What does a student learn in
California, Grade 1, Mathematics ?

Students learn which features actually make a shape what it is. A triangle is always three-sided and closed, but its color or size don't define it. Students sort shapes by their real rules, then draw or build shapes that follow those rules.

Students fit basic shapes together, like triangles and squares, to build a bigger shape. Then they use that new shape as a building block to make something bigger still.

Students cut circles and rectangles into two or four equal pieces and name each piece a half, a fourth, or a quarter. They also notice that cutting a shape into more pieces makes each piece smaller.

Students identify shapes that can be split into two equal halves, like a square cut down the middle. They learn that equal parts are the same size.

Students sort and measure objects using the same unit throughout, such as lining up paper clips end to end without gaps or overlaps. Getting this right is what makes the measurement mean something.

Students sort and describe shapes by their sides and corners, noticing what makes a triangle different from a rectangle. They look for patterns in how shapes are put together.

Students line up three objects from shortest to longest, then figure out which of two objects is longer by comparing each one to a third object, like a piece of string.

Students measure how long something is by lining up smaller objects, like paper clips or cubes, from one end to the other. The total number of those smaller objects is the length.

Students read a clock and write times like 3:00 or 3:30, for both analog and digital clocks. They also collect simple information, such as counting how many students prefer dogs or cats, and read a chart showing the results.

Students sort objects or answers into groups, count how many are in each group, and compare the groups. For example, they might tally favorite colors and figure out which got the most votes and by how much.

Students count, read, and write numbers up to 120, starting from any number, not just 1. They also show how many objects are in a group by writing the matching number.

Students learn that every two-digit number is made of tens and leftover ones. The number 37, for example, is three tens and seven ones.

Students compare two numbers under 100 and say which is greater, which is less, or whether they match. They use what they know about tens and ones to explain why.

Students add numbers up to 100 by grouping tens and ones separately. They use blocks, drawings, or written steps to show their thinking and explain why their method works.

Students pick a two-digit number and figure out what's 10 more or 10 less in their head, no counting allowed. Then they explain how they knew.

Students subtract round numbers by tens, like 70 minus 40, using blocks or drawings to show their thinking. They connect what they did with the objects to what they write on paper.

Word problems ask students to add or subtract numbers up to 20. Students figure out what's missing, whether it's the starting amount, the change, or the result.

Students add three numbers together to solve a simple story problem, keeping the total at 20 or under. They might use drawings, counters, or a number sentence to find the missing piece.

Students learn that flipping the order of two numbers still gives the same sum, and that regrouping numbers in an addition problem can make it easier to solve.

Subtraction is the flip side of addition. To solve 10 minus 8, students think "what do I add to 8 to get 10?" instead of counting backward.

Counting up or back on a number line is one way to add or subtract. Students practice seeing that counting forward 3 from 7 is the same as adding 3.

Students add and subtract numbers up to 20, and do it quickly and reliably up to 10. They use shortcuts like breaking numbers apart or using what they know about tens to find the answer without counting every finger.

Students learn that the equal sign means "both sides are the same amount," then decide whether a number sentence like 5 + 2 = 2 + 5 is true or false.

Students find the missing number in simple addition and subtraction equations, like figuring out what goes in the blank to make 8 + ? = 11 true.

Students explain *why* a math trick works, not just that it does. They use what they know about tens and ones to show why adding or subtracting in a certain order still gets the same answer.