Montana Pre-Kindergarten Math Standards

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PK.1 Children develop the ability to think and work with numbers easily, to understand their uses, and describe their relationships. Children learn the meaning of numbers in their everyday experiences (e.g., home, early childhood settings, community and nature).

• PK.1.1 experience, discover, and explore number relationships.
• PK.1.2 use the names for numbers.
• PK.1.3 understand that numbers always represent the same quantity (five objects are still five objects whether they are arranged in a vertical or horizontal arrangement) regardless of the order or physical arrangement of the objects counted.
• PK.1.4 attach meaning to visual and verbal uses of numbers (numbers on homes help to find a friend’s house).
• PK.1.5 explore the steps from inventive to accurate counting (inventive – 1,3,8,5 to accurate counting – 1,2,3,4,5).
• PK.1.6 count a series of objects in a group and tell the number (there are five cars in the block area).
• PK.1.7 recognize and match number symbols with the appropriate amounts (the number “7” corresponds to the amount of marks they made on a piece of paper).
• PK.1.8 model situations that involve the “adding to” and “taking away” using objects, pictures, and symbols.

PK.2 Children apply mathematical skills through counting, sorting, and comparing objects. Children describe their thinking and observations in everyday situations.

• PK.2.1 explore attributes of objects and begin to sort by similar traits such as shape, color, size, or function (various sizes and shapes of colored buttons).
• PK.2.2 understand the concepts of same, different, equal, more than, and less than.
• PK.2.3 count, sort, organize, and compare groups of objects.
• PK.2.4 understand one-to-one correspondence (6 napkins for 6 people at the table).
• PK.2.5 develop estimation skills related to quantity (how many blocks will fit on the shelf).

PK.3 Children learn to identify and describe patterns using mathematical language. They develop the ability to reproduce patterns they see and to create new ones.

• PK.3.1 recognize simple patterns of concrete objects (look at beads that are strung yellow, blue, yellow, blue and identify the pattern).
• PK.3.2 predict what comes next when simple patterns are extended (when asked what comes after yellow, blue, yellow, answers blue).
• PK.3.3 reproduce simple patterns of concrete objects (string beads yellow, blue, yellow, blue).
• PK.3.4 reproduce patterns of sounds and movements (clap, stomp, clap).
• PK.3.5 recognize objects arranged in a series and begin to place objects in order through trial and error (patterning blocks, by using two long blocks, one short block, two long blocks, one short block).
• PK.3.6 describe a sequence of events (to build a snowperson – first, form a large ball to put on the bottom, second, form a medium ball and put in the middle, and third, form a small ball and place on top).

PK.4 Children build the foundation for recognizing and describing shapes by manipulating, playing with, tracing, and making common shapes using real objects in a variety of activities. Children learn spatial reasoning and directional words as they become aware of their bodies and personal space within their physical environment.

• PK.4.1 recognize, describe, and name shapes (circles, triangles, rectangles, squares, diamonds, ovals).
• PK.4.2 recognize geometric shapes in the environment (playing ‘I spy’ by finding different shapes or simply noticing and commenting on familiar shapes around them).
• PK.4.3 explore geometric shapes (roll balls through a cylinder, make diamonds out of play dough).
• PK.4.4 explore the size, shape, position, and movement of objects within their physical environment.
• PK.4.5 understand space and size relationships (sneakers can fit in the small cubby, but boots need to go in the large cubby).
• PK.4.6 use position words that indicate where things are in space (inside, outside, behind, in front, above, below, over, under, next to, near, far).
• PK.4.7 experiment with mapping skills by using classroom materials to recreate their surroundings.

PK.5 Children begin to use measurement instruments to explore and discover measurement relationships. They apply the characteristics of length, quantity, volume, distance, weight, area, and time to real life situations in order to construct concepts of measurement.

• PK.5.1 use appropriate language to discuss measurement (heavy and light to describe weight, full and empty to describe volume, near and far to describe distance).
• PK.5.2 use familiar objects as measuring devices (length in relation to body parts, distance in paper clips strung together, volume in cups of sand, weight in number of blocks).
• PK.5.3 become aware of and begin to use, regardless of accuracy, the conventional language of measurement (feet, minutes, miles, gallons, tons).
• PK.5.4 show an increasing awareness of conventional measurement tools and methods (tapes, rulers, clocks, and scales).
• PK.5.5 recognize time as a sequence of events that relates to daily life (my parents pick me up after snack, we read a story before I go to bed).
• PK.5.6 realize that some activities take longer than others and develop a context for elapsed time (swim class lasts an hour, which is shorter than a full day at school).
• PK.5.7 estimate length, quantity, volume, distance, weight, area or elapsed time of familiar objects or events (number of steps to the front door, amount of water that can be poured into a glass).

PK.6 Children build a foundation for solving problems by formulating questions and possible solutions individually and with others based on their observations and experiences.

• PK.6.1 become more confident in exploring the world around him/her, while also requesting help when needed.
• PK.6.2 attempt to understand similarities and differences between objects or events.
• PK.6.3 represent newly acquired information in a variety of ways (stories, drawings, dramatic play).
• PK.6.4 explore the use and meaning of symbolic number objects (e.g., currency and coins can be exchanged for goods).
• PK.6.5 wrestle with opposing ideas and approaches to construct a new understanding of an object, process, or emotion.
• PK.6.6 look for, give clues and/or make predictions to solve a problem. (“This object is heavy and so it will sink.”, “If you stack too many blocks they may fall over.”)
• PK.6.7 develop and use systematic approaches to problems by testing new possibilities through trial and error.
• PK.6.8 work with others to achieve desired results (lifting a friend up in order to reach a desired object).
• PK.6.9 explore the concepts of whole, part, and parts that make a whole (taking apart an old appliance and trying to figure out how it worked).