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What does a student learn in ?

This is the year numbers start to mean something. Students learn to count to 100, write the numbers 0 to 20, and see that the last number they say tells how many objects are in the pile. They begin adding and taking away small groups using fingers, drawings, and real objects. By spring, they can solve simple word problems within ten and name everyday shapes like circles, squares, and cubes.

  • Counting to 100
  • Writing numbers
  • Adding and subtracting
  • Comparing groups
  • Shapes
  • Measuring and sorting
Source: Idaho Idaho Content Standards
Year at a glance
How the year usually goes. Every school and district set their own curriculum, so treat this as a guide, not official pacing.
  1. 1

    Counting and writing numbers

    Students learn to count out loud to 100 and write numbers from 0 to 20. They practice counting groups of objects and saying how many are in the pile, even after the objects are moved around.

  2. 2

    Comparing groups and numbers

    Students look at two piles and decide which has more, which has less, or whether they match. They start comparing written numbers up to ten and notice that each number is one more than the one before it.

  3. 3

    Adding and taking away

    Students put groups together and take them apart using fingers, drawings, and small objects. They solve simple word problems within ten and start to add and subtract within five without needing to count every time.

  4. 4

    Teen numbers and place value

    Students see that numbers like 13 or 17 are made of one group of ten and some extra ones. They build these numbers with blocks or drawings to get ready for place value in first grade.

  5. 5

    Measuring and sorting

    Students compare objects by length and weight, using words like longer, shorter, and heavier. They sort items into groups, count how many are in each group, and put the groups in order from smallest to largest.

  6. 6

    Shapes around us

    Students name shapes like circles, triangles, cubes, and spheres no matter how big they are or which way they are turned. They describe where objects sit using words like above, below, and next to, and build new shapes from smaller ones.

Mastery Learning Standards
The required skills a student should display by the end of Kindergarten.
Counting and Cardinality
  • Know number names and the count sequence

    K.CC.A

    Students learn the names of numbers and practice counting in order. This is the foundation for every math skill that follows.

  • Count to 100 by ones and by tens

    K.CC.A.1

    Students count from 1 to 100, one number at a time, then practice counting by tens: 10, 20, 30, all the way to 100.

  • Starting at a given number, count forward within 100 and backward within 20

    K.CC.A.2

    Starting from any number, students count forward to 100 and count backward from 20. This is the foundation for adding and subtracting later.

  • Write numbers from 0 to 20

    K.CC.A.3

    Students write the numbers 0 through 20 and match each number to a group of objects. Zero means nothing is there, and that counts too.

  • Count to tell the number of objects

    K.CC.B

    Students count a small group of objects and say how many are in it. Touching each item once while counting, then naming the total, is the core skill.

  • Understand the relationship between numbers and quantities

    K.CC.B.4

    Counting a group of objects means the last number said tells how many there are total. Students practice this by counting things they can see and touch, learning that numbers represent real amounts.

  • When counting objects, say the number names in the standard order, pairing each…

    K.CC.B.4.a

    Students count a group of objects by pointing to each one and saying exactly one number out loud for each. No object gets counted twice, and no number gets skipped.

  • Understand that the last number name said tells the number of objects counted

    K.CC.B.4.b

    The last number said when counting a group tells how many are in the group. It doesn't matter if the objects are lined up, scattered, or counted in a different order, the total stays the same.

  • Understand that each successive number name refers to a quantity that is one…

    K.CC.B.4.c

    Counting up means each next number is always one more than the last. Students practice this by adding one object at a time and saying the new total aloud.

  • Given a group of up to 20 objects, count the number of objects in that group…

    K.CC.B.5

    Students count a pile of up to 20 objects and say how many there are. If the pile gets rearranged, they know the count stays the same without starting over.

  • Compare numbers

    K.CC.C

    Students look at two groups of objects and say which has more, which has fewer, or whether they match. This is the first step in understanding that numbers have an order and a size.

  • Identify whether the number of objects in one group is greater than, less than

    K.CC.C.6

    Students look at two small groups of objects and decide which group has more, which has fewer, or whether both groups have the same amount. Groups have ten objects or fewer.

  • Compare two numbers between one and ten presented as written numerals

    K.CC.C.7

    Students look at two written numbers, both between 1 and 10, and decide which is bigger, which is smaller, or whether they match.

Operations and Algebraic Thinking
  • Understand addition as putting together and adding to

    K.OA.A

    Addition means putting groups together to get a bigger number. Subtraction means taking some away to get a smaller one. Students practice both with small groups of objects they can count and touch.

  • Represent addition and subtraction of two whole numbers within ten

    K.OA.A.1

    Students show adding and subtracting with numbers up to 10 by using fingers, drawings, or objects. They practice finding out what happens when groups come together or are pulled apart.

  • Solve addition and subtraction word problems within ten by using physical…

    K.OA.A.2

    Students hear a short story problem ("3 birds and 2 more, how many?") and solve it by counting objects, drawing a picture, or writing numbers. All problems stay within 10.

  • Decompose whole numbers from one to ten into pairs in more than one way by…

    K.OA.A.3

    Students break a number (like 7) into two groups in different ways, such as 5 and 2, or 4 and 3. They show this by using blocks, drawings, or written numbers.

  • For a given whole number from one to nine, find the number that makes ten when…

    K.OA.A.4

    Students practice finding the missing piece that completes a group of ten. Given any number from 1 to 9, they figure out how many more are needed to reach 10, using objects, drawings, or numbers.

  • Fluently add and subtract within five, including zero

    K.OA.A.5

    Students practice adding and subtracting with numbers up to 5 until the answers come quickly, without counting on fingers. That includes adding or subtracting zero.

Number and Operations in Base Ten
  • Work with numbers 11 – 19 to gain foundations for place value

    K.NBT.A

    Numbers 11 to 19 each have a ten and some leftover ones. Students break these numbers apart to see how a "ten" works, which prepares them for understanding bigger numbers later.

  • Compose (put together) and decompose

    K.NBT.A.1

    Students learn that numbers like 13 or 17 are really just ten plus a few extras. They practice building and breaking apart those numbers using objects, drawings, or written equations.

Measurement and Data
  • Describe and compare measurable attributes

    K.MD.A

    Students look at everyday objects and compare them by size, length, or weight. They notice that one crayon is longer or that one backpack is heavier.

  • Describe measurable attributes of objects, such as length or weight

    K.MD.A.1

    Students pick up an everyday object and describe what can be measured about it. A crayon, for example, has a length, a weight, and a width. Students practice noticing more than one of those qualities at a time.

  • Directly compare two objects with a measurable attribute in common, to see…

    K.MD.A.2

    Students pick two objects and compare them side by side: which one is longer, heavier, or holds more? They then say out loud what the difference is, like "the red block is shorter than the blue block."

  • Classify objects and count the number of objects in each category

    K.MD.B

    Students sort a group of objects into categories (by color, shape, or size) and count how many belong in each group.

  • Classify objects into given categories

    K.MD.B.3

    Students sort everyday objects into groups by color, shape, size, or another shared trait, count how many are in each group, and arrange the groups from smallest to largest.

Geometry
  • Identify and describe shapes

    K.G.A

    Students name and describe everyday shapes, from flat ones like squares and circles to solid ones like cubes and spheres. They notice how shapes look and where they show up in the world around them.

  • Describe objects in the environment using names of shapes

    K.G.A.1

    Students look at everyday objects around them and name their shapes, then describe where those objects are sitting using words like "above," "below," "beside," and "next to."

  • Correctly name shapes regardless of their orientations or overall size

    K.G.A.2

    Students learn that a triangle is still a triangle whether it's big, small, tilted, or flipped. The name of a shape doesn't change just because it looks different on the page.

  • Identify shapes as two-dimensional

    K.G.A.3

    Students sort shapes into two groups: flat shapes like a square drawn on paper, and solid shapes like a block or a ball you can pick up.

  • Analyze, compare, create

    K.G.B

    Students sort, compare, and build shapes by describing what makes them alike or different, such as how many sides they have or whether they stack and roll.

  • Analyze and compare two- and three-dimensional shapes, in different sizes and…

    K.G.B.4

    Squares, circles, cones, cubes: students look at shapes of different sizes and positions and describe what makes them alike or different. They talk about sides, corners, and faces using everyday words, not formal terms.

  • Model shapes in the world by building shapes from components/materials and…

    K.G.B.5

    Students build and draw basic shapes by hand, using blocks, craft sticks, or pencil and paper. The goal is to recognize that shapes like squares and triangles show up in the real world and can be made from scratch.

  • Compose simple shapes to form larger two-dimensional shapes

    K.G.B.6

    Students put smaller shapes together to build a bigger one, like fitting two triangles side by side to make a square. The focus is on how flat shapes combine to fill a larger outline.