**Middle School Number Sense Lesson 13: Converting Distance between English Units**

One of my students asked me last week if the number sense concepts I was teaching would help them in "real life." In other words, "Will I use this later on?" Well, I can say with absolute certainty that if you live in the United States, you will need to understand today's concept. (I have often wondered why we have so firmly held onto our system of measurements instead of more fully embracing the easier metric system, but that is a topic for another blog entirely).

This concept appeared a whopping

**19 times**on this year's number sense tests--more often than almost any other concept. It appeared 8 times between questions 11 & 20, 4 times between questions 21 & 30, and 7 times later than that. Interestingly, this concept appeared 6 times as an estimation question, which is why I've chosen to include some of those in today's worksheet.

**Number Dojo Level: 58**

Some of the distance conversions seen on number sense tests would be second nature to most people (feet to inches, yards to feet, etc.). But other conversions are not nearly as common (rods to feet, miles to rods, etc.). Here we will cover the gamut of conversions I've seen in the past few years of "number sensing." I will give many examples because of the wide variety of questions seen on the tests.

**The Basic Conversions**

**1 foot**(ft)

**= 12 inches**(in)

**1 yard**(yd)

**= 3 feet**(ft)

**= 36 inches**(in)

**1 mile**(mi)

**= 1760 yards**(yd)

**= 5280 feet**(ft)

**US Survey Measurements**

**1 rod**(rd)

**= 16.5 feet**(ft)

**1 furlong**(fur)

**= 40 rods**(rd)

**= 660 feet**(ft)

**1 mile**(mi)

**= 8 furlongs**(fur)

**= 320 rods**(rd)

**How to Convert between Units**

- To go from a smaller unit (like feet) to a larger one (like yard),
**divide**by the conversion factor (in this case, 3). - To go from a larger unit (like mile) to a smaller one (like feet),
**multiply**by the conversion factor (in this case, 5280). - To convert to a unit more than one step away (for example, from yards to inches), it may be easier to convert one step at a time (in this example, from yards to feet and then from feet to inches).

**Example 1: 4 yards = ___ feet**

- Consider your conversion factor: 1 yard = 3 feet.
- You are going from a larger unit to a smaller one. Multiply by your conversion factor. 4 x 3 =
**12**.

**Example 2: 60 inches = ___ feet**

- Consider your conversion factor: 12 inches = 1 foot.
- You are going from a smaller unit to a smaller one. Divide by your conversion factor. 60 ÷ 12 =
**5**.

**Example 3: 3 yards = ___ inches**

- Consider your conversion factor: 1 yard = 36 inches.
- You are going from a larger unit to a smaller one. Multiply by your conversion factor. 3 x 36 =
**108**. - It may be easier for you to solve this question in two steps (since 1 yard = 3 feet and 1 foot = 12 inches). 3 x 3 = 9, and 9 x 12 =
**108**).

**Example 4: 2640 feet = ___ miles**

- Consider your conversion factor: 5280 feet = 1 mile.
- You are going from a smaller unit to a larger one. Divide by your conversion factor. 2640 ÷ 5280 =
**.5**or**1/2**.

**Example 5: 6 feet + 2 inches = ___ inches**

- Consider your conversion factor: 1 foot = 12 inches.
- You are going from a larger unit to a smaller one. Multiply by your conversion factor. 6 x 12 =
**72**. - Now that you have both distances in inches, simply add them together. 72 + 2 =
**74**.

**Example 6: 2 yards - 1 foot - 6 inches = ___ inches**

- Since the answer is in inches, convert everything to inches. Multiply each number by the appropriate conversion factor.
- 2 yards x 36 in/yard = 72 inches. 1 foot x 12 in/foot = 12 inches.
- Now that the distances are all in inches, simply subtract. 72 - 12 - 6 =
**54**.

**Example 7: 2 feet 8 inches + 3 feet 4 inches = ___ yards**

- It is easiest for me to handle this question in baby steps. I first convert everything to inches. 2 feet =
**24**inches, and 3 feet =**36**inches. - Add the inches together: 24 + 8 + 36 + 4 =
**72**inches. - Now divide by 36 to convert from inches to yards. 72 ÷ 36 =
**2**.

**Example 8: 4 rods = ___ feet.**

- Consider your conversion factor: 1 rod = 16.5 feet.
- You are going from a larger unit to a smaller one. Multiply by your conversion factor. 4 x 16.5 =
**66**.

**Example 9: 1/2 mile = ___ rods**

- Consider your conversion factor: 1 mile = 320 rods.
- You are going from a larger unit to a smaller one. Multiply by your conversion factor. 1/2 x 320 =
**160**.

**Example 10: 1.5 furlongs = ___ feet**

- Consider your conversion factor: 1 furlong = 660 feet.
- You are going from a larger unit to a smaller one. Multiply by your conversion factor. 1.5 x 660 =
**990**.

**Here's a free worksheet to help you practice ConvDistance:**

convdistance.pdf |

**Up Next for Middle School: Mult125var**