Tag Archives: math




And so did King Henry.

And so did King Henry.


King Henry Died Drinking Chocolate Milk by Matthew S. Ray

One upon a time, in the country of Metricland,



Only chocolate milk ever appealed to him.








Sitting on his nightstand with a plate of cookies to eat.

He’d gobble them down, then swallow the drink,

Then get up and walk down to the bathroom sink.



Chocolate milk a-flowing from a chocolate milky sea.

After brushing his teeth, he’d start on his path,

To his chocolate bath tub for his chocolate milk bath.


While bathing in chocolate, Henry would sit with a straw

Drinking up the bath milk and the filth that he saw.





Lying dead in the bath tub was the king of Metricland.

Never again would he wear his robe made of silk:

King Henry Died Drinking Chocolate Milk.

Creative Commons License

Fraction Fun: Two Ways to Introduce Fractions

I introduced one of my favorite math topics, fractions, to my third graders last week. To do so, I drew on the experience of an assistant principal and our math coach. The pivotal point is that students understand that fractions are equal parts of one whole, so I really tried to stress that during the lesson. Maybe you’ll try these with your own class!

Pizza Pie Fractions

Using magnetic fraction circles, I told my class a story about dinner last week when I was so hungry that I decided to order a whole pizza for myself. When my sister arrived to bring me something, she saw the pizza, and being hungry herself, asked to have some. I gave her one slice, but she said, “That’s not fair! I want the same amount that you’re eating!” So we decided to split the pizza in half and we both got two equal pieces. Right as we were about to take the first bite, her husband called her, saying he was starving. She told him we were having pizza and he should come join us. I tried to give him one slice, too, but he also complained that everyone should get the same amount, so we cut the pie into three equal pieces.

You get the picture? This continued to fourths, fifths, sixths, and tenths. I made it funny by saying things like, “Just as I was pouring the garlic on my pizza, the bell rang again!” as well as, “At this point, I was wondering if I should just order another pizza,” and “I only had six seats at my table!” They loved the story and the visuals helped support their understanding that a fraction is an equal part of a whole.

Pizza pie fractions - hold the anchovies, double the fun and understanding.

Homemade Fraction Bars

The next part of the lesson involved students creating their own fraction bars. Each student received eight strips of brightly colored paper and followed my directions on how to create fraction bars.

The folds for thirds, fifths, sixths, and tenths were extremely difficult for the students, so I would advise having extra paper on hand!

At any rate, each time they opened their freshly folded paper, students were able to count the number of sections and therefore easily identify the fraction they created. These strips will be invaluable when we begin to study equivalent fractions!

Fraction bars - made for the students by the students.

On a side note, during the lesson, in order to help students realize that fractions didn’t just come in circles or rectangles, I encouraged students to discuss other things that were or could be made into fractions. One girl noticed her glasses could be divided into thirds (the lenses being one-third, and each arm being a third.) One student bent his arm to indicate a half (roughly). And one student mentioned that an orange could be divided into fractions. Conveniently enough, I had one in my bag, so we fractionalized and everyone enjoyed one-sixteenth.

Differentiation: Not as Bad as You Think (Trust Me)

I think a lot of people who don’t fully understand differentiated instruction mistakenly believe that a good differentiated lesson has to involve menus, six different groups doing six different things, integration of every one of Gardner’s multiple intelligences, and 12 different ways to demonstrate understanding. Or they believe that differentiation a lesson means teaching every student the same lesson and then flying around the classroom and reteaching or enriching for each group. Because differentiation is misunderstood, it gets a bad rap.

In truth, differentiation often is many of those things all in one lesson. It can be overwhelming to think about planning lessons like that for every subject every day. Yes, it is a lot of work, but, the more I hone my ability to differentiate, the more I see my students investing in the work and the less I see them becoming frustrated.

So today, I will share a very successful, highly differentiated math lesson I taught this week that had every student engaged at their own level and also incorporated a variety of concepts and modalities. I do this in the hope that it helps others better understand differentiation and see the benefits of it and perhaps provides a springboard for others’ pedagogical growth.

We are working on multiplication in my class. We kicked off the lesson by reviewing the facts for 0 and 1. We started without referring to the charts on which we had written them the day before, but of course, some kids felt more comfortable reading the facts when I called on them, so I allowed them that option. Also, even though one of my students knows many of his multiplication facts (and certainly 0 and 1), I included him in this part of the lesson because it gave him an opportunity to work on the commutative property, which is a new concept to him.

From reviewing those facts (an assessment to see who understands the concepts, by the way), we moved into arrays. It was not the first time we ever talked about arrays, but since students had never really made their own, I knew I wanted to spend the majority of our math block focusing on them and gaining a better understanding.

The essence of arrays is that they are organized sets of equal rows and equal columns. Being that my students are all ELLs, over 90 % were unfamiliar with the words “row” and “column”. So, to introduce those crucial concepts, I first drew an array. Then I boxed out a row and introduced the word. I did the same with a column. To further reinforce the concepts, every time I said the word “row,” students put their arms out horizontally. Every time I said the word “column,” they put their hands up in the sky.

With their new knowledge of these words, we watched a BrainPop Jr. video about arrays. This kept the students’ attention because it was visual, amusing, and all around entertaining. I liked the video because it really emphasized rows and columns at every turn. As we listened and watched, I paused at different spots. Often, I reinforced the physical representations of rows and columns with arms. Total physical response is huge for ELLs and students with disabilities, and because we had established a physical anchor for an important concept, my paras and I were able to consistently and constantly revisit it once we moved on to the next phase of the lesson.

After the video, each student was challenged to create an array using counters. This was the most obviously differentiated part of the lesson. Each student worked on making arrays for a different number. The number was based on their current math abilities. (Note: I use the word “current” because the expectation is that all will improve. Not using the word “current” implies students are where they are and will stay there. Back off the soapbox).

So my student who struggles the most in math worked on an array for 6. The student who knows multiplication better than others and generally is one of the better math students worked on 45. Everyone else was somewhere in between. Their work during the next 30 minutes was some of the most exciting work I’ve seen in my career. Every student was engaged and, so importantly, challenged.  The student making an array for 6 took quite some time to figure it out, but she got it. The student making an array for 45 took about 5 or 6 tries until he figured it out, but he got it. It was really exciting to witness, and the kids were truly invested.

The majority of the student work this period involved students figuring out arrays for numbers based on their math abilities.

Throughout their work, I circulated to check in and monitor for understanding of those crucial row/column concepts. For some students I simply asked “How many are in the row?” and they answered easily. For others, I needed to say “Show me a row with your arms” in order for them to remember that rows run across. For others, it went one step further, and after they showed a row with their arms, we touched the counters together to show horizontal (or in one student’s case, laid a pencil atop the row to see a linear representation). This is all differentiated formative assessment.

As students figured out their arrays, they were required to write the corresponding multiplication sentence. The students were quite proud as they finished, but I kept the rigor of the lesson going and challenged them by saying, “Make another one.” (Side note: My only assistance for most students was a reminder that the rows and columns must be equal. They were on their own more than they have been all year). They generally looked at me with mock shock and then got busy. A student who I had last year as well, and who has struggled mightily with math, actually managed to figure out four arrays for the number 10 – with minimal adult assistance. A multiplication master in the making!

Once students figured out the different possible arrays for their number, they took a piece of construction paper and drew one of their arrays using dots. After they adjusted for neatness, they took stickers and covered the dots to make the arrays look a little prettier. Then they wrote the multiplication sentence for their array and the corresponding fact based on the commutative property (ie.  4 x 7 = 28 and 7 x 4 = 28).

Each student finished and no one judged or questioned the different numbers used. It was truly wonderful.

I wrapped the lesson by having students cut out flash cards for the 2s times tables. We also sat with a 12×12 times table grid and talked about how to use it. Differentiation here came in the samples we worked on. Everyone did the same work, but there were different points of access. I had the students figure out the answers to problems like 3 x 5, but also ones like 12 x 8.

Why was this lesson a success?

  • Students were invested and engaged from the start.
  • They were working on grade level concepts at an appropriately challenging level based on their current abilities.
  • They had opportunities to talk, listen, watch, touch, move, write, and do art.
  • They experienced multiplication in several different forms (visually, orally, aurally, in arrays, on tables, and on flash cards).
  • Everyone felt comfortable and everyone had a point of access to difficult material.

This is what differentiation can look like. It does, indeed, take some extra thought during planning time, but it is an easily managed lesson and it is just so effective for the students.

Please share with us if you try something like this. Or share your own differentiation success stories!