IXL Math - Indiana sixth-grade math standards

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Skills available for Indiana sixth-grade math standards

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6.1 Number Sense

6.1.1 Understand and apply the basic concept of negative numbers (e.g., on a number line, in counting, in temperature, in "owing").
- Integers: Understanding integers (Sixth grade - C.1)
- Measurement: Working with temperatures above and below zero (Sixth grade - X.8)
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.
- Integers: Absolute value and opposite integers (Sixth grade - C.2)
- Rational numbers: Absolute value of rational numbers (Sixth grade - D.3)
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.
- Ratios, proportions, and percents: Write a ratio to describe objects in a picture (Sixth grade - Z.1)
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 Computation

6.3 Algebra and Functions

6.3.1 Write and solve one-step linear equations and inequalities in one variable and check the answers.
6.3.2 Write and use formulas with up to three variables to solve problems.
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.
- Algebra: Simplify expressions using order of operations and parentheses (Fifth grade - P.1)
- Divide fractions: Simplify expressions involving fractions (Sixth grade - W.7)
6.3.5 Use variables in expressions describing geometric quantities.
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.
- Algebra: Solve equations involving integers (Sixth grade - P.12)
- Coordinate graphing: Write the linear function shown in a graph (Sixth grade - Q.4)
6.3.9 Investigate how a change in one variable relates to a change in a second variable.
- Algebra: Complete a function table and write an equation (Sixth grade - P.9)
- Coordinate graphing: Graph linear functions (Sixth grade - Q.5)

6.4 Geometry

6.4.1 Identify and draw vertical, adjacent, complementary, and supplementary angles and describe these angle relationships.
- Geometry: Complementary and supplementary angles (Sixth grade - Y.6)
6.4.2 Use the properties of complementary, supplementary, and vertical angles to solve problems involving an unknown angle. Justify solutions.
- Geometry: Transversal of parallel lines (Sixth grade - Y.7)
6.4.3 Draw quadrilaterals and triangles from given information about them.
- Geometry: Triangle review (Sixth grade - Y.8)
- Geometry: Classify quadrilaterals (Sixth grade - Y.9)
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.
- Geometry: Find missing angles and side lengths in triangles and quadrilaterals (Sixth grade - Y.10)
- Geometry: Sums of angles in polygons (Sixth grade - Y.11)
6.4.5 Identify and draw two-dimensional shapes that are similar.
6.4.6 Draw the translation (slide) and reflection (flip) of shapes.
- Geometry: Reflection, rotation, and translation (Sixth grade - Y.16)
6.4.7 Visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids.
- Geometry: Which figure is being described? (Sixth grade - Y.25)
- Geometry: Front, side, and top view (Sixth grade - Y.26)

6.5 Measurement

6.5.1 Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles.
- Time: Time units (Sixth grade - H.2)
- Geometry: Angle review: measure and classify (Sixth grade - Y.3)
6.5.2 Understand and use larger units for measuring length by comparing miles to yards and kilometers to meters.
6.5.3 Understand and use larger units for measuring area by comparing acres and square miles to square yards and square kilometers to square meters.
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.
- Geometry: Circles: calculate area, circumference, radius, and diameter (Sixth grade - Y.23)
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.
- Geometry: Circles: calculate area, circumference, radius, and diameter (Sixth grade - Y.23)
6.5.6 Understand the concept of significant figures and round answers to an appropriate number of significant figures.
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.
- Geometry: Volume and surface area (Sixth grade - Y.27)
6.5.8 Use strategies to find the surface area and volume of right prisms and cylinders using appropriate units.
- Geometry: Volume and surface area (Sixth grade - Y.27)
6.5.9 Use a formula to convert temperatures between Celsius and Fahrenheit.
- Measurement: Convert between Celsius and Fahrenheit (Sixth grade - X.9)
6.5.10 Add, subtract, multiply, and divide with money in decimal notation.

6.6 Data Analysis and Probability

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.
6.6.2 Make frequency tables for numerical data, grouping the data in different ways to investigate how different groupings describe the data. Understand and find relative and cumulative frequency for a data set. Use histograms of the data and of the relative frequency distribution, and a broken line graph for cumulative frequency, to interpret the data.
- Charts and graphs: Create frequency tables (Sixth grade - R.5)
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.
- Probability: Compound events - find the number of outcomes by counting (Sixth grade - AA.5)
6.6.5 Use data to estimate the probability of future events.
- Probability: Make predictions (Sixth grade - AA.3)
6.6.6 Understand and represent probabilities as ratios, measures of relative frequency, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable.
- Probability: Probability of one event (Sixth grade - AA.2)

6.7 Problem Solving

Students make decisions about how to approach problems and communicate their ideas.
6.7.1 Analyze problems by identifying relationships, telling relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
6.7.2 Make and justify mathematical conjectures based on a general description of a mathematical question or problem.
6.7.3 Decide when and how to break a problem into simpler parts.
Students use strategies, skills, and concepts in finding and communicating solutions to problems.
6.7.4 Apply strategies and results from simpler problems to solve more complex problems.
- Geometry: Area of compound figures (Fifth grade - B.18)
- Geometry: Sums of angles in polygons (Sixth grade - Y.11)
6.7.5 Express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work.
- Algebra: Identify terms, coefficients, and monomials (Sixth grade - P.14)
6.7.6 Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
- Decimal numbers: Round decimals (Sixth grade - B.7)
6.7.7 Select and apply appropriate methods for estimating results of rational-number computations.
6.7.8 Use graphing to estimate solutions and check the estimates with analytic approaches.
- Coordinate graphing: Find points on a function graph (Sixth grade - Q.3)
6.7.9 Make precise calculations and check the validity of the results in the context of the problem.
Students determine when a solution is complete and reasonable and move beyond a particular problem by generalizing to other situations.
6.7.10 Decide whether a solution is reasonable in the context of the original situation.
- Algebra: Does (x, y) satisfy an equation? (Sixth grade - P.13)
6.7.11 Note the method of finding the solution and show a conceptual understanding of the method by solving similar problems.