Illuminations: Links Away

Links Away


Finding Fact Families

In this lesson, students explore the relation of addition to subtraction with books and links. Then the children search for related addition and subtraction facts for a given number. They also investigate fact families, including those where one addend is 0 and where the addends are alike.

Learning Objectives

 
Students will be able to:
  • relate addition to subtraction
  • generate fact families given two addends or given one addend and the sum

Materials

 
Counting Books
Ten in the Bed Lyrics
Links or Connecting Cubes (in two or more colors)
Student Slates or Whiteboards

Instructional Plan

To review the concept of subtraction, read Roll Over or There Were Ten in the Bed, or sing the song Ten in the Bed from the Song Lyrics sheet. For each part, ask a student to act out with links what is happening, and have each student write the related subtraction sentence on a slate.

Now read the first three pages of Quack and Count to the students, using 6 links in one color and 1 link in another to make a chain that illustrates the text on the first three pages (for example, 7 – = 6, 7 – 6 = 1, 6 + 1 = 7, 1 + 6 = 7). If you cannot obtain the book mentioned, have a volunteer tell a story that involves subtraction by taking sets away. Model as described above. Then write the fact family.

When the students seem comfortable with this procedure, distribute links of two colors to pairs of children and have them take turns making chains, taking away the indicated group of links, and writing equations as you finish the story or as additional volunteers give subtraction problems. This activity will help the students focus on the relation of subtraction to addition. When you get to the last page, have children model 7 – 7 and write the related addition and subtraction sentences (7 – 7 = 0, 0 + 7 = 7, 7 + 0 = 7) on slates.

Then call the class together and ask students to share what they think a fact family is. Invite one of the children to make a chain with 3 links of one color and 3 of another, and write the related addition and subtraction sentences (there will be only one of each). Finally, ask the students to write a fact family for one of the chains they made. This could be added to their portfolios to document their growth in understanding.

Questions for Students

 
What fact family can I write if I make a chain with 3 red links and 5 green links?
[I can write 8 – 3 = 5, 8 – 5 = 3, 3 + 5 = 8, 5 + 3 = 8.]

How are the facts in a fact family alike? How are they different?

[They are the alike because they all use the same numbers. They are different because the numbers are in different places. They are different because two equations are take away and two equations are addition.]

What is a fact family?

[A fact family is two addition sentences and two subtraction sentences with the same numbers. More specifically, a fact family is all the different addition and subtraction sentences you can write using three given numbers.]

How many addition and subtraction facts are in the fact family for a chain with 3 red and 3 blue links? Justify your answer.

[There is one addition sentence and one subtraction sentence: 6 – 3 = 3, 3 + 3 = 6]

How could you help a friend find a subtraction fact related to 5 + 4 = 9?

[Use 5 links of one color and 4 links of another color. Then, take away the 4 links and ask how many are left.]

Assessment Options

 
  1. The Assessment Option is to monitor students as they write fact families on slates. Use the Class Notes recording sheet to record whether students are emerging or mastering this skill.

Extensions

 
  1. For students who need extra support recognizing and writing fact families, place 10 two‑color chips in a cup. Have students shake up the cup and spill its contents in a shoe box lid. Then have students write the fact family illustrated by the two‑color chips. For instance, if a student spills 4 red and 2 white chips, she could write 6 – 4 = 2 and 4 + 2 = 6.

Teacher Reflection

 
  • Which students have some of the facts memorized?
  • Did most students remember the effects of adding or subtracting 0?
  • Which students met all the objectives of this lesson? What extension activities are appropriate for those students?
  • Are students prepared to move on or do they need more practice?
  • How can you incorporate/reinforce these skills in daily classroom routines?
  • Did students relate representations and terminology to previous experiences/lessons?

NCTM Standards and Expectations

 
Algebra Pre-K-2
  1. Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.
This lesson prepared by Grace M. Burton.
  
1 period   

NCTM Resources

Navigating through Number in preK‑2


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