Recording Related Facts

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The SWBAT identify related facts within 20.

Big Idea

In this lesson the children begin to make the connection that two addition sentences are related through the commutative property.

Activating Strategy

10 minutes

I like to start this lesson by giving students 20 connecting cubes (10 each of two different colors) and allowing them to create their own addition sentence.  I then ask them to break off one color to represent the corresponding subtraction fact.  I like to then have a discussion about how their addition fact is related to the subtraction fact. 

The idea of this lesson is to get the students to begin to understand that a subtraction fact is related to two addition facts.  Begin by giving the students a simple addition problem.  

(Can also be found in the resources section Recording Related Facts model)  For example:  Mike has 7 cookies.  He gets 1 more cookie.  How many cookies does he have now? 

Guide the students to determine what information they need to find, and how they can make a model to show it.  For example:

  • What do we need to find?  (how many cookies Mike has now)
  • How can we use our connecting cubes to find the answer? (I can make a cube train of 7 cubes and then add 1 more)

In order to get the students to understand the related subtraction fact, using the same example above, I like to then introduce a related subtraction fact.  For example:  Mike has 8 cookies.  He gives one to Jane.  How many cookies does he have now?

I guide the students to understand how the two examples are related.  For example, using the following questioning techniques:

  • How is this problem like the first one?  (Mike gets 1 cookie in the first problem, and he gives away 1 cookie in the second problem.)
  • Since we added in the first problem, what do we need to do in the second problem? (we need to subtract 1 from 8)
  • How can we use our cubes from the first problem to find the answer to the second problem? (we can take 1 cube away from our cube train)  

Teaching Strategies

20 minutes

The next step is to get students to model two related addition facts and two related subtraction facts.  By using models, the students will see a visual representation of how fact families are related.

For example, using connecting cubes have students model another addition sentence using two different colors (4 red + 5 blue and 5 red + 4 blue).  The point of this is to get students to understand the commutative property by using a model.  I would then ask the students how the cube trains look the same, and how they look different.  The idea is to guide the students to understanding that the addition sentences are the same, but in a different order.  I like to write the two addition sentences on the board, using two different colored markers to add to the visual representation.  We then explore the related subtraction facts.  Using the same cube train models, we show that 9-5 and 9-4 are related to our addition models.

Continue guiding the student using cube train models to demonstrate how addition and subtraction facts are related.  Here are some examples:

8 + 7 = ___                            7 + 8 = ___                15 – 8 = ___              15 – 7 = ___


5 + 9 = ___                            5 + 9 = ___                14 – 9 = ___              14 – 5 = ___


7 + 6 = ___                            6 + 7 = ___                13 – 7 = ___              13 – 6 = ___


Once students have an understanding of the concept of related facts, I like to put them with a shoulder partner.  Have students create an addition sentence and their shoulder partner will write the related subtraction fact.  The benefit of having students create their own addition sentence will further deepen their understanding of fact families.

 We then gather back on the carpet and learn the song about fact families:

Independent Practice

20 minutes

For the independent practice portion of this lesson, I use the Recording Related Facts worksheet

For those struggling students, I pulled them in a small group and used number cards to demonstrate fact families.  Each student had a set of the same number cards, we then manipulated the cards to show the two addition sentences and two related subtraction sentences.

For example:  I used 7, 3, and 10 cards (or index cards, or post it notes) 

Example 1

Example 2

Example 3

Example 4


10 minutes

To close out the lesson, I like to gather back on the carpet.  I then have students share with their shoulder partner how knowing an addition sentence will help them know the related subtraction sentence.