Illuminations: How Many More Fish?

How Many More Fish?

Fact Family Fun

In this lesson, the relation of addition to subtraction is explored with fish-shaped crackers. The students search for related addition and subtraction facts for a given number and also investigate fact families when one addend or the difference is 0.

Learning Objectives
 
Students will:
  • find missing addends
  • review the additive identity
  • generate fact families given two addends or given one addend and the sum

Materials
 
Fish-shaped crackers in resealable bags
Paper plates
Yarn
Paper and crayons
Fact Families Activity Sheet

Instructional Plan

Name two numbers, each less than 10. Then call on a volunteer to make sets of fish-shaped crackers corresponding to the numbers. It may be helpful to make the sets on different colored plates or to surround them with different colored yarn loops. Next have the student write as many addition sentences as he or she can. (If the numbers are not the same, two addition sentences are possible. For example: 1 + 9 = 10, 9 + 1 = 10] Then ask each student to use the sum and each addend to write as many subtraction sentences as they can. [In the example, the subtraction sentences would be 10 – 1 = 9; 10 – 9 = 1.)

Name a difference (for example, 4) and have each student show you the meaning of the operations for the subtraction sentence by making two sets of crackers so that one set has four more crackers than the other. [There will be several answers to this question. Encourage the students to find as many ways as they can. Some pairs will be 6 and 2, 3 and 7, and 4 and 8.] Repeat with other differences, including 0.

Next, have the students put six crackers on one plate and two on the other. Ask them to describe the relationship between the plates using a subtraction sentence and the related addition sentences. (For example, 6 - 2 = 4; 4 + 2 = 6; 2 + 4 = 6) When the students are ready, ask them to identify the addends, the sum, and the difference. Then ask what subtraction sentence can be made with the sum and the other addend. Tell them that this set of equations is called a fact family.

Then assign the students to pairs, provide them with the Fact Families activity sheet, and have them take turns making plates, recording the sums and addends, and writing equations.

Fact Families Sheet Fact Families Activity Sheet

After the students have recorded several fact families, be sure all the students have additional experiences with the additive identity by asking the students to compare two plates, one with zero fish-shaped crackers on it and one with seven crackers, and to write the related addition and subtraction sentences. [The equations will be 7 - 0 = 7; 0 + 7 = 7 ; 7 + 0 = 7] Now ask the students to make two plates each with seven crackers on them, then record the comparison and the two addition sentences. [The equations this time will be 7 - 7 = 0; 0 + 7 = 7; 7 + 0 = 7].

Then call the class together, and ask a volunteer to choose one row from the Fact Families activity sheet and demonstrate what the two plates would look like. Ask his or her partner to write the number sentences that the plates suggest. You may wish to repeat this with other volunteer pairs. Now invite one of the students to make two plates, each one with three fish-shaped crackers on it, and write the related addition and subtraction sentences in the 3, 3, 6 family. [There will be only one of each, 3 - 3 = 0; 6 - 3 = 3.] Finally, ask the students to record a set of number sentences about one of the rows they completed and illustrate it by drawing pictures of two plates that they made.

Questions for Students
 

    If you know that one plate has eight fish-shaped crackers on it and another has three fish-shaped crackers on it, how many more are in the plate with eight crackers?

    How many addition and subtraction facts can you write if you compare a plate holding three crackers and one holding five crackers? How are the facts alike? How are they different?

    Suppose I make a plate with four fish-shaped crackers and a second plate with four fish-shaped crackers. What sentences will describe a comparison of the plates?

    How could you help a friend find addition sentences related to 5 - 2 = 3? To 4 – 0 = 4?

    What addend pairs can you find for a difference of 2? What subtraction sentences do they suggest? How would you model the comparison?

Assessment Options
 
  1. The documentation you have made on the Class Notes recording sheet will be valuable as you plan appropriate remediation and enrichment opportunities for the students.

Extensions
 
  1. [A Challenge Question] Suppose I tell you that 7 is 3 more than some number. Can you write the number sentence that says that? [7 = 3 + _.] If I said 7 is 3 less than a number, what number sentence can you write? [7= _ - 3.]
  2. [A Challenge Question] How could you explain to a classmate how to find all the members of a fact family?

Teacher Reflection
 
  • Did most of the students remember the effects of adding or subtracting 0?
  • Which students were able to generate subtraction equations if they were given 2 sets to compare? Which were able to generate the related addition equations? Which students could identify addends, sums, and differences, and use this vocabulary appropriately?
  • Which students are still having difficulty with the objectives of this lesson? What additional instructional experiences do they need?
  • Which students are most dependent on the manipulatives? Which students are beginning to find the answers without them? (Encouraging the students to use manuipulatives when they need them and to compute without them when they are ready will help them build solid mathematical understandings.])
  • What will I do differently the next time that I teach this lesson?

NCTM Standards and Expectations
 
Number & Operations Pre-K-2
  1. Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
  2. Develop fluency with basic number combinations for addition and subtraction.
  3. Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.
  4. Understand the effects of adding and subtracting whole numbers.
  5. Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.
  6. Use multiple models to develop initial understandings of place value and the base-ten number system.
This lesson prepared by Grace M. Burton.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics
National Council of Teachers of Mathematics Thinkfinity Verizon Foundation
More and Better Mathematics for All Students
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