Using fingers to count and do simple math is a technique that many children utilize when first learning numbers and arithmetic. As we grow older, we often stop relying on our fingers for math and instead do mental calculations in our heads. However, using fingers can still be a helpful tool for certain types of math, even for adults. Here we’ll explore when finger counting can be useful and how to effectively use your fingers to add, subtract, multiply, and more.
When is finger counting helpful?
Finger counting can be particularly useful for:
- Learning numbers and math as a child
- Double checking mental math as an adult
- Doing math when paper/pencil not available
- Visualizing numbers and arithmetic
- Catching mistakes in mental calculations
- Doing math when distracted or under pressure
As children first learn numbers and math, using their fingers provides a visual and tactile way to understand quantities, addition, subtraction, etc. Physically counting out numbers on their fingers helps cement early math concepts. As adults, we may occasionally revert back to using our fingers when doing math in our heads as a way to double check our mental calculations or when we don’t have the luxury of pen and paper. Finger counting provides a quick way to visualize numbers and catch any errors in mental math. It can also be helpful when doing math while under distractions or time pressure.
How to count on fingers
There are a few different techniques for using your fingers to count, do arithmetic, and represent numbers:
- Counting each finger: This is what most young children do when first learning to count. You simply count one finger at a time, holding up a new finger with each number you say. This allows counting up to 10 on two hands.
- Representing quantities: With this method, you use your fingers to directly model quantities. For example, to show the number 7, you would hold up 7 fingers. This allows modeling numbers up to 10 easily on two hands.
- Base 10 system: More advanced finger counting uses your hands to represent numbers in base 10 place value columns. Each finger represents a place value column, with your pinky as the 1s column, ring finger as the 10s, etc. This allows efficiently modeling much larger numbers on just two hands.
Technique 1: Counting each finger
This is the simplest finger counting technique. You start with no fingers raised, then count out loud while raising one finger at a time with each number said. Once all 10 fingers are extended, you are at the number 10.
To use this technique:
- Start with no fingers raised, palms facing each other.
- Say “one” while raising the index finger of your left hand.
- Say “two” while raising the index finger of your right hand.
- Continue alternating hands, counting each finger as you raise it.
- Once all fingers are extended, you’ve reached 10.
While limited for larger numbers, this provides a straightforward way to visualize counting from 1-10 on your hands.
Technique 2: Representing quantities
With this method, you use your available fingers to directly represent any quantity from 1 to 10. For example:
- To show the number 5, raise 5 fingers.
- For the number 8, hold up 8 fingers.
- To represent 10, extend all 10 digits.
This provides a simple way to model one-digit numbers. To count higher quantities:
- Use your left hand pinky finger to represent “tens”.
- The remaining right hand fingers then represent ones.
- For example, raising your left pinky and 5 fingers on your right shows the number 15.
This finger counting approach helps reinforce number sense and one-to-one correspondence between quantities and symbols.
Technique 3: Base 10 system
A more advanced finger counting approach uses your hands to represent numbers in base 10 columns. This takes advantage of the fact that we have 10 fingers to model the place value system used in our number system.
In this technique:
- Left pinky = 1s place
- Left ring finger = 10s place
- Left middle finger = 100s place
- Left index finger = 1000s place
- Left thumb = 10000s place
- Right thumb = 100000s place
- Right index = 1000000s place
- Right middle = 10000000s place
- Right ring = 100000000s place
- Right pinky = 1000000000s place
You can represent any number up to 10 billion with this system. For example, to show the number 72,305:
- Hold up your left pinky, right pinky, and thumb (1s, 10,000s, and 100s place)
- Keep remaining fingers curled down
This mimics the base 10 place value structure and provides a powerful finger counting technique for working with large numbers. It does require practice to master and accurately model numbers in this finger positions.
Using fingers for basic math operations
Counting with your fingers can also help with basic addition, subtraction, multiplication, and division. Here are some tips:
Addition
- Model each addend with your fingers.
- Count total fingers extended to reach the sum.
- For example, to add 5 + 7:
- Hold up 5 fingers on left hand
- Hold up 7 fingers on right hand
- Count total fingers to reach 12
Subtraction
- Model minuend with fingers.
- Curl down fingers to represent subtracting subtrahend.
- Remaining extended fingers give difference.
- For example, to calculate 9 – 3:
- Hold up 9 fingers
- Curl down 3 fingers
- 6 fingers remain extended
Multiplication
- Model groups of fingers to show multiplication.
- For example, for 4 x 5:
- Hold up 5 fingers on left hand
- Hold up 5 fingers again on right hand
- That’s 2 groups of 5 fingers, or 10 fingers total
Division
- Model total fingers representing dividend.
- Split fingers into groups to divide.
- Number of groups gives quotient.
- For example, for 12 / 3:
- Hold up 12 total fingers
- Split into 3 groups of 4 fingers
- 3 groups means quotient is 3
Finger counting strategies
To effectively use finger counting for math:
- Start simple – begin with basic counting and modeling quantities under 10.
- Build up place value understanding – move to modeling larger numbers in base 10 columns.
- Reinforce with visuals – draw hands depicting finger positions to reinforce technique.
- Practice, practice – finger dexterity and position sense require repetition.
- Say numbers aloud – vocalize while modeling numbers with fingers.
- Double check tricky math – use fingers to validate mental calculations.
- Conceal if needed – be discreet with finger use if self-conscious.
Be patient in learning finger counting techniques. With regular practice, even adults can master using their fingers to efficiently model, calculate, and validate math problems and mental arithmetic. It provides a portable, visual approach to working with numbers wherever you are.
Benefits of using fingers for math
Using your fingers for counting, arithmetic, and representing numbers provides many benefits, including:
- Portability – Your fingers are always available whenever math is needed.
- Kinesthetic learning – Physically interacting with numbers helps reinforce math concepts.
- Multisensory – Combining touch, sight, motion engages brain in multiple ways.
- Accuracy – Provides a way to double-check mental math and catch errors.
- Speed – Finger counting is relatively fast once proficient.
- Discreet – Can subtly use finger math without attracting attention.
- Visualization – Models quantities and number relationships concretely.
Students of all ages can benefit from using their fingers appropriately to support math learning and numerical thinking. The hands-on, multisensory approach finger counting provides makes it highly effective for building math skills and number sense.
Potential limitations
While useful in many circumstances, finger counting does have some potential limitations to be aware of, including:
- Limited range – Quantity is constrained to 10 digits.
- Can be distracting – Finger motion may divert mental attention.
- Public self-consciousness – Some shy away from finger use in front of others.
- Over-reliance – May become a crutch that inhibits mental math fluency.
- Motor skills – Requires adequate finger dexterity and coordination.
However, when utilized appropriately, the benefits of finger counting generally far outweigh the limitations for most children and even many adults when learning math and arithmetic. It provides a scaffold to build up foundational math skills.
Conclusion
Using our fingers is an innately human approach to counting, visualizing numbers, and doing mental math. Finger counting techniques give us a portable, discreet, visual, and tactile way to representation quantities, model arithmetic, and reinforce our mental number sense. With some dedicated practice, even adults can master effective strategies to benefit from finger math. While fingertips may fade as our primary calculation tool, they can still serve as useful aids when doing math in a pinch or providing conceptual support for trickier arithmetic. If used judiciously, finger counting helps build computational fluency, accuracy, and confidence for math students of all ages.