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Each group will choose one of their incorrect solutions and present their corrected solution to the class. They will explain why the original solution was incorrect and what they did to make it correct. The goal is to foster general classroom discussion and understanding around equality as a whole.

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After the final rotation, students will be asked to identify two ideas they find surprising and two ideas they believe are important on their final poster paper. Each group will then share with the class, with an emphasis on promoting discussion around the ideas identified by each group.

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My main goal with these activities is to evaluate how students conceptualize the properties of equality in a context that is removed from solving equations. By having them participate in the Opposing Views Probes and the concept card mapping, I hope also to get them thinking about why the properties of equality exist and what they mean.

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FACT: Concept Card Mapping / What are you doing and why?

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FACT: Concept Card Mapping / What are you doing and why?

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Concept Card Mapping: Students are given cards with mathematical concepts and are tasked with creating an interconnected web.

What are you doing and why?: Students are asked to explain and express the purpose of an activity they are completing.

Source: Keeley's 75 Formative Assessments book

Implementation described below.

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Opposing Views: Students are presented with two or more characters that have conflicting ideas about a mathematical concept and asked to explain who they agree with.

Think-Pair-Share: Students are given individual time to compose an answer and time to discuss with a partner before sharing with the class.

Source: Keeley's 75 Formative Assessments book

Implementation described below.

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When solving equations with one variable, many students may not have a complete conception of what the equal sign means and represents. This can lead to various errors involving addition, multiplication, etc due to misconceptions about the properties of equality.

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After this class discussion, students will be brought back to the context of equations. Each group will be given four solved one-variable equations. Some of these equations will have correct solutions, and some of them will be incorrect. The task of each group will be to identify which solutions are correct and incorrect and explain why in each case. Students will be encouraged to identify specific mistakes and then relate each mistake to a property of equality. They must consider how to fix the incorrect solutions as well.

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The final exit slip will be to have students write down if their thinking changed concerning the Opposing Views Probe presented at the beginning of class. This initial activity, the concept map, the error analysis activity, and the general classroom discussion throughout should help me have a good understanding of where students stand on the properties of equality.

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Around the classroom, there will be sticky white poster paper with concepts related to the properties of equality. In groups of 3, students will be asked to make at least two connections (so two pairs of connections) between concepts with a brief explanation. After 2 minutes, they will switch to the next poster and draw two more connections while discussing the connections previous students made. They will continue rotating until each group has viewed each poster paper.

The idea is to have students seriously consider what the properties of equality represent while also getting to see what their classmates think. They will be encouraged to add their classmate's thoughts and express any points of disagreement.

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Students will be presented with two viewpoints concerning an argument friends are having about whether you can 'flip' the terms on each side of an equal sign. One friend will be arguing that you cannot because they are giving an operational definition of equality, while the other will argue that you can, because they are giving a relational definition of equality. Students must write down on a piece of paper who they agree with, then turn to a partner and discuss their answer. This will be followed by a classroom discussions.

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12 Math Rules that Expire (Karp, et al., 2015):

Table 1

Students will often interpret certain equations as easier based on what side of the equality the variable is found. Since students are taught the variable has to be on the left side of the equal sign, they are more hesitant to solve equations where the variable is on the right.

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FACT #43: POMS (Point of Most Significance)

What part of the lesson did students see as most significant?

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Source: Student's Misconception on equal sign

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Source: Student's Misconception on equal sign

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Student's Misconception on equal sign ( Kusuma, Subanti & Usodo, 2018):

Students view the equal sign as an operational symbol rather than a signifier of mathematical equivalence. They are taught to solve equations computationally without understanding the meaning behind the steps.