In pre-kindergarten, children (ages 3-5) develop a basic understanding of numbers and counting, and connect both to the idea of “how many.” They work on recognizing, grouping, and comparing objects of different sizes, colors and shapes, and identifying patterns.

Children begin to work with numbers, count objects, and associate numbers and counting with how many things are in a group. Children begin to understand how changing the number of objects in different groups – adding some, or taking some away – changes “how many” count.

By playing with blocks of many shapes, shape-sorters, snap-together construction pieces, clay and other materials, pre-kindergartners are introduced to geometry. Students begin to notice patterns in counting and in arrangements of shapes to build an understanding of how numbers relate to each other, and to anticipate what comes next.

Count out loud from 1 through 10 (or beyond). Begin to recognize and name written numbers from 1 through 10.

**Tip:** **Practice Counting**

Practice counting regularly with your child. She should know how to count to 10 and beyond and understand what the numbers represent. Play games that involve counting, such as hide and seek, and incorporate counting into everyday activities, such as climbing stairs or eating.

Count objects, one at a time, using one number name for each object, up through 10. Answer “how many?” questions about groups of objects. Use fingers to count.

Sort objects into groups by shape, color or size. Re-sort objects into different groups - for example, after sorting blocks by size, re-sort them by color. Pair objects by shape, color or size.

Develop awareness of numbers in everyday life, and think through answers to questions about what the numbers tell you.

What numbers are on this price tag? What do you think these numbers tell you? What is the number inside your shoe? Is the same number in everybody’s shoes? What do you think these numbers tell you?

Count three blocks in a row *("1, 2, 3")* then keep counting on when two more blocks are added to the row *("...4, 5")*.

**Tip: ****Practice Addition and Subtraction**

Practice basic addition and subtraction by having your child count how many objects are in a group, such as a plate of crackers, and then taking away some of those objects or adding more.

How you can help your child master the building blocks of math outside of the classroom.

Know basic number facts, such as *1 + 1 is 2*. Use fingers, blocks or other objects to answer questions such as: *If you have two nickels, and I give you two more nickels, how many nickels do you have?*

Begin to recognize and name common shapes, including circles, squares and triangles. Look for and identify shapes in the classroom, the playground, outside, and at home - for example: books, food trays and dishes, street signs, windows and doors, etc.

Create and build shapes using blocks, snap-together construction pieces, clay and other materials.

Tell if two shapes are the same shape, or the same size. Use words like *bigger/smaller*, *longer/shorter* to describe differences. Sort objects into groups by shape, color or size. Pair objects by shape, color or size.

Play and build with, arrange and line up objects, then identify the positions and direction of shapes, using words such as: *on, off, over, under, on top, on bottom, over, under, in front of, behind, above, below, etc.*

Find patterns in what they see around them – for example, prints in fabric used in their clothing, wallpaper borders, arrangement of petals on a flower. Create patterns by arranging or building with blocks, making paper chains or stringing beads, drawing or coloring, etc. Work on duplicating patterns, and extending simple patterns.

If there’s a red link, then a blue link, then a red link, what color do you think the next one is?

Begin to understand measurement as “how many” units of the same size. Identify different things in everyday life that are measured, and why – for example, how long a foot is (to get the right size shoe); how wide a door is (to cut wood the right size); how cold it is outside (so we know if we need a sweater or coat); how much water to put into the bowl (so we can follow a recipe).

Begin to connect kinds of measurements with common tools of measurement and units of measurement, including:

bathroom scales tell us how heavy a person is (weight) in pounds

rulers and yardsticks tell us how tall (height) or long (length) something is, in inches and feet

thermometers tell us how warm (temperature) something is, in degrees

Focus on how big, little, long or short things are, and figure out how to tell. Compare objects of different sizes and lengths, using the same unit of measurement. Find convenient units of measurement other than rulers – for example, cereal boxes or yogurt containers. Use measurements in daily activities – water play, cooking, science experiments.

Understand time as something measured by clocks, in hours and minutes. Begin to develop understandings of lengths of time, by having time limits set on activities – for example: *“Let’s color for 5 more minutes.” “Everyone has 10 seconds to sit down: 10, 9, 8, 7….”* Start to develop an understanding of portions of a day – *after breakfast, after lunch, before nap time* – and begin to understand time in larger units, such as days: *yesterday, tomorrow*.

**Tip: ****Use Timers to Develop a Sense of Time**Use a timer for activities like watching TV or using the computer, so that your child becomes familiar with the concept of time and how long different units of time last. If your child doesn’t want to leave the playground tell her she can stay for 5 more minutes. She’ll start to develop an understanding of time and how long different units of time last if you do this regularly.

Practice estimating measurements and amounts. For example: *How many blocks will fit in that box? How many glasses of water will it take to fill that sand pail?* Test to see how close estimates were. Repeat estimations and testing, to improve estimation skills.