Basic Concepts of Mathematics, Science and Social Studies

Basic Concepts:

Watch for: how much a child knows prior to instruction; use of knowledge base when learning new information; quantity and quality of information; use of concept at receptive level (point to, place object, nod in response); concept used at expressive level (tell name of); spontaneous use.

Most children:

• Know the concepts big/little, tall/short, long/short, high/low, wide/narrow, thick/thin, deep/shallow, on, next to, in, outside, inside, down, and up.
• Likely to make errors on underneath, below, over, and under.
• Know full/empty, light/heavy, bottom/top/middle; first, second, third; rectangle, triangle, circle, line. (4–5 yrs.)
• Can tell which of two objects is same/longer/shorter, lighter/heavier, full/less full.
• Uses spatial terms relative to own body as well as relative to other people or objects.

Color Concepts:

Watch for: ability to point to a color when asked; state color name when asked; spontaneous use of color concepts and names. Infrequently used color concepts are acquired later than those frequently used.

Most children:

• Know red, green, black, white, orange, yellow, blue, pink, brown, purple; most color names. (5 yrs.)

Mathematics Concepts:

Number and Operation

Watch for the way a child attempts to: use number to describe objects in the environment and during play; identify the number of objects in a collection without counting and with counting; identify the number of objects when objects are added or subtracted (small total number); use strategies to solve simple problems.

Many children:

• Match objects one to one and count a small collection of 1–4 items. Answer question “How many?”.
• Know number words one to five (rote counts).
• “See” and use a number to describe collections of one to three; can add and subtract with one to three objects. (3 yrs.)
• Know number words one to ten (rote counting).
• Has one to one correspondence. (3–4 yrs.)
• Count ten to twenty objects. Know that smaller numbers are first, larger numbers are later (ordinal principle).
• Know that the last number is equal to the total number (cardinal principle), and can count any collection of objects (abstraction principle). Understand that the order of the objects counted does not affect the total number. (4–5 yrs.)
• Distinguish more/same/not as much (many) as/less (fewer) than (without counting) for collections with visible differences in amount under twenty.
• Know ordinal numbers 1st to 5th.
• Know whole objects are made up of parts (fractions).
• Know that when two groups of objects have the same number, they are the same.
• Count starting on a number other than 1 (e.g., 5, 6, 7, 8, 9).
• Know that a larger number is made up of smaller numbers.
• Recognize and write numbers one to ten. (5–6 yrs.)
• Know number words to twenty.
• Know that the pattern of number words over twenty is the same as the pattern of number words one to ten (twenty-one, twenty-two, twenty-three, etc.).
• Know the concept of “half.” Can divide a whole object or collections of objects into two equal parts.
• Know if you add an object, you increase the number in the collection. If you take an object away, you decrease the number in a collection.
• Count and produce (create) a collection given the number up to 100. (6–7 yrs.)
• “See” and label patterned collection (on dice or dominos) and unpatterned collections of up to six items. (6 yrs.)
• Add or subtract using counting-based strategies, such as counting on when numbers under ten.
• Can use concrete manipulatives to solve simple word problems.
• Show an intuitive grasp of number; formal instruction in mathematics has begun. Consult curriculum guides and NCTM standards for information. (6–7 yrs.)

Geometry and Spatial Sense

Watch to see if a child can: use shapes to make pictures, name different shapes, name shapes contained in objects, label shapes in the environment (two- and three-dimensional), use geometry vocabulary.

Most children:

• Begin to match and name two-dimensional and three-dimensional shapes, first naming the object only. (3–4 yrs.)
• Know that “shape” is a constant characteristic unchanged by orientation in space.
• Use shapes to create a picture. Can find a shape in a simple picture. Link shape to object (round like a ball, etc.).
• Use spatial words like “next to,” “behind,” “under,” etc.
• Build “maps” using objects to representing places and things (houses, cars, roads, etc.).
• Describe shapes using descriptors for size and location or position (“next to the large triangle”); use spatial words “under,” “behind.” (4–5 yrs.)
• Recognize and name a variety of 2-D and 3-D shapes, such as quadrilaterals, trapezoids, rhombi, hexagons, cubes, and spheres; can identify angle, sides. (5–6 yrs.)
• Make pictures by combining shapes.
• Draw and can follow simple maps of familiar places, such as of the classroom or playground.
• Predict what a 3-D shape would look like if it were flipped or rotated in space.
• Use spatial terms relative to the position of other people or objects (“The block is in front of you but behind the chair.”).

Measurement

Watch for: attempts to measure using other objects, hand/fingers, arms, footsteps, use of measurement tools, such a scale, ruler, measuring cups, etc.

Most children:

• Recognize and label the attributes of objects using measurement terms (heavy/light, long/short, full/less full, taller/shorter, etc.). (3–4 yrs.)
• Compare and sort objects according to their attributes. (Place all the tall blocks in one pile and the short blocks in another.) Can sort by two attributes.
• Can place objects in order according to a measurable attribute (size, weight, length, etc.).
• Experiment with ways of measuring things (uses different size cups to measure water or different objects to compare length). Comment on differences in measurement between children (“I got 2 cups”) and between different types of measures (“2 small cups makes 1 big cup”).
• Understand vocabulary associated with differences in measurable attributes (smaller, smallest, smaller than, etc.).
• Uses nonstandard and standard measuring tools.
• Know time words “before,” “after,” “yesterday,” etc.
• Know that time measures the duration or length of an event.
• Know the purpose of a clock and calendar is to measure time.
• Understand basic ideas about using measuring tools (Place the ruler so the end is even with the end of the object you want to measure.). (5–6 yrs.)
• Use number with measurement (2 inches). Understand that number principles apply to measurement (You add an inch, the number is bigger).
• Estimate measurement and quantity.
• Use time words (second, minute, hour, day, week) to describe the duration of events.

Pattern/algebraic thinking

Watch for: attempts to create patterns during play with manipulatives or responses to patterns in the environment.

Many children:

• Notice and copy simple repeating patterns. (3–4 yrs.)
• Represent patterns with different objects.
• Can extend a pattern.
• Can create growing patterns. (4–5 yrs.)
• Notice and discuss patterns in arithmetic. (5–6 yrs.)

Displaying and analyzing data.

Watch for: attempts to represent counting and sorting in a display or representation in a drawing; attempts to understand graphs and tables.

Many children:

• Sort objects, count, and compare groups in terms of size of group or number of objects.
• Participate in making a simple graph (places choice in correct column of a participation chart). (3–4 yrs.)
• Compare simple graphs. (4–5 yrs.)
• Create a simple graph using a symbol, such as tally marks or blocks to stand for the objects or attribute. (5–6 yrs.) For example, places two tally marks on a piece of paper to stand for the two blue blocks in the collection.
• Represent the data using numerical summaries, such as creating a bar graph using numbers. (6–7 yrs.)
• Can read different types of graphs and tables.

Scientific Concepts:

Watch for: descriptions of scientific phenomena; use of scientific vocabulary; use observation and experimentation to understand the natural world.

Most children:

• Know that objects can be perceived by different senses and that these senses give different information. (3–4 yrs.)
• Use simple tools to make observations (magnifying glass, scales, etc.).
• Ask questions about observable phenomena. (Why are trees so big?)
• Know general properties of physical environment (seasons, weather, rock, mountains, rivers, lakes, oceans, etc.).
• Ask questions about inferred phenomena. (Why does a plant need roots?) (5–6 yrs.)
• Ask questions about details of observations. (Why are there different kinds of hair on my dog?)
• Use everyday language to explain scientific phenomena.
• Begin to use scientific words to explain phenomena.
• Know that physical properties of things can change (ice melts, etc.).
• Conduct simple experiments with adult guidance to understand phenomena.
• Know simple scientific concepts are based on the observable world. (6–7 yrs.)
• Use simple scientific concepts to explain natural phenomena.
• Understand how an investigation or experiment can answer scientific questions.
• Can classify objects and things based on inferred attributes and knows some scientific categories (mammals vs. reptiles, objects that sink and objects that float, etc.).
• Know that the life cycle for different living things is different.

Social Studies:

Watch for: interest and understanding about culture, people, places and the environment, groups and institutions, other countries, and civic ideas (good citizenship, diversity, sense of community.

The National Council for Social Studies sets the following expectations for early childhood:

Kindergarten: Awareness of self in the social setting.

First grade: The individual in school and family life.

Second grade: The neighborhood.

Third grade: Sharing the earth with others in the community.