# Math Middle School Learning Objectives

This webpage provides an overview of what your child will learn by the end of each grade in middle school by the Iowa Core, our statewide academic standards. The Math Iowa Core standards focus on key concepts in numbers, algebra, functions, modeling, geometry, and statistics, and probability.

When your child arrives at middle school, they will learn skills that are most important for college and career readiness. These skills include working with ratios and rates, and variables and variable expressions, which are the building blocks of algebra. These topics remain a major emphasis throughout middle school and into high school.

Examples of Your Child’s Work at School:

• Understand ratios and rates and solve problems that involve proportional relationships (e.g., if it took seven hours to mow four lawns, then at that rate how many lawns could be mowed in 35 hours? At what hourly rate were lawns being mowed?).
• Divide fractions and solve related word problems (e.g., how wide is a rectangular strip of land with a length of ¾ mile and an area of ½ square mile?).
• Work with variables and expressions by generalizing the way numbers work (e.g., when adding numbers, the order doesn’t matter, so x + y = y + x; likewise, properties of addition and multiplication can be used to rewrite 24x + 18y as 6(4x + 3y), or y + y + y as 3y).
• Understand the process of solving simple equations.
• Write equations to solve word problems and describe relationships between quantities (e.g., the distance D traveled by train in time T might be expressed by an equation D = 85T, where D is in miles and T is in hours).
• Reason about relationships between shapes to determine area, surface area, and volume.

Your child will continue to work in proportional relationships, equations, and positive and negative numbers. These topics will remain a major emphasis throughout the middle school years and into high school. Good command of rates and proportional relationships, including percentages, is an important life skill. Your child will begin to understand how a random sample can be used to make inferences about a population.

Examples of Your Child’s Work at School:

• Analyze proportional relationships (graphing in the coordinate plane), and distinguish proportional relationships from other kinds of mathematical relationships.
• Solve percent problems (e.g., tax, tips, and markups and markdowns).
• Add, subtract, multiply and divide positive and negative numbers, and solve related word problems.
• Solve word problems that have a combination of whole numbers, fractions, and decimals.
• Solve equations such as ½ (x – 3) = ¾ efficiently, and write equations of this kind to solve word problems (e.g., “I knocked over a carton of milk, and 3 cups were spilled before I set the carton upright again. When I poured out the remaining milk equally into two measuring cups, there was ¾ of a cup of milk in each one. How much milk was originally in the carton?”).
• Use statistics to draw inferences and make comparisons (e.g., decide which candidate is likely to win an election based on a survey).

Your child will continue to learn how to write and reason with algebraic expressions. He or she also will make a thorough study of linear equations with one and two variables. By building on previous work with relationships between quantities, your child will be introduced to the idea of a mathematical function. Your child will prepare for high school geometry by learning about congruence (same shape and size) and similarity of geometric figures.

Examples of Your Child’s Work at School:

• Understand that the slope of a line is a constant rate of change, and relate linear equations in two variables to lines in the coordinate plane.
• Solve linear equations (e.g., –x + 5(x + 1⁄3) = 2 x – 8); solve pairs of linear equations (e.g., x + 6y = –1 and 2x – 2y = 12); and write equations to solve related word problems.
• Understand functions as rules that assign a unique output number to each input number; use linear functions to model relationships.
• Analyze statistical relationships by using a best-fit line (a straight line that models an association between two quantities).
• Understand congruence and similarity by using physical models, transparencies, or geometry software (e.g., when given two congruent figures, show how to obtain one from the other by a sequence of rotations, translations, and/or reflections).
• Understand and apply the Pythagorean Theorem (a2 + b2 = c2) to solve problems.

Source: Iowa Core Parent Guides from the Iowa Department of Education.
Read the complete standards at www.iowacore.gov.