View the Frameworks for the Minnesota Mathematics & Science Standards at: http://www.scimathmn.org/stemtc

ALGEBRA

Primary Focus

Use number sentences involving addition and subtraction basic facts to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.

1.2.2.1 Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences.

1.2.2.2 Determine if equations involving addition and subtraction are true.

1.2.2.3 Use number sense and models of addition and subtraction, such as objects and number lines, to identify the missing number in an equation such as: 2 + 4 = __; 3 +__ = 7; 5 = __– 3.

1.2.2.4 Use addition or subtraction basic facts to represent a given problem situation using a number sentence.

Use number sentences involving addition, subtraction and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.

2.2.2.1 Understand how to interpret number sentences involving addition, subtraction and unknowns represented by letters. Use objects and number lines and create real-world situations to represent number sentences.

2.2.2.2 Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true.

Work on the primary focus standards and benchmarks will continue to help develop the following:

Recognize, create, describe, and use patterns and rules to solve real-world and mathematical problems.

2.2.1.1 Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts.

Recognize, create, complete, and extend patterns.

K.2.1.1 Identify, create, complete, and extend simple patterns using shape, color, size, number, sounds and movements. Patterns may be repeating, growing or shrinking such as ABB, ABB, ABB or ●,●●,●●●.

Recognize and create patterns; use rules to describe patterns.

1.2.1.1 Create simple patterns using objects, pictures, numbers and rules. Identify possible rules to complete or extend patterns. Patterns may be repeating, growing or shrinking. Calculators can be used to create and explore patterns.

Recognize, create, describe, and use patterns and rules to solve real-world and mathematical problems.

2.2.1.1 Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts.

Use single-operation input-output rules to represent patterns and relationships and to solve real-world and mathematical problems.

3.2.1.1 Create, describe, and apply single-operation input-output rules involving addition, subtraction and multiplication to solve problems in various contexts.

Use input-output rules, tables and charts to represent patterns and relationships and to solve real-world and mathematical problems.

4.2.1.1 Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table.

Recognize and represent patterns of change; use patterns, tables, graphs and rules to solve real-world and mathematical problems.

5.2.1.1 Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems.

5.2.1.2 Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system.

Recognize and represent relationships between varying quantities; translate from one representation to another; use patterns, tables, graphs and rules to solve real-world and mathematical problems.

6.2.1.1 Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts.

6.2.1.2 Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations.

Recognize proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols and graphs; solve problems involving proportional relationships and explain results in the original context.

7.2.2.1 Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations.

7.2.2.2 Solve multi-step problems involving proportional relationships in numerous contexts.

7.2.2.3 Use knowledge of proportions to assess the reasonableness of solutions.

7.2.2.4 Represent real-world or mathematical situations using equations and inequalities involving variables and positive and negative rational numbers.

Recognize linear functions in real-world and mathematical situations; represent linear functions and other functions with tables, verbal descriptions, symbols and graphs; solve problems involving these functions and explain results in the original context.

8.2.2.1 Represent linear functions with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another.

8.2.2.2 Identify graphical properties of linear functions including slopes and intercepts. Know that the slope equals the rate of change, and that the y-intercept is zero when the function represents a proportional relationship.

8.2.2.3 Identify how coefficient changes in the equation f (x) = mx + b affect the graphs of linear functions. Know how to use graphing technology to examine these effects.

8.2.2.4 Represent arithmetic sequences using equations, tables, graphs and verbal descriptions, and use them to solve problems.

8.2.2.5 Represent geometric sequences using equations, tables, graphs and verbal descriptions, and use them to solve problems.

Recognize linear, quadratic, exponential and other common functions in real-world and mathematical situations; represent these functions with tables, verbal descriptions, symbols and graphs; solve problems involving these functions, and explain results in the original context.

9.2.2.1 Represent and solve problems in various contexts using linear and quadratic functions.

9.2.2.2 Represent and solve problems in various contexts using exponential functions, such as investment growth, depreciation and population growth.

9.2.2.3 Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables and symbolic representations. Know how to use graphing technology to graph these functions.

9.2.2.4 Express the terms in a geometric sequence recursively and by giving an explicit (closed form) formula, and express the partial sums of a geometric series recursively.

9.2.2.5 Recognize and solve problems that can be modeled using finite geometric sequences and series, such as home mortgage and other compound interest examples. Know how to use spreadsheets and calculators to explore geometric sequences and series in various contexts.

9.2.2.6 Sketch the graphs of common non-linear functions such as f(x)= $\sqrt{x}$ , f(x)= $| x |$ , f(x)= $\frac{1}{x}$ , f(x)= $x^{3}$ , and translations of these functions, such as f(x)= $\sqrt{x - 2} + 4$ . Know how to use graphing technology to graph these functions.