Indiana State Standards for Mathematics: Grade 7
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IN.7.1. Number Sense
7.1.1. Read, write, compare and solve problems using whole numbers in scientific notation.
7.1.2. Recognize and compute whole number powers of positive integers.
7.1.3. Recognize the prime factors of a number and find the prime factorization of whole numbers and write the results using exponents.
7.1.4. Recognize or use prime and composite numbers to solve problems.
7.1.5. Recognize and use the inverse relationship between squaring and finding the square root of a perfect square integer.
7.1.6. Identify, write, rename, compare and order rational and common irrational numbers and plot them on a number line.
7.1.7. Solve problems that involve multiplication and division with integers, fractions, decimals and combinations of the four operations.
7.1.8. Solve problems involving percents.
7.1.8.a. Find the whole given a part and the percentage
7.1.8.b. Find percentage increase or decrease.
7.1.9. Solve problems involving ratios and proportions.
7.1.9.a. Express one quantity as a fraction of another, given their ratio, and vice versa.
7.1.9.b. Find how many times one quantity is as large as another, given their ratio, and vice versa.
7.1.9.c. Express one quantity as a fraction of another given the two quantities.
7.1.9.d. Find the whole, or one part, when a whole is divided into parts in a given ration.
7.1.9.e. Solve problems involving two pairs of equivalent ratios.
7.2.1. Use variables and appropriate operations to write an expression, equation or inequality that represents a verbal description.
7.2.2. Write and solve two-step linear equations and inequalities in one variable.
7.2.3. Evaluate numerical expressions and simplify algebraic expressions involving rational and irrational numbers.
7.2.4. Solve an equation or formula with two variables for a particular variable.
7.2.5. Find the slope of a line from its graph and relate the slope of a line to similar triangles.
7.2.6. Draw the graph of a line given its slope and one point on the line or two points on the line.
7.2.7. Identify situations that involve proportional relationships, draw graphs representing these situations and recognize that these situations are described by a linear function in the form y = mx where the unit rate m is the slope of the line.
IN.7.3. Algebra and Functions
7.3.1. Identify and use basic properties of angles formed by transversals intersecting pairs of parallel lines.
7.3.2. Identify, describe, and use transformations (translations, rotations, reflections and simple compositions of these transformations) to solve problems.
7.3.3. Draw two-dimensional patterns (nets) for three-dimensional objects, such as right prisms, pyramids, cylinders and cones.
7.3.4. Recognize, describe, or extend geometric patterns using tables, graphs, words, or symbols.
7.3.5. Identify, describe, and construct similarity relationships and solve problems involving similarity (including similar triangles) and scale drawings by using proportional reasoning.
7.3.6. Solve simple problems involving distance, speed and time.
7.3.6.a. Understand concepts of speed and average speed.
7.3.6.b. Understand the relationship between distance, time and speed.
7.3.6.c. Find speed, distance or time given the other two quantities.
7.3.6.d. Write speed in different units (km/h, m/s, cm/s, mi/hr, ft/sec).
7.3.6.e. Solve simple problems involving speed and average speed.
7.4.1. Create, analyze and interpret data sets in multiple ways using bar graphs, frequency tables, line plots, histograms and circle graphs. Justify the choice of data display.
7.4.2. Make predictions from statistical data and use proportions to make estimates about a population based on a sample.
7.4.3. Describe how additional data, particularly outliers, added to a data set may affect the mean, median and mode.
7.4.4. Analyze data displays, including ways that they can be misleading. Analyze ways in which the wording of questions can influence survey results.
7.4.5. Understand that when all outcomes of an experiment are equally likely, the theoretical probability of an event is the fraction of outcomes in which the event occurs. Use theoretical probability and proportions to make approximate predictions.
IN.PS. Process Standards
PS.1. Problem Solving
PS.1.1. Build new mathematical knowledge through problem solving.
PS.1.2. Solve problems that arise in mathematics and in other contexts.
PS.1.3. Apply and adapt a variety of appropriate strategies to solve problems.
PS.1.4. Monitor and reflect on the process of mathematical problem solving.
PS.2. Reasoning and Proof
PS.2.1. Recognize reasoning and proof as fundamental aspects of mathematics.
PS.2.2. Make and investigate mathematical conjectures.
PS.2.3. Develop and evaluate mathematical arguments and proofs.
PS.2.4. Select and use various types of reasoning and methods of proof.
PS.3.1. Organize and consolidate their mathematical thinking through communication.
PS.3.2. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
PS.3.3. Analyze and evaluate the mathematical thinking and strategies of others.
PS.3.4. Use the language of mathematics to express mathematical ideas precisely.
PS.4.1. Recognize and use connections among mathematical ideas.
PS.4.2. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
PS.4.3. Recognize and apply mathematics in contexts outside of mathematics.
PS.5.1. Create and use representations to organize, record, and communicate mathematical ideas.
PS.5.2. Select, apply, and translate among mathematical representations to solve problems.
PS.5.3. Use representations to model and interpret physical, social, and mathematical phenomena.
PS.6. Estimation and Mental Computation
PS.6.1. Know and apply appropriate methods for estimating the results of computations.
PS.6.2. Round numbers to a specified place value.
PS.6.3. Use estimation to decide whether answers are reasonable.
PS.6.4. Decide when estimation is an appropriate strategy for solving a problem.
PS.6.5. Determine appropriate accuracy and precision of measurements in problem situations.
PS.6.6. Use properties of numbers and operations to perform mental computation.
PS.6.7. Recognize when the numbers involved in a computation allow for a mental computation strategy.
PS.7.1. Technology should be used as a tool in mathematics education to support and extend the mathematics curriculum.
PS.7.2. Technology can contribute to concept development, simulation, representation, communication, and problem solving.
PS.7.3. The challenge is to ensure that technology supports-but is not a substitute for- the development of skills with basic operations, quantitative reasoning, and problem-solving skills.
PS.7.3.a. Graphing calculators should be used to enhance middle school and high school students' understanding and skills.
PS.7.3.b. The focus must be on learning mathematics, using technology as a tool rather than as an end in itself.