Grade 7

Overview

This overview provides only the highlights of the new learning that should take place at the seventh-grade level. The specific skills and subject matter that seventh graders should be taught in each of the five mathematical strands are set forth in the formal standards and indicators for these strands. To alert educators as to when the progression in learning should occur for students in this grade, specific language is used with certain indicators:

·        An indicator beginning with the phrase “Generate strategies” addresses a concept that is being formally introduced for the first time, and students must therefore be given experiences that foster conceptual understanding.

·        An indicator beginning with the phrase “Apply an algorithm,” “Apply a procedure,” “Apply procedures,” or “Apply formulas” addresses a concept that has been introduced in a previous grade: students should already have the conceptual understanding, and the goal must now be fluency.

·        An indicator beginning with the phrase “Apply strategies and formulas” or “Apply strategies and procedures” addresses a concept that is being formally introduced for the first time, yet the goal must nonetheless be that students progress to fluency.

 

Highlights of the new learning for grade-seven students are

·        understanding fractional percentages and percentages greater than 100;

·        understanding the concept of square roots and the inverse relationship between squaring and finding square roots of perfect squares;

·        understanding the meaning of absolute value;

·        generating strategies to add, subtract, multiply, and divide integers;

·        applying an algorithm to multiply and divide fractions and decimals;

·        using inverse operations to solve two-step equations and inequalities;

·        classifying and explaining proportional relationships;

·        translating between two- and three-dimensional representations of compound figures;

·        creating tessellations with transformations and explaining the angle-measure relationships among shapes that tessellate;

·        applying strategies and formulas to determine the surface area and volume of three-dimensional shapes;

·        using one-step unit analysis to convert between and within U.S. Customary System and the metric system; and

·        applying procedures to calculate the interquartile range and the probability of mutually exclusive events.

Grade 7

Mathematical Processes

 

 

 

Standard 7-1:        The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

 

 

 

Indicators

7-1.1      Generate and solve complex abstract problems that involve modeling physical, social, or mathematical phenomena.

7-1.2      Evaluate conjectures and pose follow-up questions to prove or disprove conjectures.

7-1.3      Use inductive and deductive reasoning to formulate mathematical arguments.

7-1.4      Understand equivalent symbolic expressions as distinct symbolic forms that represent the same relationship.

7-1.5      Generalize mathematical statements based on inductive and deductive reasoning.

7-1.6      Use correct and clearly written or spoken words, variables, and notation to communicate about significant mathematical tasks.

7-1.7      Generalize connections among a variety of representational forms and real-world situations.

7-1.8      Use standard and nonstandard representations to convey and support mathematical relationships.

 

Grade 7

Number and Operations

 

 

Standard 7-2:        The student will demonstrate through the mathematical processes an understanding of the representation of rational numbers, percentages, and square roots of perfect squares; the application of ratios, rates, and proportions to solve problems; accurate, efficient, and generalizable methods for operations with integers; the multiplication and division of fractions and decimals; and the inverse relationship between squaring and finding the square roots of perfect squares. 

 

Indicators

7-2.1       Understand fractional percentages and percentages greater than one hundred.

7-2.2       Represent the location of rational numbers and square roots of perfect squares on a number line.

7-2.3       Compare rational numbers, percentages, and square roots of perfect squares by using the symbols ≤, ≥, <, >, and =.

7-2.4       Understand the meaning of absolute value.

7-2.5       Apply ratios, rates, and proportions to discounts, taxes, tips, interest, unit costs, and similar shapes.

7-2.6       Translate between standard form and exponential form.

7-2.7       Translate between standard form and scientific notation.

7-2.8       Generate strategies to add, subtract, multiply, and divide integers.

7-2.9       Apply an algorithm to multiply and divide fractions and decimals.

7-2.10     Understand the inverse relationship between squaring and finding the square roots of perfect squares.

 

Grade 7

Algebra

 

 

Standard 7-3:        The student will demonstrate through the mathematical processes an understanding of proportional relationships.

 

Indicators

7-3.1    Analyze geometric patterns and pattern relationships.

7-3.2    Analyze tables and graphs to describe the rate of change between and among quantities.

7-3.3    Understand slope as a constant rate of change.

7-3.4    Use inverse operations to solve two-step equations and two-step inequalities.

7-3.5    Represent on a number line the solution of a two-step inequality.

7-3.6    Represent proportional relationships with graphs, tables, and equations.

7-3.7    Classify relationships as either directly proportional, inversely proportional, or nonproportional.

 

Grade 7

Geometry

 

 

Standard 7-4:      The student will demonstrate through the mathematical processes an understanding of proportional reasoning, tessellations, the use of geometric properties to make deductive arguments. the results of the intersection of geometric shapes in a plane, and the relationships among angles formed when a transversal intersects two parallel lines.

 

Indicators

7-4.1       Analyze geometric properties and the relationships among the properties of triangles, congruence, similarity, and transformations to make deductive arguments.

7-4.2       Explain the results of the intersection of two or more geometric shapes in a plane.

7-4.3       Illustrate the cross section of a solid.

7-4.4       Translate between two- and three-dimensional representations of compound figures.

7-4.5       Analyze the congruent and supplementary relationships—specifically, alternate interior, alternate exterior, corresponding, and adjacent—of the angles formed by parallel lines and a transversal. 

7-4.6       Compare the areas of similar shapes and the areas of congruent shapes.

7-4.7       Explain the proportional relationship among attributes of similar shapes.

7-4.8       Apply proportional reasoning to find missing attributes of similar shapes.

7-4.9       Create tessellations with transformations.

7-4.10     Explain the relationship of the angle measurements among shapes that tessellate.