8th grade (Illustrative Mathematics) | 1 Big School (By Blue Brain)

Course Content

Unit 1: Rigid transformations and congruence

Lesson 5: Coordinate moves
Reflecting points
Reflecting shapes
Lesson 6: Describing transformations
Determining reflections
Mapping shapes
Lesson 7: No bending or stretching
Rigid transformations intro
Finding measures using rigid transformations
Rigid transformations: preserved properties
Lesson 12: Congruent polygons
Congruent shapes & transformations
Non-congruent shapes & transformations
Lesson 14: Alternate interior angles
Missing angles with a transversal
Lesson 16: Parallel lines and the angles in a triangle
Angles in a triangle sum to 180° proof
Triangle exterior angle example
Worked example: Triangle angles (intersecting lines)

Unit 2: Dilations, similarity, and introducing slope

Lesson 4: Dilations on a square grid
Dilations intro
Dilating points
Dilating shapes: expanding
Dilating shapes: shrinking by 1/2
Lesson 6: Similarity
Similar shapes & transformations
Lesson 7: Similar polygons
Dilations: scale factor
Dilations and properties
Lesson 9: Side lengths quotients in similar triangles
Side lengths after dilation
Lesson 10: Meet slope
Intro to slope
Lesson 3: Representing proportional relationships
Graphing proportional relationships: unit rate
Graphing proportional relationships from a table
Graphing proportional relationships from an equation

Unit 3: Linear relationships

Lesson 4: Comparing proportional relationships
Rates & proportional relationships example
Rates & proportional relationships: gas mileage
Lesson 7: Representations of linear relationships
Linear & nonlinear functions: missing value
Lesson 8: Translating to y=mx+b
Graph from slope-intercept equation
Lesson 9: Slopes don’t have to be positive
Intro to intercepts
Slope-intercept equation from slope & point
Linear & nonlinear functions: word problem
Lesson 11: Equations of all kinds of lines
Converting to slope-intercept form
Extra practice: Slope
Worked examples: slope-intercept intro
Solutions to 2-variable equations
Worked example: solutions to 2-variable equations
Lesson 12: Solutions to linear equations
Lesson 13: More solutions to linear equations
Completing solutions to 2-variable equations
Extra practice: Intercepts
x-intercept of a line
Intercepts from an equation
Worked example: intercepts from an equation
Lesson 3: Balanced moves
Intro to equations with variables on both sides
Equations with variables on both sides: 20-7x=6x-6
Lesson 4: More balanced moves
Equations with parentheses

Unit 4: Linear equations and linear systems

Extra practice: Linear equations
Sums of consecutive integers
Sum of integers challenge
Equation practice with vertical angles
Equation practice with complementary angles
Equation practice with supplementary angles
Lesson 7: All, some, or no solution
Creating an equation with no solutions
Creating an equation with infinitely many solutions
Lesson 8: How many solutions?
Number of solutions to equations
Worked example: number of solutions to equations
Lesson 9: When are they the same?
Age word problem: Imran
Age word problem: Ben & William
Age word problem: Arman & Diya
Lesson 12: Systems of equations
Systems of equations: trolls, tolls (1 of 2)
Systems of equations: trolls, tolls (2 of 2)
Systems of equations with graphing
Systems of equations with graphing: y=7/5x-5 & y=3/5x-1
Lesson 13: Solving systems of equations
Systems of equations with substitution: y=-1/4x+100 & y=-1/4x+120
Number of solutions to a system of equations graphically
Lesson 14: Solving more systems
Systems of equations with substitution: 2y=x+7 & x=y-4
Systems of equations with substitution: y=4x-17.5 & y+2x=6.5
Systems of equations with substitution: y=-5x+8 & 10x+2y=-2
Lesson 16: Solving problems with systems of equations
System of equations word problem: no solution
Systems of equations with substitution: coins
Lesson 3: Equations for functions
Manipulating formulas: temperature
Lesson 4: Tables, equations, and graphs of functions
Linear function example: spending money
Lesson 5: More graphs of functions
Interpreting a graph example

Unit 5: Functions and volume

Lesson 8: Linear functions
Linear graphs word problem: cats
Linear equations word problems: earnings
Modeling with linear equations: snow
Comparing linear functions word problem: climb
Comparing linear functions word problem: work
Linear functions word problem: fuel
Linear functions word problem: pool
Lesson 13: The volume of a cylinder
Cylinder volume & surface area
Lesson 15: The volume of a cone
Volume of a cone
Lesson 18: Scaling two dimensions
How volume changes from changing dimensions
Lesson 20: The volume of a sphere
Volume of a sphere
Lesson 2: Plotting data
Constructing a scatter plot
Lesson 4: Fitting a line to data
Line of best fit: smoking in 1945
Lesson 6: The slope of a fitted line
Scatter plot: smokers
Interpreting a trend line
Lesson 7: Observing more patterns in scatter plots
Example of direction in scatterplots

Unit 6: Associations in data

Lesson 9: Looking for associations
Two-way frequency tables and Venn diagrams
Two-way relative frequency tables
Lesson 4: Dividing powers of 10
The 0 & 1st power
Lesson 6: What about other bases?
Exponent properties with products
Exponent properties with quotients
Negative exponent intuition
Multiplying & dividing powers (integer exponents)
Lesson 8: Combining bases
Exponent properties with parentheses
Lesson 12: Applications of arithmetic with powers of 10
Lesson 12: Applications of arithmetic with powers of 10
Approximating with powers of 10
Lesson 13: Definition of scientific notation
Scientific notation example: 0.0000000003457
Scientific notation examples

Unit 7: Exponents and scientific notation

Lesson 14: Multiplying, dividing, and estimating with scientific notation
Multiplying in scientific notation example
Multiplying & dividing in scientific notation
Scientific notation word problem: U.S. national debt
Lesson 3: Rational and irrational numbers
Intro to rational & irrational numbers
Classifying numbers: rational & irrational
Lesson 4: Square roots on the number line
Approximating square roots to hundredths
Lesson 5: Reasoning about square roots
Approximating square roots
Extra practice: Irrational numbers
Classifying numbers
Lesson 6: Finding side lengths of triangles
Intro to the Pythagorean theorem
Lesson 7: A proof of the Pythagorean Theorem
Bhaskara’s proof of the Pythagorean theorem

Unit 8: Pythagorean theorem and irrational numbers

Lesson 8: Finding unknown side lengths
Pythagorean theorem example
Lesson 10: Applications of the Pythagorean Theorem
Pythagorean theorem word problem: carpet
Pythagorean theorem word problem: fishing boat
Extra practice: Pythagorean theorem
Pythagorean theorem proof using similarity
Another Pythagorean theorem proof
Lesson 12: Edge lengths and volumes
Dimensions of a cube from its volume
Lesson 14: Decimal representations of rational numbers
Converting a fraction to a repeating decimal
Lesson 15: Infinite decimal expansions
Converting repeating decimals to fractions (part 1 of 2)
Converting repeating decimals to fractions (part 2 of 2)

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Course Content

Unit 1: Rigid transformations and congruence

Lesson 5: Coordinate moves

Reflecting points

Reflecting shapes

Lesson 6: Describing transformations

Determining reflections

Mapping shapes

Lesson 7: No bending or stretching

Rigid transformations intro

Finding measures using rigid transformations

Rigid transformations: preserved properties

Lesson 12: Congruent polygons

Congruent shapes & transformations

Non-congruent shapes & transformations

Lesson 14: Alternate interior angles

Missing angles with a transversal

Lesson 16: Parallel lines and the angles in a triangle

Angles in a triangle sum to 180° proof

Triangle exterior angle example

Worked example: Triangle angles (intersecting lines)

Unit 2: Dilations, similarity, and introducing slope

Lesson 4: Dilations on a square grid

Dilations intro

Dilating points

Dilating shapes: expanding

Dilating shapes: shrinking by 1/2

Lesson 6: Similarity

Similar shapes & transformations

Lesson 7: Similar polygons

Dilations: scale factor

Dilations and properties

Lesson 9: Side lengths quotients in similar triangles

Side lengths after dilation

Lesson 10: Meet slope

Intro to slope

Lesson 3: Representing proportional relationships

Graphing proportional relationships: unit rate

Graphing proportional relationships from a table

Graphing proportional relationships from an equation

Unit 3: Linear relationships

Lesson 4: Comparing proportional relationships

Rates & proportional relationships example

Rates & proportional relationships: gas mileage

Lesson 7: Representations of linear relationships

Linear & nonlinear functions: missing value

Lesson 8: Translating to y=mx+b

Graph from slope-intercept equation

Lesson 9: Slopes don’t have to be positive

Intro to intercepts

Slope-intercept equation from slope & point

Linear & nonlinear functions: word problem

Lesson 11: Equations of all kinds of lines

Converting to slope-intercept form

Extra practice: Slope

Worked examples: slope-intercept intro

Solutions to 2-variable equations

Worked example: solutions to 2-variable equations

Lesson 12: Solutions to linear equations

Lesson 13: More solutions to linear equations

Completing solutions to 2-variable equations

Extra practice: Intercepts

x-intercept of a line

Intercepts from an equation

Worked example: intercepts from an equation

Lesson 3: Balanced moves

Intro to equations with variables on both sides

Equations with variables on both sides: 20-7x=6x-6

Lesson 4: More balanced moves

Equations with parentheses

Unit 4: Linear equations and linear systems

Extra practice: Linear equations

Sums of consecutive integers

Sum of integers challenge

Equation practice with vertical angles

Equation practice with complementary angles

Equation practice with supplementary angles

Lesson 7: All, some, or no solution

Creating an equation with no solutions

Creating an equation with infinitely many solutions