Math Development Growth Chart: Ages 4-8

The more parents know about what to expect at each stage of their child's growth, the more realistic their expectations and the better prepared they are with appropriate activities that will further their child's learning and development. In this newsletter, we include some highlights at each age. If you'd like more details, download A Parent's Guide to the Development of Mathematical Thinking, an in-depth exploration of cognitive development, math thinking, and tips for at-home activities for ages 4 to 8.

Math learning at age 4

A four year old may easily compare sets and know which has more, but may not know how many she has. She may struggle to count each object only once, and to name the number corresponding to each counted object.

Things to do at home

Watch your child play to understand her mathematical knowledge. Is her counting sing-song or meaningful? Does she touch each object once? Is her voice in sync with her tag? Go for a walk and collect objects she likes. At home find different ways to sort this collection.

Math learning at age 5

Five year olds can not only recognize a set with more but also can count how many are in a set. They may be able to sequence sets from smallest to largest. Determining how much more one set is than another can be a struggle.

Things to do at home

Help your child think about the permanence of a set. Put 6 pennies in a row, then change the arrangement. Ask "how many are there now?" Five year olds also love repetition, which fosters mathematical thinking. Clapping patterns help him discover sequences and predict what comes next.

Math learning at age 5

Five year olds can not only recognize a set with more but also can count how many are in a set. They may be able to sequence sets from smallest to largest. Determining how much more one set is than another can be a struggle.

Things to do at home

Help your child think about the permanence of a set. Put 6 pennies in a row, then change the arrangement. Ask "how many are there now?" Five year olds also love repetition, which fosters mathematical thinking. Clapping patterns help him discover sequences and predict what comes next.

Math learning at age 6

A six year old knows that 6 can be 5 and 1, or 3 and 3. And he knows that all sets of 6, no matter what objects, are equivalent. He understands that "nothing" is represented by 0, and that any number can be written with the digits 0-9.

Things to do at home

Dice, cards, and board games can help a six year old learn addition combinations. Play "Hidden Counters." Count 8 pennies, then hide 4 under a cup. Ask, "How many are hidden?" Does he know there are 4?

Math learning at age 7

Seven year olds can better understand space and quantity, a broader range of mathematical ideas become more accessible. They have a repertoire of basic addition and subtraction combinations that they can use as tools in computing.

Things to do at home

Help your seven year old build confidence in her reasoning ability. If she knows that 4 quarters is 1 dollar, can she figure out what 6 quarters is? Prepare for multiplication by helping her think in groups. Ask "how many fingers do five people have?"

Math learning at age 8

At eight, children can think more logically to solve problems and think about the world. Children understand subtraction as the inverse of addition.

Things to do at home

Eight year olds like strategic thinking games like checkers, chess, Monopoly, and Clue. When he makes a mistake, help him develop confidence by not correcting a wrong answer. Focusing on the process helps him become an autonomous learner.

Find out more about your child's cognitive development, the math concepts your child should be learning by age, and tips for home activities in our Parent's Guide to the Development of Mathematical Thinking. download A Parent's Guide to the Development of Mathematical Thinking.

Parent Tip: Hopscotch can be outdoor math fun

Now that you can send the kids outside to play again, give them a piece of chalk and show them a new version of Hopscotch that incorporates a little math thinking.

Draw a grid to resemble a calculator. Be sure the squares are big enough to allow for a little hopping room, but small enough that your kids can jump from 1 corner to the other. Each child chooses a stone, and takes turns. Player 1 tosses his stone into 1 square, hops into another, and adds the 2 numbers together. Then he hops into 2 other squares that add up to the same number. Every time the numbers add up a point is scored. Stepping on a line means you lose your turn. The first player to score 10 wins!

You can also help them make up different versions of the game — there's nothing like making up your own rules to motivate you to play! Maybe the first player to use all 10 numerals wins, or try it with subtraction. For hopscotch rules and variations on the traditional game, go to http://www.wikihow.com/Play-Hopscotch.

Find more parent tips at http://www.dreambox.com/1st-grade-math-tips.

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Why we start kids a year early in our curriculum?

As we developed DreamBox Learning K-2 Math, through many rounds of beta testing, we learned that our curriculum is challenging. Appropriately challenging, but nonetheless challenging! This made it difficult for new users that weren't as familiar with computer games, weren't comfortable using computers for learning, and weren't confident when using virtual manipulatives for solving problems. Our academic team wanted to ensure that students experience success with math early in the product use. We learned that it's better to start kids off with easy math games and gradually increased the difficulty. By starting with curriculum one grade-level earlier in the sequencing, the new user experienced success with math, while becoming comfortable using a new learning medium. Read more on our blog: Schooled by 5-8 Year Olds: Why We Start Kids a Year Early in Our Curriculum.