We expect students to write in every subject area. Just like reading across the content areas, writing across the content areas is a key skill.
With the shift to common core standards and concept-based learning, we are asking students to do more and more written work in math. They are expected to perform in writing on assessments to complete error analysis tasks, explain problems, justify solutions, and more.
But, I've noticed that if we do not take a full day (or more) to explicitly teach this and practice it in context immediately, then we cannot expect our students to know what results we are looking for in their writing.
They really are not comfortable writing out full responses in math until we model it, show them specific examples, and explicitly outline what is required.
One of the best ways to do this is to offer a full class period or two in which you only cover writing expectations specific to math classes. Here are what I have found to be the basics to go over with kids during this lesson:
Complete Sentences. Always.
They honestly do not ever expect to have to write in full sentences, because it's math class! I have now learned to incorporate "Explain in complete sentences" into the directions for any question I want them to write for.
You can ask them to offer at least three sentences (or more) when you are looking for a complete explanation of something. At first, they probably will not know how to finish those sentences, but that is why we go on to the practice afterward.
Each statement that a student makes in writing must be supported. There are different forms of justification.
Give students examples of the different forms of "WHY" that we see in math explanations, and ask them to come up with samples on their own as you go forward. Remind them that each sentence can be followed up with a justification answering the question "why." Here are a few sample justifications that they could embed into an explanation:
• Why did you use that process?
• Why does that answer seem reasonable or not?
• Why did you choose to do that?
• Why do you think that?
• Why is it an error?
• Why will you start with that step?
Include Examples and Counter-Examples or a Picture / Diagram if Needed.
The key to a good math explanation is to be clear and complete. If students want to offer a drawing to support their explanation, this can be a great addition. Sometimes it helps. Along these lines, they can provide examples or counter-examples if it can support their writing.
However, the full sentences must always be present. Any pictures or examples are just supplements.
Now, Practice It!
Here are some of the ways that we use written explanations in math class:
You can practice each of these types of written explanations with your students.
Explaining a Mathematical Relationship
Explaining a Method, Approach, or Thinking Process
Explaining a Problem
Explaining a Choice or Answer
Be sure that students justify each and every part of their explanation with WHY!
My favorite approach for this "Writing in Math" lesson is an introductory doodle note that goes into the characteristics of a good math explanation followed up by stations where students practice right away (using the above prompts and additional ones as well). The full lesson pack for that is available for purchase here if you want it all fully assembled and ready to go.
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Take a quick peek to see what doodle notes are all about, how to get started on your own, and what's included in the eBook:
Another Free Download:
Looking for a great way to introduce this strategy to your class? This free doodle note page teaches your students about the many benefits that happen when the two hemispheres of the brain work together. It's a perfect way to kick off the process of adding coloring, doodling, or sketching into your classroom learning routine!
This one is a great first doodle note to model and introduce the concept while getting students on board! They will enjoy it plus see the results when they remember the material so well afterward!
To Read Next:
Halloween is far from my favorite holiday, but the students seem to love it!
They get pretty into it, so I decided to go ahead and make a Halloween - themed version of the equation picture challenges I wanted to make.
My goal for these is to practice algebraic concepts in a different format. These are great for practicing substitutions (an awesome lead-in to solving systems of equations).
But they can also be an application of the transitive property in some cases on the challenging level of the cards.
I love the conversations that these types of problems inspire. It's so cool to see how some kids work in pictures, while some instantly can figure it out mentally without even thinking they are using any "Algebra."
These are great for partner work, because they can talk through different methods of solving (so common-core-friendly!).
You can also try using one each day during the week of Halloween as a warm-up.
I included an easier set of 4 problems for younger students too (or a basic starter set before using the 4 challenging ones).
I hope your students enjoy these!
Here is the link for the free download: Halloween Equations
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