Tell
students that they will be rolling clay into "fish food." Divide
students into groups of 3 to 6, and distribute play dough to each
group. For students at the pre-K level, rolling clay can be a tedious
task. Demonstrate for them how to do this, and offer assistance as
needed. For students who have difficulty rolling the dough into a ball,
you may wish to demonstrate how to pinch off pieces. As they roll the
clay, encourage them to separate the fish food into two groups.
Then give each group the cut-outs of the fish. Explain that this
fish is hungry. Ask, "Do you notice anything about the fish that shows
he is hungry?" Students may respond, "His mouth is open." Respond
positively to their observations, and reinforce the idea of the open
mouth. (Note:
You may wish to print a copy of this activity sheet for all students,
but the mat itself will not be used until later in the lesson.)
Fish and ClamNext, tell students that the fish wants to eat from the group
with the most food. Point to the two groups of food and demonstrate for
the students how they can choose the fish which points toward the group
with more food. During this time, reinforce the direction by having the
children look carefully at the fish’s mouth and place it in the
direction of the clay group with the larger quantity. The open mouth of
the fish serves as the students' introduction to the greater than
(>) and less than (<) symbols.
Encourage students to look at their own groups of fish food and think about the model, with the following questions.
- “The fish is hungry, his mouth is open, and he is looking for the most food. From which pile will your fish eat?”
While students are exploring with the clay and fish, ask leading questions to assess their understanding of the most.
- While pointing to the appropriate group, ask, “How do you know there is more here?”
A student may respond, “Because I counted the food,”
“Because this side has a lot, and this side has a little,” or “Because
I looked at the food, and I just know.” Respond to each of the
comments, but focus on the aspect of counting to find out which set has
more.
As a group, you and students might begin counting the modeling clay
balls, comparing two amounts, and distinguishing which set has more.
Make this initial introduction very informal.
Using the Island Mat
For The second part of the lesson, utilize the Island Equation Mat.
Island Equation Mat
(Instead of using the mat given here, you can have students create
their own. They could cut two islands from light brown paper and glue
them to an 11" × 15" piece of blue construction paper.)
Note:
Rather than using paper versions of the mat, you may wish to use the
fish and clam images and the greater than and less than symbols on an
electronic whiteboard. Draw two piles of fish food on the whiteboard,
and then have students drag the appropriate image between the piles.
This technology works well, because the greater than or less than
symbol can be dragged over top of the fish’s lips, and then the image
of the fish can be removed. The replacement of the lips by the symbol
provides a nice transition from concrete to pictorial to symbolic.
Allow students working in small groups to make different sized
piles of fish food from modeling clay. This time, have students add or
remove amounts of fish food from each island. Again, tell them that the
fish likes to swim (with mouth open) toward the island that has more
food. At this point, student groups do not have to be working with the
same numbers in their piles of food. They are still investigating more
in terms of quantity, not necessarily specific amounts. As students
attempt to answer your question, listen for rote counting, and visually
observe the direction in which students are placing their fish. The
focus objective here is still on more and less, but also on the correct order of rote counting and on subitizing (identifying amounts without counting) up to six.
Once students are able to identify the island with more based on
the groups of food that they made, you can begin to suggest specific
amounts to place on the island mats. “Place two on this island and six
on the other island.” Watch the techniques that students use to
identify two and six.
- Does the student count two and then count six? or subitize two and count out six? or subitize two and subitize six?
Observing this will tell you where students are in understanding the quantities of two and six.
Introducing the Clam
As a subsequent step, state a set of equivalent amounts. (To make it
less obvious that equivalent amounts are being used, you may wish to
simply add some food to 1 of the islands. For instance, if the islands
originally had 5 and 3 clay balls, you could tell students to add two
pieces of food to the appropriate island.) Then, watch as students
attempt to solve the problem. “Which way does the fish swim if both
islands have the same amount of food?” After listening to their ideas
of where the fish might swim, introduce the clam cut-out. Say something
like, “When both islands have the same amount of food, the fish gets
confused and swims away. A clam takes his place instead.” The clam
figure introduces the equal sign. Students love the idea that they can
choose between the fish and the clam. They begin to understand, with
practice, that they use the fish to identify sets that are unequal
(more, greater, less, fewer) and they use the clam to identify sets
that are the same (equal).
During the remainder of the lesson, call out different sets of amounts,
visually observe students as they manipulate their fish or clam, listen
for rote counting, watch for counting techniques (such as subitizing),
and individually check for understanding of more than, less than, and equal to.