Subtraction A Better Way
www.subtractionabetterway.com
For years my students struggled with learning their subtraction facts. Addition
strategies were so powerful, but I could not find any comparable strategies for subtraction.
The seed of the idea for these strategies started many years ago in a “Math Their Way”
workshop. I have been teaching these four strategies with my “Tower of Twenty” for the
past seven years with promising results. My prayer is for your students to have the same
success as mine.
Ginnie Luce
2nd grade teacher, retired
Otterbein Elementary
Otterbein, Indiana
0
1
2
3
4
5
6
7
8
9
18 17 16 15 14 13 12 11 10 9
9
9 8
9 8 7
9 8 7 6
9 8 7 6 5
9 8 7 6 5 4
9 8 7 6 5 4 3
9 8 7 6 5 4 3 2
9 8 7 6 5 4 3 2 1
9 8 7 6 5 4 3 2 1 0
8
8
7
6
5
4
3
2
1
0
7
7
6
5
4
3
2
1
0
6
6
5
4
3
2
1
0
5
5
4
3
2
1
0
4
4
3
2
1
0
3
3
2
1
0
2
2
1
0
1
1
0
0
0
This table represents the basic subtraction facts that children need to know.
There are 100 basic facts illustrated in blue, yellow, purple, and tan.
BLUE-Strategy One-18 facts
Strategy One facts are problems in which one takes away 0, 1, and 2. When I present these facts,
we use the first ten in the Tower of Twenty and we practice taking away 0, 1, and 2.
YELLOW-Strategy Two-27 facts
Strategy Two facts are problems that have a difference of 0, 1, and 2. When I present these facts
to learn, we work with partners to compare our towers. Thus students are introduced to the idea
that subtraction can be thought of as the difference between numbers.
TAN-Strategy Three-45 facts
These are the hardest facts for children to learn. They are difficult because young children have
trouble when they run out of fingers. I've found that my Tower of Twenty helps them visualize
those numbers above ten. This is a very powerful strategy. When students internalize this
strategy, they have mastery of 45 of the toughest problems.
PURPLE-Misfits-10 facts
These are the last ten facts to learn. They are not difficult, but do not fit into the other strategies.
Strategy One
In Strategy One, students will be exploring subtraction problems, which require them to subtract
zero, one, or two from a number.
This is a very easy strategy to learn by showing a number and then breaking off zero cubes, one
cube, or two cubes. Accordingly, the concept of adding to check a subtraction problem will be
introduced.
Depending on the age of the student, this step could be mastered very quickly.
If you take away zero, you get the very same
number.
If you take away one, you count back one, just like
they do in mission control.
If you take away two, you count back the even and
odd numbers.
Strategy Two
In the second strategy, the teacher focuses on the mathematical term “difference”. Students work
in partners to compare numbers that have a difference of zero, one, and two.
Each lesson is designed to include discovery opportunities for finding the difference. These
problems would be analyzed so that students would know what to do when they see a subtraction
problem involving two numbers that are the same, two numbers right next to each other on the
number line, and two numbers that are said when counting backward by the odd or even
numbers.
I teach strategy One and Two in tandem. Songs, activities, and worksheets help reinforce these
two strategies that make up 45 of the 100 basic subtraction facts.
Difference of 0
Difference of 1
Difference of 2
Strategy Three—Ten Buddies
This is the strategy that takes the most time. I have come to believe that taking the time
needed to internalize this strategy is well worth it. The great thing about this strategy is
that once they learn the principle behind this strategy, they have at their fingertips 45 of
the toughest math facts! Excited? Here’s how it works.
Step 1: Build the Problem
During this step, students will need to be encouraged to think of the difference as 3 to the
10 plus five above the ten that equals 8. Practice with this step is very important to
prepare for the next step, illustrated in Step 2.
Each lesson will immerse students in the language of this strategy. The two colors in the
Tower of Twenty help students see where one unit of ten ends and the other unit of ten
begins.
Notice how the student broke off the
cubes above 15 and put them aside.
Next the student cracks 7 cubes off
the bottom of the tower. Last, they
say 3 to the 10, plus 5=8
Step 2: Moving to the Abstract
During the teaching of this
step, I unashamedly require
that students verbalize going
to the 10 first and then the
cubes above the ten. When
students know their "ten
buddies" or the sums of ten as
some texts call it, this step
becomes no harder than a
small addition fact. The
speech bubbles show the language
I require when solving
these "ten buddy facts".
3 to the 10
+5
8
3 to the 10
+6
9
16
-7
5 to the 10
+3
8
13
-5
15
-7
Strategy Four--Misfits
These 10 facts are not necessarily hard, but they don’t fit in any of the strategies. Some
time should be set aside to learn these ten facts.
I use visualization strategies to help students picture these facts. Then, practice,
practice, practice.
8
-3
8
-4
9
-4
9
-5
9
-3
7
-3
6
-3
8
-5
7
-4
9
-6
Ginnie Luce
Box 98
Otterbein, IN 47970
ginnie.luce@gmail.com
765 583 4578 (home)
765 490 9998 (cell)