Read Draw Write

When I think of the number one struggle a majority of my students have when it comes to math each year, it would be word problems. The entire process of reading through the problem, figuring out how to solve it, and explaining their thinking afterward is so challenging for first graders. We work on this skill daily over the course of the school year because it is such an important skill. We focus on not only solving word problems, but on explaining our thinking when answering them.  

When I was young, word problems were my nemesis! I understood that the steps below were what was expected of me to solve a word problem, but I had no clue how to get past step 1!

1. Understand the Problem
2. Come up with a Plan for Solving 
3. Carry out the Plan
4. Reflect or Check Your Work

As much as these steps always seemed like a logical idea and did get me thinking through the math problem I was facing, they didn't get the job done.  What do you do when you can't get past step 1?  You stare at and then read the question over and over and still can't figure it out. You recognize the known information, you underline the key terms and circle the numbers, but you can't figure out what to do. Under this problem-solving method, you are expecting students to understand the problem before making any diagrams, drawings, patterns, tables, etc. which can leave many students stumbling to succeed. This is why I love the  "Read, Draw, Write" (RDW) approach!      

What is so great about the Read, Draw, Write approach?

This approach works because students can draw a model of what they are reading to help them understand the problem. In other methods, the drawing usually came after understanding. When faced with story problems, children will often add whatever numbers they see. In the RDW approach, the drawing helps lead to knowledge; it gives students the tools to think about and model the relationships in the problem. Drawing a model helps students see what patterns might arise, which operations are needed, and which models work and don't work. Students must go deeper into the problem by drawing representations and determining which representations are relevant to solve the problem. While students are utilizing the RDW process, they are using the Standards for Mathematical Practice. Some of these would include: model with mathematics, make sense of problems and persevere in solving them, use appropriate tools strategically, and look for and make use of structures.  

Read

Read the problem. Read it over and over again. And then reread it. Answer- What am I trying to solve/answer? Identify-What information is given to me in this problem? Deconstruct- Can I box the question? Can I circle the parts? Can I find a total? Can I find missing parts? Can I underline important information? I always ask students to read the problem and think about what information is given. My goal is to get students to tell me what they believe or wonder before they model. Students can tell me, for example: I see the total and one part, which means we can count on or subtract to find the missing part. This is a great time to practice academic language and use collaboration with your students.   

Draw

Draw a picture that represents the information given. During this step, students ask themselves: Can I draw something from this information? What can I draw? What's the best model to show the information? What conclusions can I make from the drawing? My students know they can use multiple strategies to solve problems. They chose different, yet similar ways to model and label their work. Each student's work shows detailed, specific choices rather than arbitrary combinations of numbers. It also helps me know if they are confused and helps me to find common errors that can direct my instruction. 

Write

Write your conclusions based on your drawings. This can be done as an equation, a number sentence, or a statement--or all three. It's an essential skill to have your students write a statement. It ensures they are answering the exact question being asked. The ability to turn a question into a statement is an important skill. Writing is the time to check your answer for reasonableness. I choose students who used different strategies to share their responses with the class using the document camera.  The class can see multiple strategies and understand why certain students chose certain strategies. 

Do you use the Eureka Math "Read Draw Write" strategy? Has it changed the way your students go about solving word problems?

Positively Teaching,  

Randi Muehlen

Integrating Visuals in Order to Build Connections in Math

"Numbers, Pictures, Words!" I am a broken record as I walk around the room and gently remind students that when completing word problems, they should have all of these three criteria by using the Read Draw Write process. As we all know, if students can use the skill successfully in a word problem, chances are they have mastered it. In 6th grade, I have come to realize, few lessons introduce a new concept without a word problem or two, so as I collect their exit tickets or tests, I am looking for these three criteria. I expect students to struggle, but the part that amazes me is what the struggle is. Some students complete the problem correctly, but their picture does not match their numeric solution. Others provided a perfect model with an inaccurate and illogical answer. The worst scenario is when they all seem to get it just to present you with wide eyes the next day when you give them a similar problem to the day before! *Cue sad music here*. Students haven't internalized the connection between their pictures and numbers, which leads to difficulty when they are trying to provide reasonableness to their answer. Is this important? Yes, because as well all know, it wouldn't be Eureka or common core if it didn't have a picture or strategy when teaching a skill. The great thing is that the solution requires 1 question and some old fashion color coding! 

                

                                                                                

                                                                               I see it!!! Can't you??

When I look at our program, I am thankful that we teach multiple methods and models to assist our students in their understanding of something as simple as addition. Models were something I wish I had growing up. As a visual learner, multi-step word problems were tricky if I was unable to picture it. I still remember the problems that sounded like this "Now Jerry lives 3. 8 miles from school and 2.6 miles from his house lives Sherry in the opposite direction. Jack can travel to the school and back in 8.6 miles. If they walked to school tomorrow, how many miles would they walk all together to arrive to school? So there I was, drawing squares to represent buildings and arrows to represent paths to their destination. Most students today could solve this problem with three simple tape diagrams and a few labels. So why the disconnect? After countless examples of a problem side by side with a tape diagram/model, they still didn't see it!  So I did what I do best when I want things to stand out--I color-coded, and the students helped me. When you make the students find the connection, they are more likely to see it and internalize it on their own. 

Bridging the GAP and making the connection

Incorporating this strategy can be completed or every lesson. The following steps to incorporating this into your lesso is simple. This is how I embed it into my daily lesson. 
1. Complete problem with your picture and your drawing. 

2. Once your model is side by side with its corresponding drawing, you break up the equation and ask students to connect it to their picture by using the following stems using my example.
          "I see 45 in my equation, but where do I see it in my picture/model?" 

3. Have students look at the picture and tell me once they see the 45. Once they have done this I color code them the same color-in the example it is represented in pink. 

4. I continue this process with all the pieces within the equation. "I see 3/4 as my divisor, where do you see it in my picture?" and then color code it--in the example it is represented in blue. 

5. I continue this process with the answer of my problem. " I see 60 as my quotient, where do you see it within my picture?"

6. Now lets look at my answer and see if based on my picture if it logically makes sense. During this time I discuss that the whole tape is bigger than the 45 which makes sense because it is only 3/4 of the tape and 15 + 15+ 15+ 15= 60. 

7. Once we have completed this together then I reveal my overall anchor chart for that lesson that have the same colors. I then leave this up throughout the entire lesson for students to refer to. You can complete this on any following problems and that way throughout the entire lesson you are building that connection. 

8. In my class I wll have students complete a seperate problem color coding their work OR provide them with a copy of my anchor chart that we colored together to glue in. Students can continue to refer to it as the module progresses. 

I have seen a big change in my students when they are required to make connections between their numbers and pictures. This is a valueable tool that not only allows for class discussion and reasonableness. 


                                                                  Lively Teaching, 

Jessica Magana

Mathematically Speaking!

Mathematically Speaking!

Getting our students to use and clearly comprehend academic language in math (and any other subject area for that matter) is not an easy task.  We know how difficult the Lexile level is for most standardized tests and understand how imperative it is that students can read and take in the terminology.  What if you could address these academic vocabulary words daily without taking a lot of time out of your busy day?



In this blog post, you’ll read about some different ways to turn your students into mathematical speakers!

Asking my students again and again what the word “sum” means always gets quite irritating.  “Boys and girls, I know you’ve heard this word ever since ___(insert grade level here).”  I don’t want to make my students feel bad, but I also want to hold them accountable for knowing their academic language especially when the word is not new to them!  How can I get my students to proficiency on a test if they can’t understand the language provided?  After thinking logically about ways to increase comprehension and vocabulary in math, I realized that a good old point system with rewards always seemed to do the trick.  However, I also knew that I couldn’t stop there.

Using some of these strategies will not solve all of your students’ academic language needs, but they’ll at least get kids motivated to participate and try harder to use more mathematical words.  Here are some of the things I do:

1.   Write “Mathematical Speakers” on the board.  I write this on my white board because it needs to be seen the entire week.  Every time students use math vocabulary, I reward a tally mark next to their name.  The board starts off blank and each name only makes it onto the board once they earn a point (see picture at the top of the blog).  I use sticker charts in my class, so for each point received, a sticker is earned.  Once students fill up their sticker charts, they get to choose a prize from the prize box.  Each time a student receives a point, the class cheers for him or her.  I’ve even heard one of my boys say, “Alright!  You’re a mathematical speaker now!  Woo hoo!” :)
2. When a student shares a response and does not use academic language, I simply say, "Can you restate that like a mathematician would?" The student then has to reach into his or her academic tool bag to come up with the proper vocabulary.
3. Include important academic language/math vocabulary in your room where kids can access it.  Underneath my mathematical speakers area, I have “Math Words of the Week”.  Some of your words might stay up the whole year, and others you’ll need to update weekly.  When my students find a word during the lesson that is not on the board, they share it out loud and receive a Mathematical Speaker point.
4. Box, underline or highlight important vocabulary words within your lessons.  When we read directions together and/or word problems, we always box the verbs so that we are aware of the action that needs to be taken.  For every verb, we number the steps.  If a problem has three verbs, then the students have three steps to complete.  We also identify and annotate other key words.  For example, if we come across the word product, we’ll highlight it and draw a multiplication sign or annotate “the answer to a x problem” above the word.
5. During cooperative learning structures, I walk around to listen to my students' conversations.  I let them know that I'm looking for students to use their math vocabulary like mathematicians.  When I hear students using these words, they receive more stickers.  I also might stop the class to bring attention to an awesome word or conversation that I heard.
6. Create diagrams for students to copy or paste into their math journals.  Ask students to help you label each part of the diagram. See example below:
7. Design a Kahoot or some other formative assessment to continuously spiral through math vocabulary words. The more they practice and have access to this language, the better.

These are just some of the things we like to use during math time.  I’m sure you have many creative and helpful ideas, and I’d love to hear about them!  Please comment below about some of the things that work well for you!

Educating together,

Kimberly Smith Loya