Grade level: 2
Focus: Spatial issues and patterns leading to the mathematical issues of
addition, multiplication and even fractions.
Activity A: Rod Cover-up A
Activity B: Rod Cover-up B
Activity C: Fractions of Rods
A. Introduction:
Rod Cover-up activities are puzzles which require spatial reasoning and lead to the understanding of the different lengths of the Cuisenaire Rods. These activities also can explore mathematical operations as addition, multiplication and fractions.
(1)This a generative activity which allows for various responses from the students. (4)The space is open enough for students to work alone or in small groups allowing time to make independent discoveries. (5)At the same time these activities allow space for the teacher to expand on issues of patterns, addition, subtraction, and fractions. (10)Students are urged to use their mathematical knowledge and imagination to explore the characteristics of the rods and patterns of the puzzles.
(3)This is a challenging activity for second graders
based on their limited knowledge of fractions and the need to create their
own puzzles using the Cuisenaire Rods. (2)The students
need to have had prior experience working with patterns, length and an introduction
to fractions. Students are going to use their learned skills of mathematics
and will also be coached into future lessons to be learned such as fractions.
B. (6)Class Plans:
(9)Materials:
Cuisenaire Rods
Grid paper (one-centimeter)
colors/markers
Students should be allowed to work in groups of two or three.
Allow students to explore and discover characteristics of the Cuisenaire Rods. Using the one-centimeter grid page that has been provided enables the students to record their own observations pictorially.
Next, these ideas need to be shared among the entire class. A good way
to do this is after the groups have written down their discoveries the teacher
should make an accumulated list on the board or overhead of the main observations
made from each group.
C. Rod Cover-up A:
Students are to cover each rectangle with the appropriate color rod.
One color will not work. Have each group predict which one it is before
they begin. Have students record their findings and discuss what they have
noticed thus far.
D. Rod Cover-up B:
The idea for activity B is much the same as it was for activity A. However,
this time the patterns are formed more into puzzles. Have students predict
which puzzle will not be cover completely before they begin. After they
have finished have the students write their findings.
E. Challenges:
Challenge the students to design their own puzzles much like Rod Cover-up
B. For example, they can look for outlines that can be completely covered
by four different colored rods. Then, find a fifth color that will not work
for the same outline. The one-centimeter grid paper is good for the students
to trace the exact outlines of their puzzles.
F. Possible Observations by Students (7):
Beginning observations will mostly be related to individual size of each
rod, such as, the white rods can fit in all puzzles, or the orange rod is
the largest. Other issues related to size and leading to fractions can be
made, for example, two red rods are the same length as one purple, or a
red rod is _ of a purple rod. With more time working with all the rods other
observations such as two purple rods are the same as one brown rod can also
be made. This leads to the idea that if the outline could be covered by
a brown rod, it could also be covered by purple. In addition to emphasizing
spatial reasoning, this activity provides an informal experience with the
concept of fractions.
G. Class Discussion(8):
Review what the students have observed. First of all the emphasis is on spatial issues. However, the students' discoveries may also lead to ideas connecting other mathematical ideas such as addition, multiplication, even fractions.
To help direct students to other observations the teacher may wish to ask such questions as (15):
"What rod is as long as a train of a light green rod and a dark green rod?"
lg + dg = _____
"What rod together with a red rod makes a train as long as a dark green rod?" dg - r = ____
"What rod is as long as a train made from three red rods?"
r x r x r = ____
"If you cut a brown rod in the middle, what rod would be the same size?"
b/2 = ____
H. Other activities(13):
Activity C:
Fractions of Rods
This activity is useful for understanding both the naming of fractions and the equivalence of fractions.
What to do: Have the students work with each rod in the set. Let each rod be 1, then find all the ways to make one-color trains, only, that equal the chosen rod. The students should name and record each rod they use and compare their results.
Using the idea of building trains of rods can be helpful in understanding
operations with fractions. After sufficient experience of naming the rods
as fractions the teacher can begin to introduce math operations, such as
adding fraction.
Activity A:
Rod Cover-up A
Cover each rectangle exactly with the color of rod indicated. One color
does not work. Predict which one it is before you begin.
red yellow
white light green
purple
Activity B:
Rod Cover-up B
Cover each shape exactly with the color that is indicated under the shape.
One color will not work. Make a prediction on which on you think it is before
you begin: ___________
light green dark green
red yellow
Activity C:
Fractions of Rods
A. Place the brown rod in the top row of the outline shown. Find all the ways to make one-color trains that are as long as the brown rod. Place them in the outline.
If the brown rod is 1,
_ what is the value of the purple rod. _________
_ what color of rod is 1/4 of the brown rod. __________
_ what color of rod is 1/8 of the brown rod. __________
_ show 1/2 = 2/4 = 4/8
with the rods.
B. Tape a brown and black rod together. Place them on the top row of the outline shown. Find all the ways to make one-color trains that are as long as the brown-black rod. Place them on the outline.
If the brown-black rod is 1,
_ what color of rod is 1/3 of the brown-black rod. ________
_ find the rod that is 1/6 of the brown-black rod. ________
_ show 1/3 = 2/6 = 3/9
with the rods.
Grid Paper (One-centimeter)
Grid Paper (One-Centimeter)
