mathematics instruction. These eight standards can only be addressed by having students solve math problems on a regular basis, use mathematical tools, and discuss their thinking and reasoning with others. If you download the Standards for Mathematical Practices chart above, you'll see that they range from "Making sense of problems and persevering in solving them," to "Look for and express regularity in repeated reasoning." All eight practices can be integrated into math instruction when you have a daily problem solving program in place.

All four of the Daily Math Puzzler books are included in my Math Problem Solving Bundle, along with Math Mindset Challenges and a Math Problem Solving Webinar. Click here to preview the entire bundle on TpT.

Problem Solving Assessment Freebie

Before you begin a problem solving program, it's a good idea to assess your students to determine how they solve problems. You'll find this free Problem Solving Assessment packet to be really helpful because each page of the assessment requires students to show their work. You can also require students to explain their answers in writing if you want to gain a more complete understanding of their thought processes. You can download this freebie when you sign up for my Candler's Classroom Connections newsletter. Just follow the links in the welcome message to a page called Laura's Best Freebies.

The Common Core State Standards have definitely raised the bar for all students in mathematics. Incorporating math problems into your instruction on a daily basis is one of the best way to ensure success with the new standards.