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

Lesson 1 of 7

## Objective: SWBAT show what they know about solving for the unknown.

*In order to start this unit, I want to have a clear idea of what my students understand about the equals sign. If students have not been taught to think about the equals sign as a symbol that means to balance, I know that trying to master addition and subtraction algorithms, solve equations with variables, understand the concepts of inequality, solve function rules and solve for the unknown as expected in standards 4.NBT.B.4,4.OA.A.1, 4.OA.A.2, and 4.OA.A.1, will be more difficult.*

*Math Practice Standard 1 expects that students are proficient in making sense of problems. Math Practice 2 expects that my students can reason abstractly and quantitatively, looking at relationships of expressions within an equation. Math Practices 6 & 7 expect students to be accurate and look for structure in their problem solving. These equations and the writing in this quiz will reveal their abilities to do all of the aforementioned. It shows me the level of their reasoning and problem solving using all four operations. It gives me a clear idea of their understanding of solving for the unknown and whether they understand the meaning behind the equals sign.*

I opened up this lesson by telling them that I was going to give them a short quiz that would tell me a lot about their thinking about the equals sign. We talked about how the equals sign is something we see all of the time and that we have been using since we first started to add and subtract. The students talked about how way back in Kindergarten and preschool, they were using it to put things together (manipulatives) and that they knew it meant either getting more or less depending on what they were doing.

I asked them to clear their workspace and get ready to show me what they knew!

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#### The assessment...

*20 min*

This short quiz quickly shows me whether or not my fourth graders have mastered understanding of the equals sign.This article from the University of Wisconsin Madison helped me understand the importance of this little test and made me think about how the rigorous expectations of CCSS must have solid foundations and the transition needs to provide this.

This assessment examines four essential things:

1. Placement of the unknown. ( Can the student solve if the box is moved in different places?)

2. Understanding how to use the inverse to solve problems.

3. Using different operations within an equation.

4. Using words to explain what equals means.

I passed out the quiz and hoped it would reveal their understanding.

#### Resources

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- UNIT 1: Place Value and Multi-Digit Addition & Subtraction
- UNIT 2: Metric Measurement
- UNIT 3: Graphing and Data
- UNIT 4: Concepts of Multiplication
- UNIT 5: Geometry
- UNIT 6: Fractions 1: Understanding Equivalence in Fractions and Decimals
- UNIT 7: Fractions 2: Addition and Subtraction Concepts/ Mini unit
- UNIT 8: Fractions 3 Mini Unit: Multiplying Fractions by Whole Numbers
- UNIT 9: Division Unit
- UNIT 10: Addition and Subtraction: Algorithms to One Million
- UNIT 11: Place Value
- UNIT 12: Addition and Subtraction Word Problems
- UNIT 13: Multiplication Unit

- LESSON 1: Understanding of What "Equals" Means: A Formative Assessment of an Essential Concept
- LESSON 2: RTI Understanding the Equals Sign: What does it really mean?
- LESSON 3: Addition: Getting Kids to "Talk Through" Their Regrouping
- LESSON 4: Assessment: Addition
- LESSON 5: Subtraction Quiz: Algorithms, Estimation & Word Problems
- LESSON 6: Subtraction and Addition of Multi-digit Numbers: Assessing Our Growth
- LESSON 7: Bunnies, Bunnies, Bunnies: A quick lesson in exploring the Fibonacci Sequence