Math Standards

1. Draws pictures to represent problems
2. Uses discussions with teachers and other students to understand problems
3. Explains to others how she or he went about solving a numerical problem
4. Makes organized lists or tables of information necessary for solving a problem
5. Uses whole number models (e.g., pattern blocks, tiles, or other manipulative materials) to represent problems
6. Uses a variety of strategies to understand problem situations (e.g., discussing with peers, stating problems in own words, modeling problem with diagrams or physical objects, identifying a pattern)
7. Represents problems situations in a variety of forms (e.g., translates from a diagram to a number or symbolic expression)
8. Understands that some ways of representing a problem are more helpful than others
9. Uses trial and error and the process of elimination to solve problems
10. Knows the difference between pertinent and irrelevant information when solving problems
11. Understands the basic language of logic in mathematical situations (e.g., "and," "or," "not")
12. Uses explanations of the methods and reasoning behind the problem solution to determine reasonableness of and to verify results with respect to the original problem
13. Understands basic valid and invalid arguments (e.g., counter examples, irrelevant approaches)

1. Understands that numbers are symbols used to represent quantities or attributes of real-world objects
2. Counts whole numbers (i.e., both cardinal and ordinal numbers)
3. Understands symbolic, concrete, and pictorial representations of numbers (e.g., written numerals, objects in sets, number lines)
4. Understands basic whole number relationships (e.g., 4 is less than 10, 30 is 3 tens)
5. Understands the concept of a unit and its subdivision into equal parts (e.g., one object, such as a candy bar, and its division into equal parts to be shared among four people)
6. Understands the relationships among fractions, decimals, mixed numbers, and whole numbers
7. Understands equivalent forms of basic percents, fractions, and decimals (e.g., « is equivalent to 50% is equivalent to .5) and when one form of a number might be more useful than another
8. Understands the basic difference between odd and even numbers
9. Understands the basic meaning of place value
10. Understands the relative magnitude of whole numbers, fractions, decimals, and mixed numbers
11. Uses models (e.g., number lines, two-dimensional and three-dimensional regions) to identify, order, and compare numbers

1. Adds and subtracts whole numbers
2. Solves real-world problems involving addition and subtraction of whole numbers
3. Understands common terms used with estimation (e.g., "about," "near," "closer to," "between," "a little less than")
4. Understands the inverse relationship between addition and subtraction
5. Adds, subtracts, multiplies, and divides whole numbers and decimals
6. Adds and subtracts simple fractions
7. Uses specific strategies (e.g., front-end estimation, rounding) to estimate computations and to check the reasonableness of computational results
8. Performs basic mental computations (e.g., addition and subtraction of whole numbers)
9. Determines the effects of addition, subtraction, multiplication, and division on size and order of numbers
10. Understands the properties of and the relationships among addition, subtraction, multiplication, and division (e.g., reversing the order of two addends does not change the sum; division is the inverse of multiplication)
11. Solves real-world problems involving number operations (e.g., computations with dollars and cents)
12. Knows the language of basic operations (e.g., "factors," "products," "multiplication")

1. Understands the basic measures length, width, height, weight, and temperature
2. Understands the concept of time and how it is measured
3. Knows processes for telling time, counting money, and measuring length, weight, and temperature, using basic standard and non-standard units
4. Makes quantitative estimates of familiar linear dimensions, weights, and time intervals and checks them against measurements
5. Understands the basic measures perimeter, area, volume, capacity, mass, angle, and circumference
6. Selects and uses appropriate tools for given measurement situations (e.g., rulers for length, measuring cups for capacity, protractors for angle)
7. Knows approximate size of basic standard units (e.g., centimeters, feet, grams) and relationships between them (e.g., between inches and feet)
8. Understands relationships between measures (e.g., between length, perimeter, and area)
9. Understands that measurement is not exact (i.e., measurements may give slightly different numbers when measured multiple times)
10. Uses specific strategies to estimate quantities and measurements (e.g., estimating the whole by estimating the parts)
11. Selects and uses appropriate units of measurement, according to type and size of unit

1. Understands basic properties of (e.g., number of sides, corners, square corners) and similarities and differences between simple geometric shapes
2. Understands the common language of spatial sense (e.g., "inside," "between," "above," "below," "behind")
3. Understands that geometric shapes are useful for representing and describing real world situations
4. Understands that patterns can be made by putting different shapes together or taking them apart
5. Knows basic geometric language for describing and naming shapes (e.g., trapezoid, parallelogram, cube, sphere)
6. Understands basic properties of figures (e.g., two- or three-dimensionality, symmetry, number of faces, type of angle)
7. Predicts and verifies the effects of combining, subdividing, and changing basic shapes
8. Understands that shapes can be congruent or similar
9. Uses motion geometry (e.g., turns, flips, slides) to understand geometric relationships
10. Understands characteristics of lines (e.g., parallel, perpendicular, intersecting) and angles (e.g., right, acute)
11. Understands how scale in maps and drawings shows relative size and distance

1. Understands that observations about objects or events can be organized and displayed in simple graphs
2. Understands that one can find out about a group of things by studying just a few of them
3. Understands that data represent specific pieces of information about real-world objects or activities
4. Understands that spreading data out on a number line helps to see what the extremes are, where the data points pile up, and where the gaps are
5. Understands that a summary of data should include where the middle is and how much spread there is around it
6. Organizes and displays data in simple bar graphs, pie charts, and line graphs
7. Reads and interprets simple bar graphs, pie charts, and line graphs
8. Understands that data come in many different forms and that collecting, organizing, and displaying data can be done in many ways
9. Understands the basic concept of a sample (e.g., a large sample leads to more reliable information; a small part of something may have unique characteristics but not be an accurate representation of the whole)

1. Understands that some events are more likely to happen than others
2. Understands that some events can be predicted fairly well but others cannot because we do not always know everything that may affect an event
3. Understands that the word "chance" refers to the likelihood of an event
4. Recognizes events that are sure to happen, events that are sure not to happen, and events that may or may not happen (e.g., in terms of "certain," "uncertain," "likely," "unlikely")
5. Understands that when predictions are based on what is known about the past, one must assume that conditions stay the same from the past event to the predicted future event
6. Understands that statistical predictions are better for describing what proportion of a group will experience something (e.g., what proportion of automobiles will be involved in accidents) rather than which individuals within the group will experience something, and how often events will occur (e.g., how many sunny days will occur over a year) rather than exactly when they will occur
7. Uses basic sample spaces (i.e., the set of all possible outcomes) to describe events

1. Recognizes regularities in a variety of contexts (e.g., events, designs, shapes, sets of numbers)
2. Extends simple patterns (e.g., of numbers, physical objects, geometric shapes)
3. Recognizes a wide variety of patterns (e.g., basic linear patterns such as [2, 4, 6, 8 . . .] ; simple repeating and growing patterns) and the rules that explain them
4. Understands that the same pattern can be represented in different ways (e.g., geometrically or numerically; the pattern of numbers [7, 14, 21, 28 . . .] is equivalent to the mathematical relationship 7 n)
5. Knows that a variable is a letter or symbol that stands for one or more numbers
6. Understands the basic concept of an equality relationship (i.e., an equation is a number sentence that shows two quantities that are equal)
7. Solves simple open sentences involving operations on whole numbers (e.g., + 17 = 23)
8. Knows basic characteristics and features of the rectangular coordinate system (e.g., the horizontal axis is the X axis and the vertical axis is the Y axis)

1. Understands that numbers and the operations performed on them can be used to describe things in the real world and predict what might occur
2. Understands that mathematical ideas and concepts can be represented concretely, graphically, and symbolically