Math Facts Strategies
Gloria Cuellar-Kyle
As your child is learning basic math facts, it will help him or her to understand a few simple strategies
to solve these facts.
Children that are able to identify the relationship between addition and subtraction can readily master
both addition and subtraction facts. At the elementary grade level these relationships are called the
Fact Families. The bar or strip diagrams below illustrate the relationship between the members of the
same Fact Family:
5
2
3
2+3=5
5
3
2
3+2=5
5
2
?
5 – 2 = ? (3)
5
3
?
5 – 3 = ? (2)
Fact Families are a building block for MANY math skills. At the most basic level Fact Families help
children easily recall basic facts. But as in any foundational construct, Fact Families are critical
bridges to more advanced mathematics. Fact Families help children solve for unknown values, lay
the groundwork for the Associate and Commutative Properties, serve as a base for inverse math
relationships, and numerous other concepts. Please check out the link below for an article describing
the value of leaning and applying an understanding of Fact Families.
http://eduplace.com/math/mathsteps/1/b/index.html
Math Facts Strategies
Gloria Cuellar-Kyle
Addition
addend + addend = sum
6
+
4
= 8
The above vocabulary is primarily for parents and utilized in descriptions for addition strategies on
this page.
Counting On – Plus One
This strategy is used when adding small numbers such as 1,2, or 3 to any number.
Children can use counter or a number line (sometimes I use the cm side of a ruler) to help children
visualize the addition.
Once children have a solid understanding of adding with counters or a number line there is another
example that may be helpful.
7+1= __. Tell your child to “hold” the larger number in their mind and count up 1. (think 7,8) Other
examples would be 1 + 6 =__ (think 6, 7) or 8 + 2 =__ (think 8, 9,10)
Addition Facts When One Addend is Plus Two
Spend some time reviewing odd and even numbers. Children that are familiar with odd and even
numbers will easily see the commonalities in adding two and counting by odd or even numbers.
When adding 2 to an even number the sum will be the next consecutive even number. For instance
when adding 4 (even number) + 2 = 6 (next consecutive even number)
When adding 2 to an odd number the sum will be the next consecutive odd number. For instance
when added 5 (odd number) + 2 = 7 (next consecutive odd number)
Addition Facts for Addends that are Doubles
1+1
2+2
3+3
4+4
5+5
6+6
7+7
8+8
9+9
10+10
Use counters, beans, coins or buttons to model addition of doubles. Line up 3 buttons on the left and
3 buttons on the right. Discuss how the two addends are equal or represent a double. Giving
children a visual for adding doubles will be of great value when children begin to multiply and divide.
Math Facts Strategies
Gloria Cuellar-Kyle
Math Facts Strategies
Gloria Cuellar-Kyle
Addition Facts for Sums of Ten
1+9
2+8
3+7
4+6
5+5
6+4
7+3
8+2
9+1
10 + 0
A ten-frame is a perfect tool to help children visualize addends that yield a sum of ten.
What is a ten-frame? Simply put a ten-frame is a rectangle cut into 10 equal sections (see illustration
below). Students place counters in the ten-frame to model the numbers 1 through 10. Ten-frames
are highly useful tools for developing number sense within the context of ten. Arranging counters in
different ways on the ten-frame prompts students to form mental images of the numbers represented.
The National Council of Teachers’ of Mathematics points out, "The ten-frame uses the concept of
benchmark numbers (5 and 10) and helps students develop visual images for each number."
When using a ten-frame, students can easily see that 6 is 1 more than 5 and 4 less than 10, or that 8
can be seen as "5 and 3 more" and as "2 away from 10." Once students are able to visualize the
numbers 1 through 10, they begin to develop mental strategies for manipulating those numbers, all
within the context of the numbers' relationship to ten.
Ten-frame resources
See the Dot Card and Ten Frame Package 2005 file for suggested activities.
http://www.youtube.com/watch?v=p6RaMGDPfJg&NR=1
http://illuminations.nctm.org/Activity.aspx?id=3565
Math Facts Strategies
Gloria Cuellar-Kyle
Math Facts Strategies
Gloria Cuellar-Kyle
Addition Facts for Addends that are Ten Plus an Addend
10 + 1
10 + 4
10 + 7
10 + 2
10 + 5
10 + 8
10 + 3
10 + 6
10 + 9
10 + 10
Once children learn the basic addition ten facts they can then easily begin to add multiples of ten to a
number. The ability to add ten to a number is one of the essential precursors to adding and
regrouping larger numbers.
Addition Facts When Addends are Consecutive Numbers- Doubles Plus One
A review of doubles would be most helpful before beginning Doubles Plus One.
Using counters will greatly benefit children in visualizing the doubles plus one strategy.
Below are some steps to consider when adding a doubles plus one fact, like 6 + 7
* Double the lower number, which in this case would provide you with 6 + 6 =12.
* Now add one: (The second 6 was a 7, remember?)
* Think 6 + 6 + 1 = 13 or 12 + 1 = 13.
* Now say the fact: 6 + 7 = 13
One of the tactics that we can use help children is to recognize when to use a particular strategy. For
the Doubles Plus One strategy, explain to the children "when the numbers are next door neighbors
(the numbers are consecutive like 6 and 7) then we can use the doubles plus one strategy.
Addition Facts When One Addend is 2 Greater - Doubles Plus Two
If a child is faced with the 5 + 7, think through the same steps as Doubles Plus One except add 2
instead of one. This works for facts that have number that are separated by two. When helping a
Math Facts Strategies
Gloria Cuellar-Kyle
child to recognize when to use this strategy explain them to use it "when the numbers are NOT next
door neighbors, but two doors down from one another."
Subtraction
minuend - subtrahend = difference
6
4
= 2
The above vocabulary is primarily for parents and utilized in descriptions for subtraction strategies on
this page.
Count Backward
As the name implies, children begin with the Minuend and count backward the amount indicated in
the subtrahend to solve for the difference. A cm ruler is a great tool to help students visualize
counting backward. In addition, you may wish to place a counter at each cm and as the child counts
backward remove (or subtract) the counter to further reinforce the concept of subtraction.
Minus One,
Have children place the number of minuend counters on the table then take away one. Also, you may
wish to place a counter at each cm and as the child removes one (or subtract) the child can easily
see that minus one yields the number that precedes the minuend.
Minus Two
Spend some time reviewing odd and even numbers before working on subtraction by two. Children
that are familiar with odd and even numbers will readily see the relationship in subtracting or taking
away two and counting backward by odd or even numbers. Using a 120’s chart can help children to
visualize the process. Simply place a counter on the minuend and then “jump back” two.
Once children are comfortable with the “jumping back” on the 120’s chart, begin to ask your child
questions that will help them to see a commonality for all instances when subtracting 2. Questions
such as, “When subtracting 2 from an even number the answer/difference always seems to be ___
(the preceding even number). Example: 6 (even number) - 2 = 4 (preceding even number). When
subtracting 2 from an odd number the difference will be the preceding odd number. Example: 5 (even
number) - 2 = 3 (preceding even number)
Math Facts Strategies
Gloria Cuellar-Kyle
This line of questioning expands children’s understanding of subtraction from a rote or isolated
process to a deeper relational understanding of how math concepts are interdependent.
Minus a Double
Before beginning to subtract Doubles, review the Doubles Facts for addition. Students that know the
Doubles Addition Facts will have a big advantage and will help them to more easily understand the
subtraction connection. When students see the members of a double fact family they can clearly see
the association. For instance:
6
3
3
3+3=6
6
3
?
6–3=3
One additional strategy is to have children use counters. Counters could be beans, coins, or buttons
– any object that children can easily manipulate. Have the child use the counters to represent the
minuend. Then ask the child to separate the counters into two equal groups, or doubles. Children
will quickly see that the resulting subtrahend and difference are the same amount. It is important that
children master this skill as it is a precursor to the later skill of division.
Minus from Ten
Before beginning to subtract from ten, review the Sums of Ten. The students that know the Sums of
Ten will have a giant head start. Knowing the Sums of Ten Facts helps students to more easily
subtraction from a minuend of 10. An additional strategy is to have students build bar/strip diagrams
to visualize the relationship between the Sums of Ten and the Minus from Ten facts.
10
2
8
2+8=
8 + 2 = 10
10 – 8 = 2
10 – 2 = 8
For Subtraction I can use the Bar/Strip diagram above. If I know that 10 is the total and I take away 8
I am left with 2. Conversely, if 10 is the total and I take away 2 I am left with 8.