3-Dimensional Fraction Blocks

Author: jrsnyder, published on 2013-11-17

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Do not underestimate the many effective uses for this manipulative!! These Fraction Blocks have applications from early grades and introductory fraction concepts through Algebra 2 and beyond! Much of the effectiveness of this tool lies in its simplicity, and files are very easy to print; the blocks are perfect for the beginning 3-D printer operator.

Fractions are often taught using 2-dimensional figures, graphics or manipulatives. Using 3 dimensions, students can better understand fractions through increased spatial awareness while introducing area and volume concepts at an earlier age. The fractional nature of the blocks can be expanded to concepts of volume, surface area, growth and scale factors, ratios and proportions, etc.

Various files can be printed based on the concept being taught or the grade level of the student. Blocks can be printed both with or without fraction labels.

See the instructions for a few ideas on how to use the Fraction Blocks to teach various concepts at different levels of mathematical ability.


One of the greatest things about this manipulative is the fact that it is scalable to grade level and depth of concept being taught. The instructions below provide instructions for printing and using your Fraction Blocks based on these factors.

The given files are scaled so that the largest block, the one-unit block, will measure exactly 10cm x 10cm x 10cm. This is most likely too large for student use, but can make a great demonstration tool for the teacher. Student models should be scaled down by 50% to produce a student unit cube that measures 5cm x 5cm x 5cm.

A. Introductory Fraction Concepts

  1. Print the base and the labeled blocks: one, one-half, one-third, one-fourth (a), one-fifth, one-sixth (a), one-seventh, and one-eighth (a). It is recommended that you print each type of block in a different color if possible, for easy identification. Print enough of each block so that together they can form one whole (i.e. print two one-half blocks, three one-third blocks, etc.)

  2. Use the blocks to explore how a whole can be divided into equal parts.

Sample prompts:
“How many thirds does it take to equal one whole?”
“How many sixths does it take to equal one whole?”
“If a whole is divided into seven equal parts, what is the size of one part?”

  1. Use the blocks to explore equivalent fractions or missing parts of the whole.

Sample prompts:
“How many fourths does it take to create one-half?”
“One-eighth plus one-eighth is equal to what other fractional part?”
“Given one fourth and one eighth, what fraction combinations would you use to complete the whole?”

  1. Extension. The one-fourth, one-sixth and one-eighth blocks have more than one block shape. These are labeled as b and c blocks. These blocks can be used to show that equivalent fractional parts can come in different forms, and can be used for an early discussion about equivalent volumes in relation to different shapes. Print these blocks in the same color as their fractional equivalents for easy identification.

B. Length, Surface Area and Volume Relationships.

  1. Print the one-unit cube, the one-eighth (c) cube and the one-sixty-fourth cube. Choose either the labeled or unlabeled versions of each. These three cubes can be used as an introduction to the scale factor relationships between length, surface area and volume.

Sample Prompts:
“How does the length of one edge of the one-eighth cube compare to the length of one edge of the unit cube?” (it is one-half the length)
“How does the area of one face of the one-eighth cube compare to the area of one face of the unit cube?” (it is one-fourth the area)
“How does the volume of the one-eighth cube compare to the length of the volume of the unit cube?” (it is one-eighth the volume)

Extend these ideas to the 1/64 cube and ask students to find a pattern (the linear scale factor is squared to find the surface area and cubed to find the volume). Extend these ideas by printing other non-regular blocks and explore the change in dimensions, surface area and volume.

There are many, many more exciting way to use these blocks! Share your ideas!

License: Creative Commons – Attribution – Share Alike

Tags: 3d, blocks, curriculum, fractions, MakerBotAcademyMath, manipulative, math, proportion, ratio, surface_area, volume