Building Number Intuition: Estimation
What Is Estimation?
Estimation is the ability to make a good guess without calculating exactly. We can, for example, say roughly how many buttons are in a jar without counting them one by one. Or we might be able to predict how many digits will be in the answer to a problem without actually doing the math. To do this, we use different strategies — for instance, counting out 50 buttons and then guessing how many such groups of ten might fit in the jar, or replacing all the numbers in a problem with “round” ones to get a quick sense of the answer.
Why Does It Matter for Kids?
Estimation helps not only in predicting an answer but also in spotting calculation errors — whether our own or a calculator’s. For example, if you multiply two two-digit numbers and see a one-digit result on the screen, chances are you pressed the wrong button. Today, these skills are especially important: while calculators are always at hand, kids still need to know whether the answer makes sense.
Research shows that preschoolers’ ability to visually estimate quantities is a strong predictor of future success in math and other academic areas — even more so than reading skills. Conversely, a lack of number sense often leads to persistent difficulties in learning math. Games and activities that involve estimating quantities or placing numbers on a number line can significantly boost math achievement in kids at risk of falling behind.
In one study, kids aged 7–9 were asked to place numbers on a number line (for example, to show where 250 would go on a line from 0 to 1000). The results showed that estimation skills develop systematically and are closely tied to a child’s ability to work with numbers. Kids who practiced estimating quantities and making approximate calculations demonstrated a more developed number sense.
Experts also emphasize the importance of discussing and reflecting on estimates in everyday situations: the cost of groceries, the length of a wall, the volume of a container, or the time needed for a trip. This kind of practice builds numerical thinking, encourages critical discussion, boosts confidence in calculations, and helps kids apply math effectively outside the classroom. For instance, when looking at a café menu, a person can quickly figure out roughly how much lunch will cost. They can check if the travel time suggested by a navigation app seems realistic, spot possible errors in an electricity bill, or estimate how many apples are hanging on a tree. In real life, it’s useful to be able to gauge the size of a room, the number of people at a concert, or the speed of a moving line — and much more.
How Do We Teach?
We start with simple “Which has more?” activities, where kids compare groups of objects without counting them. This helps develop the skill of quickly estimating quantities at a glance.
Interested in how kids learn to estimate quantities at a glance? Take a look at our article on subitizing!
Next, we focus on understanding scale — what one, ten, or a hundred objects look like, and how to tell a small amount from a large one just by looking.
Gradually, kids begin estimating not only quantities but also measurements. For example, they might guess an area or length and compare objects without actually measuring them.
Once a kid has mastered counting by tens, we introduce number lines to help them understand which numbers are “close” to each other, which are “far apart,” and how to roughly estimate the difference between them.
This builds a valuable skill — the ability to estimate without counting or calculating precisely. It is just as useful in everyday life as it is in the classroom.
First Steps
Estimating “Which Has More”
At ages 4–5, kids can often look at a picture and tell which group has more objects without counting each one.
Subitizing & comparison
Subitize and compare up to 10 (objects only)
Sometimes those objects are partly hidden. For example, they might need to figure out how many dots in a pattern are tucked under a pocket, or which of the face-down cards showed more coffee beans.
When kids compare “more” and “less,” they use some pretty clever reasoning. They might realize that a jar holds fewer big objects than small ones, or that many fives plus one one make more than many ones plus one five.
Area
Estimate area
Estimation
Subitizing
Estimations
Use estimation to compare quantities.
Estimations
Patterns
Deep Understanding
Number Scale
By ages 5–6, kids learn to roughly estimate quantities at a glance. For example, they get a sense of what one button, ten buttons, and one hundred buttons look like.
Estimation
Counting
Understanding what 10 objects look like helps them recognize when a group has a two-digit number of items.
They also start estimating visual geometric measures like length, area, and perimeter. Choosing between multiple options encourages kids to make quick judgments instead of calculating exact values. This helps them notice, for example, that a square plot with the same area will have a shorter perimeter than a long, narrow rectangle.
Measurements
Indirect measurements
Areas
Compare areas
Perimeter and area
Length and perimeter
Confident Mastery
Close and Far Numbers on the Number Line
As kids begin to understand place value, they also develop a sense of which numbers are close together and which are far apart on the number line. Close numbers have a small difference, while far numbers have a large one. Usually, close numbers share the same first digit and have similar second digits — but if a round number happens to be between them, the digits can look very different.
Subtraction
Subtraction as a difference
When moving on to multi-digit numbers, it becomes especially important to understand number scale and to recognize which numbers are close together on the number line and which are far apart.
Estimation
Counting
Big numbers
Place value
Big numbers
Beyond 100
Big numbers
Beyond 100
Big Ideas
A sense of scale becomes especially important when working with decimal numbers — it’s all too easy to put the decimal point in the wrong place.
The idea of replacing a number with a smaller or larger one that’s easier to work with later proves very useful in algebra and mathematical analysis, where operations are performed not on numbers themselves but on inequalities, functions, or sequences.
