Summary
Understanding fact families in math and how they help with the understanding of the relationship between addition and subtraction and multiplication and division math facts.
Are you wondering what are the fact families and how they are so powerful? I’ll delve into what fact families are and why they play a crucial role in building number sense. We will explore how fact families help students understand the relationship between addition and subtraction and multiplication and division, laying a solid foundation for future math concepts.
With easy-to-understand explanations, practical examples, and helpful tips, this guide will equip you with the knowledge and tools to teach fact families effectively. Discover engaging activities and games to make learning fun and reinforce the concept.
- ☀Download this BONUS Guide with everything you need to cultivate a positive classroom community.
- ➕Includes definitions, lesson ideas, mindset surveys for students and teachers, and printable posters.
- 🧠💪Research shows a link between a growth mindset and math success. Kids with a growth mindset about their abilities perform better and are more engaged in the classroom.
- 👉Includes everything you need to start cultivating a more positive math classroom and students who love math. Download and get started today! Click here to download the Mindset Guide & Survey.
What is Number Sense in Mathematics?
Number sense refers to understanding number concepts, operations, and applications of numbers and operations. It is the ability to be flexible with numbers and have a variety of strategies to use. Students know how to use and adapt the strategy to meet different situations.
Flexible and fluent thinking with numbers is necessary for students to develop an understanding of math concepts. It is the building block of mathematics, and learning fact families is a great way to develop number sense.
How to Build Number Sense
Children with good number sense enjoy playing with and exploring numbers. Putting numbers together and taking them apart (composing and decomposing numbers), and finding the parts of a whole (part-part-whole) are ways to help students become flexible in their thinking.
These Part-Part-Whole activities are a great way to practice this strategy. Click HERE to see them.
Talking, playing, and solving math throughout the day—not just during math class—builds number sense and a love of mathematics.
Get this Freebie of 71 Math Puzzles to use with your students. These are great for warm-up, whole class, small group, or independent work. In addition, you can print and put the puzzles up on a bulletin board. Then, have strips of paper for students to write down their answers. It is a great early-finisher activity and allows students to see math as fun.
Read more at How to Use Engaging Math Puzzles for Fun to Build Number Sense.
Foundation for Understanding Fact Family Addition
Composing and decomposing numbers and using the part-part-whole model are the foundations for learning fact families. This helps students understand how sets of numbers relate to each other.
Compose and Decompose Numbers Break Down
It involves helping children break numbers into parts (decompose) and back together ( compose). For example, a student who can compose and decompose numbers understands that 1 and 3 together make 4 and can break 4 into 1 and 3.
It is important to use concrete and pictorial representations to understand that numbers can be put together and taken apart in various ways. Students need many opportunities with numbers up to 5 and later extending to 10. This forms the foundation for future work with place value and helps students develop mental images and strategies as they work with basic facts.
Read more… Discover Fun and Exciting Activities and Unpack What is Decomposing in Math?
What is Part-Part-Whole Math?
The part-part-whole model represents a problem that helps students see the relationship between a “whole” and its components. Partitioning is the act of splitting a number into parts.
Children using this model will see the relationship between the whole number and its parts, helping learners to make the connections between addition and subtraction, as well as fact families.
Read more.. How to Use the Powerful Part-Part-Whole Strategy to Improve Number Sense
What are Addition 1 Digit Facts?
Facts with addends of 0-10 are considered basic facts. Sometimes, 0-9 are considered basic facts.
As math teachers, we want our students to become fluent in addition 1, digit, and subtraction facts. We call these basic math facts because they provide the foundation for more complex problems.
Students should develop both automaticity and an understanding of math facts. Automaticity is a student’s ability to recall a fact effortlessly. We also want our students to understand these essential facts. Here is a breakdown of when students are expected to have automaticity with their basic facts. Seeing how facts are related into fact families makes learning the facts so much easier.
Read more… 3 Guaranteed and Fun Resources to Practice Addition 1 Digit Problems with Students
Addition and Subtraction Facts to 20 Standard
2.OA.B.2 Fluency add and subtract within 20 using mental strategies. By the end of Grade 2, know all sums of two one-digit numbers from memory. Students should review and extend strategies with explicit activities connected to facts using concrete materials, number lines, and the hundred chart for addition and subtraction facts with sums to 20.
By understanding the communicative property fact families, students see there aren’t really that many facts to learn!
Read more… 7 Guaranteed Effective Teaching Strategies For Add And Subtract Facts
math-fact-practice-sheetMultiplication Facts to 100
Students begin by modeling multiplication and division situations using concrete models, pictorial representations, and number lines. They solve various multiplication and division problems focusing on the meaning of numbers in the situation and identifying what they know (number of groups, number of items in a group, or total number) and use that information to figure out that they do not know.
They progress to writing equations for those situations. This all leads to fluently multiplying and dividing within 100. Just like addition and subtraction, they will learn to understand how multiplication and division are related and understand the fact families.
Grade 3 Multiplication
3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division. By the end of Grade 3, know all products of two one-digit numbers from memory.
Read more.. Do You Need Exciting and Fun Online Multiplication Fact Practice Ideas and Games?
Array Multiplication Definition
An arrays math definition is a number of mathematical elements that are arranged in rows and columns.
A multiplication array is simply an arrangement of rows or columns that matches a multiplication equation. You can make arrays out of objects or pictures, and you can use any sort of shape.
3 rows of 5 or 3 X 5= 15
Reasons to Use Multiplication Arrays
Multiplication arrays make it easy to visualize multiplication problems.
Arrays show a number of objects in rows and columns. Then, they can use the array and repeated addition to come up with the total. ______ rows of _______.
Multiplication arrays make it easy for kids to see the commutative property.
The commutative property says you can multiply numbers in any order and still get the same answer. For example, 2 × 7 and 7 × 2 equal the same answer: 14.
To show your child this fact, use the dot array to show a multiplication fact. Then, turn the array 90 degrees. The dot array shows the related multiplication fact, but the number of dots didn’t change. These arrays also help students see the total, divided into rows and columns, which connects to division and forms a fact family.
Read more.. What’s a Multiplication Arrays Math Definition and Fun Activities to Use?
Understanding the Concept of Fact Families
A fact family is a collection of math facts that express the relation between the same set of numbers. It is also known as a “number family” and generally uses three numbers.
It helps to understand basic arithmetic operations (addition, subtraction, multiplication, and division) and solve their problems.
Fact Family Definition
A collection of related facts involving the same numbers.
What is a Fact Family?
Most addition and subtraction fact families include two addition and two subtraction facts. What is the addition/subtraction fact family for the numbers 7, 8, and 15?
7 + 8= 15, 8 + 7= 15, 15 – 7=8, 15 – 8= 7.
Most multiplication and division fact families include two multiplication and two division facts.
What is the fact family of 15, 5, and 3?
5 X 3= 15, 3 X 5 = 15, 15 / 3= 5, 15 / 5 = 3
Importance of Fact Families in Math Education
Fact families play a significant role in math education by providing a structured approach to learning basic arithmetic operations. Students can better comprehend mathematical concepts by understanding how numbers are related through fact families. This understanding goes beyond memorization and encourages critical thinking and problem-solving skills.
In addition, fact families promote number sense by emphasizing the relationships between numbers. Students gain a holistic view of numbers and operations, enabling them to make connections and apply mathematical concepts in different contexts. This holistic approach fosters a deeper understanding of math and promotes mathematical reasoning and logical thinking skills.
How to Identify Fact Families
Identifying fact families involves recognizing the group of related math facts that revolve around a set of numbers. To determine the members of a fact family, you need to identify the three interconnected numbers through addition and subtraction operations. For instance, in the fact family 5, 2, and 7, the related facts include 5 + 2 = 7, 2 + 5 = 7, 7 – 2 = 5, and 7 – 5 = 2.
One approach to identifying fact families is to list all the addition and subtraction combinations for a given set of numbers. Systematically exploring these combinations can uncover the relationships between the numbers and form the corresponding fact family.
Why Teach the Basic Math Facts in Terms of Fact Families?
Math fact families can be a gateway to greater mathematical understanding for students. In addition, understanding the commutative property reduces the number of basic math facts (equations with single-digit numbers) that need to be learned in half. Understanding the relationship of inverse math operations makes learning subtraction and division facts simply a matter of reversing equations.
Understanding of the Commutative Property and Fact Families
When students begin thinking in terms of math fact families or math fact family triangles, they are being given their first introductions to the commutative properties of both addition and multiplication.
- The commutative property of addition means that a + b = b + a; order does not matter in addition. For example, 7 + 4 = 4 + 7.
- The commutative property of multiplication is similar: a x b = b x a. Like with addition, order does not matter in multiplication. For example, 7 x 4 = 4 x 7. Like with commutativity in addition, when a student sees time, and again that order does not matter when working with the basic multiplication facts, they will feel confident in knowing that 8 x 7 can be considered as either 7 eights or 8 sevens, whichever happens, to be easier for them to solve.
Recognition of both of these commutative properties almost cuts the number of math facts in half that need to be learned. Students don’t have to learn 6 + 8 and 8 + 6; learning one means learning the other. The same, of course, would be true for 6 x 8 and 8 x 6.
Increased Understanding of the Inverse Relationship between Operations
When students see that they can make four equations with just the three numbers composing a math fact family, it helps them recognize that addition and subtraction (multiplication and division) are opposite operations: one undoes the other.
Thinking about fact families helps foster the mathematical understanding that one property of operations is that they have an inverse operation. The result is that students build number sense, and math fact learning is simplified.
Strategies for Teaching Fact Families
Encouraging students to practice identifying fact families through hands-on activities and visual aids can enhance their understanding and retention of math facts.
Another strategy is to use fact family houses or triangles to represent the relationships within a fact family visually. This visual representation can simplify identifying fact families and reinforce the connections between numbers.
Fact Family Triangle
Fact families are usually represented in the form of a triangle. The three numbers forming the fact family are written in the three corners (near the vertices) of the triangle.
The operation’s sign connecting the three numbers is usually written in the middle. For the addition fact family, the sum of the numbers is generally written at the top vertex, and the numbers being added are written at the vertices at the bottom.
Fun and Interactive Activities for Practicing Fact Families
Both these activities are building blocks for learning about fact families.
Arrays Project– Students build multiplication arrays with tiles and then color on the multiplication with arrays worksheets.
Multiplication Arrays Worksheets and Slides– Use the counters to represent the multiplication problems equal group or use the multiplication arrays worksheet. Then, fill in the addition and multiplication equation for each repeated addition leading to multiplication problem.
Decompose and Compose Numbers– Decompose and compose numbers with 6 sets of Google Slides. This Bundle has 6 sets with 80 slides with compose and decompose numbers with several different formats. These slides build number sense with students. Composing and decomposing numbers to 10 into multiple ways is an important number sense activity.
Resources and Tools for Teaching Fact Families
Part-Part-Whole Mat Activity– Students identify the part that is shown and the part that is covered and enter the numbers in the text boxes. Part-part-whole activities are great for warm-ups, whole group, or small-group instruction. Students use addition or subtraction to find the missing part. This shows students how addition and subtraction are related by using part-part-whole mats.
Math Fact Practice Sheet Slides– In each set there are 16 addition fact practice slides with ten frames and counters. There are 24 subtraction fact practice –12 with movable pieces, 12 with text boxes. These slides help students to practice their addition and subtraction facts.
Easier Learning of the Basic Math Facts
Counting all four math operations, there are close to 500 basic math facts that students are expected to develop fluency with. Consider how bewilderingly daunting it would be to have to memorize 500 facts.
- ☀Download this BONUS Guide with everything you need to cultivate a positive classroom community.
- ➕Includes definitions, lesson ideas, mindset surveys for students and teachers, and printable posters.
- 🧠💪Research shows a link between a growth mindset and math success. Kids with a growth mindset about their abilities perform better and are more engaged in the classroom.
- 👉Includes everything you need to start cultivating a more positive math classroom and students who love math. Download and get started today! Click here to download the Mindset Guide & Survey.
When students learn the commutative property, that huge number is cut almost in half. When students understand inverse operations, that number gets cut by about half again. Thinking (and teaching) with math fact families in mind reduces the task by almost three-fourths! (From there, a range of math fact strategies will dramatically reduce that number further.) What are the fact families activities you want to use with students?
