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In this 3D Printing Lesson Plan, students will verify (A+B)³ as a mathematical expression based on physical measurement through the use of modeling and 3D printing.

• Lesson Plan: Math Expressions (A+B)³
• Creator: Venkateswaran
• Subject: Math
• Grade Level: 7th-9th
• Level of Difficulty: Easy

Standards covered

MS-ETS1-3 ENGINEERING DESIGN Analyze data from tests to determine similarities and differences among several design solutions to identify the best characteristics of each that can be combined into a new solution to better meet the criteria for success.

HS-ETS1-4 ENGINEERING DESIGN Use a computer simulation to model the impact of proposed solutions to a complex real-world problem with numerous criteria and constraints on interactions within and between systems relevant to the problem.

CCSS.MATH.CONTENT.7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Teacher instruction

TinkerCAD software was used to design the cubes. The dimensions are provided in the images for reference. The side A was chosen to be 2 cm and B was chosen to be 3 cm. Rest of the calculations follow as per the equation:

(A+B)³ = A³ + 3A²B + 3B²A + B³

Student instructions

Theoretical Explanation of the Math Expression with 3D Models

A³ and B³ Model Dimensions

A²B and B²A Model Dimensions

Project Info:

Apply the knowledge of modeling primitive shapes using TinkerCAD Utilize physical measurement and modeling technique to other complex mathematical expressions and formulae Explain the concept of Pascal’s Triangle in an intuitive and novel approach Make use of technology to simplify the teaching approach for better and quicker understanding amongst students

Pascal’s Triangle:

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
...

For example:

(a+b)⁰ = 1
(a+b) ¹ = a¹+b¹ = a+b
(a+b) ² = a²+2ab+b²
(a+b) ³ = a³+3a²b+3ab²+b³
(a+b) ⁴ = a⁴+4a³b+6a²b²+4ab³+b⁴

...

Key questions

How will you apply this learning session in your classroom?

What are the subject areas in Mathematics and Physical Measurement wherein this modus of operand will help the students grasp the concept?

How will this technique help the students to apply it to their real life problems and applications?

Author notes

For a group of 30 Students, you may have to split them into a batch of 5 students each. So for each batch you would need one set of cubes without names engraved on them and one more set of cubes with names engraved in them. During the first 75% of the teaching pedagogy you would need only the cubes without the names engraved.

After the printing of a cube is initiated, you may collect the cubes (without names) back and then hand over the cubes with names and teach them the mathematical expression and ask them to assemble.

The A²B and B²A models need to be printed in quantities of 3 each. The A³ and B³ models need one quantity each.

Remember: in order to print them in different colors, you will have to load them separately.