Conceptual Math Lessons

Last week, I mentioned that there were three different types of math lessons. Considering which type of math lesson can help you differentiate and consider how the lesson should unfold. You can find out more by accessing this blog post here or by checking out this quick video:

Today, I want to focus on one specific type of lesson and discuss the small differences to consider. Let's talk about a conceptual lesson, which just happens to be my favorite type of lesson to teach.


Take a look at this standard or objective:

Partition circles and rectangles into two, three and four equal shapes; describe the shares using the words halves, thirds, etc and describe the whole as two halves, three thirds, and four fourths. Recognize that equal shares of identical wholes need not to have the same shape.


How do I know this is a conceptual lesson? Let's look at the main points below:

  • By looking at the continuum of standards and objectives across grade levels, I can tell that this is the first time students have begun creating fractions. They have decomposed shapes into parts but have not used the fraction language.

  • The vocabulary is a key factor, as well. Note the language equal shares and halves, thirds and fourths. These are all words that students will have to create a mental definition while piecing together the concept.

  • The objective also states that students will describe and recognize these common fractions. Again, that tells me that students will need to discuss fraction concepts to develop their own meaning.

Now that I have recognized this is a conceptual lesson, I have to decide how it changes my lesson. The first consideration is to set the lesson up with a great real-life task. I need a question that will engage my learners and have them thinking about the problem.

This problem allows students to think about how they could divide the circle into equal shares. I would provide the students with paper already cut into circles for them to fold and see what happens when they try to make pieces for my friends. Questions I might ask include:

  • What does it mean to get an equal piece?

  • How are you sure your pieces are equal? How did you prove it?

  • What different ways did you share the pie? Is that the only way?

  • How would you describe the piece each friend received?

I would even provide students with scissors to cut apart the pieces and lay them on top of each other to ensure that each piece is equal. I am trying to get students to internalize the idea of equal shares and the idea that shapes can be partitioned into smaller equal shares.


We would then look at each model and introduce the vocabulary necessary for the objective. I may even take out some fraction circles and allow students to explore them for a few minutes to think about how the fraction circles relate to the task.


But then, I have to move it to the next level. The students have a base understanding. What happens when I challenge their thinking?

I would provide students with rectangle cut outs and allow them to continue the process. My goal is to get students to see that they can make equal groups that have the same name but describe a different whole. My questions might include:

  • What ways did you divide the cake?

  • How would you describe the piece each friend received?

  • How is this different from the pie?

  • How is this the same as the pie?

We would add our responses to our anchor chart and compare. I would then provide fraction strips and allow students to continue to explore fractional concepts.


As an extension to the lesson, I would create a discovery station where students can play with fraction strips and circles. The goal would be to allow students to explore and build understanding. There would not be a specific task, but I would ask students to journal their discoveries or even add their generalizations to a giant anchor chart. Again, the goal is discovery and conceptual understanding by allowing play.


This is easily an example of a conceptual lesson, because students are building a foundation. Others include:

  • Measure lengths using feet, inches, centimeters and meters. (2.MD.3)

  • Measure areas by counting unit squares (3.MD.6)

  • Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to the right (4.NBT.1)

There are conceptual standards and objectives across every grade level, and they help students to truly understand a concept. Remember when planning these lessons that conceptual lessons rely on using hands-on materials and a meaningful task. Without these, students may struggle to build the foundational understanding necessary to move to the next stage in a procedural type lesson. If you missed my checklist from the last post, you can grab it by clicking on the image below. It can help you consider the lesson type and a few things to consider when planning.

Next week, I will continue this process by outlining a procedural lesson. I hope you will check in out! In the meantime, leave me a comment about some of your favorite conceptual lessons!


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