Page 123 - NUMINO Challenge_B1

14 Measurable Lengths and Weights

Basic Concepts Measuring Lengths Using Unmarked Rulers

Lengths can be measured by joining or overlapping unmarked rulers. For
example, the following lengths can be measured by using these unmarked
rulers that are 1 cm, 2 cm, and 6 cm long:
By using only one unmarked ruler:

12 6
1 cm 2 cm 6 cm

By joining unmarked rulers:

12 16 26 12 6
3 cm 7cm 8 cm
9 cm

By overlapping and joining unmarked rulers:

1 5 cm 2 4 cm 1 7 cm 2 5 cm
6 6 26 16

Therefore, the measurable lengths are 1 cm, 2 cm, 3 cm, 4 cm, 5 cm, 6 cm,
7 cm, 8 cm, and 9 cm.

Example Here are three unmarked rulers that are 2 cm, 3 cm, and 7 cm
long. How many lengths can be measured using these rulers?

23 7

Class Notes

Lengths that can be measured by using one ruler are 2 cm, 3 cm, and cm.

Lengths that can be measured by joining two rulers are 5 cm, 9 cm, and cm.

A length that can be measured by joining these three rulers is cm.

Lengths that can be measured by overlapping two rulers are 1 cm, 4 cm, and cm.

Lengths that can be measured by overlapping or joining these three rulers are 2 cm,

cm, and 8 cm.

Therefore, there are measurable lengths from 1 cm to 12 cm, excluding cm.

120 NUMINO Challenge B1