Students will:

• Create questions that need data collection, focusing on making histograms.
• Figure out what data you need to answer your question and collect it using different methods like observing, measuring, surveys, or experiments.
• Make sure your data sample is big enough and collected randomly to represent a larger group accurately.
• Organize and show your data using histograms, either by hand or with technology.
• See how using different intervals (groupings) in your histogram can change how the data looks.
• Compare histograms with other graphs like line plots, circle graphs, and stem-and-leaf plots. Explain which graph shows the data best.
• Look at the data in histograms, make observations, and draw conclusions. See how histograms can show patterns that might not be obvious from just looking at the data.

Students will:

• Explore and explain patterns with powers of 10 that have negative exponents.
• Show how a power of 10 with a negative exponent looks as a fraction and a decimal.
• Change numbers from scientific notation to decimal form and vice versa.
• Compare and arrange up to four numbers written in scientific notation in order from smallest to largest or largest to smallest.
• Use different methods like benchmarks, number lines, and equivalency to compare rational numbers written as integers, fractions, mixed numbers, decimals, and percents (positive and negative, limited to the thousandths place). Arrange up to four rational numbers in order (ascending or descending) and explain the reasoning using symbols (<, >, =), talking, writing, or visual models.
• Find the positive square root of perfect squares between 0 and 400.
• Explain how square roots and perfect squares are related.

Students will:

• Use the order of operations and properties of real numbers to simplify numerical expressions. Exponents will be 1, 2, 3, or 4, and bases will be positive integers. Braces { } are not included, but brackets [ ] and absolute value bars | | may be used. Square roots are only for perfect squares.
• Use concrete tools like colored chips or algebra tiles to show equivalent algebraic expressions in one variable.
• Simplify and create equivalent algebraic expressions in one variable by following the order of operations and properties of real numbers. This may involve combining like terms. These expressions will only have linear and numeric terms, and coefficients and numeric terms can be positive or negative rational numbers.
• Use the order of operations and properties of real numbers to solve algebraic expressions by replacing variables with given values. Exponents will be 1, 2, 3, or 4, and bases will be positive integers. Braces { } are not included, but brackets [ ] and absolute value bars | | may be used. Square roots are only for perfect squares. No more than three replacements per expression. Replacement values can be positive or negative rational numbers.

Students will:

• Use different materials and pictures to represent and solve two-step linear equations with one variable.
• Use properties of real numbers and equality to solve two-step linear equations with one variable. The numbers used will be rational.
• Check that the solutions to the linear equations in one variable are correct.
• Write a two-step linear equation with one variable to describe a given situation, including real-life contexts.
• Create a real-life situation based on a given two-step linear equation with one variable.
• Solve real-life problems that involve finding the solution to a two-step linear equation.
• Use properties of real numbers and operations (addition, subtraction, multiplication, and division) to solve one- and two-step inequalities with one variable. The numbers used will be rational.
• Explore and explain how the solution set of a linear inequality changes when you multiply or divide both sides by a rational number less than zero.
• Show the solutions to one- or two-step linear inequalities with one variable using algebra and graphs on a number line.
• Write one- or two-step linear inequalities with one variable to describe a given situation, including real-life contexts.
• Create a real-life situation based on a given one- or two-step linear inequality with one variable.
• Solve real-life problems that involve finding the solution to a one- or two-step inequality.
• Identify which numbers are part of the solution set for a given one- or two-step linear inequality with one variable.
• Explain the differences and similarities between solving linear inequalities and linear equations with one variable.

Students will:

• When given a proportional relationship between two quantities, make and use a ratio table to find missing values.
• Write and solve a proportion that shows the proportional relationship between two quantities to find a missing value, including real-life situations.
• Use proportional reasoning to solve real-life problems, such as converting units of measurement when given the conversion factor.
• Estimate and find the percentage of a given whole number, using benchmark percentages and other methods.
• Find the slope (m) as the rate of change in a proportional relationship between two quantities using a table, graph, or real-life situation. Write the equation as y = mx to show the direct variation. The slope can be positive or negative, but it will only be positive in real-life situations.
• Look at a graph and identify if the line has a positive, negative, or zero (0) slope, and describe it.
• Draw a line on a graph to show a proportional relationship between two quantities using an ordered pair and the slope (m) as the rate of change. The slope can be positive or negative.
• Draw a line on a graph to show a proportional relationship between two quantities using the equation y = mx, where m is the slope as the rate of change. The slope can be positive or negative.
• Connect and understand how proportional relationships between two quantities are shown through real-life problems, tables, equations, and graphs. The slope can be positive or negative, but it will only be positive in real-life situations.

Students will:

• Use geometric markings to find and identify angles that are the same (congruent) in similar quadrilaterals and triangles.
• Identify the sides that match (corresponding sides) in similar quadrilaterals and triangles.
• Given two similar quadrilaterals or triangles, write statements showing their similarity using symbols.
• Write proportions to show the relationships between the lengths of matching sides in similar quadrilaterals and triangles.
• Recognize and explain if two quadrilaterals or triangles are similar by comparing the ratios of their matching side lengths.
• Solve a proportion to find a missing side length in similar quadrilaterals or triangles.
• Given some angle measures in a quadrilateral or triangle, find the unknown angle measures in a similar quadrilateral or triangle.
• Use proportional reasoning to solve real-life problems, including scale drawings. The scale factors will have denominators no greater than 12 and decimals no smaller than tenths.
• Given a starting shape on a coordinate plane, identify the coordinates of the new shape after it has been resized (dilated) by a scale factor of 1/4, 1/2, 2, 3, or 4, with the center of resizing (dilation) being the origin.
• Draw the new shape of a polygon after it has been resized (dilated) by a scale factor of 1/4, 1/2, 2, 3, or 4, with the center of resizing (dilation) being the origin.
• Identify and explain examples of resizing (dilations) in real-life situations, such as in scale drawings and graphic design.

Students will:

• Figure out the likelihood of an event happening based on what should happen in theory.
• Use the results from a study or experiment to find the actual likelihood of an event happening.
• Explain how the actual likelihood changes as you do more trials or experiments.
• Explore and explain the difference between what should happen in theory and what actually happens in an experiment or simulation.
• Estimate, solve, and explain answers to real-life problems using addition, subtraction, multiplication, and division with whole numbers, fractions (both positive and negative), and decimals (up to the thousandths place).

Students will:

• Compare and contrast the features of different quadrilaterals (parallelogram, rectangle, square, rhombus, and trapezoid), focusing on:
  • Parallel and perpendicular sides and diagonals
  • Equal angle measures, sides, and diagonal lengths
  • Lines of symmetry
• Sort and classify quadrilaterals (parallelograms, rectangles, trapezoids, rhombi, and squares) based on:
  • Parallel and perpendicular sides and diagonals
  • Equal angle measures, sides, and diagonal lengths
  • Lines of symmetry
• Look at a diagram to find an unknown angle measure in a quadrilateral using its properties.
• Look at a diagram to find an unknown side length in a quadrilateral using its properties.
• Learn and use the formulas for finding the volume of right cylinders to solve problems, including real-life scenarios, with the help of objects, diagrams, and formulas.
• Learn and use the formulas for finding the surface area of rectangular prisms and right cylinders to solve problems, including real-life scenarios, with the help of objects, diagrams, nets, and formulas.
• Identify whether a problem involving a rectangular prism or right cylinder is about volume or surface area.
• Understand and explain how the volume of a rectangular prism changes when one measurement is multiplied by 1/4, 1/3, 1/2, 2, 3, or 4, including real-life scenarios.
• Understand and explain how the surface area of a rectangular prism changes when one measurement is multiplied by 1/2 or 2, including real-life scenarios.

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