Geometry and
spatial reasoning
Activity 4.10
Connections to the mathematics TEKS
(4.10) The student recognizes the connection between numbers and their
properties, and points on a line.
The student is expected to locate and name points on a number line
using whole numbers, fractions such as halves and fourths, and decimals
such as tenths.
Students work in groups of four. Each student is given a transparency with a number
line printed on it. The locations for 0 and 1 are marked, but nothing else. One student
0
1
records whole numbers on one transparency, one student records halves ( 2 , 2 , 22 ,
3
, etc.), one student records fourths ( 04 , 41 , 24 , etc.), and one student records decimals
2
(0.0, 0.1, 0.2, 0.3, 0.4, etc.). The students place their transparencies on top of one
another, staggered so that the number lines appear as shown below:
1
0
0
0
1/2
1/4
0
2/4
2/2
3/4
4/4
1.0
0.5
Students compare the number lines and identify equivalent fractions and decimals that
name the same points on the number line.
Questioning...
Open with...
Describe your number line.
Probe further with...
• How did you decide where to place the halves?
• How did you decide where to place the fourths?
• How did you decide where to place the decimals?
1
• What other numbers are equal to ?
Equal to 1? Equal to 1.5? Equal to 2?
2
• What patterns do you notice?
140
Chapter 2 – Grade 4
Geometry and
spatial reasoning
Listen for...
• Does the student use mathematical vocabulary such as five-tenths, threehalves, or equals?
• Does the student notice patterns and relationships? (For example, one-fourth is
between zero and one-half.)
Look for...
• Is the student’s number line accurate?
• How does the student determine fractional parts? (folding, measuring,
estimating)
• Does the student use mathematical notation to label points on the number line?
• Is the student able to self-correct errors as the transparencies are placed on top
of one another?
Chapter 2 – Grade 4
141