This activity is about doing calculations using upper and lower bounds.

As a quick recap ...

To find the upper and lower bounds of a value, we **add **and **subtract** half of the rounding unit to our rounded value.

In this activity, we will be using upper and lower bounds when calculating using addition, subtraction, multiplication and division to find the maximum and minimum values.

**For example**

One piece of wood is 170 cm long (rounded to the nearest 10 cm) and another is 160 cm long (rounded to the nearest 10 cm).

What is the largest possible total length of the two pieces?

To find the largest possible total we need to use the upper bounds for both of the lengths.

170 + 5 = 175 cm

160 + 5 = 165 cm

Total = 175 + 165 = 340 cm

In general, we use the following rules

**Addition**

Maximum Value = Upper Bound + Upper Bound

Minimum Value = Lower Bound + Lower Bound

**Subtraction **

Maximum Value = Upper Bound - Lower Bound

Minimum Value = Lower Bound - Upper Bound

**Multiplication**

Maximum Value = Upper Bound x Upper Bound

Minimum Value = Lower Bound x Lower Bound

**Division**

Maximum Value = Upper Bound ÷ Lower Bound

Minimum Value = Lower Bound ÷ Upper Bound

If you ever need a recap of the rules - head on back to this page by clicking on the red help button on the screen.

Now let's give these questions a go!