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IN.7.1. Number Sense
Students understand and use scientific notation and square roots. They convert between fractions and decimals.
7.1.1 Read, write, compare and solve problems using whole numbers in scientific notation.
7.1.2 Compare and order rational and common irrational numbers and place them on a number line.
7.1.4 Understand and compute whole number powers of whole numbers.
7.1.5 Find the prime factorization of whole numbers and write the results using exponents.
7.1.6 Understand and apply the concept of square root.
7.1.7 Convert terminating decimals into reduced fractions.
Students solve problems involving integers, fractions, decimals, ratios, and percentages.
7.2.1 Solve addition, subtraction, multiplication, and division problems that use integers, fractions, decimals, and combinations of the four operations.
7.2.2 Calculate the percentage increase and decrease of a quantity.
7.2.3 Solve problems that involve discounts, markups, and commissions.
7.2.5 Use mental arithmetic to compute with simple fractions, decimals, and powers.
IN.7.3. Algebra and Functions
Students express quantitative relationships using algebraic terminology, expressions, equations, inequalities, and graphs.
7.3.1 Use variables and appropriate operations to write an expression, a formula, an equation, or an inequality that represents a verbal description.
7.3.10 Identify and describe situations with constant or varying rates of change and know that a constant rate of change describes a linear function.
7.3.2 Write and solve two-step linear equations and inequalities in one variable and check the answers.
7.3.3 Use correct algebraic terminology such as variable, equation, term, coefficient, inequality, expression, and constant.
7.3.4 Evaluate numerical expressions and simplify algebraic expressions by applying the correct order of operations and the properties of rational numbers (e.g., identity, inverse, commutative, associative, distributive). Justify each step in the process.
7.3.5 Solve an equation or formula with two variables for a particular variable.
7.3.6 Define slope as vertical change per unit of horizontal change and recognize that a straight line has constant slope or rate of change.
7.3.7 Find the slope of a line from its graph.
7.3.8 Draw the graph of a line given the slope and one point on the line, or two points on the line.
Students deepen their understanding of plane and solid geometric shapes by constructing shapes that meet given conditions and by identifying attributes of shapes.
7.4.1 Understand coordinate graphs and use them to plot simple shapes, find lengths and areas related to the shapes and find images under translations (slides), rotations (turns), and reflections (flips).
7.4.3 Know and understand the Pythagorean Theorem and use it to find the length of the missing side of a right triangle and the lengths of other line segments. Use direct measurement to test conjectures about triangles.
Students compare units of measure and use similarity to solve problems. They compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less regular objects.
7.5.2 Use experimentation and modeling to visualize similarity problems. Solve problems using similarity.
7.5.3 Read and create drawings made to scale, construct scale models, and solve problems related to scale.
7.5.4 Use formulas for finding the perimeter and area of basic two-dimensional shapes and the surface area and volume of basic three-dimensional shapes, including rectangles, parallelograms, trapezoids, triangles, circles, right prisms, and cylinders.
7.5.6 Use objects and geometry modeling tools to compute the surface area of the faces and the volume of a three-dimensional object built from rectangular solids.
IN.7.6. Data Analysis and Probability
Students collect, organize, and represent data sets and identify relationships among variables within a data set. They determine probabilities and use them to make predictions about events.
7.6.1 Analyze, interpret, and display data in appropriate bar, line, and circle graphs and stem-and-leaf plots, and justify the choice of display.
7.6.2 Make predictions from statistical data.
7.6.4 Analyze data displays, including ways that they can be misleading. Analyze ways in which the wording of questions can influence survey results.
IN.7.7. Problem Solving
Students determine when a solution is complete and reasonable and move beyond a particular problem by generalizing to other situations.
7.7.11 Decide whether a solution is reasonable in the context of the original situation.
7.7.12 Note the method of finding the solution and show a conceptual understanding of the method by solving similar problems.
Students make decisions about how to approach problems and communicate their ideas.
7.7.1 Analyze problems by identifying relationships, telling relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
7.7.2 Make and justify mathematical conjectures based on a general description of a mathematical question or problem.
7.7.3 Decide when and how to divide a problem into simpler parts.
Students use strategies, skills, and concepts in finding and communicating solutions to problems.
7.7.10 Make precise calculations and check the validity of the results in the context of the problem.
7.7.4 Apply strategies and results from simpler problems to solve more complex problems.
7.7.5 Make and test conjectures by using inductive reasoning.
7.7.6 Express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work.
7.7.7 Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
7.7.8 Select and apply appropriate methods for estimating results of rational-number computations.
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