Scales on Number Lines

When drawing a number line to show, say, 3.45 with 3.4 and 3.5 as the end points, students easily lose track of the position of 0 on the line. Being able to solve such a problem is a powerful indicator that the students’ knowledge of the decimal place value system is good. This activity is not easy and needs careful teaching.

Using Materials

Problem: “If 3.4 and 3.5 are marked 10 divisions apart on a number line where is the number 0?”

Get the students in groups to mark 3.4 and 3.5 on a number line with 10 1-centimetre gaps between the 2 numbers. 

Discuss why 3.4 needs 34 x 10 centimetres from 0. Get the students to use a metre rule to locate 0.

Problem: “Outside place 2 pegs, representing 4.5 and 4.6 on a number line, 1 pace apart. Your task is to locate where 0 would be on the number line.”

Put the students into groups of 3 or 4 and discuss what they are going to do outside on the field.Show them the task on the board. They will put a marker on the ground to represent 4.5. One student in each group takes a pace to represent 4.6, and this point is marked  with 4.6. The students’ task now is to mark where 0 is. (The group moves 45 paces back from 4.5 using the pace of the selected student.)

Examples: The space between the given numbers represents one pace. Find 0 in each case:
2.2 to 2.3, locate 0. (Answer: 0.1 is 1 pace, so they need 22 paces back from 2.2.)

0.45 to 0.46, locate 0. (Answer: 0.01 is 1 pace, so they need 45 paces back from 0.45.)

0.023 to 0.024, locate 0. (Answer: 0.001 is 1 pace, so they need 23 paces.)

150 to 160, locate 0. (Answer: 10 is 1 pace, so 150 is 15 paces.)

3 300 to 3 400, locate 0. (Answer: 100 is 1 pace, so 3 300 is 33 paces.)

Using Number Properties

Examples: 2.02 to 2.03 are 10 centimetres apart on a number line. How far is it to 0?

(Answer: 0.01 unit = 10 centimetres so 1 unit is 100 x 10 centimetres = 10 metres. So 2.02 is 2.02 x 10 = 20.2 metres back to 0.)

67.5 to 67.6 are 1 metre apart on a number line. How far is it to 0?

907.05 to 907.06 are 10 centimetres apart on a number line. How far is it to 0?