Solved Exercises on Fact Families in Grade 2

Master fact families: addition and subtraction relationships, fact family triangles, number bonds, related facts within 20 through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic fact family
Exercise 1
Write the fact family for the numbers 5, 3, and 8.
Definition:

Fact family: A group of related addition and subtraction facts using the same three numbers.

Fact family method:
  1. Use the three numbers to create two addition facts
  2. Create two subtraction facts using the same numbers
  3. Verify that all facts are related
8
5
3
5 + 3 = 8
→
3 + 5 = 8
→
8 - 5 = 3
→
8 - 3 = 5
Step 1: Write the addition facts

5 + 3 = 8 and 3 + 5 = 8

Step 2: Write the subtraction facts

8 - 5 = 3 and 8 - 3 = 5

Step 3: Verify all facts are correct

Check: 5 + 3 = 8 ✓, 3 + 5 = 8 ✓, 8 - 5 = 3 ✓, 8 - 3 = 5 ✓

5 + 3 = 8
3 + 5 = 8
8 - 5 = 3
8 - 3 = 5
Final answer:

The fact family for 5, 3, and 8 includes: 5 + 3 = 8, 3 + 5 = 8, 8 - 5 = 3, 8 - 3 = 5.

Applied rules:

• Family principle: Three numbers create four related facts

• Commutative property: Addition can be done in either order

• Inverse relationship: Addition and subtraction are inverse operations

2 Fact family triangle
Exercise 2
Complete the fact family triangle for 6, 4, and 10.
Definition:

Fact family triangle: A visual representation showing the relationship between three numbers in a fact family.

10
6
4
Step 1: Identify the largest number

10 is the largest number, goes at the top

Step 2: Place the smaller numbers at the bottom

6 and 4 go at the bottom corners

Step 3: Write the addition facts

6 + 4 = 10 and 4 + 6 = 10

Step 4: Write the subtraction facts

10 - 6 = 4 and 10 - 4 = 6

6 + 4 = 10
→
4 + 6 = 10
→
10 - 6 = 4
→
10 - 4 = 6
Final answer:

The fact family triangle shows: 6 + 4 = 10, 4 + 6 = 10, 10 - 6 = 4, 10 - 4 = 6.

Applied rules:

• Triangle placement: Largest number at top, smaller numbers at bottom

• Addition facts: Bottom numbers add to top number

• Subtraction facts: Top number minus bottom number equals other bottom number

3 Missing fact in family
Exercise 3
Complete the fact family: 7 + 5 = 12, 5 + 7 = 12, 12 - 7 = ?, ? - ? = ?.
Definition:

Missing fact: Finding the unknown equation in a partially completed fact family.

7 + 5 = 12
→
5 + 7 = 12
→
12 - 7 = 5
→
12 - 5 = 7
Step 1: Identify the three numbers

The numbers are 7, 5, and 12

Step 2: Complete the known facts

7 + 5 = 12 and 5 + 7 = 12 (addition facts)

12 - 7 = 5 (given subtraction fact)

Step 3: Find the missing subtraction fact

12 - 5 = 7 (top number minus other bottom number)

Step 4: Verify all four facts

7 + 5 = 12 ✓, 5 + 7 = 12 ✓, 12 - 7 = 5 ✓, 12 - 5 = 7 ✓

7 + 5 = 12
5 + 7 = 12
12 - 7 = 5
12 - 5 = 7
Final answer:

The missing fact is: 12 - 5 = 7. The complete fact family is: 7 + 5 = 12, 5 + 7 = 12, 12 - 7 = 5, 12 - 5 = 7.

Applied rules:

• Completeness principle: Every fact family has exactly four related facts

• Pattern recognition: Use known facts to deduce missing ones

• Verification: Always check that all four facts are correct

Fact Families Rules and Methods
5 + 3 = 8, 3 + 5 = 8, 8 - 5 = 3, 8 - 3 = 5
Complete Fact Family
Rule 1
3 numbers = 4 facts
Always same numbers
Rule 2
2 addition facts
Order doesn't matter
Rule 3
2 subtraction facts
Start with largest
Key definitions:

Fact family: A set of related addition and subtraction facts using the same three numbers

Related facts: Addition and subtraction equations that use the same numbers

Fact family triangle: A visual tool showing the relationship between three numbers

Missing fact: An unknown equation in a partially completed fact family

Complete methodology:
  1. Identify the three numbers: Find the numbers in the fact family
  2. Write addition facts: Two facts using commutative property
  3. Write subtraction facts: Two facts starting with largest number
  4. Verify completeness: Ensure all four facts are correct
Tip 1: Always start with the largest number in subtraction facts.
Tip 2: Addition facts can be written in either order (commutative property).
Tip 3: Use fact family triangles to visualize the relationships.
Tip 4: Check that addition and subtraction facts are inverses of each other.
Common errors: Forgetting to write all four facts, mixing up addition and subtraction, not using the same three numbers consistently.
Memory aid: "Family of 3 makes 4 facts" - three numbers create four related equations.
Rules to remember:

• Step 1: Every fact family has exactly 3 numbers and 4 facts

• Step 2: Two addition facts using the smaller numbers

• Step 3: Two subtraction facts starting with the largest number

• Step 4: Verify all facts use the same three numbers

a + b = c, b + a = c, c - a = b, c - b = a
General Fact Family
Solution: Exercises 4 to 5
4 Finding missing number
Exercise 4
If one fact in a family is 9 + 4 = 13, what are the other three facts?
Definition:

Deriving facts: Using one known fact to generate the complete fact family.

13
9
4
Step 1: Identify the three numbers from the given fact

From 9 + 4 = 13, the numbers are 9, 4, and 13

Step 2: Write the second addition fact

4 + 9 = 13 (commutative property)

Step 3: Write the first subtraction fact

13 - 9 = 4 (largest number minus first addend)

Step 4: Write the second subtraction fact

13 - 4 = 9 (largest number minus second addend)

9 + 4 = 13
→
4 + 9 = 13
→
13 - 9 = 4
→
13 - 4 = 9
Final answer:

The other three facts are: 4 + 9 = 13, 13 - 9 = 4, 13 - 4 = 9.

Applied rules:

• Derivation principle: One fact determines the entire family

• Commutative property: Addition facts can be reversed

• Subtraction principle: Start with largest number in subtraction

5 Word problem
Exercise 5
Tom has 15 marbles. He gives 6 to his sister. How many does he have left? Write the fact family for this situation.
Definition:

Word problem: A real-world scenario that can be represented by a fact family.

15
6
9
Step 1: Identify the numbers in the problem

Total marbles: 15, given away: 6, remaining: ?

Step 2: Solve the subtraction problem

15 - 6 = 9 marbles left

Step 3: Identify the three numbers in the fact family

The numbers are 15, 6, and 9

Step 4: Write all four facts

6 + 9 = 15, 9 + 6 = 15, 15 - 6 = 9, 15 - 9 = 6

6 + 9 = 15
→
9 + 6 = 15
→
15 - 6 = 9
→
15 - 9 = 6
Final answer:

Tom has 9 marbles left. The fact family is: 6 + 9 = 15, 9 + 6 = 15, 15 - 6 = 9, 15 - 9 = 6.

Applied rules:

• Problem translation: Convert word problems to mathematical facts

• Context application: Apply fact families to real situations

• Completeness: Always write all four related facts

Fact Families Laws, Methods, and Definitions
a + b = c ↔ c - a = b and c - b = a
Inverse Relationship
Key definitions:

Fact family: A group of four related addition and subtraction facts using the same three numbers

Related facts: Addition and subtraction equations that share the same numbers

Fact family triangle: A visual representation showing the relationship between three numbers in a fact family

Commutative property: The order of addends does not affect the sum (a + b = b + a)

Inverse operations: Addition and subtraction are opposite operations that undo each other

Missing fact: An unknown equation in a partially completed fact family

Complete methodology:
  1. Identification: Find the three numbers involved in the fact family
  2. Addition facts: Write two addition facts using the smaller numbers
  3. Subtraction facts: Write two subtraction facts starting with the largest number
  4. Verification: Check that all four facts use the same three numbers
  5. Application: Use fact families to solve related problems
Tip 1: The largest number in a fact family is always the sum in addition facts and the minuend in subtraction facts.
Tip 2: Use the fact family triangle to visualize the relationships between numbers.
Tip 3: If you know one fact, you can derive all other facts in the family.
Tip 4: Always verify that addition and subtraction facts are inverses of each other.
Common errors: Forgetting to write all four facts, mixing up addition and subtraction, not using the same three numbers consistently, confusing the order of numbers in subtraction.
Memory aids: "Family of 3 makes 4 facts" and "Biggest number stays on top in subtraction."
Essential laws and rules:

• Family composition: Exactly 3 numbers and 4 related facts

• Addition facts: Two facts using commutative property (a + b = b + a)

• Subtraction facts: Two facts starting with the largest number

• Inverse relationship: Addition and subtraction are opposite operations

• Completeness principle: All four facts must be present in a complete family

8 + 2 = 10, 2 + 8 = 10, 10 - 8 = 2, 10 - 2 = 8
Example Fact Family
Visual representation: Fact family triangles help students understand the relationship between numbers.
Real-world connection: Fact families represent real situations like combining and separating groups of items.

Questions & Answers

Question: Why do we call them "fact families"? They're just numbers and equations.

Answer: Great question! They're called "fact families" because:

  • Like a family: The three numbers are related and belong together
  • Four "relatives": Just like a family might have parents and children, a fact family has four related facts
  • Connected: All four facts use the same three numbers, like family members sharing the same last name

Just like in a family, these numbers and facts are all connected and related to each other!

The "family" idea helps us remember that the facts are related and help each other.

Question: Why do we need both addition and subtraction facts in the same family? Why not just addition?

Answer: Addition and subtraction are like opposite actions - they help each other:

  • Addition: Puts numbers together (combining)
  • Subtraction: Takes numbers apart (separating)
  • Connection: If you know 5 + 3 = 8, then you know 8 - 3 = 5

Having both helps you:

  • Solve subtraction problems using addition facts
  • Check that your answers are correct
  • Understand that addition and subtraction are opposites

It's like knowing both how to build with blocks and take them apart!

Question: My child gets confused about which number should go first in subtraction. How can I help?

Answer: The largest number always goes first in subtraction facts:

  • In the fact family 5, 3, 8: The subtraction facts start with 8 (the largest)
  • Correct: 8 - 5 = 3 and 8 - 3 = 5
  • Incorrect: 5 - 3 = 8 (you can't take away more than you have)

Help your child remember:

  • The "biggest number" is always the "starting number" in subtraction
  • Use the triangle: largest number at the top
  • Think: "I start with the total and take away part of it"

Practice with physical objects to make it concrete!

Question: What happens if I only know one fact? Can I still figure out the others?

Answer: Yes! If you know one fact, you can figure out all the others:

  • If you know 4 + 6 = 10: The numbers are 4, 6, 10
  • Second addition: 6 + 4 = 10 (switch the order)
  • First subtraction: 10 - 4 = 6 (start with biggest, take away first number)
  • Second subtraction: 10 - 6 = 4 (start with biggest, take away second number)

One fact tells you:

  • What the three numbers are
  • How they relate to each other
  • All the other related facts

It's like having a map - one location helps you find all the others!

Question: Why do we learn fact families? Isn't it easier to just memorize each fact separately?

Answer: Fact families are actually easier and more helpful than memorizing separately:

  • Learn one, get four: Instead of memorizing 4 separate facts, you learn them as a group
  • Better understanding: You see how addition and subtraction connect
  • Problem solving: If you forget 8 - 5, you can think "5 + ? = 8"
  • Mental math: Helps you solve problems faster

Think of it like learning words that rhyme - once you know one, the others are easier to remember!

Fact families help you understand math, not just memorize it.