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PK.1 Children begin to develop processes and strategies for solving mathematical problems.
- PK.1.1 Try to solve problems in their daily lives using mathematics (e.g., how many napkins are needed).
- PK.1.2 Generate new problems from every day mathematical situations and use current knowledge and experience to solve them (e.g., distribute crackers).
- PK.1.3 Begin to develop and use various approaches to problem solving based upon their trial and error experiences.
- PK.1.4 Begin to talk about the processes and procedures they used to solve concrete and simple mathematical situations.
- PK.1.5 Begin to generate problems that involve predicting, collecting, and analyzing information and using simple estimation.
PK.2 Children begin to use the language of mathematics by applying emerging skills in representing, discussing, reading, writing, and listening (e.g., by translating a problem or activity into a new form; a picture, diagram, model, symbol, or words).
- PK.2.1 Participate regularly in informal conversations about mathematical concepts and number relationships.
- PK.2.2 Begin to record their work with numbers in a variety of simple concrete and pictorial formats, moving toward some use of number and other mathematical symbols.
- PK.2.3 Begin to use symbols to represent real objects and quantities.
- PK.2.4 Make progress from matching and recognizing number symbols to reading and writing numerals.
- PK.2.5 Talk about their own mathematical explorations and discoveries using simple mathematical language and quantity-related words.
- PK.2.6 Begin to recognize that information comes in many forms and can be organized and displayed in different ways.
- PK.2.7 Begin to describe comparative relationships (e.g., more/less/same number of objects or quantities).
PK.3 Children begin to develop skills of recognizing, comparing and classifying objects, relationships, events and patterns in their environment and in everyday life.
- PK.3.1 Recognize, describe, copy, extend, and create simple patterns with real objects and through pictures.
- PK.3.2 Identify patterns in their environment.
- PK.3.3 Investigate patterns and describe relationships.
- PK.3.4 Recognize patterns in various formats (e.g., things that can be seen, heard, felt).
PK.4 Children extend their understanding of numbers and their relationship to one another and things in the environment.
- PK.4.1 Develop an increasing interest and awareness of numbers and counting as a means for determining quantity and solving problems.
- PK.4.2 Match, build, compare, and label amounts of objects and events (e.g., birthdays in the week) in their daily lives.
- PK.4.3 Make progress in moving beyond rote counting to an understanding of conceptual counting (e.g., one-to-one correspondence).
- PK.4.4 Recognize and match number symbols for small amounts with the appropriate amounts (e.g., subitizing).
- PK.4.5 Show progress in linking number concepts, vocabulary, quantities and written numerals in meaningful ways.
- PK.4.6 Show growth in understanding that number words and numerals represent quantities.
- PK.4.7 Use cardinal (e.g., one, two) and ordinal (e.g., first, second) numbers in daily home and classroom life.
- PK.4.8 Understand how numbers can be used to label various aspects of their lives (e.g., house number, phone number, ages of classmates).
- PK.4.9 Develop an increasing ability to count in sequence up to ten and beyond, typically referred to as “counting on.”
PK.5 Algebraic Thinking. Children begin to develop skills of sorting and organizing information, seeing patterns, and using information to make predictions and solve new problems.
- PK.5.1 Begin to develop the ability to solve problems involving joining, separating, combining, and comparing amounts when using small quantities of concrete materials.
- PK.5.2 Can generate problems that involve predicting, collecting, and analyzing information.
- PK.5.3 Use simple estimation to make better guesses.
- PK.5.4 Identify likenesses and differences.
- PK.5.5 Can place objects or events in order, according to a given criterion (e.g., color, shape, size, time).
- PK.5.6 Recognize that the same group can be sorted and classified in more than one way and describe why they would group or sequence in a particular way.
- PK.5.7 Begin to understand that simple concrete and representational graphs are ways of collecting, organizing, recording, and describing information.
PK.6 Children explore and discover simple ways to measure.
- PK.6.1 Show awareness that things in their environment can be measured.
- PK.6.2 Begin to understand concepts of weight.
- PK.6.3 Show an awareness of the concept of time, beginning with the recognition of time as a sequence of events and how time plays a role in their daily life (e.g., breakfast, snack, lunch, dinner).
- PK.6.4 Show an awareness of temperature as it affects their daily lives.
- PK.6.5 Use beginning skills of estimation in solving everyday measurement problems (e.g., about how many cookies are needed for a small group of children).
- PK.6.6 Begin to use non-standard measures (e.g., length of hand) for length and area of objects.
- PK.6.7 Begin to understand that tools (e.g., rulers, scales, counters) can be used to measure properties of objects and amounts.
PK.7 Children build their visual thinking skills through explorations with shape and the spaces in their classrooms and neighborhoods.
- PK.7.1 Can make models, draw, name, and/or classify common shapes and verbally describe them in simple terms.
- PK.7.2 Investigate and begin to predict the results of combining, subdividing, and changing shapes.
- PK.7.3 Begin to recognize and appreciate geometric shapes in their environment.
- PK.7.4 Begin to build an understanding of directionality, order, and positions of objects through the use of words (e.g., up, down, over, under, top, bottom, inside, outside, in front of, behind). Identify patterns in their environment.
- PK.7.5 Recognize, describe, copy, extend and create simple patterns with real objects and through pictures.
- PK.7.6 Investigate patterns and describe relationships.
- PK.7.7 Recognize patterns in various formats (e.g., things that can be seen, heard, felt).