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- books enhance children's natural interest and curiosity about math.
- books also help children see numbers in many contexts.
- they are a meaningful tool for exploring, thinking, and exchanging math concepts.

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- cooking and outdoor activities  help introduce temperature concepts.
- include words like: thermometer, hot, cold, warm, and cool.

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- time is a difficult concept for children to understand, partly because time can stand for so many situations.
- past present, future, soon, hours, days, yesterday, tomorrow, and today are examples of time concepts.
- young children have only a vague concept of time.
- children cannot usually read a clock or watch until about the age of seven.
- offer time experiences to children by using the correct time words.
- some words are: day, night, before, after, minute, second, now, later, morning, afternoon, evening, yesterday, today, tomorrow, early, late, spring, summer, autumn, winter, new, and old.
- children should also learn about the passing of time.

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- sand tables and water tables are useful for offering children many opportunities to explore volume.
- provide many containers of varying volumes and shapes for measuring.
- introduce volume concepts such as: empty, full, little, much, a lot, and some.
- when children use these concepts, they think about their world in terms of quantity.

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- children develop size concepts only through experience.
- use words like: big, little, large, small, long/tall, short, wide, thin, big, bigger, biggest, small, smaller, smallest, inches, feet, pounds, smaller than, bigger than, thick, thin, high, low, large, larger, longer, taller, and shorter.

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- spatial relationships: the position of people and objects in space relative to each other.
- space concepts can be taught during cleanup time, art time, block-building, and other activities.
- games like "Simon Says" and "Hokey Pokey" are good ways to teach children about space concepts.
- give children frequent review so they can maintain this information.

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- counting is a key problem-solving tool.
- one-to-one correspondence: the understanding that one group has the same number as another.
- most basic part of the concept of numbers.
- finger counting is helpful and fun for children.
- cardinality: the last number of the counting sequence tells how many objects exist in a set.
- children are often exposed to counting by listening to adults count objects.
- after they know the names of the numbers, they can identify them and make the connection between the word and the numeral.
- the ability to count occurs in two stages:
- rote counting
- rational counting
- rote counting is learned before rational counting.
- rote counting is recitation of numbers in order. This involves memory, not understanding.
- rational counting involves attaching a number to a series of grouped objects.
- children should always be exposed to rational counting using concrete objects.

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- set: group of objects that are alike  in some way and, therefore, belong together.
- common features of a set may be:
- color
- shape
- size
- material
- pattern
- texture
- name
- use
- a set can have few or many members.
- empty set: a set with no members.
- the concept of set can be strengthened by asking a small group of children to divide themselves into a set.
- may divide by gender, age, color of eyes, or color of clothing.
- can use snack time as an example of an empty set, when everything is eaten off of the plate.

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- numerals: the symbols that represent numbers.
- children gain these recognition skills as they are continually exposed to numerals.
- there are many easy ways to expose children to numerals, like taking a walk or looking at a number line.

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- classification: the process of mentally sorting and grouping objects or ideas by a common attribute.
- attribute examples:
- size
- color
- shape
- pattern
- function
- matching: a form of classification. Involves putting like objects together.
- sorting: involves classification. The process of physically separating objects based on unique features.
- sequencing: the process of ordering real-life objects from shortest to tallest or tallest to shortest.
- children begin to learn classification skills in their first few weeks of life.
- recognizing: gathering information to make classifications by using senses through repeated experiences. This gives a child the ability to relate past and present experiences.
- as children build classification skills, increase the number of common features in the activities.

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- children will first say that circles and squares are the same shapes because they both have closed boundaries. Over time, they will become aware of the features they have.
- usually, roundness is the first one that children learn.
- to learn basic shape concepts, use a variety of activities that stress touching, holding, and matching of shapes.
- shape: what "goes around the outside" or the outline of the object, to help the child grasp the concept of shape.
- parquetry blocks: geometric pieces that vary in color and shape.
- do not teach shape and color concepts at the same time, wait until color concepts are well understood.

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- well-planned settings provide developmentally appropriate play experiences that also help promote math skills.
- these experiences help with color and shape recognition, classification, measurement, counting, time, temperature, space, and volume concepts.
- the math experiences should stress:
- observing and describing concrete objects
- recognizing colors, patterns, and attributes
- classifying sets of objects
- comparing objects and using terms that describe quantity, such as more than and lighter than
- copying patterns
- recognizing shape concepts
- recognizing and writing numerals
- using logical words such as all, none, and some
- using one-to-one correspondence
- estimating quantity and measurement
- developing problem-solving skills

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- color is considered a math concept since it helps children learn to discriminate among objects.
- using color, children can classify, pattern, and sequence.
- identifying color can also help language development. It requires the skill to recall a name and associate it with a visual image.
- children learn to identify colors before shapes. It is also common for a preschool child to confuse color and shape.
- color blindness can be discovered through careful observation of children as they try to learn colors.
- color blind children see shades of green and red as grayish brown.
- they may even see all colors as gray.
- the director will usually discuss this problem with the child's parents. Then, the parent decides if their child should be tested for color blindness.
- color concepts can be taught formally or informally.
- color recognition can be taught at transition times.
- sorting objects by color will help with recognition.

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- determine children's skill levels before planning math activities.
- two common forms of assessment:
- observation assessment
- specific task assessment
- observation involves formal viewing of a child during self-selected activities.
- specific behaviors to watch for:
- identifying colors and shapes
- sorting and classifying objects
- counting objects
- setting a table correctly
- pouring liquids and carefully watching the amount poured
- constructing patterns
- writing numerals
- specific task assessment involves giving children set activities to determine skill and/or needs.

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- encourage the children by providing an active, stimulating environment to foster mathematical thinking.
- provide the children with a variety of 3D objects that promote physical and mental activity.
- Include items for counting, observing, creating, sorting, discussing, construction and comparing.

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- a quality curriculum provides a rich environment and developmentally appropriate activities to help children explore key concepts.
- children should learn to count and recognize numbers and understand the concepts of space, size, volume, and time