## Fish Food, More or Less

• Lesson
• 1
• 2
Pre-K-2
1

Students are introduced to the concepts of greater than, less than and equal to by observing quantities and making comparisons. Using various instructional materials such as modeling clay, buttons, beans, and cotton balls, students create amounts to compare using the open-mouthed fish. Depending which fish is chosen, the fish cut-out (with its mouth open) represents either greater than or less than. For equivalent amounts, a clam cut-out represents equal to.

This introductory lesson can be assessed through visual observation and verbal questioning. A group size of 3 – 6 students per group is optimal.

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 Clam

Next, 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.

(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.

Assessment Options

1. Observe student participation during the group activity. Work with smaller quantities until students are successful, then advance to larger quantities. Listen for rote counting and watch for other counting techniques. Observe students as they place the fish and clam cut-outs on the mat. Do they construct correct equations as they manipulate the cut-outs and the modeling clay? Ask questions that encourage students to verbalize their understanding of more, less, and equal to, and to demonstrate their understanding by manipulating the cut-outs appropriately.
2. This lesson should assess students’ understanding of more and most as being greater than less and least. The lesson should also address students’ ability to identify the group (or set) that has the most. If focusing on equal groups, students should understand that the same refers to equal quantities. Encourage students to use the island mat to construct visual quantities appropriate to their developmental ability and place the fish or clam cut-outs accordingly. When students successfully manipulate the fish and use the open fish mouth to indicate the greater quantity, they are ready to proceed to the next lesson.
3. Students may observe that some clay balls of “food” are larger than others and declare that one island has more food than the other, particularly when the counts differ by one. While this is a good observation, the objective of this lesson is to measure the food by counting and not by volume.  Help students identify the attribute in focus and reinforce counting the clay balls of food

Extensions

1. Have students progress from comparing smaller quantities to comparing larger amounts.
2. Have students progress from comparing balls of modeling clay to comparing various other items. They could also compare dots (such as on a domino) or numerals.
3. Move on to the next lesson, From Fish Food to Pictures to Symbols.

Questions for Students

1. Why do you think the fish has his mouth open?

[Because he is hungry, OR because he wants to eat a lot of food.]

2. Where do you think the fish will swim? (to which island)? Why?

[The fish will swim here, because there is more food here than over there.]

3. How do you know that there is more in this group (on this island)?

[I counted the pieces of modeling clay OR I just looked and saw that there is more here.]

4. What will happen if I move two play clay balls from one island to the other island?

[Responses will vary, depending on the quantity on each island.]

5. Who in our group has the most on one island? Who has the least? How do you know?

[Responses will vary, but may include counting as a means of finding out who has more and who has less.]

6. What can you do to the clay to show none? What number represents none?

[Take all the clay food away. The number zero, or the numeral 0, represents none.]

7. What happens when both groups are the same?

[They have the same amount of fish food, and I put the clam in between them. Both groups (islands) have the same number of clay balls.]

8. If this group (island) has the most, how much does the other group (island) have?

[It has less OR it has a smaller amount that the other group (island).]

Teacher Reflection

• What learning styles does this lesson address?
• In what ways was this lesson different when students used modeling clay and when they used objects like blocks or beads?
• How did students perform in relation to the stated learning objectives?
• What was most effective when presenting this lesson? What was least effective? Why?
• What did you learn from observing the students as they participated in this activity?
• How did students demonstrate their understanding of the connection between the fish and the concepts of greater than and less than?
• How did the students demonstrate their understanding of the connection between the clam and the concept of equal to?
• How did you adjust the lesson to meet the needs of all learners?

### Island Inequality Mat

Pre-K-2
The concepts of greater than, less than, and equal to are explored in this 2-lesson unit.

### From Fish Food to Pictures to Symbols

Pre-K-2
Students build upon their understanding of greater than, less than, and equal to by observing quantities and making comparisons using various instructional materials. The fish cut-out, with its mouth open, represents the greater than or less than symbol; the clam cut-out represents the equal to symbol. Using fish lips as a transition point, students will apply their understanding of greater, less, and equal to the standard symbols (>, <, =) as you introduce symbolic notation at a developmentally appropriate level.

### Learning Objectives

Students will:

• Compare a set of quantities and determine which is greater.
• Determine when sets are equal.
• Understand the terms greater thanless than, and equal to.

### NCTM Standards and Expectations

• Count with understanding and recognize "how many" in sets of objects.
• Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.
• Model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols.

### Common Core State Standards – Mathematics

-Kindergarten, Counting & Cardinality

• CCSS.Math.Content.K.CC.A.2
Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

-Kindergarten, Counting & Cardinality

• CCSS.Math.Content.K.CC.C.6
Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.

-Kindergarten, Counting & Cardinality

• CCSS.Math.Content.K.CC.C.7
Compare two numbers between 1 and 10 presented as written numerals.

-Kindergarten, Algebraic Thinking

• CCSS.Math.Content.K.OA.A.1
Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

• CCSS.Math.Content.1.OA.D.7
Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

• CCSS.Math.Content.1.NBT.B.3
Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

• CCSS.Math.Content.2.NBT.A.4
Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

### Common Core State Standards – Practice

• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.