## Reflection: Data Analysis Equivalent Numerical Expressions, Day 2 of 2 - Section 5: Closure and Post-Assessment

Once students turned in the post assessment I compared the pre-assessment and post assessment of each student.  It was interesting to see how students’ thinking developed between these two assessments.  Here are my reflections on three examples of student work.

Student 1:

On the pre-assessment, this student chose expressions based on the numbers he observed in the picture and how the numbers were organized in the expression.  He failed to find the area of the figure himself and compare it to the value of each expression.   He also thought that expression (ii) and (iii) were equivalent (Unit 1.14 Student 1 Pre Assessment)

On the post assessment, he was able to correctly find the area of the diagram (Unit 1.14 Student 1 Post Assessment AUnit 1.14 Student 1 Post Assessment B). For expression (i), (ii), and (iii) he was able to correctly use the order of operations to simplify the expression.  His work on expression (iv) and (v) show that he is still struggling with the concept of exponents and multiplication.  It is interesting that in his work on expression (iii) he correctly multiples 25 x 6, but in expression (v) he multiplies 25 x 6 and gets 116.  He confuses 5 x 6 as being 36 and then he adds 6+2, instead of multiplying, and then adds 8+3 to get 11.  This student’s thinking around area and expressions has advanced, but he is still struggling concepts that are preventing him from consistently solving the problems.

Student 2:

On the pre-assessment, this student struggled to figure out the area of the larger square.  She had difficulty labeling the picture and came up with an area of 80 (Unit 1.14 Student 2 Pre Assessment)

On the post assessment she was able to correctly find the area and identify all the matches and non-matches correctly (Unit 1.14 Student 2 Post Assessment A.jpeg Unit 1.14 Student 2 Post Assessment B).  She correctly applied the order of operations and understands the meaning of exponents.  She is using the box method to multiply multi-digit numbers.  I will work with her in the next unit to see the connection between the box method and the traditional method.  I want students like Student 2 to transition to using the traditional method because it is more efficient.

Student 3:

On the pre-assessment, this student was able to correctly find the area of the figure but she only found one expression that matched her work (Unit 1.14 Student 3 Pre Assessment).

On the post assessment she was able to find the area of the diagram and correctly identify matches and non matches using the order of operations (Unit 1.14 Student 3 Post Assessment AUnit 1.14 Student 3 Post Assessment B). For expression (iv) she found that 15 squared was equal to 125, instead of 225.  She forgot to multiply the 10 x 10 in the probelm.  This was a mistake that I saw frequently with other students so I am going to include similar problems in do nows.  Up to this point much of their work with exponents has included bases that are 12 or less, so I think they will benefit from being exposed to problems where the bases are larger.

Data Analysis: Comparing the Pre-Assessment and Post Assessment

# Equivalent Numerical Expressions, Day 2 of 2

Unit 1: Intro to 6th Grade Math & Number Characteristics
Lesson 14 of 16

## Big Idea: How can you represent the area of a diagram using numerical expressions? Students connect their knowledge of area and equivalent expressions to the commutative and distributive properties for day 2 of this investigation.

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Standards:
Subject(s):
Math, order of operations, commutative property of addition, commutative property of multiplication, Number Sense and Operations, 6th grade, master teacher project, area model, distributive property, equivalent expressions
60 minutes

### Andrea Palmer

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