Author: jrsnyder, published on 20131117
Summary
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 3D printer operator.
Fractions are often taught using 2dimensional 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.
Instructions
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 oneunit 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

Print the base and the labeled blocks: one, onehalf, onethird, onefourth (a), onefifth, onesixth (a), oneseventh, and oneeighth (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 onehalf blocks, three onethird blocks, etc.)
 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?”
 Use the blocks to explore equivalent fractions or missing parts of the whole.
Sample prompts:
“How many fourths does it take to create onehalf?”
“Oneeighth plus oneeighth is equal to what other fractional part?”
“Given one fourth and one eighth, what fraction combinations would you use to complete the whole?”
 Extension. The onefourth, onesixth and oneeighth 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.
 Print the oneunit cube, the oneeighth (c) cube and the onesixtyfourth 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 oneeighth cube compare to the length of one edge of the unit cube?” (it is onehalf the length)
“How does the area of one face of the oneeighth cube compare to the area of one face of the unit cube?” (it is onefourth the area)
“How does the volume of the oneeighth cube compare to the length of the volume of the unit cube?” (it is oneeighth 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 nonregular 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