## Math

Time Kindergarten Math Shapes Kindergarten Math Colors Kindergarten Math Addition Kindergarten Math Whole Numbers Kindergarten Math Whole Numbers Kindergarten Math Over & Under Kindergarten Math ### MN.6.1. Number & Operation

#### 6.1.1. Read, write, represent and compare positive rational numbers expressed as fractions, decimals, percents and ratios; write positive integers as products of factors; use these representations in real-world and mathematical situations.

##### 6.1.1.1. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid.

##### 6.1.1.2. Compare positive rational numbers represented in various forms. Use the symbols <, = and >.

##### 6.1.1.3. Understand that percent represents parts out of 100 and ratios to 100.

##### 6.1.1.4. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems.

##### 6.1.1.5. Factor whole numbers; express a whole number as a product of prime factors with exponents.

##### 6.1.1.6. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions.

##### 6.1.1.7. Convert between equivalent representations of positive rational numbers.

#### 6.1.2. Understand the concept of ratio and its relationship to fractions and to the multiplication and division of whole numbers. Use ratios to solve real-world and mathematical problems.

##### 6.1.2.1. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction.

##### 6.1.2.2. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations.

##### 6.1.2.3. Determine the rate for ratios of quantities with different units.

##### 6.1.2.4. Use reasoning about multiplication and division to solve ratio and rate problems.

#### 6.1.3. Multiply and divide decimals, fractions and mixed numbers; solve real-world and mathematical problems using arithmetic with positive rational numbers.

##### 6.1.3.1. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms.

##### 6.1.3.2. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions.

##### 6.1.3.3. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts.

##### 6.1.3.4. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers.

##### 6.1.3.5. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem.

### MN.6.2. Algebra

#### 6.2.1. 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.

#### 6.2.2. Use properties of arithmetic to generate equivalent numerical expressions and evaluate expressions involving positive rational numbers.

##### 6.2.2.1. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers.

#### 6.2.3. Understand and interpret equations and inequalities involving variables and positive rational numbers. Use equations and inequalities to represent real world and mathematical problems; use the idea of maintaining equality to solve equations. Interpret solutions in the original context.

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

### MN.6.3. Geometry & Measurement

#### 6.3.1. Calculate perimeter, area, surface area and volume of two and three dimensional figures to solve real-world and mathematical problems.

##### 6.3.1.1. Calculate the surface area and volume of prisms and use appropriate units, such as cm2 and cm3. Justify the formulas used. Justification may involve decomposition, nets or other models.

##### 6.3.1.2. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid.

#### 6.3.2. Understand and use relationships between angles in geometric figures.

##### 6.3.2.1. Solve problems using the relationships between the angles formed by intersecting lines.

#### 6.3.3. Choose appropriate units of measurement and use ratios to convert within measurement systems to solve real-world and mathematical problems.

##### 6.3.3.1. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units.

### MN.6.4. Data Analysis & Probability

#### 6.4.1. Use probabilities to solve real-world and mathematical problems; represent probabilities using fractions, decimals and percents.

##### 6.4.1.2. Determine the probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions and decimals between 0 and 1 inclusive. Understand that probabilities measure likelihood.

##### 6.4.1.3. Perform experiments for situations in which the probabilities are known, compare the resulting relative frequencies with the known probabilities; know that there may be differences.

##### 6.4.1.4. Calculate experimental probabilities from experiments; represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown.

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