## Open Middle Problems

That’s the problem I presented to my students today for our math warm-up. It seems like a basic problem, but the conversation it started was wonderful.

I got the idea for the problemfrom Open Middle. As his website states, most of these problems have:

1. a closed beginning meaning that they all start with the same initial problem;
2. a closed end meaning they all end with the same answer;
3. an “open middle” meaning that there are multiple ways to approach and ultimately solve the problem.

We started with this basic problem today. Students were given time to work on their whiteboard and talk with a partner before we shared as a class. One student, Jimmy, pointed to his partner and asked, “Mr. Rashid, we have two different answers. Can we have different answers and both be right?”

My answer was, “Can you prove that you’re both correct?”

Jimmy and his partner took turns explaining why each answer was correct. Then I asked, “Jimmy, can you have different answers and both be right?”

He smiled and said yes.

Students were excited to share their thinking with the class. Each student shared their answer and explained how they solved the problem. We will increase the complexity of the problems as we move forward, but this was a great way to introduce the idea to students and help them understand the process.

There are many great examples on the Open Middle website. They are organized by grade level and standard. This resource makes diving into the process a little easier. I hope it works as well for you as it did for my students.

## Mystery Science

About a month ago a colleague told me about a website called Mystery Science. The site has great lessons with hands-on activities. You can search for topics or browse by grade level. Best of all, it’s free!

Earlier this week I used a lesson with my students to explore how sound travels. They used paper cups, string, and paperclips to make telephones. Students “talked” through the phones to learn about sound waves. It was an engaging, hands-on activity that really helped them understand how sound travels.

If you teach elementary school, you should definitely check out this website.

## I know… So I… To find… Therefore…

Teaching problem solving is a tough task. Students have to read a word problem, understand what to do, complete the computation, give an answer, and then determine if the answer is reasonable. So how do teachers best support students in that endeavor?

There is no magic bullet to help students become better problem solvers. They need to be exposed to different problem types. They need to see, hear, and learn how other mathematicians around them are solving problems. Some students also need a structure to help them solve problems and explain their thinking.

One strategy I’ve use is called “I know… So I… To find… Therefore…” This helps students work through a problem and explain their thinking. Here’s a breakdown of each of those parts.

• I know… What important information was given in the problem?
• So I… What did you do to solve the problem?
• To find… What answer did you get?
• Therefore… What is the answer with the correct label?

Let’s look at the following problem to walk through the process.

David started his coin collection with 14 coins. He added 3 coins to his collection at the end of each month for 5 months. How many coins are in David’s collection after 5 months?

Students would answer the question with: I know David has 14 coins in his collection. He adds 3 coins each month, and this happens for 5 months. So I added 14 + 3 + 3 + 3 + 3 + 3 because he gets 3 coins after each of the 5 months to find 29. Therefore, David has 29 coins in collection after 5 months. (Students could also say they added 14 + (3 x 5) instead of using repeated addition.)

This takes some modeling at the beginning of the year, and I always supply a graphic organizer with the “I know.. So I… To find… Therefore…” components already listed. I created a copy of the graphic organizer on Google Docs.

Students pick up on the process pretty quickly. Using the graphic organizer slows their thinking, which improves focus during the problem solving process. It also helps improve a student’s explanation by giving them a structure to follow.

Last week, my students were working on problem involving fractions. The problem was: A quarter is 1/4 dollar. Noah has 20 quarters. How much money does he have? Explain.

I gave my students graphic organizers. (We’re not quite ready to take the training wheels off yet.) Here are two examples of how an average student completed the graphic organizer.

I have adjusted this approach over the years. I’m sure I’ll continue to make slight changes in the future to try and improve the supports I’m providing for my students. What strategies and supports do you use with your students to help them be better problem solvers?

## 50 Books in 2020… #1

I mentioned in my “One Word for 2020” post that I set a personal goal to ready 50 book in 2020. The goal seemed a little daunting at first. One book into the challenge, and it still seems a little too ambitious. Now that the ball is rolling, however, it seems a little more attainable.

The first book I read for the new year is One of Us Is Lying by Karen M. McManus. This is a thrilling mystery with twists and turns throughout. Five high school students are given detention. Only four come out alive, and everybody has a secret to hide… and a motive. It is very Breakfast Club – a jock, an outcast, a brain, etc.

One of Us Is Lying is not a genre I normally read. Typically I read either adult nonfiction, mystery, or thriller. I love anything by authors like Malcolm Gladwell and David Baldacci. One of my goals with this book challenge is to read texts outside of my comfort zone. So, for my first book of 2020 I chose a young adult novel. Granted, it is not exactly going out on a limb since it is a mystery/thriller, but it’s the first young adult novel I’ve read. Baby steps.

I got the idea to read new genres from a familiar place – my classroom. Throughout the school year I encourage my students to read books from different genres and try to get them into books they might not normally read. Students get a “What Genres Am I Reading?” form at the beginning of the year. As, they read a book they mark the genre they read. The goal is the fulfill the requirements for each genre by the end of the year. I check in with them periodically to see which genres they’ve completed and where they might need some encouragement or guidance.

Last year, I had one student who is a voracious reader. After completing a couple genres, she came up to me a little worried. “Mr. Rashid, I don’t really like poetry,” she said anxiously. We talked about this, and I introduced her to some Shel Silverstein books. The next week she was sitting with one of her friends laughing at some of his poems in Where the Sidewalk Ends. It’s not that she wouldn’t have found a love of poetry without the genre challenge but maybe not as early as she did.

Other students found books and genres which were new to them. I had an entire group of students become mystery fans because of the challenge. Do all students achieve the goal? No. Does every student love each genre? No. But even if they read half the genres I outlined and find one new genre they like, that is better than not trying. That way, we all win.

## Monday Morning Check-In

Recently I saw a viral post by a teacher named Erin Castillo. She has her students write their name on the back of a Post-it and place it on a chart each Monday. The chart had headings such as “I’m Great,” “I’m Okay,” and “I’m Meh.” After students placed their sticky notes on the board, the teacher can check in with them as necessary.

First, let me say, thank you Erin Castillo. This is such a wonderful idea. The social-emotional aspect of a student’s life has an enormous impact on their academic life. (You can’t get to Bloom unless you’ve taken care of Maslow.) This was such a powerful idea, I wanted to use it with my students. My only concern was a room full of 26 fourth graders all going up to the board in the morning to place their Post-its. Would they be completely honest when their peers were watching? (I don’t know that I would with my peers watching me.) Would students place their sticky note in the category where the majority of the other students did? I might follow the pack in such a situation.

The way I addressed this possible issue was to create a digital version of the chart. On this Google Form, I have a consistent eight questions students answer every Monday morning when they enter the classroom:

• Name – This is a dropdown menu with students’ names already entered. (I’ve changed their names in the linked Google Form for privacy purposes.)
• How was your weekend? (It was wonderful. It was okay. It was difficult.)
• Today I am… (Great, Okay, Hanging in there, Struggling, I’m having a tough time and wouldn’t mind a check-in)
• Is there anything you want me to know?
• What book are you reading right now?
• Would you recommend this book to a friend?
• What is the next book you’re going to read?

A QR code is projected on the board, so students can grab an iPad and get started right away. They usually complete the form in less than five minutes, and I can easily view all their responses in a Google Sheet or Excel document. It has worked really well so far, and it gives me a great insight into how my students feel when they walk in the door, how their weekend was, and their overall outlook.

I’ve also found this to be a conversation starter with my students. Here’s some of what they’ve shared the last few weeks:

• I almost made it up the warped wall. (We have an American Warrior gym near our school.)
• My stomach hurts.
• I baked cookies with my grandma this weekend.
• I went to my dad’s house yesterday.
• I got 2nd all around at my gymnastic meet.
• I love school.
• My team won our basketball game 30-4.

Nothing is better to build relationships than asking a question about one of these responses when we are lining up for lunch, transitioning between subjects, or at another point throughout the day.

Feel fee to use, adapt, and make this work for you classroom.

Happy Monday!