School City of Hobart Mathematics The ISTEP+ assessment measures the academic performance of students in Mathematics. IN: Grade 7 The Indiana Academic Standards for Mathematics include standards for students in seventh grade. |
Algebraic Concepts |
The Algebraic Concepts Unit includes Competencies/Objectives which focus on algebraic equations and operations. Students explore the symbolic nature of algebraic concepts by identifying and extending patterns in algebra, by following algebraic procedures, and by proving theorems with properties. |
Vocabulary: Algebra
The learner will be able to determine and/or apply the correct algebraic terms and/or vocabulary.
|
Expressions: Evaluate/Rational Number
The learner will be able to use the correct order of operations and the properties of rational numbers to evaluate numerical expressions and simplify algebraic expressions, justifying each step during the process.
|
Rate: Recognize/Explain Change
The learner will be able to recognize and explain scenarios with constant or varying rates of change and understand that a constant rate of change explains a linear function.
|
Formulas: Solve/Two Variable
The learner will be able to solve for the value of a variable in a two variable formula.
|
Variables: Apply
The learner will be able to apply variables and suitable operations in the writing of an expression, a formula, an equation, inequality, or inequalities that illustrate a verbal description.
|
Computation: Precision
The learner will be able to perform precise computations.
|
Basic Operations: Integers/Fractions
The learner will be able to use combinations of the four basic operations with integers, fractions, and decimals to solve problems.
|
Solve Equations: Two Variables
The learner will be able to solve for the value of a variable in two variable equations.
|
Decimals |
The Decimals Unit includes Competencies/Objectives which focus on number sense and operations with decimals. Students compare and compute decimals, study money, estimate decimals, problem solve using decimals, and reason using decimals. |
Decimals: Converting
The learner will be able to convert decimals to fractions and fractions to decimals.
|
Decimals: Convert/Terminating
The learner will be able to convert terminating decimals into fractions in simplest form.
|
Problem Solving: Decimals
The learner will be able to obtain solutions to problems that involve decimals.
|
Problem Solving: Use/Basic Operations
The learner will be able to use the basic arithmetic operations with decimals when solving problems.
|
Fractions |
The Fractions Unit includes Competencies/Objectives which focus on number sense and operations with fractions. Students compare and order fractions, study fraction parts, estimate with fractions, reason using fractions, and problem solve using fractions. |
Problem Solving: Fractions
The learner will be able to solve problems that involve fractions.
|
Problem Solving: Operations/Fractions
The learner will be able to obtain solutions to problems involving the four basic operations with fractions.
|
Functions |
The Functions Unit includes Competencies/Objectives which focus on exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions. |
Functions: Recognize
The learner will be able to recognize functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.
|
Geometry |
The Geometry Unit includes Competencies/Objectives which focus on exploring geometric concepts from multiple perspectives. Students study properties and construction of figures, proofs and theorems, history of geometry, transformations, logic, and problem solving. |
Figures: Construct/Understanding
The learner will be able to deepen their understanding of two- and three-dimensional figures and properties by constructing figures that meet given criteria and by identifying characteristics of figures.
|
Similarity: Apply/Modeling
The learner will be able to apply experimentation and modeling to visualize similarity problems (with spreadsheets and drawing programs applying scaling and aspect ratios).
|
Solids: Create/Patterns
The learner will be able to create two-dimensional patterns for solid objects.
|
Triangles: Test Conjectures
The learner will be able to apply direct measurement to test conjectures about triangles.
|
Pythagorean Theorem: Understanding
The learner will be able to have knowledge and/or comprehension of the Pythagorean Theorem.
|
Pythagorean Theorem
The learner will be able to use the Pythagorean Theorem to determine an unknown side length of a right triangle.
|
Pythagorean Theorem: Find Lengths
The learner will be able to apply the Pythagorean Theorem to find the lengths of line segments.
|
Transformations: Comprehend/Length
The learner will be able to comprehend that the length of segments remain the same after undergoing a transformation.
|
Transformations: Comprehend/Results
The learner will be able to comprehend that the result from slides, turns, and flips are congruent to the original shape.
|
Inductive Reasoning: Conjecture
The learner will be able to apply techniques of inductive reasoning to formulate a conjecture.
|
Inductive Reasoning: Conjecture
The learner will be able to apply techniques of inductive reasoning to test conjectures.
|
Similarity: Applying
The learner will be able to solve problems by applying concepts of similarity.
|
Integers |
The Integers Unit includes Competencies/Objectives which focus on number sense and operations with integers. Students compare integers, perform operations with integers, convert integers to other number forms, use manipulatives to demonstrate integers, and solve problems with integers in real world contexts. |
Integers: Comprehend/Powers
The learner will be able to comprehend positive integer powers of positive integers.
|
Integers: Calculate/Powers
The learner will be able to calculate positive integer powers of positive integers.
|
Problem Solving: Apply/Basic Operations
The learner will be able to apply the basic operations on integers to obtain solutions to problems.
|
Problem Solving: Integers
The learner will be able to obtain solutions to problems involving integers.
|
Mathematics Processes |
The Mathematics Processes Unit includes Competencies/Objectives which focus on mathematical connections. Students communicate and model concepts and procedures. |
Reasoning: Approach Problems
The learner will be able to decide about the manner in which to approach a given problem.
|
Mathematics as Communication
The learner will be able to state solutions clearly and logically using suitable mathematical vocabulary and notation, and support solutions with verbal and symbolic evidence.
|
Conjecture: Create/Justify
The learner will be able to create and justify conjectures based on a general description of the mathematical question or problem that was posed.
|
Communication: Ideas/Problems
The learner will be able to communicate their ideas about how to approach problems.
|
Measurement |
The Measurement Unit includes Competencies/Objectives which focus on measurement concepts, applications, and analysis. Students study length, area, circumference, perimeter, volume, weight, formulas, distance, calendar, money, tools, accuracy, units, constructions, patterns, and problem solving. |
Area: Approximate/Calculate
The learner will be able to approximate and calculate the area of more complex or irregular two-dimensional shapes by dividing them into more basic geometric figures.
|
Perimeter/Area/Volume: Common Objects
The learner will be able to calculate the perimeter, area, and volume of everyday objects and apply them in determining those measures for less familiar objects.
|
Area/Volume: Objects/Modeling
The learner will be able to use objects and geometric modeling tools to calculate the surface area of the faces and the volume of a three-dimensional object made from rectangular solids.
|
Scale Drawings: Construct/Read
The learner will be able to create and/or read scale drawings and/or models.
|
Formulas: Perimeter/Area
The learner will be able to apply formulas for determine the perimeter and area of simple two-dimensional shapes and the surface area and volume of simple three-dimensional shapes.
|
Units: Compare
The learner will be able to make comparisons of measurement units.
|
Problem Solving: Scale
The learner will be able to solve problems involving scale.
|
Measurement: Compare/Within Systems
The learner will be able to make comparisons of the measures of lengths, areas, volumes, weights, capacities, times, and temperatures within the same system.
|
Number Theory |
The Number Theory Unit includes Competencies/Objectives which focus on manipulating number forms and classifications. Students make connections between number forms and their real world applications. |
Exponential Notation: Prime Factors
The learner will be able to determine the prime factorization of whole numbers and express the results using exponential notation.
|
Scientific Notation: Read/Write/Compare
The learner will be able to read, write, make comparisons, and obtain solutions to problems using whole numbers in scientific notation.
|
Ratio: Problem Solving
The learner will be able to use the concept of ratio in problem solving scenarios.
|
Square Roots: Understand
The learner will be able to understand square roots.
|
Square Roots: Apply
The learner will be able to apply square roots.
|
Scientific Notation: Understand
The learner will be able to comprehend scientific notation.
|
Scientific Notation: Apply
The learner will be able to apply scientific notation.
|
Numeration |
The Numeration Unit includes Competencies/Objectives which focus on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships. |
Quantities: Express Relationship
The learner will be able to relate quantitative relationships through the application of algebraic terms, expressions, equations, inequalities, and their graphs.
|
Estimate/Problems: Reasonableness
The learner will be able to use approximation to determine whether solutions are reasonable in problems involving fractions and decimals.
|
Mental Math: Use/Decimals
The learner will be able to use mental math to calculate with decimals.
|
Mental Math: Use/Fractions
The learner will be able to use mental math to calculate with basic fractions.
|
Mental Math: Use/Powers
The learner will be able to use mental math to calculate with powers.
|
Percents |
The Percent Unit includes Competencies/Objectives which focus on the concepts of percent. Students perform operations with percents, convert percents to other number forms, use manipulatives to demonstrate percents, and solve problems with percents in real world contexts. |
Problem Solving: Discount
The learner will be able to obtain solutions to problems involving discounts.
|
Problem Solving: Percents
The learner will be able to obtain solutions to problems involving percents.
|
Percent Increase: Compute
The learner will be able to compute the percentage of increase of a quantity.
|
Percent Decrease: Compute
The learner will be able to compute the percentage of decrease of a quantity.
|
Perspective/Role in Society |
The Perspective/Role in Society Unit includes Competencies/Objectives which focus on real world mathematics. Students study the mathematics of society and the role of mathematics in personal finance and careers. |
Consumer: Markups
The learner will be able to obtain solutions to problems involving markups.
|
Consumer: Commission
The learner will be able to obtain solutions to problems involving commissions.
|
Probability/Statistics |
The Probability/Statistics Unit includes Competencies/Objectives which focus on data analysis and probability concepts. Students collect, analyze, and make sense of real world data (including overlapping data, inconclusive data, etc.). |
Probability: Determine/Predict
The learner will be able to determine the probabilities of events and predict outcomes.
|
Data Management: Data Sets
The learner will be able to gather, organize, and illustrate data sets and recognize relationships between variables within a data set through the use of an electronic spreadsheet program as well as manually.
|
Graphing: Use/Check
The learner will be able to use graphing to approximate answers and check the approximations with analytic approaches.
|
Data Display: Study/Interpret/Display
The learner will be able to study, interpret, and display data in suitable bar, line, and circle graphs, and stem-and-leaf plots, and justify their decisions for using a particular display.
|
Probability: Comprehend/Disjoint
The learner will be able to comprehend that the probability of either of two disjoint events happening is the sum of the probabilities of each event.
|
Probability: Comprehend/Event
The learner will be able to comprehend that if P is the probability of an event occurring, 1-P is the probability of an event not occurring.
|
Measures of Central Tendency: Explain
The learner will be able to explain how adding data, particularly outliers, to a data set may affect the mean, median, and mode.
|
Statistical Data: Predicting
The learner will be able to make predictions based on given statistical data.
|
Survey: Create/Question/Appropriate
The learner will be able to study the manner in which the wording of questions can influence survey results.
|
Trees: Determine/Combinations
The learner will be able to determine the number of possible combinations of several objects using a tree diagram.
|
Data Display: Analyze
The learner will be able to analyze displays of data including how they can be misleading.
|
Problem Solving |
The Problem Solving Unit includes Competencies/Objectives which focus on analyzing problems, evaluating solutions, exploring problems, and developing strategies for solving problems. |
Solution: Determine/Communicate
The learner will be able to determine and communicate answers to problems using strategies, skills, and ideas.
|
Strategies: Solve/Similar
The learner will be able to express the strategy for determining the solution to a problem and illustrate a conceptual understanding of the strategy by obtaining solutions to similar problems.
|
Strategies: Break Up Problem
The learner will be able to figure out when and how to break up a problem into less difficult components.
|
Analyzing Problems: Relationships
The learner will be able to analyze problems by recognizing relationships, differentiating between relevant and irrelevant information, recognizing missing information, sequencing and prioritizing information, and observing patterns.
|
Problem: Generalizations
The learner will be able to progress past a given problem through generalizations to other situations.
|
Evaluating Solutions: Completeness
The learner will be able to determine when an answer is complete.
|
Solutions: Exact or Approximate
The learner will be able to identify the advantages of exact and approximate answers to problems.
|
Solutions: Degree of Accuracy
The learner will be able to present solutions to a specified degree of accuracy.
|
Solutions: Validity in Context
The learner will be able to verify the validity of solutions based on the context of the problem.
|
Solution: Reasonableness
The learner will be able to determine the reasonableness of results.
|
Solutions: Evaluate Reasonableness
The learner will be able to evaluate the reasonableness of a given solution within the context of the original problem.
|
Strategies: Apply
The learner will be able to apply strategies and/or results obtained from simpler problems to those that are more complex.
|
Rational and Irrational Numbers |
The Rational and Irrational Numbers Unit includes Competencies/Objectives which focus on number concepts. Students manipulate, compare, and perform operations with rational and irrational numbers. |
Rational Numbers: Estimate/Strategies
The learner will be able to apply strategies in the estimation of results of calculations with rational numbers of various forms.
|
Compare: Order/Rational Numbers
The learner will be able to make comparisons among rational numbers, and/or place them in order.
|
Irrational Numbers: Recognize/List
The learner will be able to recognize common irrational numbers from a list.
|
Irrational Numbers: Number Line
The learner will be able to place common irrational numbers on a number line.
|
Irrational Numbers: Compare/Order
The learner will be able to make comparisons and place in order common irrational numbers.
|
Rational Numbers: Recognize/List
The learner will be able to recognize rational numbers from a list.
|
Rational Numbers: Number Line
The learner will be able to place rational numbers on a number line.
|
Rational Numbers: Choose/Strategies
The learner will be able to choose strategies for the estimation of results of calculations with rational numbers of various forms.
|
Real Numbers and the Coordinate Plane |
The Real Numbers and the Coordinate Plane Unit includes Competencies/Objectives which focus on graphing concepts. Students graph equations and make connections between algebraic concepts and their geometric correspondences. |
Coordinate Geometry: Comprehend/Apply
The learner will be able to comprehend and apply coordinate graphs to plot basic figures, determine lengths and areas related to them, and find their image under translations, rotations, and reflections.
|
Linear Equations/Inequalities: Solve
The learner will be able to create and solve two-step linear equations and inequalities in one variable and check the solutions.
|
Slope: Identify/Straight Line/Constant
The learner will be able to identify that a straight line has a constant slope or rate of change.
|
Slope: Determine/Definition
The learner will be able to determine the definition of slope to be the vertical change per unit of horizontal change.
|
Slope: Determine From Graph
The learner will be able to use the graph of a linear equation to determine the slope.
|
Linear Equations: Graph
The learner will be able to make graphs of lines when two points and/or the slope and a point are known.
|