What are Math Fact Families

Recipe updated: April 5th, 2024

Hello, my name is Ken Ray, and I have a master’s degree in elementary education. I have taught every primary grade from pre-kindergarten jumpstart to second grade. Usually, children are introduced to fact families in first grade math. The specific purpose of math fact families is to help students understand how addition and subtraction facts are connected. In this post, I will teach you the basic facts every 1st grade and 2nd grade student should know about fact families.

💡 Understanding Math Fact Families

To understand math fact families, you must understand the pieces of a math equation. The basic pieces of a math equation include 2 parts and the whole. These 3 pieces can be represented in a variety of ways depending on the type of math equation you are being presented with.

🔢 Part – Part – Whole

The basic idea of a fact family triangle is that you are stating the 3 pieces, part-part-whole, of math without the actual equation (addition or subtraction). For instance, 1 + 2 = 3 is a simple math equation. In an addition equation, the two parts are connected with the + sign and the whole is by itself on the other side of the = sign. The same addition sentences can look like 3 = 2 + 1. This does not change the whole or the 2 parts, it just changes how it is read.

The fact family in this scenario is (1,2,3). You just take the three numbers out of the equation. The whole number will always be the largest number in the fact family. The smaller numbers are the parts.

How is Knowing This Useful

Knowing math fact families lets you solve subtraction much easier. Subtraction fact families is usually a tougher skill to learn. Once you know that 1,2,3 is a fact family, with 1 being a part and 2 being a part, 3 is the whole through addition, a subtraction fact family becomes easier. All you have to do is know the subtraction equations for Part-Part-Whole and you have your answer. In subtraction, the equation is Whole – Part = Part, so 3 is the whole. The whole always goes first. Depending on the setup of the equation just plug in the missing numbers of the fact family piece.

3 – 2 = ?

2 = ? – 1

3 – ? = 1

1 + ? = 3

3 = 2 + ?

Being equipped with the fact family of 1,2,3 and part-part-whole strategy, it makes all of these equations relatively simple.

Learning Fact Families

Initially, you must learn the basics of addition. 1 apple plus 2 apples make 3 apples. Seeing the different groupings is called subitizing. Once you have learned how to count and recognize how many apples you have, this is where you can start learning fact families. I teach part–part–whole on a regular basis. Print out number bonds and part-part-whole models. Put them in plastic sleeves and have your child use dry-erase markers to save paper. Then you can put the problems in the 2 models and have your child pull out the fact families. I would start with addition as that is the easiest for most students.

First, let’s take the example, 5 + 4 = __. If your child knows how to do simple addition, then finding the fact family is very simple.

5 + 4 = 9 therefore, the fact family is 5,4,9. You can rearrange the fact family in a number of ways. Part + Part = Whole and Whole – Part = Part.

5 + 4 = 9

4 + 5 = 9

9 – 5 = 4

9 – 4 = 5

Now that you know what fact families are, you deserve a cookie! I recommend the Ranger cookie!

Fact Families Connection to Number Lines

Number lines show fact family relations in a concrete way. The whole number will always be the largest number. The parts are represented by the starting point on the number line and the number of spaces used to get to the whole number. This is a great way for students to solidify their understanding of both the part-part-whole and fact families concepts. Once they understand the concepts you can test your child by giving them a set of numbers and having them plot the numbers on the number line.

Which Math Fact Families Should We Learn First?

Start with easy ones first and then progress with ones that will lead to more complex strategies. You could do the Plus 1 fact families. The Plus 1 fact family will always have a 1, so kids only have to connect 1 or 2 new numbers in the family. Learning the Plus 1 fact family will also give your child a better number sense as they will better understand immediately that 1 more than 5 is 6 and one less than 6 is 5.

Group of Math Facts with Plus 1 Examples:

1 + 0 = 1	0 + 1 = 1	1 – 0 = 1	1 – 1 = 0
1 + 1 = 2	1 + 1 = 2	2 – 1 = 1	2 – 1 = 1
1 + 2 = 3	2 + 1 = 3	3 – 1 = 2	3 – 2 = 1
Continue	with	the	pattern
1 + 9 = 10	9 + 1 = 10	10 – 1 = 9	10 – 9 = 1

The next anchor I would use is the Make 10 facts as this will be an extremely useful skill in addition and also has a 10 in every equation. The only difference is that the 10 is the whole piece.

Make 10 Fact Family Numbers Examples:

0 +10 = 10	10 + 0 = 10	10 – 0 = 10	10 – 10 = 0
*1 + 9 = 10	9 + 1 = 10	10 – 1 = 9	10 – 9 = 1
2 + 8 = 10	8 + 2 = 10	10 – 2 = 8	10 – 8 = 2
3 + 7 = 10	7 + 3 = 10	10 – 3 = 7	10 – 7 = 3
4 + 6 = 10	6 + 4 = 10	10 – 4 = 6	10 – 6 = 4
5 + 5 = 10	5 + 5 = 10	10 – 5 = 5	10 – 5 = 5

(*Your child should recognize this one from the plus 1 fact family)

🥳 A Fun Way to Learn Math Fact Families

A fun way to learn basic addition and subtraction problems is to use M&Ms with the kids while teaching math fact families. Create fact family cards by writing numbers 0-9 on separate pieces of paper for each number. Randomly select a number and put the same color M&Ms to match the number on the corresponding piece of paper. Repeat this step using a different color of M&M to match the number on the paper. Have the students combine both colors and count the total. Have the students subtract one color of M&Ms from the total to see what is left. This number should equal the other part. Conclude this fun way of learning by eating the M&Ms! The kids will love it!

✅ Conclusion

Hopefully, this post has helped you understand what math fact families are and has explained their usefulness in understanding the connection between addition and subtraction. If a child knows his/her addition facts and math fact families, then he/she can solve 9 – 5 = _ without even knowing how to subtract because they can now flip the equation to an addition sentence 5 + _ = 9, the answer is 4. I routinely use these concepts to build fact fluency in my math small groups during morning work.

There are a lot of games and fact family worksheets out there, so I didn’t include any in this post. If you are looking for some you could go to Pinterest or just search google, but I would recommend joining TPT. TeachersPayTeachers is a site you can join for free and download free material, there are resources you can pay for, but you can find what you need for free most of the time. Search for your topic, in this case, math fact families, and select the price free and it will pull up all of the material it has. Trust me, you won’t regret the one-minute sign-up!

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• Strategies for Addition – Teach your kids these 5 strategies to do mental math quickly and efficiently.