Your child’s developmental process is unique. To guide you, education experts have mapped a few basic first and second grade math skills to help you track your child’s development in different mathematical areas. See the Child Development Tracker for more information.
Many six-year-olds will be able to correctly compute — in their heads — basic addition and subtraction problems with answers up to 10. Seven-year-olds may be able to complete problems with answers in the teens.
During their sixth year, some children will begin to solve basic word problems. For instance, they will be able to answer the following: If Jill has five pennies and Joe has three, how many more pennies does Jill have? Or: How many more pennies does Joe need to have in order to have the same number of pennies as Jill?
In their sixth year, many children discover that one of two is one half, one of three is one third, one of four is one fourth, and one of five is one fifth. By their seventh year, many may be able to compare fractions such as one half and one fourth and say which is more.
Nearing their seventh year, many children will be able to count out loud by fives to 100. Some will be able to count by twos to 20. And a few will be able to count by threes up to 18 and fours to 24.
Throughout their seventh year, children will continue reading number words (“one,” “two,” “first,” “second,” etc.). They will also be able to read and understand mathematical terms such as equal, unequal, greater than, and less than, and match them to their symbols.
Seven- and eight-year-olds begin to understand and get pretty good at estimating the number of objects in a collection, such as jellybeans in a jar. Some children will be able to estimate or make a close guess at a collection of several hundred objects!
Geometry: Shapes & Space
Toward the end of their sixth year, and throughout their seventh year, children will be able to combine two-dimensional shapes to make a new shape. For instance, they can arrange six triangles to form a hexagon, or combine a square and two triangles to make a rectangle.
Many seven-year-olds will be able to flip, turn, and move a two-dimensional shape, such as a triangle, until it matches a similar shape.
Some seven-year-olds and many eight-year-olds will be able to look at a shape and break it down into a number of different shapes. For instance, looking at a rectangle, some children might see four triangles or two squares.
Seven-year-olds will be able to look at a three-dimensional object, like a cube, and re-create it. For instance, to make a die, they would connect six same-size squares along their edges.
Many seven- and eight-year-olds will be able to look at objects in and outside their homes (television, refrigerator, windows, cans, and boxes, for example) and recognize their simple shapes, such as squares, rectangles, circles, and triangles.
Some seven-year-olds and many eight-year-olds will be able to use a tool, such as a yardstick or a length of string, over and over again to measure a large area like a hallway or a room.
Soon after they begin to use tools for measuring, many seven- and eight-year-olds will discover that their methods aren’t always accurate and so their measurements are really just estimates or guesses. They will begin to see this when two people measure the same space with the same tools but come up with different results.
Seven-year-olds become increasingly aware of and use different ways to measure weight, moving from simple balance tools to standard scales.
By their eighth year, many children will discover that differently shaped containers can still hold similar amounts. For instance, a half-gallon milk carton holds the same amount as a half-gallon plastic juice bottle, although their shapes are different.
Patterns, Reasoning & Algebra
By their sixth year, many children will figure out how to make their own repeating ABC pattern using different symbols or objects. For instance, triangle, circle, square, triangle, circle, square follows an ABC pattern, as does penny, dime, nickel, penny, dime, nickel.
Six-year-olds understand that five pennies can be exchanged for one nickel. And many children this age can play games where they trade one object for a specific number of another object of equal value.
Throughout their sixth year, many children discover number patterns. As seven- and eight-year-olds, they will recognize patterns of larger and larger numbers, For instance, the pattern 3, 6, 9, 12 … can be continued by adding 3. And later, a pattern of 7, 14, 21, 28 … can be continued by adding 7.
Statistics & Probability
During the later part of their seventh year, children figure out how to “collect” information and use what they find in a discussion. For instance, the child who is looking for an increase in allowance may poll her friends and discover that they are all getting a dollar more than her. She will then bring back this collected information and present it to her parents in hopes of getting an increase in her own allowance.
Eight-year-olds begin to understand the probability or chance that something will happen. For instance, when given a bag with two blue marbles and a red marble, they will recognize that if they reach in without looking and pull one out it is more likely that they would draw a blue marble.
Many eight-year-olds may also be able to say that when flipping a coin, the chances of it landing heads up are 50/50.