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Learning mathematics through Minecraft
Author(s): Beth Bos, Lucy Wilder, Marcelina Cook and Ryan O'Donnell
Source:
Teaching Children Mathematics,
Vol. 21, No. 1 (August 2014), pp. 56-59
Published by: National Council of Teachers of Mathematics
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56 August 2014 • teaching children mathematics | Vol. 21, No. 1 www.nctm.org
iSTEM
Learning mathematics
through Minecraft
Beth Bos, Lucy Wilder, Marcelina Cook,
and Ryan O’Donnell
Technology has a natural drawing power
for today’s youth. It stimulates their inter-
est, curiosity, and creativity (Dawley and
Dede 2012). Students are naturally inquisitive
and explore without fear of failure when using
technology. All these traits help them investigate
mathematics within game-based technology.
One of the popular game-like environments
that children enjoy is Minecraft, a Web-based
environment that can be downloaded from the
Internet (https://minecraft.net/) onto a smart-
phone, iPod®, iPad®, or computer.
Interacting with a virtual world
Minecraft, created by Markus Persson and Jens
Bergensten, has captured the attention of many
users and has a special appeal for the younger
user because of its three-dimensional Lego®-
like environment in which the user can build
and interact with a virtual world. Minecraft is
an open-world game within a sandbox environ-
ment that has no specifi c goals for the player
to accomplish while in default settings, thus
allowing students a large amount of freedom
in choosing how to play the game. The world is
made of blocks of different colors and simple
patterns that represent a variety of organic and
hand-crafted materials.
Initially, play is from a fi rst-person perspec-
tive in a 360 degree environment and involves
breaking and placing blocks. Although players
move freely across the world, objects and items
can be placed only at fi xed locations relative to
positioning on a grid. Players can gather these
material blocks and place them elsewhere,
allowing for various building projects.
The game has two modes: creative and sur-
vival. In the creative mode, players have access
to unlimited blocks and can fl y freely around
the world. The survival mode has four levels.
The easiest (peaceful) level removes any hos-
tile creatures; the harder the level, the more
advanced the hostile creatures. For teaching
mathematics, the creative mode is a perfect
sandbox environment to explore such concepts
as algebraic patterns, measurement, perimeter,
area, and volume.
Building a coastal community
Within a three-day math unit in a third-grade
classroom, students used Minecraft to explore
area and perimeter. First, the teacher reviewed
the defi nition of perimeter and area. Using a
class set of iPods with Minecraft downloaded
and installed, students were asked to go to the
creative mode to build a coastal town with a
pier area of 12 square meters, a bait shop with a
perimeter of 12 meters, a restaurant with an area
of 24 square meters, and a square store with an
area of 16 square meters (see fi g . 1 and g . 2 ).
Notice the Lego-like feel of the virtual world.
Each square block represented a cubic meter.
The units were carefully chosen to give students
choices of stone with different dimensions.
After building their structures, they compared
and discussed the similarities and differences
among one another’s confi gurations. Questions
were raised about the different choices of shapes
for the buildings (narrow and thin or almost
square). The variety of possible dimensions
inspired a rich discussion. Students found that
only one set of dimensions was possible for the
store (a square building). This discovery led to
making conjectures about the structures’ shapes
and their relationship to perimeter and area.
The difference between the two terms became
clearer with the visual imagery as students used
the length of the side of one cube repeatedly to
measure the distance around (perimeter of) a
shape and counted the number of squared units
forming the base shape (area).
Designing a scenario means providing a
purpose for students to use the skills they have
learned in class to explore and achieve a greater
depth of understanding. Minecraft forms a
medium to explore possibilities.
Copyright © 2014 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved.
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www.nctm.org Vol. 21, No. 1 | teaching children mathematics • August 2014 57
Playing with mathematical ideas
Minecraft can be used for instruction, reme-
diation, or extension activities for anytime,
anywhere learning. Students typically play
Minecraft at home, at the game field, and riding
in the car—extending their learning outside the
walls of the school. Offering a Minecraft video,
posted on the class website, is a great way to get
your students started. Encourage them to do the
activity on video and take a screenshot of their
final product to share with others at school. Play
becomes an opportunity to explore mathemati-
cal ideas within an online community.
Students working with Minecraft are unafraid
to try a different configuration, to make a new
tool, or to discover the attributes of a stone.
Their only limitations may be what questions
to ask and which problems to solve, and that
is where the teacher contributes meaningful
scenarios and pertinent questions reflective of
the curriculum. See table 1 (pp. 58–59) for more
Minecraft activities.
REFERENCE
Dawley, Lisa, and Chris Dede. 2012. “Situated
Learning in Virtual Worlds and Immersive Sim-
ulations.” In The Handbook of Research for
Educational Communications and Technology.
4th ed. Edited by J. Michael Spector, M. David
Merrill, Jan Elen, and M. J. Bishop, pp. 723–34.
New York: Springer.
Beth Bos, bb33@txstate.edu, an associate professor
at Texas State University, is interested in elementary
school mathematics and micro-identities. Lucy Wilder,
law143@txstate.edu, has been an elementary school
instructional coach for six years in San Marcos CISD,
Texas. She is interested in mathematical problem
solving. Marcelina Cook, marcelina.cook@
austinisd.org, a math and science instructional
coach at Campbell Elementary School in Austin ISD,
Texas, is interested in creating alternative ways of
demonstrating geometric concepts and its applications
to real-world problems as well as technological uses
that pique the interest of her students.
Ryan O’Donnell, ryan.odonnell@austinisd.org,
works as a senior associate of student learning and
assessment for the Of fice of Educator Quality in the
Austin ISD in Texas. He is interested in numeracy and
building students’ numerical fluency foundation.
Edited by Terr i K ur z, terri.kurz@asu.edu, who
teaches mathematics and mathematics methodology
at Arizona State University, Polytechnic in Mesa, and
Jorge Garcia, Jorge.garcia@csuci.edu, who teaches
at California State University Channel Islands.
Each month, this section of the Problem Solvers
department features a new challenge for students.
Readers are encouraged to submit problems to be
considered for future columns. Receipt of problems
will not be acknowledged; however, those selected
for publication will be credited to the author. Find
detailed submission guidelines for all departments
at www.nctm.org/tcmdepartments.
On class iPods that had the Minecraft application already
installed, students used the creative mode to build a coastal
town. This is a screenshot of a pier area and bait shop.
FIGURE 1
This screenshot shows the restaurant.
FIGURE 2
LUCY WILDER LUCY WILDER
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58 August 2014 • teaching children mathematics | Vol. 21, No. 1 www.nctm.org
iSTEM
Kindergarten CCSSM Use of Minecraft
Understand addition as putting
together and adding to, and understand
subtraction as taking apart and
taking from.
Use cubes to build trains with a certain number of cubes (numbers
11–19); have student count and then group in trains of 10 to gain
foundation for place value.
Identify and describe shapes. Analyze,
compare, create, and compose shapes.
Students can identify and create squares, rectangles, and triangles.
Analyze, compare, create, and compose shapes in two and three
dimensions.
Grade 1 CCSSM Use of Minecraft
Represent and solve problems involving
addition and subtraction. Understand
and apply properties of operation. Add
and subtract within 20.
Add and subtract blocks using numbers 1–20. Work with simple
equations and have students create block structures to illustrate
problem. Have them create structures by following an equation,
and have another student guess the equation they used.
Measure lengths indirectly and by
iterating length units.
Measure length of buildings by iterating length of cubes.
Grade 2 CCSSM Use of Minecraft
Represent and solve problems involving
addition and subtraction. Add and
subtract within 20. Work with equal
groups of objects to gain foundations for
multiplication.
Build solid towers with a base of 2 and count by twos to fi nd the
total number of cubes used. Repeat with a base of 3, base of 5,
and base of 10. Use fl ats of 10 and towers of 10 × 10 to add and
subtract three-digit numbers.
Reason with shapes and their attributes. Partition rectangles made with twelve cubes into two, three, or four
equal shares. Describe the shares using the words halves, thirds,
fourths, and quarters; and use the phrases two-halves, three-thirds,
and four-fourths. Recognize that equal shares of identical wholes
need not have the same shape.
Grade 3 CCSSM Use of Minecraft
Numbers and operations in base ten Build solid towers with base of 10 and chimneys with various
heights. Estimate the number of cubes. Write an equation using
both multiplication and addition to fi nd the number of cubes in the
structure. Take a picture and send it to the teacher. What would you
build to show 3 × 10 – 8? Take a picture and send it to the teacher.
Geometric measurement: recognize
perimeter as an attribute of plane fi gures
and distinguish between linear and area
measures.
Have students build buildings with the same perimeter and
different areas, and with the same area and different perimeters.
The following activities are organized by grade and the Common Core State Standards for Mathematics
(CCSSM) (CCSSI 2010) to show different mathematics activities possible with Minecraft.
TABLE 1
Additional Minecraft mathematics activities
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www.nctm.org Vol. 21, No. 1 | teaching children mathematics • August 2014 59
REFERENCE
Common Core State Standards Initiative (CCSSI).
2010. Common Core State Standards for
Mathematics. Washington, DC: National
Governors Association Center for Best
Practices and the Council of Chief State
School Officers. http://www.corestandards
.org/wp-content/uploads/Math_Standards
.pdf
Grade 4 CCSSM Use of Minecraft
Gain familiarity with factors and
multiples.
Determine whether a given whole number in the range 1–100
is a prime or composite number. See www.youtube.com
/watch?v=IDr6v9HsmxQ
Use the four operations with whole
numbers to solve problems.
Have students build representations of houses, complete with
windows and doors. Students figure out the total cost of the
house if each cube is worth $12. Students must determine how
many cubes they used by multiplying to find the area of sides and
subtracting the area of the windows and door. Then they add wall
areas together and multiply by $12 and set a budget they cannot
exceed.
Build fractions from unit fractions
by applying and extending previous
understandings of operations on
whole numbers.
Use rods made in lengths of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
Each rod must be a different color. Represent the value of 1 with
the rod that is 12 units long. Add and subtract fractions as joining
and separating parts referring to the whole. Decompose a fraction
into a sum of fractions with the same number in the denominator
in more than one way. Record each decomposition by using an
equation. Justify with your visual fraction model made of cubes.
Grade 5 CCSSM Use of Minecraft
Analyze patterns and relations. Build a triangle by beginning with a base of sixteen cubes (row 8).
On the next row, decrease cubes by two, (row 7), and continue
in this pattern until you have two cubes on top (row 1). Write an
equation showing the relationship between the number of the
row and the number of blocks on that row. Have students develop
similar but original patterns and write as equations showing the
relationship between the row number and the number of blocks.
Interpret multiplication as scaling
(resizing).
Using 1 cube = 1 meter, re-create a model of a historical building
or your school.
Geometric measurement: understand
concepts of volume and relate volume to
multiplication and to addition.
Build towers (solid rectangles) by packing the cubes close together
without gaps. Measure the volume in unit cubes. Apply the formula
V= l × h × w. Recognize volume as additive. Have students find
volumes of solid figures composed of two nonoverlapping right
rectangular prisms formed by cubes by adding the volumes of the
nonoverlapping parts. Also, counting the number of blocks that
were dug out when making a 6 × 6 × 3 cave can support concepts
of volume and area.
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