Ch 35: NMTA Middle Grades Math: Rates, Ratios & Proportions

About This Chapter

The NES Middle Grades Mathematics exam has replaced the NMTA Middle Grade Mathematics in the state of New Mexico. As you prepare for this NES certification exam, complete the lessons of this chapter to improve your understanding of solving problems with rates, ratios and proportions as well as the real life applications of them.

NMTA Middle Grades Mathematics: Rates, Ratios & Proportions - Chapter Summary

Watch the lesson videos of this chapter to improve your abilities solving problems with rates, ratios and proportions as you prepare for the NMTA Middle Grades Mathematics. These lessons are taught by expert instructors who walk you through example problems with real life applications. Be sure to ask any questions you may have about the topics of these videos so that you can effectively improve your skills:

  • Calculating unit rates, ratios and proportions
  • Finding solutions for one-step problems with ratios and rates
  • Solving example problems, including those with money, time and other real life examples
  • Finding unknowns in proportions
  • Determining proportional relationships between quantities
  • Using equations and graphs to represent proportional relationships
  • Solving multi-step ratio and percent problems using proportional relationships

Use the on lesson quizzes to reinforce your retention of the information and test your skills. The results of the quizzes can also help determine what topics you need to review further. Return to the lesson videos to reinforce you understanding of these topics with video tags that allow you to skip over material you've already mastered.

NMTA Middle Grades Mathematics: Rates, Ratios & Proportions Chapter Objectives

NMTA Middle Grades Mathematics is the certification exam used in the state of New Mexico to certify middle grade math teachers. This is a computer-based exam with 150 multiple-choice questions, administered in a four-hour and 15-minute testing session. Of the material covered in these questions, 17% are in the Number Sense and Operations domain. You can expect to find questions about ratios and proportions in this domain. This chapter can help you prepare for these questions by demonstrating examples problems with rates, ratios and proportions which you can follow along with.

16 Lessons in Chapter 35: NMTA Middle Grades Math: Rates, Ratios & Proportions
Test your knowledge with a 30-question chapter practice test
Ratios & Rates: Definitions & Examples

1. Ratios & Rates: Definitions & Examples

If we have two items, or two numbers, and we want to compare them, what language can we use? How do we write the comparison? Find out as we learn about ratios and rates in this lesson.

How to Find the Unit Rate

2. How to Find the Unit Rate

If we are going to use math to predict outcomes, one of the most useful measures we can establish is the unit rate of change. In this lesson, you'll learn how to find the rate of change and apply the formula to real-life examples.

How to Solve a One-Step Problem Involving Ratios

3. How to Solve a One-Step Problem Involving Ratios

Ratios show the relationship between different things. They can be very useful in math and everyday life. Learn how you can quickly and easily solve one-step ratio problems.

How to Solve a One-Step Problem Involving Rates

4. How to Solve a One-Step Problem Involving Rates

One of the most useful aspects of math is the ability to take a rate and use it to solve questions of time or quantity. In this lesson, we'll learn how to use rates, time, and quantity to solve for each other.

How to Solve Problems with Money

5. How to Solve Problems with Money

Money matters, and knowing how much things cost will be useful no matter where you go. In this lesson, we'll learn the steps for solving word problems involving money.

Proportion: Definition, Application & Examples

6. Proportion: Definition, Application & Examples

When we want to compare one ratio, or fraction, to another equivalent ratio, it's a proportion. Learn all about proportions and practice solving proportion problems in this lesson.

Calculations with Ratios and Proportions

7. Calculations with Ratios and Proportions

Even if only 99 out of 100 people need to know how to work with ratios, the odds that they'll be useful to you are very high. In this lesson, we'll practice performing calculations with ratios and proportions.

How to Solve Problems with Time

8. How to Solve Problems with Time

It's amazing how much time can be saved when people work together. In this lesson, we'll practice figuring out just how much time we're talking about as we solve problems involving time.

How to Find an Unknown in a Proportion

9. How to Find an Unknown in a Proportion

Artists, engineers, athletes, and accountants all use proportions in their daily lives, and setting them up is really quite easy, once you know the rules. In this lesson, you'll learn how to solve proportions when there is an unknown value and work on some practice problems.

Calculating Unit Rates Associated with Ratios of Fractions

10. Calculating Unit Rates Associated with Ratios of Fractions

This lesson demonstrates a few different ways to calculate unit rates. We use them to solve problem such as how many beats per minute, or how many miles per hour. To master this lesson, you must understand how ratios and fractions will help to find the unit rate based off of a higher ratio of values.

Proportional Relationships Between Two Quantities

11. Proportional Relationships Between Two Quantities

When two values always maintain the same ratio, forming the same fraction when you divide them, they have a proportional relationship. In this lesson, you can learn about proportional relationships between two quantities.

Identifying the Constant of Proportionality

12. Identifying the Constant of Proportionality

Constants of proportionality might sound like something complicated, but chances are, you've encountered them before. In this lesson, we'll explore the constant of proportionality and how to find it.

Representing Proportional Relationships by Equations

13. Representing Proportional Relationships by Equations

After you read this lesson, you'll see just how easy it is to find an equation that represents your proportional relationship. You'll learn the formula you can use to find your equation for any proportion you have.

Graphing Proportional Relationships

14. Graphing Proportional Relationships

Two values are proportional if they maintain the same ratio and their graph will always be a straight line that goes through the origin (0,0). In this lesson we'll explore how to draw proportional graphs and use them to solve desperate situations!

Proportional Relationships in Multistep Ratio & Percent Problems

15. Proportional Relationships in Multistep Ratio & Percent Problems

This lesson introduces the concepts of ratios, rates, and proportions. It will show you how to use rates and ratios to develop proportional relationships. Using proportions to solve problems is very common in mathematics, because oftentimes many rates and ratios are constant.

Constructing Proportions to Solve Real World Problems

16. Constructing Proportions to Solve Real World Problems

In this lesson, we will concentrate on proportions. Through definition and example, we will learn how to construct proportions and how to use proportions to solve real world problems.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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