#### 6.1: Students compare and order positive and negative integers, decimals, fractions, and mixed numbers. They find multiples and factors.

6.1.1: Understand and apply the basic concept of negative numbers (e.g., on a number line, in counting, in temperature, in “owing”).

6.1.2: Interpret the absolute value of a number as the distance from zero on a number line, and find the absolute value of real numbers.

6.1.3: Compare and represent on a number line positive and negative integers, fractions, decimals (to hundredths), and mixed numbers.

6.1.4: Convert between any two representations of numbers (fractions, decimals, and percents) without the use of a calculator.

6.1.5: Recognize decimal equivalents for commonly used fractions without the use of a calculator.

6.1.6: Use models to represent ratios.

6.1.7: Find the least common multiple and the greatest common factor of whole numbers. Use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction).

#### 6.2: Students solve problems involving addition, subtraction, multiplication, and division of integers. They solve problems involving fractions, decimals, ratios, proportions, and percentages.

6.2.1: Add and subtract positive and negative integers.

6.2.2: Multiply and divide positive and negative integers.

6.2.3: Multiply and divide decimals.

6.2.4: Explain how to multiply and divide positive fractions and perform the calculations.

6.2.7: Understand proportions and use them to solve problems.

6.2.8: Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.

6.2.9: Use estimation to decide whether answers are reasonable in decimal problems.

6.2.10: Use mental arithmetic to add or subtract simple fractions and decimals.

#### 6.3: Students write verbal expressions and sentences as algebraic expressions and equations. They evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results. They investigate geometric relationships and describe them algebraically.

6.3.1: Write and solve one-step linear equations and inequalities in one variable and check the answers.

6.3.3: Interpret and evaluate mathematical expressions that use grouping symbols such as parentheses.

6.3.4: Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations.

6.3.6: Apply the correct order of operations and the properties of real numbers (e.g., identity, inverse, commutative, associative, and distributive properties) to evaluate numerical expressions. Justify each step in the process.

6.3.7: Identify and graph ordered pairs in the four quadrants of the coordinate plane.

6.3.8: Solve problems involving linear functions with integer values. Write the equation and graph the resulting ordered pairs of integers on a grid.

#### 6.4: Students identify, describe, and classify the properties of plane and solid geometric shapes and the relationships between them.

6.4.1: Identify and draw vertical, adjacent, complementary, and supplementary angles and describe these angle relationships.

6.4.2: Use the properties of complementary, supplementary, and vertical angles to solve problems involving an unknown angle. Justify solutions.

6.4.4: Understand that the sum of the interior angles of any triangle is 180º and that the sum of the interior angles of any quadrilateral is 360º. Use this information to solve problems.

6.4.6: Draw the translation (slide) and reflection (flip) of shapes.

6.4.7: Visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids.

#### 6.5: Students deepen their understanding of the measurement of plane and solid shapes and use this understanding to solve problems. They calculate with temperature and money, and choose appropriate units of measure in other areas.

6.5.1: Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles.

6.5.4: Understand the concept of the constant pi as the ratio of the circumference to the diameter of a circle. Develop and use the formulas for the circumference and area of a circle.

6.5.5: Know common estimates of PI (3.14, 22/7 ) and use these values to estimate and calculate the circumference and the area of circles. Compare with actual measurements.

6.5.7: Construct a cube and rectangular box from two-dimensional patterns and use these patterns to compute the surface area of these objects.

6.5.8: Use strategies to find the surface area and volume of right prisms and cylinders using appropriate units.

#### 6.6: Students compute and analyze statistical measures for data sets. They determine theoretical and experimental probabilities and use them to make predictions about events.

6.6.1: Organize and display single-variable data in appropriate graphs and stem-and-leaf plots, and explain which types of graphs are appropriate for various data sets.

6.6.3: Compare the mean, median, and mode for a set of data and explain which measure is most appropriate in a given context.

6.6.4: Show all possible outcomes for compound events in an organized way and find the theoretical probability of each outcome.

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.