Base-Ten Blocks
Why Is This Strategy Useful?
Interestingly, the English language lacks distinct words to describe named-value or base- ten
concepts. In order to use and understand base-ten written marks and to add and subtract multidigit numbers, children need to link the words and the written marks to each other. Base-Ten
Blocks can make abstract ideas like place value and regrouping visible and tangible for
elementary students when teaching subtraction. Base ten blocks are an excellent teaching tool
for helping children learn math concepts because they allow children to touch and manipulate
something real while learning important skills that translate well into paper and pencil addition.
Base-Ten blocks are a physical representation of numbers, and are appropriate for use with
young elementary students.
Description of Strategy
Base-Ten blocks are a tangible representation of numbers that can direct students’ attention to
crucial meanings and help to understand their actions. Base-Ten blocks can be purchased for
use, made or drawn when teaching students this technique. Generally, there will be three
symbols used to show students the value of numbers: a single cube will represent tens place, a
rod of cubes usually 10 cubes long will represent the tens place and a board of 10 rods together
represents the hundreds’ place value (see Sample Activity for a visual representation of this).
Students may use sets of blocks to perform addition or subtraction problems. While using these
tools, students begin to generalize mathematical concepts, making it easier for them to
reproduce correct answers.
Research Evidence
At least one quasi-experimental study supports this strategy. This experiment included two
studies which examined the effects of the base-ten block strategy. Participants were 169 firstgraders and 79 second graders from two schools in Chicago. Each class had at least one set of
base-ten blocks. The first phase of instruction focused on exploration of the relationships
between the different blocks and on use of the blocks word, the blocks were then used to make
three and four digit numbers. Results indicated that the second graders and high-ability first
graders showed multi-digit addition and subtraction computation performance that was
considerably above that shown by third graders receiving traditional instruction. These children
also showed competence far above that usually demonstrated by third graders in verbally
labeling tens and hundreds places.
Sample Studies Supporting this Strategy
Fuson, K.C., & Briars, D.J., (1990). Using a Base-Ten Blocks Learning/Teaching
Approach for First- and Second-Grade Place-Value and Multi-digit Addition and
Subtraction. Journal for Research in Mathematics Education, 21(3), 180-206
This quasi-experimental study examined the effects of base-ten learning/teaching approach on
the performance of first and second graders when adding and subtracting multi-digit numbers.
Steps in addition and subtraction of four-digit numbers were motivated by the size of the blocks
and then were carried out with the blocks; each step was immediately recorded with base-ten
numerals. Children practiced multi-digit problems of from five to eight places after they could
INQUIRE summaries available at schools.nyc.gov/inquire
Study abstract reproduced with permission, copyright © 1990, National Council for Teachers of Mathematics,
www.nctm.org. All rights reserved.
successfully add or subtract smaller problems without using the blocks. There were two studies
performed: in Study 1, six of the eight classes of first and second graders totaling 169 students,
demonstrated meaningful multi-digit addition and place-value concepts up to at least four-digit
numbers; average-achieving first graders showed more limited understanding. Three classes of
second graders, 75 students, completed the initial subtraction learning and demonstrated
meaningful subtraction concepts. In Study 2 most second graders in 42 participating classes,
totaling 783 students, in a large urban school district learned at least four-digit addition, and
many children in the 35 classes, totaling 708 students, completing subtraction work learned at
least four-digit subtraction.
Source: (http://www.math-drills.com/baseten.shtml)
INQUIRE summaries available at schools.nyc.gov/inquire
Study abstract reproduced with permission, copyright © 1990, National Council for Teachers of Mathematics,
www.nctm.org. All rights reserved.