Patterns & Relationships

Seeing, making, and generalizing patterns and relationships, and reasoning about change.

K–12 objective ladder

• K D05.S2.K.01 Continue or copy a simple repeating pattern of colors, shapes, or sounds.
• 1 D05.S2.01.01 Identify, extend, and create repeating patterns using objects, sounds, or colors, and tell the rule of the pattern.
• 1 D05.S2.01.02 Find the missing number in a simple number sentence such as 3 + ? = 7 and explain how they know.
• 2 D05.S2.02.01 Identify and extend growing patterns and describe how the pattern changes from one step to the next.
• 2 D05.S2.02.02 Solve one-step addition and subtraction problems with a missing number in a real context, such as sharing or spending.
• 3 D05.S2.03.01 Identify arithmetic patterns in tables and number grids and explain them using the properties of operations.
• 3 D05.S2.03.02 Solve two-step word problems using the four operations and explain the relationship between addition and subtraction or multiplication and division.
• 4 D05.S2.04.01 Generate and analyze a number or shape pattern that follows a given rule and describe its features.
• 4 D05.S2.04.02 Use a letter or symbol to stand for an unknown number in a simple equation and find its value.
• 5 D05.S2.05.01 Plot points and graph relationships in the first quadrant of a coordinate grid to represent real situations.
• 5 D05.S2.05.02 Write and evaluate simple expressions and interpret what they mean in a real situation.
• 6 D05.S2.06.01 Use variables to write expressions and equations that represent real situations, and solve one-step equations.
• 6 D05.S2.06.02 Represent the relationship between two quantities with a table and graph, and tell when one quantity depends on the other.
• 7 D05.S2.07.01 Write and solve two-step equations and inequalities to represent and solve real problems.
• 7 D05.S2.07.02 Identify proportional relationships in tables, graphs, and equations, and express them in the form y = kx.
• 8 D05.S2.08.01 Define, evaluate, and compare functions and use function notation to describe how one quantity depends on another.
• 8 D05.S2.08.02 Solve linear equations in one variable and analyze a pair of simultaneous linear equations by graphing.
• 9 D05.S2.09.01 Model real situations with linear and exponential functions and interpret slope and intercept in context.
• 9 D05.S2.09.02 Solve quadratic equations using several methods and interpret what their solutions mean in real situations.
• 10 D05.S2.10.01 Build and interpret polynomial and rational functions that model real relationships and describe their key features.
• 10 D05.S2.10.02 Model exponential growth and decay in population, finance, or environmental systems and explain the effect of the rate.
• 11 D05.S2.11.01 Model periodic phenomena with trigonometric functions and interpret amplitude, frequency, and shift in context.
• 11 D05.S2.11.02 Use logarithmic and exponential relationships to solve problems involving growth, decay, and large ranges of scale.
• 12 D05.S2.12.01 Model systems of relationships with equations or matrices and interpret the meaning of a solution in a real context.
• 12 D05.S2.12.02 Describe an algorithm as a step-by-step procedure for a real problem and analyze whether it works correctly and fairly.

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