Order of Operations

[Alex]

When I taught middle school math, I found order of operations to be a major point of confusion for students of all levels.  This is a fun activity we made that helps students gain a deeper understanding of order of operations through visualization and problem solving:

https://classroom.tilefarm.com/activityPreview/5/warmups/6

Below are some teacher notes to go along with this activity.  Over the next few weeks we will be adding this type of resource to all of the activities in Tile Farm Classroom.  Let us know if you have any feedback or suggestions!

Overview

This activity develops students’ problem solving and spatial skills, while giving students a visual understanding of order of operations. Many students struggle with the overall concept of order of operations, but simple visualization activities such as this one quickly lead to a deeper understanding of the subject.

Estimated Time:  5-15 minutes

Best For:  Individuals, Pairs, Small Groups, Class Discussions

Discussion Questions and Prompts

-For each puzzle, first solve it, then using pen and paper, write an expression for the total number of tiles in the puzzle.

-For each problem, there is more than one correct answer, but elegant solutions generally will contain parentheses.

-After writing an expression using parentheses, evaluate it, then confirm with a classmate that your evaluated expressions yield the same number of tiles.

Reflection & Extension Ideas

-Students who enjoy building puzzles such as this, can find a wider range of puzzles playing Copycat and Shadow in Tile Farm Playground

-A more creative, open ended extension of this activity can be found in 5th Grade > Builders > Number Builders > Order of Operations.

[Alex]

Here is an image showing the four steps of solving one of these problems, along with the annotation for number of tiles and how that relates to order of operations:

[MrGold]

This looks fantastic! My 6th graders really struggle with conceptualizing PEMDAS and I think this will help!

[Alex]

Glad you like it!  If you look in Big Thinkers in Tile Farm Homeroom for middle school, we have a whole suite of puzzles focused on developing a deeper understanding of order of operations through visualziation.

[Author]

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