Grade 7 Math

Length: Full-Year Grade: 7 Required: Yes

Course Description

Grade 7 Math forms a crucial link in the chain between the foundational mathematical learning of elementary school and the more sophisticated elaboration and application of mathematics of High School. Superficially, the curriculum covers elementary-level concepts, but it does so in a way that provides reinforcement and development, especially of critical concepts that often weaken during middle school, such as fractions, percents, and common denominators. On a deeper level, the theoretical knowledge is developed through practice in situational word problems and in-class projects that put ideas into action. By the end of the course, basic ideas of algebra--already being developed in elementary school--are expressed more fully, preparing students for Grade 8 Math and pre-algebra.

Enduring Understandings

• Number systems and the societies in which they develop mutually influence each other.

• Place value governs all basic arithmetic operations, as well as exponential operations.

• Variables can represent changing values in an expression.

• Algebraic expressions can be used to model real-world scenarios and to show relationships between quantities in a system.

• Fractions, decimals, and percents are equivalent ways of expressing numbers.

• Probabilities can be measured, estimated, or predicted quantitatively.

• Numbers and shapes can be used to represent one another, and they can both be grouped into sets.

• Number lines are one-dimensional coordinate systems in which numbers can be graphed.

• Number lines give a geometric representation of additional and subtraction of positive and negative numbers.

• A relationship between two variables that involves a constant rate of change of one variable with respect to the other can be represented as a line.

• A line can be represented as a linear equation.

Essential Questions

• How can numbers be represented symbolically?

• What is the meaning of a negative number?

• How are functional relationships between elements of a process represented as mathematical symbols?

• What are the limitations of mathematical expressions?  That is, what kinds of questions cannot be answered using mathematics?

• How does the shape of a graph relate to the mathematical relationship between two or more variables?

Major Texts/Resources Used:

• Viktora, S.S., Cheung, E., Highstone, V., Capuzzi, C., Heeres, D., Metcalf, N., Sabrio, S., Jakucyn, N. & Usiskin, Z. (2016):  Transition Mathematics, The University of Chicago Mathematics Project, Chicago.

• Miller, C.D., Heeren, V.E. & Hornsby, E.J., Jr. (1990):  Mathematical Ideas, 6th Edition, Harper Collins, New York.

Units

Unit 1: Reading and Writing Numbers

Enduring Understandings:

• Numbers are a symbolic representation of quantities.

• Some abstract quantities must be represented with negative numbers.

• Different counting systems provide a greater understanding of mathematics as a whole.

• Place value reinforces understanding of fractions, division, and exponents.

• Numbers can be represented as points in a coordinate system.

Major Concepts:

• Numbers in everyday use

• Positive and negative numbers

• Rational numbers and their uses

• Powers of ten and other numbers

• Order of operations

• Grouping symbols

• Scientific notation

• Plotting points in coordinate systems

Major Content:

• The decimal system, decimal place-value

• Whole numbers, integers, negative numbers

• Inequality and double inequalities

• Rate, rate units

• Ratios

• Rational numbers

• Bases, exponents, powers of ten, multiplying by powers of ten

• Order of operations

• Numerical expressions

• Evaluation, grouping

• Fractions

• Square roots and other radicals

• Scientific notation

• Coordinates & coordinate axes, coordinate systems, quadrants, graphs

Unit Assessments:

• Section Quizzes

• Unit 1 Test

Unit 2: Using Variables

Enduring Understandings:

• Some physical and abstract scenarios and processes can be represented and modelled using mathematical expressions.

• Quantities related to these scenarios and processes may be represented symbolically as variables when the quantities change in response to another change in the system.

• Variables may be assembled into expressions that describe and predict relationships in the system. 

Major Concepts:

• Describing patterns with variables

• Translating words into algebraic expressions

• Evaluating algebraic expressions

• Expressions and formulas

• The Pythagorean Theorem

• Open sentences

• Graphing inequalities.  

Major Content:

• Patterns

• Variables

• Algebraic expressions

• Evaluation

• Equations

• Formulas

• Using units in calculations

• Choosing variables in formulas

• The Pythagorean Theorem

• Right triangles

• Pythagorean triples

• Independent and dependent variables

• Sentences, open sentences and solutions, 

• Inequalities, graphing inequalities.  

Unit Assessments:

• Section Quizzes

• Unit 2 Test

Unit 3: Representing Numbers

Enduring Understandings:

• The integers do not include all of the real numbers.

• Many of the numbers that lie between integers may be represented as fractions, and those fractions have decimal and percent equivalents.

• Fractions with equal denominators may be added and subtracted by adding or subtracting their numerators.

• All non-negative real numbers can be written equivalently as pairs of equal factors called square roots.

• Probabilities can be quantified as ratios, which themselves can be expressed as decimals or percents. 

Major Concepts:

• Decimals for numbers between integers

• Equal fractions

• Adding and subtracting fractions

• Estimating by rounding

• Fraction-decimal equivalence

• Fractions, decimals, and percents

• Using percents

• Square roots

• Probability

Major Content:

• Intervals

• Unit distance

• Comparing decimals

• Decimals on the coordinate plane

• Numerator and denominator

• Comparing fractions

• Factors

• Simple fractions

• Lowest terms

• Greatest common factor (GCF)

• Prime numbers, prime factorization, relative primes

• Common denominator

• Least common multiple (LCM)

• Least common denominator (LCD)

• Converting mixed numbers to simple fractions

• Rounding

• Dividends

• Divisors

• Quotients

• Fraction-decimal conversion

• Percent, using percents

• Taxes, simple interest

• Square roots

• Irrational numbers

• Probability, frequency, relative frequency, randomness, events, outcomes. 

Unit Assessment:

• Section Quizzes

• Unit 3 Test    

Unit 4: Representing Sets of Numbers and Shapes

Enduring Understandings:

• Because numbers have properties (such as the property of being odd or even), they can be grouped into sets according to those properties.

• The concepts of grouping ideas into sets can extend to logical statements constructed from simple ideas.

• Sets can interact with one another, and logic operations may be performed on sets.

• Because numbers can represent points in a coordinate system, the concepts of sets and set operations can be used to construct and investigate geometric figures composed of sets of points.

• Geometric figures, themselves, may in turn be grouped into sets based on their properties. 

Major Concepts:

• Logical statements

• Properties of numbers

• If-then statements

• Unions and intersections of sets

• Geometric figures

• Unions of geometric figures

• Definitions

• Classifying shapes

• Classifying numbers

Major Content:

• Sets, relationships between sets

• Venn Diagrams

• Real numbers

• Additive identities

• Opposites of numbers

• Additive inverses

• Conditional statements

• Truth and falsity

• Converses of statements

• Unions and intersections of sets

• The empty set

• Figures

• Points, lines, segments, rays

• Angles, measuring angles

• Triangles and quadrilaterals, polygons

• Writing good definitions

• Classification systems, classifying shapes, classifying numbers

Unit Assessment:

• Section Quizzes

• Unit 4 Test 

Unit 5: Addition, Subtraction, and Linear Equations

Enduring Understandings:

• Addition and subtraction can be modelled numerically, abstractly, or geometrically.

• Adding a negative number to another number is equivalent to subtracting a positive number of equal magnitude.

• Subtracting a negative number from another number is equivalent to adding a positive number of equal magnitude.

• Even numbers of nested minus signs cancel and become addition.

• Odd numbers of nested minus signs remain subtraction.

• The concept of adding or subtracting two numbers to yield a third naturally leads to the idea of a linear equation.

• Linear equations are equations 1) whose variables only have exponents of one and 2) whose graphs are lines.

• Linear equations can model relationships between variables whose mutual rate of change is constant.   

Major Concepts:

• Models for addition

• Absolute value

• Rules for adding positive and negative numbers

• Models for subtraction

• Solving x+a=b

• Understanding x+y=k

• Basic linear equations

• Slope & intercept

• Graphing linear equations, solving problems using linear equations

Major Content:

• Algebraic and geometric models for addition

• Measures of segments and angles

• The commutative property of addition

• Graphs of addition operations

• Absolute value

• Rules for negative signs

• The associative property of addition

• Algebraic and geometric models for subtraction

• Solving equations

• The addition property of equality

• Ordered pairs

• Points on a graph as solutions to an equation

• Slope of a line

• Y-intercept

• Slope-intercept form of a linear equation, graphing linear equations, word problems involving linear equations

Unit Assessment:

• Section Quizzes

• Unit 5 Test