Elementary Mathematics Benchmarks, Kindergarten
Number (N)
N.K.1 Count objects and use numbers to express quantity.
a. Count up to 25 objects and tell how many there are in the counted group of objects.
Note: Accuracy depends on not skipping objects or counting objects twice. Counting objects foreshadows the important mathematical concept of one-to-one correspondence.
Note: Going past 20 is important to move beyond the irregular "teen" pattern into the regular twenty-one, twenty-two, . . . counting routine.
b. Read aloud numerals 1 through 25 and match numerals with the numbers used in counting.
Note: In early grades "number" generally means "natural number" or, more mathematically, "non-negative integer."
c. Place numbers 1 through 25 in their correct sequence.
Note: The emphasis in kindergarten is on the sequence of numbers as discrete objects. The "number line" that displays continuous connection from one number to the next is introduced in grade 2.
d. Count to 20 by twos.
- Recognize 20 as two groups of 10 and as 10 groups of two.
e. Recognize and use ordinal numbers (e.g., first, fourth, last).
Example: The fourth ladybug is about to fly.
N.K.2 Use number notation and place value up to 20.
a. Understand that numbers 1 through 9 represent "ones."
b. Understand that numbers 11 through 19 consist of one "ten" and some "ones."
- Relate the "teen" number words to groups of objects ("ten" + some "ones").
Example: 13 can be called "one ten and three ones," with "thirteen" being a kind of nickname.
N.K.3 Compare numbers up to 10
a. Compare sets of 10 or fewer objects and identify which are equal to, more than, or less than others.
- Compare by matching and by counting.
- Use picture graphs (pictographs) to illustrate quantities being compared.
b. Recognize zero (0) as the count of "no objects."
Note: Zero is the answer to "how many are left?" when all of a collection of objects has been taken away.
Example: Zero is the number of buttons left after 7 buttons are removed from a box that contains 7 buttons.
N.K.4 Understand addition as putting together and subtraction as breaking apart.
a. Add and subtract single-digit numbers whose total or difference is between 0 and 10.
- Write expressions such as 5 + 2 or 7 - 3 to represent situations involving sums or differences of numbers less than 10.
b. Understand "add" as "put together" or "add onto" and solve addition problems with numbers less than 10 whose totals are less than 20.
- Understand the meaning of addition problems phrased in different ways to reflect how people actually speak.
- Use fingers and objects to add.
- Attach correct names to objects being added.
Note: This is especially important when the objects are dissimilar. For example, the sum of 3 apples and 4 oranges is 7 fruits.
c. Understand "subtract" as "break apart" or "take away" and solve subtraction problems using numbers between 1 and 10.
- Understand the meaning of addition problems phrased in different ways to reflect how people actually speak.
Example: 7 – 3 equals the number of buttons left after 3 buttons are removed from a box that contains 7 buttons.
- Recognize subtraction situations involving missing addends and comparison.
- Use fingers, objects, and addition facts to solve subtraction problems.
d. Express addition and subtraction of numbers between 1 and 10 in stories and drawings.
- Translate such stories and drawings into numerical expressions such as 7 + 2 or 10 – 8.
- Model, demonstrate (act out), and solve stories that illustrate addition and subtraction.
N.K.5 Compose and decompose numbers 2 through 10.
a. Understand that numbers greater than 2 can be decomposed in several different ways.
Note: Decomposition and composition of single-digit numbers into other single-digit numbers is of fundamental importance to develop meaning for addition and subtraction.
Example: 5 = 4 + 1 = 3 + 2; 10 = 9 + 1 = 8 + 2 = 7 + 3 = 6 + 4 = 5 + 5.
- Recognize 6 through 10 as "five and some ones."
Note: This is an important special case because of its relation to finger counting.
Example: 6 = 5 + 1; 7 = 5 + 2; 8 = 5 + 3; 9 = 5 + 4; 10 = 5 + 5.
Measurement (M)
M.K.1 Compare the length, weight, and capacity (volume) of objects.
a. Make direct comparisons between objects (e.g., recognize which is shorter, longer, taller, lighter, heavier, or holds more).
b. Estimate length, weight, and capacity, and check estimates with actual measurements.
- Select and use appropriate measurement tools (rulers, tape measures, scales, containers, clocks, thermometers).
- Relate direct comparisons of objects to comparisons of numerical measurements or estimates.
Example: Tom, who is four feet tall, is shorter than Jose, who is five feet tall, because 4 is smaller than 5.
Probability and Statistics (PS)
PS.K.1 Recognize and use words that represent time, temperature, and money.
a. Recognize and use the words day, night, morning, afternoon, evening, yesterday, today, tomorrow.
- Identify daily landmark times such as bedtime or lunch time.
b. Recognize the role of clocks and calendars in measuring and keeping track of time.
c. Know that thermometers measure temperature and that degree is the word used to name a temperature.
d. Identify U.S. coins by name.
Geometry (G)
G.K.1 Create, explore, and describe shapes.
a. Identify common shapes such as rectangle, circle, triangle, and square.
- Draw a variety of triangles (equilateral, right, isosceles, scalene) in a variety of positions.
- Draw squares and rectangles of different proportions (tall, squat, square-like) both horizontally and vertically positioned. Recognize tipped squares and rectangles.
Note: Squares are a type of rectangle.
Note: Drawing of tipped rectangles is typically too hard for kindergarten.
- Describe attributes of common shapes (e.g., number of sides and corners).
b. Use geometric tiles and blocks to assemble compound shapes.
- Assemble rectangles from two congruent right triangular tiles.
- Explore two-dimensional symmetry using matching tiles.
c. Recognize and use words that describe spatial relationships such as above, below, inside, outside, touching, next to, far apart.
Algebra (A)
A.K.1 Identify, sort, and classify objects.
a. Sort and classify objects by attribute and identify objects that do not belong in a particular group.
- Recognize attributes that involve colors, shapes (e.g., triangles, squares, rectangles, and circles) and patterns (e.g., repeated pairs, bilateral symmetry).
Example: Identify the common attribute of square in a square book, square table, and square window.
Example: Distinguish different patterns in ABABABA,
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b. Recognize related addition and subtraction facts.
- Use objects to demonstrate "related facts" such as 7 - 4 = 3, 3 + 4 = 7, 7 - 3 = 4.