Storyline

Standards

Teacher Background

### Grade 6-8 | 9 (45 min) Classes

Students will answer the question “How are ratios and proportions used when creating scale models of rockets?” They will explore the concept of proportional figures by making drawings of model rockets with different scale factors. Students will use ratios to compare components of the actual Blue Origin New Shepard with the model rocket version. For the assessment, students will demonstrate their understanding of scales and ratios by creating a scale drawing of the Earth, Moon, and Sun to compare their sizes and distances from each other.

## Standards

## Targeted Performance Expectation(s):

## Common Core Math Standards

### CCSS.MATH.CONTENT.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

### CCSS.MATH.CONTENT.6.RP.A.3

Use ratio and rate reasoning to solve real-world and mathematical problems

### CCSS.MATH.CONTENT.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

### CCSS.MATH.CONTENT.7.G.A.1

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing, and reproducing a scale drawing at a different scale.

## Next Generation Science Standards

### SEPs

- Developing and using models
- Using mathematics and computational thinking
- Obtaining, evaluating, and communicating information

### CCCs

- Scale, proportion, and quantity
- Systems and system models

## Common Core ELA Standards

### CCSS.ELA-LITERACY.RST.6-8.3

Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

## Vocabulary

### EQUIVALENT RATIOS

**Ratios that can be simplified to the same value**

### MODEL

**A representation of an object that is larger or smaller than the actual size of the object**

### PROPORTION

**When two ratios are equivalent**

### RATIO

**A quantitative relationship between two numbers that defines the quantity of the first number by comparing it to the second number**

### RATIO TABLE

**A structured list of equivalent ratios**

### SCALE DRAWING

**Drawings that have been carefully measured and accurately reduced or enlarged using a consistent scale factor**

### SCALE FACTOR

**The ratio of any two matching lengths in similar figures**

### TAPE DIAGRAM

**A rectangular drawing that looks like a piece of tape but is divided to support mathematical calculations**

## Teacher Background

### Ratios

**A ratio shows the relative size of two or more values.**

A ratio is a **quantitative relationship** between two numbers that defines the quantity of the first number by comparing it to the second number. It describes how much of one thing there is by comparing it with how much there is of another thing, therefore neither of the quantities may be zero. The numbers in a ratio are quantities, for example, counts of specific items or measurements like length, weight, or time.

A ratio is written with a colon (:) between each number, with “to” between each number or as a fraction.

### Proportions

When two ratios are equivalent, they are said to be proportionate. You can test this by using the equality test for fractions, or by cross multiplying.

Ratios can be described using

**Tape diagrams**: rectangular drawings that look like a piece of tape but are divided to support mathematical calculations**Ratio tables**: data tables that list equivalent ratios

### Scale

A scale describes the relationship of the size of one thing to the size of another thing. It tells us how enlarged or reduced an item has been from its original size. Scale factors are ratios that describe a relationship between two images, models or representations.

**Scale drawings** are drawings that have been carefully measured and accurately reduced or enlarged using a consistent scale factor. Scaled images maintain the same ratio and have the same shape but are a different size. The difference between the ratio numbers represents the factor by which the scaled image is enlarged or reduced.

### Blue Origin

Blue Origin was founded by Jeff Bezos in 2000 with the vision of enabling a future where millions of people are living and working in space for the benefit of Earth. The rockets are reusable and fully autonomous. Every person onboard is a passenger—there are no pilots.

The Blue Origin logo, a feather in flight above the Earth, represents the perfection of flight, freedom, exploration, mobility and progress.

The New Shepard vehicle has a pressurized Crew Capsule with room for six. It is named after Alan Shepard, who was the first American in Space in 1961.

### Modeling in Aerospace

Scientists and engineers use scale models when it may be impossible or impractical to use the real item. Models may be safer and less expensive to use than the real thing. In aerospace, scale models are used for many reasons, such as demonstrating how aircraft respond in different conditions, testing stability, and improving efficiency of existing planes and rockets. Blue Origin uses models to test functions of individual parts of the rocket such as the engine, capsule, fins, and recovery system to save time and money before building the full-scale rocket with all the parts together.

Scale model rockets may be based on an existing or historical guided missile, rocket vehicle, or space vehicle. The Estes scale model of Blue Origin’s New Shepard used in this unit is a 1/66th scale model.

**Important note:** Scale models should be proportional to the real object. However, sometimes the scale of a specific feature of a rocket (such as the fins) must be changed in order to make the model rocket stable. The mechanics of flight are also different at such a smaller size, which means the thrust, weight, and therefore altitude may not be proportional for a scale model rocket.

*For example, the Blue Origin New Shepard’s BE-3 engine fires for 110 seconds and produces 110,000 lbs of thrust. The model rocket Blue Origin New Shepard, using a C 6-3 engine, has a time delay of 3 seconds, a thrust duration of 1.85 seconds, and produces 4.6 lbs of thrust.*

## Materials

### Each Student Needs:

Student Portfolio

Safety Goggles

Graph Paper

Ruler

Tape Measure

### The Class Needs:

## Unit Plan

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## Student Portfolio

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## Resources

### Slide Presentations

How are scale models used in science and engineering?

What are ratios?

Ratios and Scale

Making Scale Drawings