If I could do last year’s lessons on solving equations all over again I would begin with CGI. As a whole, 7th graders at my school struggled with solving equations last year. And as I’ve been in 8th grade classes and had conversations with 8th grade teachers I see the struggle continues. I’ve concluded that many students do not understand the real meaning of the equal sign.

When you ask students what the equal sign means the overwhelming answer is “equals”. When you ask if they can give another meaning the look of confusion covers their faces as they respond, “equal to?”

Starting with CGI, Cognitively Guided Instruction, helps students to make sense of a concept through making sense of a context. Through this process of thinking, students are able to conceptually understand a mathematical idea such as dividing fractions, addition and subtraction and even solving equations.

This past week I worked on a few CGI problems for middle school concepts. My plan is to do a couple of professional learning sessions where we can focus on this instructional strategy. 8th grade is my first group. An 8th grade teacher asked if Number Talks could be used to introduce systems of equations. What a perfect fit for CGI.

Here’s a problem I wrote. Students were instructed to only draw diagrams with labels to solve the problem.

Pictured above are two students beginning thoughts.

How two students served in a special education resource class thought about it.

More processing going on.

Students realized the answers needed to be 18, not more and not less. They had to use reasoning to determine how much of each fish was needed in order for it to be equivalent to 18. Within their explanations, students expressed they had to determine one unknown in order to determine the other unknown. Imagine students being able to develop their understanding of systems of equations in this manner. Making the bridge to the abstract would make more sense.

Here are other CGI problems I have written and examples of more. If you have a source for more please let me know.

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Once again Ms Sexton you have saved the day! I have learned more about CGI, CC Standards of Math Practices, Inquiry based learning and how to facilitate opened ended math tasks through classes and institutes and workshops this summer. I am looking for this type of problem for the first standard we will teach this year in solving equations with one variable. I mentioned teaching this concept in the inquiry based class I took with an internationally known researcher in science. He said that if he was going to teach solving equations he would start with the meaning of the equal sign. God has sent you and your amazing teaching skills to help me and other teachers become the best that we can be! Thank you for sharing with us.

Aww thanks Pam! This is a great work we are all doing and I’m thankful God has allowed me to be a part of it. I look forward to hearing how great things are for you this year.