Grade 7

NUMBER SYSTEM including FRACTIONS: Students develop an understanding of numbers, ways of representing numbers, relationships among numbers and number systems.

OPERATIONS and ALGEBRAIC THINKING: Students use basic and advanced procedures to understand the meaning of operations in relation to advanced properties of functions and algebra

Geometry:  Mathematics is helpful in describing the physical world and the patterns of God’s creation, students analyze characteristics and properties of two and three dimensional geometric shapes and develop mathematical arguments about geometric relationships and specify locations and describe spatial relationships using coordinate geometry and other representational systems.

Measurement: Students understand measurable attributes of objects and the units, systems, and processes of measuremen

STATISTICS, PROBABILITY, AND DATA ANALYSIS: Design investigations, select, use and appropriate statistical methods to analyze data in order to make inferences and predictions based on data.

Work flexibly with fractions, decimals, and percents to solve problems

Compare and order fractions, decimals and percents efficiently and find their approximate location on a number line

Understand and use ratios and proportions to represent quantitative relationships

Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation

Use factors, multiples, prime factorization, and relatively prime numbers to solve problems

Develop meaning for integers and represent and compare quantities using them

Represent, Analyze, and generalize a variety of patterns with tables, graphs, words, and when possible, symbolic rules

Relate and compare different forms of representation for a relationship

Represent and analyze mathematical situations and structures using algebraic symbols and expressions

Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Use mathematical models to represent and understand quantitative relationships

Precisely describe, classify, and understand relationships among types of two and three – dimensional objects using their defining properties

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationships.

Use coordinate geometry to represent and examine the properties of geometric shapes

Apply transformations and use symmetry to analyze mathematical situations

Examine the congruence, similarity , and line or rotational symmetry of objects using transformations

Use visualization, spatial reasoning, and geometric modeling to solve problems

 Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life

Understand and use both metric and customary systems of measurement

Understand relationships among units and convert from one unit to another within the same system

Understand, select and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume

Use common benchmarks to select appropriate methods for estimating measurements

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more complex shapes

Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders

Solve problems involving scale factors, using ratio and proportion

Solve simple problems involving rates and derived measurements for such attributes as velocity and density

Formulate questions, design studies, and collect data about characteristics shared by two populations or different characteristics within one population

Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatter plots.

Select and use appropriate statistical methods to analyze data

Develop and evaluate inferences and predictions that are based on data

Convert between decimals, fractions and percents

Identify the fraction to the decimal equivalent (and vice versa) for halves, thirds, fourths, and fifths

Solve problems using scientific notation with positive exponents

Solve percent problems for real life situations (mark-ups, discounts, commissions, sales tax, etc.)

Calculate percent increase and percent decrease up to 100 percent

Compare and order fractions and decimals

Compare and order percents, fractions, and decimals

Develop meaning for percents greater than 100 and less than 1

Develop meaning for percent increase greater than 100%

Identify equal ratios and write them as a proportion

Find the unknown in a proportion containing integers or decimals using cross multiplication

Calculate a unity rate for a given relationship

Demonstrate movement of the decimal point to support understanding of the powers of 10

Use scientific calculators to show scientific notation

Use scientific calculators to compute exponents or roots

State if a value (between 1 and 50) is prime, composite or neither

Write the prime factorization of a number in expanded and exponential form

Use prime factorization to find greatest common factor (GCF) and least common multiple(LCM)

Represent everyday values (gains and losses) using integers

Compare an order integers on a number line

Understand and compute absolute value of integers

Understand and find opposites of integers

Find the expression from a given function table

Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations

Compare the relationships that exist between decimals, fractions, mixed numbers and percents

Write algebraic expressions from words to symbols and symbols to words

Write expressions from word problems

Describe what each variable represents in a given formula or problem

Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope

Write simple multi-step equations to solve word problems

Combine like-terms to simplify basic algebraic expressions

Evaluate numerical expressions and simplify algebraic expressions by applying the correct order of operations and the use of properties

State if a given value is a solution for the equation

Solve one step equations using inverse operations

Model and solve contextualized problems using various representations such as graphs, tables, and equations

Use graphs to analyze the nature of change in quantities in linear relationships

Classify and describe two dimensional shapes by angle measures/or side length

Classify and describe three dimensional shapes as prisms, pyramids, cylinders, cones, and spheres

Determine the difference between regular and irregular polygons

Compare similar objects to determine how the attributes are affected by changing in the dimensions of figures

Identify congruent figures and angles.

Identify complementary and supplementary angles

Find the missing complementary or supplementary angle measurement

Identify vertical and adjacent angles

Identify and compare similar figures.

Find the length of a side in a right triangle using Pythagorean Theorem

Use angle relationships (supplementary/complement ary angles, vertical/adjacent angles) to find missing angles when parallel lines are cut by a transversal

Locate and graph points on a coordinate plane and state the axis or quadrant on which they lie

Use coordinate geometry to examine special geometric shapes such as regular polygons or those with pairs of parallel or perpendicular sides

Determines the coordinates of missing vertices of geometric figures in the first quadrant given the coordinate of the other vertices

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling 

Recognize transformations as translations, reflections, and rotations

Use translations, reflections, and rotations to transform geometric shapes

Use scale to determine actual measurements

Use actual measurements to construct a scale model

Calculate the scale factor of two similar figures

Identify line symmetry and rotational symmetry in a variety of figures

Identify tessellations and shapes that can tessellate

Use two-dimensional representations of three- dimensional objects to visualize and solve problems such as those involving surface area and volume

Use nets to compose and decompose three dimensional shapes

Use given formulas to find perimeter, circumference, and area

Break a polygon into simpler shapes to find its area

Use indirect measurement to solve problems

Use the metric system and its units

Use the customary measurement system and its units

Make conversions with the customary system

Make conversions within the metric system

Use estimation to determine whether a measurement is reasonable

Use benchmarks angles (45o angle, right angle, and straight angle) to estimate angle measurement

Explain and use formulas to develop strategies to determine the area of complex shapes

Determine the volume of prisms, pyramids, and cylinders

Determine the surface area of prisms, pyramids, and cylinders

Use ratio and proportion to solve scale problems

Use ratio and proportion to solve problems involving unit rate

Formulate questions, design experiments or surveys to collect relevant data to compare characteristics

Given a set of data, select an appropriate representation

Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots and scatter plots

Find, use, and interpret measures of center and spread, including mean and interquartile range

Explain how outliers affect central tendencies

use observations about differences between two or more samples to make conjectures about the populations for which the samples were taken

make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit 

make conjectures to formulate new questions and plan new studies to answer them