## Reflection: Relevance Understanding of What "Equals" Means: A Formative Assessment of an Essential Concept - Section 2: The assessment...

What am I looking for? I see so many things in just these few samples! The data I gather from this little quiz will help drive my instruction for this unit on place value, addition and subtraction.

In Sample 1 This student simply looked at the equals sign as an infinite horizontal process. Sometimes they will draw another equals sign after the second expression. This student didn't even think about what the second expression meant. It is linear thinking. It is apparent in the subtraction problem, he understood the idea of inverse, which I suspect is because he studied fact families and memorized his facts. That is fine, but it isn't enough as far CCSS is concerned.

The last equation has me stumped. I am guessing that he simply placed the three in the box to have the problem over with! Students are uncomfortable sometimes with leaving things they don't understand, blank. Fill it in with a number and there might a chance you might be right! The written answer is  key in understanding that he really does not know what an equals sign means.

For Sample 2, this student can solve the problem. He does not show understanding of why he got the answers he did in his written sentence. This should be an easy thing to fix!

Sample 3 shows no understanding beyond the first problem. Although he addressed the concept of "total" ( which partially relates to the idea of equals), he clearly shows that he does not understand where the total should be in a subtraction equation, an shows no understanding of the inverse. He is not showing thinking about the difference between addition and subtraction as a concept.

Sample 4 shows mastery!

I am going to plan on setting  clear learning goals individually or in small groups for students who have not mastered the concepts over the course of the next week. I will record my findings and figure out groups using my Student Checklist. This should make learning how to solve multistep problems much easier for them later on when I need to teach equations and variables.

I am going to advance their thinking by setting up these goals according to my checklist and differentiate. Students will have their own checklist that will look like this. This checklist reflects the standards I mentioned in the the beginning.

*I will be able to explain what equals means.

*I will be able to use the inverse to solve an unknown.

*I will be able to use the four different operations in equations to solve.

*I will learn how to use the numbers I already have to help me solve for the unknown.

Setting up these clear goals will help them master more rigorous work in the future. I will revisit this quiz again about mid year to reflect on their progress and my teaching.

This little clip finalizes my thoughts about my next steps after looking at all of my data.

Relevance: Assessing the Situation

# Understanding of What "Equals" Means: A Formative Assessment of an Essential Concept

Unit 10: Addition and Subtraction: Algorithms to One Million
Lesson 1 of 7

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