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Fact Family Fun

Number and Operations
Grace M. Burton
Location: unknown

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.

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.

pdficonFact 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.

Assessment Option

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.


  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?
  3. Move on the last lesson, Wrapping Up the Unit.

Questions for Students 

  1. 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?
  2. 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?
  3. 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?
  4. How could you help a friend find addition sentences related to 5 - 2 = 3? To 4 – 0 = 4?
  5. What addend pairs can you find for a difference of 2? What subtraction sentences do they suggest? How would you model the comparison?

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?
Number and Operations

Counting Back

Students count back to compare plates of fish-shaped crackers, and then they record the comparison in vertical and horizontal format. They apply their skills of reasoning and problem solving during this lesson in several ways. [Because students have associated the word "more" with addition, the comparative approach to subtraction is typically more challenging for the students to understand.]
Number and Operations

How Many More?

Students write subtraction problems, model them with sets of fish-shaped crackers, and communicate their findings in words and pictures. They record differences in words and in symbols. The additive identity is reviewed in the context of comparing equal sets.
Number and Operations

Hopping Backward to Solve Problems

In this lesson, students determine differences using the number line to compare lengths. Because this meaning is based on linear measurement, it is a distinctly different representation from the meanings presented in Lessons One and Two. At the end of the lesson, the students use reasoning and problem solving to predict differences and to answer puzzles involving subtraction.
Number and Operations

Balancing Equations

This lesson encourages the students to explore another meaning for operations of subtraction, the balance. This meaning leads naturally into recording with equations. The students will imitate the action of a pan balance and record the modeled subtraction facts in equation form.
Number and Operations

Wrapping Up the Unit

During this final lesson in the unit, the students use the mathematical knowledge and skills developed in the previous lessons as they visit five stations to review comparative subtraction.

Learning Objectives

Students will:

  • Find missing addends.
  • Review the additive identity.
  • Generate fact families given two addends or given one addend and the sum.

NCTM Standards and Expectations

  • Use multiple models to develop initial understandings of place value and the base-ten number system
  • Understand the effects of adding and subtracting whole numbers.
  • Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.
  • Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
  • Develop fluency with basic number combinations for addition and subtraction.
  • Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.

Common Core State Standards – Mathematics

-Kindergarten, Algebraic Thinking

  • CCSS.Math.Content.K.OA.A.5
    Fluently add and subtract within 5.

Grade 1, Algebraic Thinking

  • CCSS.Math.Content.1.OA.B.4
    Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.

Grade 1, Algebraic Thinking

  • CCSS.Math.Content.1.OA.C.6
    Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Grade 1, Number & Operations

  • CCSS.Math.Content.1.NBT.C.4
    Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

Grade 2, Algebraic Thinking

  • CCSS.Math.Content.2.OA.B.2
    Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

Grade 2, Number & Operations

  • CCSS.Math.Content.2.NBT.B.7
    Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Common Core State Standards – Practice

  • CCSS.Math.Practice.MP6
    Attend to precision.