Elaine Chan
Joan Elliott
Natalie Ralphs
Karen Norwood

Goldfish In The Pond

Grade Level: K-3

Purpose: The purpose of these activities is to provide children with a concrete introduction to different math concepts. This lesson plan shows how you, as an educator, can manipulate one activity to cover various math operations (addition, subtraction, multiplication, division). It gives children a visual, kinesthetic, and concrete way to learn a new concept and problem solve.

Objective: Students will understand new concepts (addition, subtraction, etc.)

Resources/Materials:

1. Pepperidge farms Goldfish

2. Coffee Filters, Cupcake Holders

3. Addition, Subtraction, Multiplication, Division cards (depends on what concept the students are working with). These cards will consist of fact families or number families. For example, in addition, you might want to make cards for all the ways you can add to 5, i.e. 5+0, 4+1, and 3+2.

4. Record Sheet, which looks different depending on math concept
 
 

 Activities and Procedures: 1. As with all other manipulatives, discuss proper use of materials. Be clear about when children will be able to eat the goldfish.

2. Demonstrate how students will use materials.

You can find specific procedures and extensions for each math concept on the following pages.
 
 
 
 

Evaluation: 1. Observation Do children know what operation sign means?

2. Collect record sheets. Are they writing numbers in correct order when they have to?

3. Story problems. Can have children make up story problems as they work with manipulatives and cards. In the end, you can have children make any story problem they want and share it with a neighbor.
 
 

 Diversity: 1. Can manipulate these activities more and have students work with two or three digit numbers.

2. Model the activity for students, so students who may not be as English proficient can observe and follow along.
  1. You can do this activity with different kinds of groupings. You can do it pairs, groups of four, or individually. Be sure to divide groups unbiasedly.
  2. Language and Cultural Diversity: Because of the modeling and hands-on


    3. activity of the lesson, students can understand concepts and applications despite language difficulty.

  3. Gender Diversity: The connection to real-life images and ideas is
interesting to both girls and boys, and the activity allows for mixed gender groups for cross-gender interaction. Standards:
  1. Mathematics as Problem Solving


    2. -Use problem-solving approaches to investigate and understand mathematical content

    -Formulate problems from everyday and mathematical situations

    -Acquire confidence in using mathematics meaningfully

  2. Mathematics as Communication


    3. -Relate physical materials, pictures, and diagrams to mathematical ideas

    -Relate their everyday language to mathematical language and symbols

  3. Mathematics as Reasoning


    4. -Use models, known facts, properties, relationships to explain their thinking

    -Justify their answers and solutions processes

    -Use patterns and relationships to analyze mathematical situations

  4. Mathematical Connections


    5. -Use mathematics in their daily lives

  5. Whole-Number Computation
-Select and use computation techniques appropriate to specific problems and determine whether the results are reasonable
 
  Addition Procedure and Extension

Activities and Procedure:

  1. First demonstrate proper use. Depending on the way you group, talk about how we treat each other in a
  2. group.
  3. Invite them to eat a couple of goldfishes as to avoid having them eat them during the lesson. Let them know that they can have more when they are through with the lesson.
  4. Model how to use cards, manipulatives, and record sheet. Model story problems as you do the problem on the card. For example, once upon a time there was only 1 very lonely goldfish in the pond. It wanted some roommates and then 3 goldfish decided to move in. How many goldfishes were in the pond living happily ever after?
  5. Ask children what I needed to do to find how many fishes were in the pond. Did I put (add) some in or take some out? Talk to students about what (+) means.
  6. Pass out materials
  7. Have students work on their card set and have them record their answers on record sheet.
  8. Invite students to share some story problems they made up using the cards.
  9. Collect record sheets for evaluations.
Tying It All Together and Extensions:
  1. Ask class what (+) means.
  2. Have children make up story problems for their neighbor.


Addition Record Sheet
 

Subtraction

Procedure (1st or 2nd grade)

  1. Invite students to eat a few goldfish crackers if they wish. This should deter them from sneaking too many during their lesson.
  2. Show students a "pond" and say, "I am going to tell you a little story." Tell a subtraction story using the goldfish. For example: Once there were five little fishes. One decided to sneak away and hide near the edge of the pond. (Put one goldfish just outside the pond.) How many fish were left? Ask students to hold up number of fingers of fish left in the pond.
  3. Introduce the index card number sentences/stories.
  4. Model one story.
  5. Pass out index card stories and direct students to make their fish look like the ones in the story. Let them experiment here. Older students may need more challenging number sentences or sentences with different spaces blank (not just the answer).
  6. Hand out the record sheet (see example at the bottom). Ask student to record their stories on their own record sheets.
  7. Collect the record sheet for assessment.
Extensions
  1. Students make up their own number sentences/stories and record on the record sheet.
  2. Students make up a problem for a partner to complete.
  3. Older students who are beginning to learn about place value and subtracting larger numbers may also be able to use these activities. For example, in one pond, one fish might represent ten and in another pond one fish might represent just one.


Subtraction Record Sheet
 

LESSON TOPIC: MULTIPLICATION

GRADE LEVEL: 3

LESSON PURPOSE: To learn the multiplication concept and to apply it

OBJECTIVES:

Students will learn the concept behind multiplication through being taught the "fishes in a pond" method (drawing ponds with fish in them to understand the concept of multiplication.)

Students will apply the multiplication concept to functions as they solve and create their own problems.

 ANTICIPATORY SET: Ask about the students’ experiences with fishing and catching fish. Ask if they’ve been to a pond and if they could see any fish in the pond. Tell the class that they’re going to learn how to multiply numbers by making their own ponds and putting fish in them. After they’re done, they’ll get to catch their own fish and eat them. LESSON DEVELOPMENT: I. Here’s How A. The Ponds 1. Draw a card. Say what is on the card and show the students. FOR EXAMPLE--The card says 2 ponds x 3 fishes.

2. Put out the number of filters for the number of ponds and explain what you are doing. (The card says two ponds, so here are one, two ponds.)

3. Write the number (2) on the worksheet. Say you are going to be multiplying, and write the multiplication symbol next to the number. Tell the students: This is the multiplication symbol.

 B. The Fishes 1. Put the number of fish in each pond and explain (The card says three fishes, so we put three fishes in each pond--one, two, three--one, two, three.)

2. Write the number (3) and the equal sign on the worksheet after the multiplication symbol.

 C. How Many Fishes in All? 1. Review how many ponds you have with the number of fish in each, while referring to the equation that was written on the worksheet. (We have two ponds with three fishes in each. That’s 2 x 3.)

2. Pose the question: How many fishes are there in all?

3. Count the fishes in the ponds. Write the number after the equal sign.

4. Distinguish between adding the numbers and multiplying them.

 D. Let’s Try Another--Model another time, and have the students do it with you. II. Guided Work A. Pass out the filters, the goldfish, and personal stacks of cards.

B. Instruct the students of the directions while writing them on the board:

1. Draw a card.

2. Make the ponds and put the fish in them. (Write the problem)

3. Count all the fishes. (Write the answer)

 B. Let the students work. Give instruction and guidance as needed. III. Make Your Own A. Tell the students that once they have done all of their cards, they can make their own problems.

B. Students can continue to use their worksheet to record their own problems.

C. When time is up, students can eat their fishes.

 LESSON CLOSURE I. Multiplication Equations A. Write a multiplication equation on the board. Ask if anybody made that number of ponds with that number of fishes in each. Ask: When you multiplied, what did you get?

B. Repeat for a number of problems, allowing students to come up to the board and write down problems they made.

C. Give a problem that nobody would have made, and ask: How many fishes would we get? Try another one.

 EXTENSIONS A Circles & Stars Book. On each page, students can draw circles in replace of ponds and stars in replace of fish and write the corresponding equation. They can give their book a title and decorate it. Other--circles and dots, hearts, etc. Primary Grades. Addition and Subtraction--Students can add and subtract goldfish.

Division. Students can begin with a school of fish in one pond (the first number to be written is the number of total fish--say 12) and can separate the fish equally among a number of ponds (the second number to be written--say 2). Students will count the number in each pond.

 For our example, students will write 12 ÷ 2 = 6

Multiplication Record Sheet
 
 

Division Procedure and Extension

GRADE LEVEL: 4

LESSON PURPOSE: To learn the division concept and to apply it

OBJECTIVES:

Students will learn the concept behind division through being taught the "fishes in a pond" method (having a coffee filter for a pond with schools of fish in cupcake holders to understand the concept of division.)

Students will apply the division concept to functions as they solve given division problems and create their own problems.
 
 

 ANTICIPATORY SET: First discuss ponds, lakes, the sea and the fish in them. Relate to experiences seeing fish, catching fish or any previous knowledge about fish. Talk about schools of fish how they swim in the water. Talk about how you can have more than one school of fish in one lake or pond. Demonstrate how 20 fish in a pond could be in 4 schools of 5 fish. Discuss the proper use of the goldfish, coffee filters and the cupcake holders. Inform the students they will be able to eat their schools of fish after they are done.
 
  Activities and Procedure:
  1. Model how to use cards, manipulatives, and record sheet. Model division problems as you do the problem on the card. For example, there was only 32 goldfish in the pond. They split up into schools of 6. How many schools of goldfishes were there, how many were left over?
  2. Ask children what I needed to do to find how many schools were in the pond and why were there some left over. What is this called - division? Talk to students about what division means.
  3. Pass out materials
  4. Have students work on their card set and have them record their answers on record sheet.
  5. Collect record sheets for evaluations.
Tying It All Together and Extensions:
  1. Ask class what division means and how it is like multiplication.
  2. Have children make up story problems to exchange.
NAME:___________________________

# of Goldfish (Total) # of Schools # of Goldfish (in Schools) Left Over Goldfish

1. _____________ __________ ______________ _________

2. _____________ __________ ______________ _________

3. _____________ __________ ______________ _________

4. _____________ __________ ______________ _________

5. _____________ __________ ______________ _________

6. _____________ __________ ______________ _________

7. _____________ __________ ______________ _________