Making numbers
There are interviews with children doing this activity given in the Case Study section.

Goals:
  • To diagnose shorter-is-larger misconceptions and stimulate students' reconsidering decimals in terms of place value.
  • To prompt consideration of which zeros matter.
Year level:  Year 5 to 8
Group size: Whole class, small group or individuals
Equipment: 
  • (all optional)
  • Place holders such as 3.__ __ __ __ written on cardboard.
  • A large supply of cards bearing the digits 0,1,2....9.
Time: 10 - 15 minutes


Activity Instructions: 
1. Use the cards 9, 8, 6, and 2 to make the largest number in the template below:

Possible
student
response:

3.9862

Most students will get this correct. Students who make errors may have one of the shorter-is-larger misconceptions. An answer like 3.2 would indicate this thinking pattern.

2. Use the 9, 8, 6, and 2 cards to make the smallest number in the template below:

Possible
student
response:

3.9862

Students who give this answer have a shorter-is-larger misconception such as reciprocal thinking.

3. Use the 0, 0, 1 and 5 cards to make the smallest number in the template below:

Possible
student
response:

2.0015

2.1500

This item may draw a large number of responses as many students have difficulty deciding which zeros matter.

Variations:
A more difficult variation is to ask the students to make the closest number to 3.7 (using all 4 cards from example 1) OR to make a number less than or greater than a particular number.