Work with radicals and integer exponents.
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8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.
8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes.
8.EE.3 Use numbers expressed in scientific notation to estimate very large or very small quantities, and to express how many times as much one is than the other.
World Bank (Operations with Scientific Notation)
The World Bank is an international financial institution that provides loans and grants to the governments of low—and middle-income countries to pursue capital projects. James, a data analyst at the World Bank, has been tasked with calculating the GDP per capita for a list of countries and making a list ranking these countries, including the United States and the GDP per Capita for the entire world since 1998. Make a list ranking these countries, including the United States and the world. Use the data for 2022 for the world.
Solar System (Operations with Scientific Notation)
Nia and her dad, James, are exploring the new space posters in her room. She has some questions about the mass of the planets. She wonders if all the planets together have a bigger mass than the Sun. How does the mass of all the planets combined compare to the mass of the Sun?
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8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.
Oceans
Sunlight (Operations with Scientific Notation)
Nia knows that the light that we are looking at from the Sun takes time to get to Earth. The Sun is approximately 149,600,000,000 meters from Earth, and light travels at about 3.3 × 10^8 meters per second. How long does the light take to get here? And are we, therefore, looking into the past?
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Understand the connections between proportional relationships, lines, and linear equations.
8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
Ski Lift (Slope of a Line)
The initial plans for the new ski lift are complete, but we need to do some last-minute calculations. The ski lift's incline or gradient cannot exceed 0.275. James and Nia are leading the team that will make the last-minute adjustments. You must check all the sections and ensure they are safe; if they are not, how do we fix them?
Analyze and solve linear equations and pairs of simultaneous linear equations.
8.EE.7 Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results.
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
Butcher (Solving Linear Equations)
James has a new job at a butcher shop. Andrew has set up some weighing challenges in the back of the shop to prepare for it. The question James has to answer is: What is the weight of the ham in each setup?
The Italian Job
Pirates
8.EE.8 Analyze and solve pairs of simultaneous linear equations.
a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.
c. Solve problems leading to two linear equations in two variables.
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