## Time Rate Distance Problems

## Standards

**CCSS.Math.Content.7.EE.B.3**

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

**CCSS.Math.Content.4.NBT.B.5 **Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. (Common Core Standards)

## Summary

Time-rate-distance problems are word problems that involve the distance an object will travel at a certain average rate for a given period of time. Because we have found many students struggle with this type of problem, we find it so helpful to have multiple examples through videos, slides, and through a video game. In all of these problems, students solve for distance. Video, game and presentation resources are available in both English and Spanish.

**The formula for distance problems is: **

**distance = rate × time or d = r × t**

## Technology required

The game AzTech: The Story Begins can be played for free on iOS (iPad and iPhone) and in a web browser on any computer. The game can be installed in an iPad and played off-line by students who do not have reliable Internet access.

## Time required

15-25 minutes – time varies depending upon discussion of questions and length of game play allowed.

## Lesson Plan

### Watch video introducing students to Time-Rate-Distance problems

This brief video uses number bonds as one means of finding the total number of hours, then multiplies hours by rate to find the total distance. We work step by step through an example to find how far Spanish troops needed to ride to attack the Aztecs.

### 2. Video or Presentation of time-rate-distance example

#### Teaching Options

Students can watch another video solving for distance. If it takes 2 1/2 days to get to Honduras from Iowa, and Grandma drives 60 miles per hour without stopping, what is the distance from Iowa to Honduras? This video solves the problem step by step, beginning with converting 2.5 days to hours.

Alternatively, teachers can use this presentation as PowerPoint or in Google slides to present the same material either in class or in a web meeting. These presentations are also available in Spanish as PowerPoint and in Spanish as Google slides.

### 3. Video or Presentation of a second time-rate-distance example

#### Teaching Options

Students can watch another video solving for distance. If it takes Grandpa one day to get from Iowa to Texas and he drives 55 miles per hour, what is the distance from Iowa to Texas? This video shows, step by step, how to solve this problem.

Alternatively, teachers can use this presentation as PowerPoint or in Google slides to present the same material either in class or in a web meeting. These presentations are also available in Spanish as PowerPoint and in Spanish as Google slides.

## Assessment

Play AzTech: The Story Begins. Not only will students have fun and be exposed to educational content on Latin American history, but they will also have to answer mathematics questions to progress. Instruct students to be sure to answer the first bonus question, shown above. Remind them that the icon at the bottom of the screen can be used to pull up a calculator. (There is no arrow on the screen in the game. It is merely shown above for emphasis.) Once students have played the game, you can look in the AzTech teacher reports to see an individual students response. You will need to know your students’ usernames. To see an example of a report, enter the username “ddtester” .

State Standards

**Minnesota Math Standard 6.2.3.2** – Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results.

**Minnesota Math Standard 7.1.2.1** – Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating decimals; use efficient and generalizable procedures, including standard algorithms; raise positive rational numbers to whole-number exponents.

**Minnesota Math Standard 4.1.1.3** – Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms.