The volume (in cm^{3}) of 0.55 kilogram piece of iron (Density = 7.9 g/cm^{3}) is _________

When I read a math problem, I often draw a diagram. Of course it doesn’t have to be fancy–it is just to help me understand what each of the facts in the problem mean.

I also list all the facts and label them. This also helps me when I do start solving the problem.

**Facts:**

**density = 7.9 g/cm ^{3}**

**mass = 0.55 kg (NOTE: I have to know what each of the units measure and kilograms is a mass unit.)**

**Problem Map: **

This is a plan that shows you where to** Start** and the units of the answer at the **Finish.**

**Start————————————————————————–>Finish**

**UMM! Maybe I need to help you decide where to start.**

**Think!**

**1. **When density is given, you will use it as a conversion factor, this means that it is **NEVER** the starting point. Instead, it is used to change either grams to cubic centimeters or vise versa.

**2. **For this problem, the only other fact is the mass of the piece of iron. So this has to be what you will use as your starting point.

**3. **The answer is to be the volume of the piece of iron measured in cm^{3.}

With this information, you are ready to express your problem map.

**Start—————————————————————————>Finish**

**0.55 kg———————————————————————–>? cm ^{3}**

**Think!**

**1. **The problem is to change the** kg **unit to ** cm ^{3}**

**2. **Density is a conversion factor that can be used to change the** g **unit to ** cm ^{3}**

**3. **Since your mass is given in kg, and the density has mass in grams, you will have a second conversion factor, and it is one you must know. This is a conversion between grams and kilograms, which is 1000 g = 1 kg.

**3. **Write down the **starting fact** and the multiplication sign (X) , and then draw a line that will separate the numerator from the denominator.

**0.55 kg X = ? ****cm ^{3}**

**4. **Now you are ready to eliminate the kg unit. You do this by multiplying by a fraction that has the kg unit in its denominator. **REMEMBER THAT ANY AND ALL CONVERSION FACTORS ARE FRACTIONS AND CAN BE FLIPPED OVER TO MEET THE NEEDS OF THE PROBLEM. **