What does a student learn in StateCalifornia,GradePre-Kindergarten,SubjectMathematics?

Counting out loud from 1 to 10 in order, with only a small stumble here and there. Students say the numbers by heart, not by reading them.

Students count aloud from 1 to 30, making only a small slip or two along the way. They can also start counting from the middle, like picking up at 7 instead of always starting from 1.

Students count a small group of objects by touching or pointing to each one and saying one number out loud per object. The goal is five objects or more.

Counting a pile of blocks or crayons, students touch or move each one while saying a number out loud. They practice making sure every object gets exactly one number, up to ten or more.

Counting a group of objects and saying how many are there total. Students are just starting to understand that the last number they say when counting tells them the size of the whole group.

The last number said when counting a group tells how many things are in that group. Students count a pile of blocks, and whatever number they land on last is the total.

Students recognize at a glance how many objects are in a small group, up to four, without counting them one by one.

Students look at a small group of objects and say how many there are without counting them one by one. This works with groups of up to five things.

Students recognize a handful of written number symbols, like 2 or 5, and say their names aloud. This is the first step toward connecting a written digit to a word.

Students look at written numbers from 0 to 10 and say each one by name. This is the foundation for all the counting and number work that comes next.

Students look at two small groups of objects and decide which group has more or if both groups have the same amount.

Students count two small groups of objects and decide which has more, which has less, or whether they match.

Adding an object to a group makes the total go up. Taking one away makes it go down. Students practice this with small groups of toys or blocks.

Adding one toy to a small group makes the count go up by one. Taking one away makes it go down by one. Students practice this with real objects they can touch and move.

Students learn that a group of things can be split into smaller groups, and that the whole group is bigger than any piece of it. Think of a bowl of grapes divided between two hands.

Students break a small group of objects into two smaller groups, then put two groups back together to make a larger one. For example, 5 blocks can split into 3 and 2, or 4 and 1.

Students figure out simple adding and taking-away problems using a handful of real objects, like toys or snacks, in everyday moments.

Students add and subtract groups of everyday objects, like toys or snacks, with totals up to 10. They work through these problems in real, familiar situations rather than on a worksheet.

Students split a small pile of objects, like four crackers or six blocks, so two people each get the same amount.

Students divide a small pile of objects (like 9 crayons) into equal shares for two or three people, making sure everyone gets the same amount.

Students spot what makes objects alike or different, then sort them into groups by one shared trait, like color, shape, or size.

Students sort everyday objects into groups by one or two features, such as color and shape, and can re-sort the same objects a different way without getting confused.

Students spot repeating patterns in everyday objects, like red-blue-red-blue blocks, and copy that pattern with adult help.

Students copy and extend repeating patterns, like red-blue-red-blue with blocks or claps, then say which part repeats. A grown-up helps them figure out the repeating piece.

Students copy and continue a simple repeating pattern, like red-blue-red-blue, with help from an adult.

Students make repeating patterns using toys, shapes, or other objects, like lining up red-blue-red-blue blocks, then copy that same pattern using different objects.

Students notice that objects can be longer, heavier, or fuller than each other and say what they see, like telling a teacher that one block is bigger than another.

Students pick up two objects, compare them side by side, and say which one is longer, heavier, or holds more.

Students line up two or three objects from shortest to tallest, smallest to biggest, or least full to most full. It is an early step toward measuring and comparing the world around them.

Students line up four or five objects, like crayons or cups, from shortest to tallest or smallest to biggest. They practice putting things in order by size.

Students line up small objects (like blocks or crayons) from one end of something to the other to measure how long it is. A grown-up may help.

Students sort real objects into two groups and show the results by lining them up, making tally marks, or drawing simple pictures. A teacher helps guide the work.

Students sort real objects or draw simple pictures to show information in two groups, like red apples versus green apples. Each object or mark stands for exactly one thing counted.

With help from a teacher, students look at two groups of objects and say which group has more and which has less.

Students look at two groups of objects or pictures and say which group has more and which has less. A grown-up helps them compare and talk about what they see.

Shapes like circles, squares, triangles, and rectangles get a name. Students point to them and say what they are, in pictures and in everyday objects around the room.

Shapes like circles, squares, and triangles are everywhere. Students learn to spot them, name them, and describe what makes each one different, like how many corners it has or whether its edges are straight or curved.

Students start naming basic 3D objects they see every day, like calling a ball a ball or a box a box, without needing the formal math terms yet.

Spheres, cubes, and cylinders are 3D shapes that take up space, like a ball, a block, or a can. Students learn to recognize and name a few of these shapes by sight.

Two circles are still both circles even if one is bigger or tilted. Students look at flat shapes side by side and decide whether they match in type, no matter the size or which way they point.

Students compare shapes like circles, squares, and triangles to figure out if two shapes are the same kind, even when one is bigger or tilted. They notice how many sides or corners each shape has.

Students pick shapes like circles, squares, and triangles and arrange them to build a picture, using a circle for the sun or a square for a house.

Kids snap or stack two or more shapes together to build something new, like using a square block and a triangle block to make a house.

Students learn words like "under," "over," "inside," and "outside" to describe where things are. They can say where a toy is hiding or whether a ball is on top of or beneath something.

Students use position words like "under," "behind," and "next to" to describe where objects and people are. They can point to the cup on the table, the toy inside the box, or the friend standing between two chairs.

Students figure out how to make a shape fit into a space by turning it, flipping it, or sliding it around until it clicks into place.

Students picture in their head how a shape would look if turned or flipped, then fit it into place without having to test every position by hand.