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Modeling Multiplication and Division with Watermelon Plates

I live for classroom hacks! I enjoy discovering new ways to deliver math instruction. Recently, I found a fantastic package of watermelon plates at Wal-mart. I was attracted to the seeds in the middle of each plate. The seeds are great for counting in primary grades, but kids can also use them for lessons highlighting the importance of multiplying and dividing.

Items Needed:

Watermelon plates
Counting Cards
Sharpies
Paper or Journal
Pencil

The Hook:

How can watermelons help us learn about multiplication and division?

After passing out plates to students, tell them you need to know how many seeds are "in the watermelons." Next, ask students "How can we find the total number of seeds?" Students can answer this question in journals or discuss possible responses with partners, small groups, or in a whole group format. Based on responses, extend the conversation by asking them to choose the fastest method.

Watermelon Work:

Distribute "counting cards." The cards should indicate the number of seeds students should group together. For example: "Circle groups of 3 seeds." Another option is the "A, B, C, D, E." Assign students groups based on the letter they call in a whole group format,

Recommended groupings: two seeds through seven seeds.

Student asked to group seeds by five.

After students group seeds, ask them how the groupings can help them count faster. Students should be able to respond that they can count the number of groups and multiply by the number of seeds in each group. There may be seeds left over. Students can add the remaining seeds to the product. Make sure students write the multiplication expressions in their journals or worksheets. Extend this part of the lesson by allowing students to discuss how and why different groupings resulted in various multiplication expressions.

Wide Divide:

After students determine the number of watermelon seeds on each plate, discuss how the groupings also represent the inverse of multiplication (division). First, ask students how the groupings model division. Seek input and responses from students. The goal: students realize that the total number of seeds divided by the number of seeds in each group results in the quotient (the number of groupings created with a possible remainder).

Beyond the Plates:

Watermelon is healthy, nutritious, and TASTY! If possible, offer watermelon cubes or slices to bring a little bit of the "real-world" into this delicious summer math lesson.

Happy Hacking!

Error Analysis in Mathematics

It will happen. Students will make mistakes when solving math inquiries. In the past, these errors were met with red ink and low grades, leaving generations of students feeling as if math was a bottomless pit they could never escape. Now, errors can serve as learning opportunities students can use to master mathematical concepts.

Why error analysis?

Error analysis is the process of reviewing solutions to math inquiries, identifying mistakes, explaining why they were made, and making corrections. For example, if a student completes 20 problems focused on multiplying rational numbers, and two of the answers are incorrect, did the student make calculation errors or does the student have an issue understanding the proper algorithm? Would your response change if the student answers 15 out of 20 incorrectly? 

While it is important for educators to understand the types of mistakes students make, there is a crucial element missing. Students also need to learn how to identify and correct mistakes. The most effective types of error analyses focus on 5 common mathematical errors: conceptual, operations, reading comprehension, procedural, and silly (EA CORPS).

Conceptual errors

Conceptual errors arise from the failure to recognize, understand, or connect math ideas and principles. Indicators of conceptual errors include errors based on definitions of math concepts or repeated procedural or calculation errors. A student who identifies a four-sided curved figure as a quadrilateral may not recognize that quadrilaterals are formed by four straight line segments. Conceptual errors are the hardest to address and require planning and consistent practice to overcome. 

Operations errors

Operations errors - also called calculation errors - can be a major roadblock to students trying to master mathematics. Addition, subtraction, multiplication, and division are at the core of the subject, and mistakes here can cause major frustrations. Many times, operations errors are minor, and students can prevent them by checking their work and taking additional time when solving problems. Repeated operations errors may indicate issues with conceptual or procedural understanding.

Reading comprehension errors

Some would argue that math has become "reading comprehension with numbers." Indeed, mathematics is a language. Therefore, it should come as no surprise that reading comprehension is a major issue in error analysis. This type of error occurs when a student misreads or misunderstands the text. It can stem from a lack of focus, rushing, or the inability to analyze text. Students understand the basic concept and apply correct procedures. There are also no calculation errors. Review the example below:

There are 5 cars and 3 trucks in the parking lot. Write the ratio of trucks to cars in three different ways.  

Jon's response: 5 to 3, 5 : 3, and 5 / 3 

Jon's response shows that he understands the concepts of ratios and how to write them. Jon's mistake stems from failing to order the objects being compared based on the prompt. Students can avoid reading comprehension pitfalls by highlight key words, close reading, using context clues, and using graphic organizers. 

Procedural errors

Procedural errors are mistakes in processes when solving math problems. Errors include incorrect operations, incorrect algorithms, and incorrect or missing steps. This type of error can manifest when students work with the order of operations, for example. Some students will perform multiplication before division and addition before subtraction despite the order of the operations (left to right). Procedural errors also arise when students learn "shortcuts" before understanding concepts. They rely on shortcuts and fail to develop the conceptual or procedural fluency needed to master concepts.

Silly errors

Silly errors are not really silly, but they are the easiest types of error to fix. Many silly error excuses are easy to identify:

"I ran out of time."
"I thought the answer was right."
"I changed my answer."
"I didn't pay attention."

There are two important ways students can combat silly errors: focus and confidence. Focusing on problems, one at a time, can alleviate problems caused by failing to pay attention. Practice builds confidence, which is needed when nervous guts tell students to change the answers, but clear minds know the first answer is correct.

Join the EA CORP!

We're looking for a multitude of great teachers and students who are ready to improve classroom environments by embracing mistakes and not condemning students for making them. There's nothing to sign and no phone calls to make. Just commit to using error analysis as a tool for growth in math classrooms. Want a way to get started? Download the guide students can use to analyze errors in class. It's perfect for back-to-school and useful all year round.

Click here for student error analysis guide. 


Join the conversation on Twitter using #eaCORP.

Further reading:

Simple Activities can Help Reveal Students' Issues with Math Concepts

Is Reading Comprehension the Real Problem with Math?

Test Prep Hack: Integer Activity Using Cups

It is test prep season, and teachers and students everywhere are gearing up for those BIG tests by using questions and activities. Studies have shown that using a variety of methods for test prep keep students engaged and prevent them from reaching a plateau before test day. Since the stakes are high, alleviating stress and anxiety by incorporating games in a test prep environment is important.

Of course, games are fun, and saving money creating those games makes it even more fun. What if you could use 6 cups and 1 permanent marker to create an engaging lesson? What if I told you it is possible? (*Are you smiling yet?)

Cups Full of Integers

Cups Full of Integers is an activity I created to provide a challenge for students learning about comparing and ordering integers. It is simple to create. Basically, you stack 5 cups and then write integers in order the cups. You can choose greatest to least or least to greatest. Use the sixth cup as a guide to make sure your numbers are aligned.

Once you separate the cups, you have created a puzzler that, at first glance, seems simple to solve. Trust me, it is not as easy as it looks to order the cups correctly if you choose a good set of integers. Cups Full of Integers can be used as a station activity for test prep review. Consider making more than one set for the stations so that students can work together to solve the puzzler. Remind them to separate the cups and shuffle them so that the next group of students will have the same experience with the challenge.

This is a great activity for less than 50 cents!!!

If you are pressed for time, I created a version of the activity with a set of numbers to use and recording sheets. Click on the image for details.

Only Mice Like Useless Socks: The Power of Mnemonics

It's no secret that mnemonics can help people remember steps and processes in mathematics and other subjects. Many people have heard (and used) the mnemonics for the order of operations: PEMDAS and Please Excuse My Dear Aunt Sally. I've personally witnessed the power of mnemonics and their usefulness. They help make learning "sticky" and help calm students during testing situations.

Have your students had trouble with interquartile range? The concept was added to our sixth grade standards last year. Interquartile range is quite different from the simplicity of dot plots and bar graphs. It requires students to find the median of a set of data, the median of the lower half of the data, and the median of the upper half of the data. When I first introduced the concept to students, they had that classic "what?" look. I had to think of a way to help students remember how to find interquartile range.

I listed the steps for finding interquartile range, and the idea of mice and socks formed in my mind. A short time later, I wrote down the mnemonic "Only Mice Like Useless Socks."

Order the data from least to greatest
find the Median of the data
find the median of the Lower half of the data (Q1)
find the median of the Upper half of the data (Q3)
Subtract Q1 from Q3

The quirkiness of the mnemonic is perfect for middle school students. To "hook" them in, ask them how they think mice and socks can help them remember interquartile range. The responses you get will probably be hilarious, but the question and the responses add to the "stickiness" of the lesson. The mnemonic transformed a normally tricky lesson into one where students have a little fun. Maybe it will work for you as well.

Click here to download a copy of the worksheet I use to introduce interquartile range. It's available for FREE until Saturday, February 20, 2016.

Have a great week!!!

Classroom Hack: Think Outside the Box Plot

Learning is Love...and I love classroom hacks! During a recent trip to the dollar store, I picked up some great finds for Valentine's Day. I've been thinking about how to help students better understand box plots and interquartile range. I like students to explore various ways to make learning "sticky." Once I found a bag of foam heart-shaped stickers, I hoped I could create an activity that would make box plots sticky for students.

I always like to start off with a crazy question. For this lesson, I may ask students, "How can hearts help us learn about box plots?" At first glance, there is no obvious answer (one student did mention that we could display the data for heartbeats:. ;-)

100 Hearts for $1. What a deal!

For this activity, I used box plot task cards with various scenarios. They vary in difficulty, which allows for differentiation. In addition to task cards, students need 5 foam heart-shaped stickers, a sharpie or pen, and their interactive notebooks or pieces of paper for their box plot full of hearts. For an added touch, I used red yarn for the whiskers.

Students will use the task cards to determine the median, first and third quartiles, and the upper and lower extremes. They will create a number line with the appropriate scale and intervals. Next, they will write the labels of the five summaries on the hearts. Now, they can construct their box plot using the stickers and the string.

What's great about this activity is that it's quick and simple. Plus, kids will have a little bit of fun while learning about or review box plots. Win-win for $1 plus tax. We can all love that!!!

Learning to Love Hacks: Groundhog Day

I'm celebrating "Learning is Love" this week with my fellow Texas teachers Lauren of Leaf and STEM Learning and Randi of Teaching in an Organized Mess. We want to share why we love learning, and we hope our love will bring inspiration to educators as we close out January 2016.

Click Here to get this Groundhog Day Freebie on TPT!

If you have followed my blog long enough, you know that I'm addicted to shopping at dollar stores and finding materials that can spark a love of learning in students. My recent trip was no different; I found some plates and tape. I just had to find a groundhog. And I knew I couldn't dig for it. Instead, I found a wonderful set of groundhog images from Educlips on TPT.

My mission (and the mission of my students) is to create a sundial and take it outside to see if the groundhog can see its shadow. It's a great activity for elementary grades, but middle school students can benefit from it as well.

What shape is it?

First, students should cut the groundhog to size. I ask students to identify the shape of the cutout. Most students will immediately answer triangle. Prepare to ask them again, but tell them you want to know the shape of the entire cutout.

Hint: It's a trapezoid. :-)

Find the area

Yep, break out those rulers. Once students identify the shape of the cutout, they'll need to find its area. What looks like a print out, a plate, and some tape is turning into a nice, engaging lesson. To facilitate this part of the lesson, students round measurements to the nearest half-inch (or half-centimeter).

Fold it up

After students find the area, I ask them to fold the shape along the dotted line. Now, there are two shapes. Students must identify them and find the area of those two shapes. Next, they'll reflect on the area of the first shape and the area of the two shapes.

Finally, the sundial

Never one to lose out on a chance to review, I'll ask students to identify the shape of the plate before marking the center. Students should place the plate face down. If you are working on circumference and area of circles in your classes, its a great time for students to review those concepts.

• After marking the center of the plate, students should write the numbers for their "clock" around the perimeter of the plate.
• Students can attach the groundhog to the center of the plate using tape. The groundhog should line up with the 12 and the 6.
• Take the plates outside (or to a well-lit room). Will the groundhog see its shadow?
• If you have an outside area or room that receives sunlight for an extended period of time, set of the groundhog sundial and observe how the shadow changes over time.

The plate before attaching groundhog

Hopefully, you can use this quick and fun activity in your classroom this Tuesday. If you're looking for other blogs in our Learning to Love series, please check out Lauren's blog or Randi's blog.

Want to win a $25 TPT gift card? Click here to find out how!!!

What FREEBIES: Click here!

Tell the world what you love about learning on Twitter: #learningislove

TPT "Learning is Love" Crave - Win a $25 Gift Card

Learning is Love. Teaching is Heart. If you're like me, you love to teach, but sometimes the budget we need to instill a love of learning in our students is tight. Three Texas Teachers have joined together to help lighten the budget burden with a chance to win a TPT Gift Card!
Click Here for Your Chance to Win!

A Tale of Two Homeworks

"It was the best of times; it was the worst of times." That classic line from Charles Dickens' A Tale of Two Cities pretty much sums up my feelings about homework. I believe that students need to complete work outside of the classroom to prepare for the rigors of college and professional work life, but there are times when the homework return rate is abysmal. I've often asked myself: "What's the point of assigning homework when only a small percentage of students turn it in?" I've personally witnessed kids copying a classmate's work right before class or scribbling as hard as they can to get a little credit. I've been given every excuse (from kids and parents) and have tried almost trick in my toolbox. Some teachers at my school have given up on homework for this very reason. It's definitely the "worst of times."

I've taken some time to review my homework success rates. There are several approaches I take that has led to more success.

Get 'Em Moving at Home

We have all used them...that worksheet with column after column of problems. I can totally understand how this type of homework can lead to extreme boredom at home. I think kids benefit when they can use concepts we learn during class to explore the real world of math. For example, for part of our geometry unit, students learn about the volume of rectangular prisms. I do have a traditional homework sheet available, but I also give students the opportunity to explore volume at home by measuring a household object and finding the volume. Guess which one the students prefer?

Traditional Homework

Get 'Em Moving Homework

I've found that students are more engaged when they can interact with their homework and make it personal. They are still learning about the volume of rectangular prisms, but in a way that can help them better retain the fundamentals of this important math concept.

Flip the Script

Flipping the classroom has definitely helped students complete work outside of the classroom. I started posting videos on my online classroom (I use Quia, but your district may have Schoology, Edmodo, or Moodle). Instead of doing math problems at home, students work on note-taking skills. I have two particular formats we use for notes. We then focus on math problems during class. Some days, I give students who don't watch the videos at home the opportunity to complete them during class while other students are working in groups.

Nothing New, Home for Review

In the past, the homework I assigned focused on the topic we covered in class that day. I realized that one of the reasons students didn't complete the work is because they were stuck on a problem and gave up or decided to wait and ask me how to approach the problem during the next class period. To address this issue, I started assigning spiral review homework. It focuses on topics we've already covered with varying degrees of difficulty. I saw homework completion rates increase with this approach.

Ten or Less is Best

I've taken some heat for this approach. Generally, I assign ten or fewer problems for homework. There are times it increases to 15 or so, but not very often. I've found that if students "get it," ten problems helps them get the review or reinforcement they need to be successful in my math classes. If they get ten problems wrong, they're going to get 20 problems wrong. There is no need to have them complete problem after problem if I need to work with them to make sure they understand a particular math concept.

Paperless Homework

Google forms and Quia have definitely helped me save a ton of paper! I post the problems online and students submit it. Simple, yet effective. It has the added benefit of allowing me to see when students are completing their homework. What I love most about paperless homework is that it allows me to give students the opportunity to fix problems before they submit it for a final grade. I often ask them, "Why not go for 100% mastery?"

Variety is the Spice of Life

Instead of assigning one type of homework all the time, I use all of these approaches to "keep it fresh." I'm also researching more ways to get students to enhance their learning outside of the classroom. Do you have an innovative way to get kids to complete homework? I'd love to read about your tips and tricks.

My challenge to you this week: try a different approach to homework and see if it makes a difference.

What's the Connection between Fashion and Math?

I love asking my students questions such as the one in the title. The answer can be found on a wonderful website called Get the Math. Don't just get the math - grab it! Once you start using the materials from this wonderful website, you will understand why it is one of my favorites. Oh, maybe you're wondering where the link is to the awesome goodness that is Get the Math...

Get the Math

Get the Math offers excellent representations of using math in the real world. As a true fan of Project Runway, the lesson with Chloe Dao - who won season two - is one of my go to lessons from this website. Her lesson focuses on how fashion designers use math to design clothing for different sizes. It starts with an introductory video about Dao and ends with a challenge. Students have to calculate the costs of manufacturing a design that will have a 220% markup. To plan for this lesson, I picked up a few inexpensive t-shirts from a discount retailer. I rearranged the desks so students could work in groups to complete the challenge. The kids had a lot of fun and learned at the same time.

To extend the lesson, students could design their own simple t-shirts and set a price for them. They would have to research the cost of the t-shirt as well the cost for printing images or adding embellishments. Their mark-up would have to be a certain percentage. In my classes, they would meet in small groups with their finished products. Each group would present one t-shirt to display and explain why they chose it.

I love Get the Math because it offers real-world math connections along with inspiration for project-based learning. This is a win-win in my view. The diversity of the lessons gives teachers the opportunity to reach the interest levels of all students. Hopefully, you'll find it useful as well.

Classroom Hack: Student-made Rational Number Cubes

If you're like me, you love using number cubes and dice in the classroom. They are versatile tools perfect for a variety of math games and enrichment. There are times when I find the number cubes limiting because the cubes that include fractions and decimals are basic. They include unit fractions and decimals to the tenths place. I've been searching everywhere for cubes with different types of rational numbers. My search ended with a trip to my favorite dollar store!

There, I found packages of blank foam counting blocks. Each package contains 50 blocks. The price - $1.00. I grabbed a couple of packages for my classes and rejoiced in the knowledge that I would soon have the best number cubes ever!





First, I separated the number cubes and placed sets of them in small cups. The cubes come in colors of red, blue, green, and orange.



Although students normally carry Sharpies, I also placed them on the desks for each group. I gave the students simple instructions:

(1) Make a list of 6 rational numbers in your spirals. The rational numbers must include at least two negative numbers, 1 integer, 1 decimal, 1 fraction, and 1 percent.

(2) Review your numbers with your group members to make sure none of you have the same rational numbers. Make modifications if necessary.

(3) Select one number cube and one Sharpie (fine point). Write your numbers on the six sides of the number cube.



Within two days, I had 150 number cubes with a wide variety of rational numbers. Not only did my students practice the important skill of generating rational numbers, but there was also 100% engagement! So, how do we use the number cubes?

• Comparing rational numbers: roll two cubes and compare
• Ordering rational numbers: roll four cubes and order the numbers from least to greatest or greatest to least
• Rational number operations
• Graphing rational numbers on number lines

You can't go wrong with this classroom hack. And, you can't beat 50 number cubes for $1.00 (*okay, full disclosure. I purchased 4 packages and spent $4.00...plus tax ;-).