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Age-by-age learning skills

# Math Skills: What to Expect at Different Ages

Your baby begins learning math the moment she starts exploring the world. Each skill—from identifying shapes to counting to finding patterns—builds on what she already knows. Here’s how math skills typically develop at different ages.

Math Skills: What to Expect at Different Ages

Children develop at their own rate, but you can generally expect them to meet certain milestones. Take a look at how kids build math skills throughout the years.

Babies
• Begin to predict the sequence of events (running water means bath time)
• Start to understand basic cause and effect (shaking a rattle makes a noise)
• Begin to classify things in simple ways (some toys make noise and some don’t)
• Start to understand relative size (baby is small, parents are big)
• Begin to understand words that describe quantities (more, bigger or enough)

Toddlers
• Understand the “how many” of basic numbers, such as using their fingers to show “how many” years old they are
• Begin reciting numbers, but skip some of them
• Understand basic math language,such as how objects relate to each other (under, behind, fast and heavy)
• Match basic shapes (triangle to triangle or circle to circle)
• Explore measurement by filling and emptying containers
• Start seeing patterns in daily routines and in things like floor tiles

Preschoolers
• Recognize shapes in the real world
• Start sorting things by color,shape, size or purpose
• Compare and contrast using classifications such as height, size or gender
• Count up to at least 20 and accurately point to and count items in a group
• Understand that numerals stand for number names (5 stands for ve)
• Use spatial awareness to put puzzles together
• Start predicting cause and effect (such as what will happen if they drop a toy in a tub full of water)

Kindergarteners
• Add by counting the fingers on one hand—1, 2, 3, 4, 5—and starting with 6 on the second hand
• Identify the larger of two numbers and recognize numerals up to 20
• Copy or draw symmetrical shapes
• Start using very basic maps to find a “hidden treasure”
• Begin to understand basic time concepts like morning or days of the week
• Follow multi-step direction words like first and next
• Understand the meaning of words like unlikely or possible

• Predict what comes next in a pattern and create own patterns
• Know the difference between two and three-dimensional shapes and name the basic ones (cubes, cones, cylinders)
• Count to 100 by ones, twos, ves and tens
• Write and recognize the numerals 0 to 100, and the words for numbers from one to twenty
• Do basic addition and subtraction up to 20
• Read and create a simple bar graph
• Recognize and know the value of coins

• Move from using hands-on methods to using paper and pencil to work out math problems
• Work with money
• Do addition and subtraction with regrouping (also known as borrowing)
• Understand place value well enough to solve problems with decimal points
• Know how to do multiplication and division, with help from fact families (collection of related math facts, such as 3 x 4 = 12 and 4 x 3 = 12)
• Create a number sentence or equation from a word problem

• Start applying math concepts to the real world (such as when helping you cook)
• Practice using more than one way to solve problems
• Put different types of numbers in order on a number line
• Compare numbers using > (greater than) and < (less than)
• Start two- and three-digit multiplication (312 x 23)
• Complete long division, with or without remainders
• Estimate and round

Middle-Schoolers
• Begin basic algebra with one unknown number (such as 2 + x = 10)
• Use coordinates to locate points on a grid, also known as “graphing ordered pairs”
• Work with fractions, percentages and proportions
• Work with lines, angles, types of triangles and other basic geometric shapes
• Use formulas to solve complicated problems and to find the area, perimeter and volume of shapes

High-Schoolers
• Understand that numbers can be represented in many ways (fractions, decimals, bases and variables)
• Use numbers in real-life situations (such as checking accounts or calculating tips)
• Begin to see how math ideas build on one another
• Begin to understand that some math problems don’t have real-world solutions
• Use mathematical language to convey thoughts and solutions
• Use graphs, maps or other representations to learn and convey information

## What’s Next

Amanda Morin is a parent advocate, a former teacher and the author of The Everything Parent’s Guide to Special Education.

## Reviewed by

Donna Volpitta, Ed.D., is coauthor of The Resilience Formula: A Guide to Proactive, Not Reactive, Parenting.

## Chat With an Expert

Tue Sep 26 at 1:00pm ET