Christ the Redeemer

7th Grade Math Curriculum Scope and Sequence

Numbers and Operations

 (Whole Numbers, Decimals, Fractions)

Algebra

(Proportionality)

  • Add, subtract, multiply and divide rational numbers.
  • Change a rational number in fraction form to its decimal form.
  • Demonstrate that the distance between two numbers on a number line is the absolute value of their difference.
  • Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with rational numbers.
  • Locate rational numbers on a number line.
  • Compare rational numbers based on their position on the number line.
  • Use addition, subtraction, multiplication, and division to solve problems involving fractions and decimals and integers and connect actions to algorithms.  
  • Understand what proportions are and what they mean in the context of a real-word problem.
  • Determine if two quantities form a proportional relationship.
  • Create and interpret equivalent ratios.
  • Understand the meaning of and compute the constant of proportionality (unit rate).
  • Write and solve proportions.
  • Use proportions to solve problems involving percent.
  • Estimate and use common applications of percentages including tax, tip, discount, mark-up interest, commission.
  • Estimate and solve problems involving percent of increase and decrease.

Algebra

(Functional Relationships)

  • Recognize the constant rate of change as slope.
  • Solve multi-step inequalities involving rational numbers in various forms.
  • Graph solutions to equations and inequalities on a number line.
  • Translate real life stories and verbal expressions into algebraic expressions.
  • 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.
  • Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations

Algebra

(Expressions and Equations)

Geometry

  • Understand the opposite of a number and use it in expressions like – x when x=-2.
  • Use the properties and order of operations to simplify numeric and algebraic expressions.
  • Evaluate expressions including expressions with square roots.
  • Translate real life stories and verbal expressions into algebraic expressions.
  • Understand the difference between an expression and an equation.
  • Add and subtract monomial expressions with rational coefficients.

Demonstrate equivalent forms of the same expression.

Use the distributive property when simplifying expressions.

Simplify algebraic expression by combining like terms.

Solve multi-step problems involving rational numbers presented in various forms.

  • Find scale factor and understand the relation between scale factor and similar figures.
  • Use supplementary, complementary, adjacent and vertical concepts to find missing angles including work where angle measurements are given as expressions.
  • Determine perimeter and circumference.
  • Calculate area of triangle, trapezoid, parallelogram and circle directly and then the area of polygons composed of these figures.
  • Calculate the surface area of prisms, pyramids, and cylinders.
  • Draw nets of prisms, pyramids, and cylinders.
  • Identify the shapes from a cross section of a 3-D figure.
  • Locate and name points on a coordinate plane using ordered pairs of integers.  
  • Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures.
  • Examine congruence, similarity, and line or rotational symmetry on an object using transformations.

Measurement

Data Analysis

  • Use proportions to convert among different units of measurement.
  • Apply proportionality to areas of measurement including area, volume, circumference, radius and diameter.
  • Use proportions for indirect measurement in similar figures.
  • Analyze the structure and uniformity of the metric system and contrast with the customary system.  
  • Surface area and volume of prisms, cylinders, and quadrilaterals.
  • Select and use appropriate tools and units of measure when measuring and calculating angles, surface areas, and volumes of rectangular prisms.
  • Understand the difference between surface area and volume, and demonstrate that two objects may have the same surface area, but different volumes—or may have the same volume, but different surface areas.
  • Use ratios and proportions to solve problems involving scale factors.

 

  • Understand the necessity of using samples to make inferences as opposed to surveying entire populations.
  • Determine if a sample is biased or unbiased.
  • Use proportions to make estimates relating to a population on the basis of a sample.
  • Construct data displays including box and whisker and stem and leaf plots. Analyze and interpret data from these displays to make generalizations.
  • Apply percentages to make and interpret histograms and circle graphs.
  • Make predictions from scatter plots using or estimating a line of best fit.
  • Determine correlation shown from scatter plot.
  • Analyze and interpret measures of central tendency including mean, median, mode, range, and outliers, and recognize that changes in data sets can affect these measures.
  • Compare the distribution of data and variability between two data sets, comparing the ranges and centers of the data.
  • 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.
  • Understand the probability of an event is a number between 0 and 1 (unlikely and likely) and a probability of 1⁄2 is equally likely.
  • Estimate the probability of an event by collecting data on the chance the event occurs.
  • Create sample spaces using lists, tree diagrams, and tables.
  • Compare theoretical and experimental probabilities.
  • Determine if two events are independent or dependent and how that affects the outcome.
  • Find the probability of compound events and create sample spaces of compound events that occur in everyday life.
  • Describe a set of data using mean, median, mode, range.  

Objective

Skills

Quarter 1

Numbers and Operations

(Whole, Decimals, Fractions)

Algebra

(Proportionality)

Review of 6th Grade Skills

Operations with Whole Numbers and Decimals

  • Add, Subtract, Multiply, Divide Whole Numbers and Decimals
  • Compare and Order whole numbers and Decimals on a number line
  • Properties of Addition and Multiplication

Fractions and Mixed Numbers

  • Add, Subtract, Multiply, and Divide Mixed Numbers and Fractions with common and not common denominators
  • Solve word problems with fractions and Mixed numbers

Integers and Rational Numbers

  • Relate Integers and their opposites
  • Order positive and negative numbers
  • Order of operations and exponents
  • Understand difference between Rational and Irrational numbers
  • Classify numbers in the real number system

Add and Subtract Integers and Rational Numbers

  • Add Integers
  • Subtract Integers
  • Add and Subtract Rational Numbers

Multiply and Divide Integers and Rational Numbers

  • Multiply Integers
  • Divide Integers
  • Multiply and Divide Rational Numbers
  • Solve word problems with the four operations and rational numbers

Ratios, Rates, and Unit Rates

  • Write and use ratios and rates
  • Write and solve proportions

Create and interpret equivalent ratios

Proportional Relationships

  • Describe Proportional Relationships
  • Understand the constant of proportionality
  • Graph proportional relationships
  • Apply Proportional Reasoning to Solve Problems
  • Find Scale Factors

Quarter 2

Algebra

(Proportionality)

Algebra

(Functional Relationships)

Algebra

(Expressions and Equations)

Percent

  • Analyze Percents of Numbers
  • Connect percents and proportions
  • Write and solve percent equations
  • Use proportions to solve problems involving percents

Analyze Percent of Change

  • Estimate and use common applications of percentages including tax, tip, discount, mark-up, interest, and commission
  • Solve percent of change and percent error problems
  • Solve simple interest problems
  • Recognize the constant rate of change as slope

Algebraic Expressions

  • Understand the opposite of a number and use it in expressions like – x when x = -2
  • Understand difference between expression and equation
  • Expressions with square roots
  • Write and evaluate algebraic expressions
  • Generate equivalent expressions
  • Simplify expressions by combining like terms

-     Expand expressions

Operations with Expressions

  • Factor Expressions
  • Add and Subtract Expressions
  • Analyze equivalent Expressions

-     Solve multi-step expressions

Solve problems using Equations

  • Write two step equations
  • Solve two step equations
  • Solve Equations using Distributive Property
  • Graph solutions to equations on a number line

Solve Inequalities

  • Add and Subtract Inequality Equations
  • Multiply and Divide Inequality Equations
  • Solve two step inequalities
  • Solve Multi-step inequalities
  • Graph solutions to inequalities on a number line

Functions

  • Introduce functions
  • Visualize constant rate of change as slope
  • Identify functions and linear vs. nonlinear

Quarter 3

Geometry

Measurement

Scale Drawings

  • Find scale factor of figures
  • Solve Problems involving scale drawings
  • Identify types of angles

Solve Problems with Polygons

  • Draw triangles with given conditions
  • Solve problems involving angle relationships
  • Polygons
  • Quadrilaterals

Perimeter and Area

  • Find area of triangle, trapezoid, parallelogram, and other polygons

Circles

  • Circumference and Area of a Circle

Nets and Cross Sections

  • Nets of 3-D figures
  • Describe Cross Section

Surface Area and Volume of 3-D figures

  • Use proportions to convert between different areas of measurement
  • Use proportionality to solve Surface Area and Volume
  • Use proportions to measure similar figures

Quarter 4

Data Analysis

Data Interpretation

  • Identify Populations and Samples
  • Draw Inferences from Data
  • Create surveys
  • Determine if a sample is biased vs. unbiased

Populations

  • Make Comparative Inferences about populations
  • Draw mathematical models

Graphs

  • Create data displays
  • Histograms
  • Circle Graphs
  • Scatter Plots
  • Box and Whisker Plots

Statistics

  • Calculate Mean, Median, Mode, Range
  • Show comparisons and differences in data sets by graphs and tables
  • Outliers
  • Compare distribution of data and variability

Probability

  • Understand Likelihood and Probability
  • Theoretical Probability
  • Experimental Probability
  • Use probability models

Samples Spaces

  • Create lists, tree diagrams, and tables

Compound Events

  • Determine Outcomes of Compound Events
  • Find probabilities of Compound Events
  • Simulate Compound Events