Chance—This strand of mathematics treats understanding how probable it is that events will occur or recur.
Data collection, representation and distribution—Information can be collected and displayed to make it more easily understood. Various measures can be used to analyze data, each being more appropriate for some purposes than others.
Equivalence—There are many ways to express one quantity and students should be able to compare expressions and determine whether equivalence exists. If not, they should know which represents more. Very closely related is the concept of the equal sign. Quantities on two sides of an equal sign must be equivalent.
Estimation—This is a legitimate skill that relies on a good understanding of numbers, number systems and operations. Estimation helps students decide whether their solutions are reasonable.
Functions and relations—If a quantity changes in a regular way (e.g., always +5), the change is a linear function. If the changing quantity is graphed, it creates a straight line. If all the changes are not the same, the graphed line is not straight.
Measurement—This allows precise description and construction of both physical objects and abstract ideas such as time. It plays a large role in everyday life.
Numbers—Students should understand the meaning of numbers, the quantities they stand for and be able to order real numbers on a number line. They develop number sense through counting, using benchmarks, doing mental math and being able to make reasonable estimates.
Operation meanings and relationships—Different expressions or numbers can express the same situation; one expression can represent different situations. Meanings of operations remain the same regardless of the numbers involved. Sometimes different operations can be used to solve the same problem. For example, Jimmy has 12 crayons now. He gave away some but had 15 earlier. How many crayons did he give away? Children can think 15-12 or add 12 + ? = 15.
Patterns—Patterns can be described, generalized and used to make predictions. Pattern recognition is often a clue for solving problems.
Ratio and Proportion—Ratio is the relationship between two quantities (1 kit for every 4 students). If the relationship remains constant as the number of students (or kits) increases the relationship is proportional. Two equivalent ratios create a proportion.
Rational numbers are points on the number line—These numbers acquire meaning in the context of what they refer to: 1/4 inch or 1/4 of the crowd? 0.8 of a meter or 0.8 of a dollar? The effects of multiplication and division are different when fractions and decimals between zero and 1 are used.
Shapes and solids—These are used to describe physical aspects of the environment. Changing position or orientation does not change a shape. But shapes, like numbers, can be decomposed, recomposed or completed to enable problems to be solved.
Solving word problems—To solve word problems, students must understand what is happening in a situation and not simply look for one or two words that are supposed to tell them what to do.
Some relationships are always true—Understanding them can help people navigate new situations. Generalizing those relationships creates algebraic expressions.
Variables are an underlying foundation of algebra—Situations can be described mathematically without using numbers with a variable representing a range of possible numbers. For example, no matter how many squares you place end to end, if the side of a square is “1,” the perimeter will always be two times the number of squares (top and bottom) plus 2 (ends), so we can say p = n + 2 and find the perimeter for any number of squares easily.