Students will:

• Come up with questions that need data collection, focusing on boxplots.
• Decide what data is needed to answer the question and collect the data using different methods, like observations, surveys, or experiments.
• Understand how statistical bias could impact whether the collected data accurately represents the larger group.
• Organize and display a numeric data set of up to 20 items using boxplots, with or without technology.
• Identify and explain the minimum, maximum, median, upper quartile, lower quartile, range, and interquartile range from a data set shown in a boxplot.
• Explain how an extreme data point (outlier) changes the shape and spread of the data in a boxplot.
• Look at the data shown in a boxplot, make observations, and draw conclusions.
• Compare and analyze two data sets that are shown in boxplots.
• In a real-life situation, decide which type of graph (like bar graphs, line graphs, or boxplots) best shows the data.
• Identify parts of a graph that might be misleading.

Students will:

• Estimate and figure out the two whole numbers between which the positive square root of a given number lies. Explain which whole number is the better guess. This will only be for numbers from 1 to 400.
• Use rounded approximations (to the nearest hundredth) of irrational numbers to compare, order, and place them on a number line. This includes both positive and negative square roots of numbers from 0 to 400 that result in an irrational number.
• Use different strategies, like benchmarks, a number line, or finding equivalencies, to compare and order up to five real numbers. These numbers could be integers, fractions, decimals, mixed numbers, percents, numbers in scientific notation, square roots, and π. Explain your reasoning using words, writing, or a model.
• Explain and show the connections among different groups of numbers within the real number system using tools like diagrams or number lines. These groups include rational numbers, irrational numbers, integers, whole numbers, and natural numbers.
• Identify and explain why a specific number belongs to a certain group or groups within the real number system.
• Describe each group within the real number system, providing examples of numbers that belong to each group and numbers that do not.

Students will:

• Estimate and solve real-life problems where you need to calculate either a discount or markup and find the final sale price.
• Estimate and solve real-life problems where you need to figure out the sales tax, tip, and the total cost.
• Estimate and solve real-life problems where you need to calculate how much something has increased or decreased by a certain percentage.
• Figure out if two events are independent or dependent, and explain how replacing or not replacing items affects the chance of something happening.
• Compare and explain the difference between the chances of independent events and dependent events.
• Calculate the probability of two independent events happening.
• Calculate the probability of two dependent events happening.

Students will:

• Decide if a relation (shown by ordered pairs, a table, or a graph with specific points) is a function. You'll work with sets of no more than 10 ordered pairs.
• Find the domain (all possible input values) and range (all possible output values) of a function when it’s shown as ordered pairs, a table, or a graph with specific points.
• Understand how adding a number (b) to the equation y = mx will move the line on a graph.
• Learn about important features of linear functions, like the slope (m), y-intercept (b), and how the variables are connected.
• Draw a graph of a linear function when given a table, equation, or real-life example.
• Make a table of values for a linear function when given a graph, equation (y = mx + b), or real-life example.
• Write an equation for a linear function (y = mx + b) when you have a graph, table, or real-life example.
• Come up with a real-life situation that matches a graph, table, or equation in the form y = mx + b.

Students will:

• Use tools like colored chips or algebra tiles to represent algebraic expressions, including those that use the distributive property.
• Simplify and create equivalent algebraic expressions with one variable by following the order of operations and properties of numbers. You may need to expand expressions using the distributive property or combine like terms. These expressions will involve linear and numeric terms, and both coefficients and numeric terms can be rational numbers.
• Use tools like algebra tiles or drawings to represent and solve multistep linear equations (up to four steps) with the variable on one or both sides.
• Solve multistep linear equations (up to four steps) by applying properties of numbers and equality. You might need to expand expressions using the distributive property or combine like terms. The equations will involve rational numbers.
• Write a multistep linear equation to describe a situation or story.
• Create a story or situation that matches a given multi step linear equation.
• Solve real-world problems that require you to solve a multistep linear equation.
• Understand and explain the meaning of your solution to a linear equation in the context of a problem.
• Check your work to make sure your solution to a linear equation is correct.

Students will:

• Solve multistep linear inequalities (up to four steps) with the variable on one or both sides by using properties of numbers and inequalities. You might need to expand expressions using the distributive property or combine like terms. The inequalities will involve rational numbers.
• Show the solutions to inequalities both algebraically and by graphing them on a number line.
• Write multi step linear inequalities to describe a situation or story.
• Create a story or situation that matches a given multi step linear inequality.
• Solve real-world problems that require you to solve a multistep linear inequality.
• Identify numbers that are part of the solution to a given inequality.
• Understand and explain the meaning of your solution to a linear inequality in the context of a problem.

Students will:

• Learn about and describe how different pairs of angles relate to each other, such as vertical angles (angles that are opposite each other when two lines cross), adjacent angles (angles that are next to each other), supplementary angles (angles that add up to 180°), and complementary angles (angles that add up to 90°).
• Use your understanding of these angle relationships to find and solve for unknown angles in various problems, including real-life situations.
• Confirm the Pythagorean Theorem by using drawings, physical tools, and measurements.
• Check if a triangle is a right triangle by looking at the lengths of its three sides.
• Recognize the different parts of a right triangle, like the hypotenuse (the longest side) and the legs (the two shorter sides), no matter how the triangle is positioned.
• Find the length of one side of a right triangle if you know the lengths of the other two sides.
• Use the Pythagorean Theorem to solve real-world problems involving right triangles, and also use the reverse of this theorem to check if a triangle is a right triangle.
• Identify the new coordinates of a shape on a grid after it has been moved up, down, left, right, or a combination of these directions.
• Identify the new coordinates of a shape on a grid after it has been flipped over the x-axis or y-axis.
• Identify the new coordinates of a shape on a grid after it has been moved and then flipped, or flipped and then moved, over the x-axis or y-axis.
• Draw the new position of a shape after it has been moved up, down, left, right, or a combination of these directions.
• Draw the new position of a shape after it has been flipped over the x-axis or y-axis.
• Draw the new position of a shape after it has been moved and then flipped, or flipped and then moved, over the x-axis or y-axis.
• Recognize and explain how shapes are moved or flipped in real-life situations (e.g., tile patterns, fabric designs, wallpaper, art).

Students will:

• Break a flat shape into smaller shapes like triangles, rectangles, squares, trapezoids, parallelograms, circles, and half-circles. Find the area of each smaller shape, then add them up to find the area of the entire shape.
• Break a flat shape into smaller shapes like triangles, rectangles, squares, trapezoids, parallelograms, and half-circles. Use the sides of each smaller shape to figure out the perimeter of the entire shape.
• Use formulas for perimeter, circumference, and area to solve real-life problems involving shapes made up of multiple smaller shapes.
• Find the surface area of square-based pyramids by using physical models, flat layouts (nets), pictures, and formulas.
• Find the volume of cones and square-based pyramids by using physical models, pictures, and formulas.
• Explore and explain how the volume of cones compares to cylinders and how square-based pyramids compare to rectangular prisms.
• Solve real-life problems involving the volume of cones and square-based pyramids, as well as the surface area of square-based pyramids.

Students will:

• Create questions that need data to be collected, focusing on scatterplots.
• Decide what data is needed to answer a question and collect data (up to 20 items) using different methods like observations, measurements, surveys, or experiments.
• Organize and display two sets of related numeric data using scatterplots, with or without technology.
• Look at scatterplots and describe whether the data points show a positive trend, negative trend, or no trend.
• Analyze and explain the relationship between the two sets of data shown in scatterplots.
• Draw the best-fitting line for the data on a scatterplot.

In this unit, teachers will provide differentiated opportunities for students to review previous content and/or explore content at a deeper level.