Learn math the easy way


Learning Math With Manipulatives - Base Ten Blocks (Part II)

In part one of this article, you read aboutvalue blocks until there are enough smaller
representing and adding numbers using baseplace value blocks to remove. The resulting
ten blocks. Once these two skills arepiles after the subtrahend is removed
mastered, it is time to move onto many arepresents  the  difference.
child's nightmare: subtraction. Subtraction,
as you may have heard, is essentiallyIn the example, begin by representing 234
addition in reverse. It can be an arduouswith 2 flats, 3 rods, and 4 cubes. The goal
task on paper, but it can be quite easy withis to remove 187 or 1 flat, 8 rods, and 7
base  ten  blocks.cubes from these piles. Removing one flat is
simple enough, but 8 rods and 7 cubes are
Recall that there are four different base tendifficult to remove if there are only 3 rods
blocks: cubes (ones), rods (tens), flatsand 4 cubes! To solve this problem, trade in
(hundreds), and blocks (thousands). Groups ofone flat for 10 rods, and one rod for 10
ten base ten blocks can be regrouped orcubes. The result would be 1 flat, 12 rods,
traded for equivalent amounts of other baseand 14 cubes. Removing the subtrahend - 1
ten blocks; for instance, ten cubes can beflat, 8 rods, and 7 cubes - at this point
traded for one rod because both are worthwould leave no flats, 4 rods, and 7 cubes.
ten. For subtraction, it is useful to knowThe difference is whatever is left after
how to trade down rods, flats, and blocks.removing the subtrahend, so the difference is
Trading down means converting larger place47.
value blocks into smaller place value blocks.
For instance, one flat can be traded for tenFor beginners, it would be wise to start with
rods  since  they  are  both  worth  100.subtraction that does not require trading.
For example 1954 - 1831 would require no
Before describing the subtraction procedure,trading because there are enough blocks in
let's  go  over  some  vocabulary  .  .  .the minuend to remove the subtrahend. For
more advanced students, questions that
Minuend - The amount from which you areinclude zeros can present a bit of a
subtracting.challenge. For example, 4000 - 3657 would
require several trading steps all starting
Subtrahend - The amount that you arewith four blocks. has several thousand free
subtracting.math worksheets including subtraction
questions with no regrouping (trading). One
Difference  -  The  answer.of the nice features of this website is that
answer keys are provided, so students can get
In the equation, 234 - 187 = 47, the minuendfeedback  on  their  results.
is 234, the subtrahend is 187, and the
difference is 47. Most people don't botherWith enough experience, students learn
with the terms minuend and subtrahend, butsubtraction on a conceptual level and are
they are useful in describing the subtractionbetter equipped to apply it to pencil and
procedure  using  base  ten  blocks.paper methods later on. Students who only
learn the paper and pencil method don't
To begin, represent the minuend with base tenalways develop a conceptual understanding of
blocks. Try to keep the blocks in order fromsubtraction and are less able to identify
largest to smallest as this will help toerrors  in  their  work.
transfer knowledge and skills to paper and
pencil methods later on. Remove from theBase ten blocks are not limited to just
minuend piles, enough blocks to represent theaddition and subtraction of whole numbers. In
subtrahend. If there aren't enough blockspart III of this series, several other uses
available, trade some of the larger placeof base ten blocks will be explored.



1 A B C D 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106