Skills without mastery are useless. Mastery is impossible without the right methods. BlitzGrok platform makes mastery effortless and fastest with proven, smart practice.
Skills without mastery are useless. Mastery is impossible without the right methods. BlitzGrok platform makes mastery effortless and fastest with proven, smart practice.
Ten Plus Facts
Understanding Teen Numbers
The numbers from 11 to 19 have a special name—we call them teen numbers. These numbers are unique because they're the first numbers we encounter that have two digits, and they all share something important: they all contain one ten plus some extra ones. Understanding "ten plus facts" is about recognizing this structure and using it to work with teen numbers confidently and efficiently.
What Are Ten Plus Facts?
Ten plus facts are addition equations where we start with ten and add a single-digit number (0 through 9). These facts create all the teen numbers:
- 10 + 0 = 10
- 10 + 1 = 11
- 10 + 2 = 12
- 10 + 3 = 13
- 10 + 4 = 14
- 10 + 5 = 15
- 10 + 6 = 16
- 10 + 7 = 17
- 10 + 8 = 18
- 10 + 9 = 19
Each teen number is simply ten plus some ones. This simple pattern is the foundation for understanding our entire number system!
The Structure of Teen Numbers
Every teen number can be broken down into two parts: one ten and some ones. Let's explore what this means.
Place Value Foundation
Understanding teen numbers helps you learn about place value—the idea that where a digit appears in a number determines its value:
- In the number 13, the 1 is in the tens place (representing 1 ten = 10)
- The 3 is in the ones place (representing 3 ones = 3)
- Together: 10 + 3 = 13
This pattern works for every teen number. The first digit always represents one ten (10), and the second digit represents the ones.
Visualizing with Base-Ten Blocks
Base-ten blocks help us see the structure of teen numbers: - A tens rod represents 10 (ten unit cubes stuck together) - Unit cubes represent ones - For 15: you'd have 1 tens rod + 5 unit cubes
This visual representation makes it crystal clear that teen numbers are composed of one ten plus some ones.
Why Ten Plus Facts Matter
Understanding ten plus facts is not just about knowing addition—it's about understanding how our number system works and developing mathematical thinking that will help you for years to come.
Building Number Sense
When you understand teen numbers as "10 plus something," you develop strong number sense: - You can quickly compose and decompose numbers - You see patterns in how numbers work - You can estimate and compare more easily - You understand the structure of larger numbers
Foundation for Place Value
Ten plus facts are your first introduction to place value, which is one of the most important concepts in all of mathematics: - Understanding that 15 = 10 + 5 prepares you for understanding that 150 = 100 + 50 - The same pattern continues: 1,500 = 1,000 + 500 - This pattern is the foundation of our entire number system!
Mental Math Speed
When you know ten plus facts automatically, you can: - Add and subtract teen numbers quickly in your head - Use strategies like "make ten" efficiently - Work with larger numbers more confidently - See shortcuts in calculations that others might miss
Strategies for Learning Ten Plus Facts
There are several effective strategies to help you master ten plus facts. Let's explore each one.
The "Teen" Name Pattern
Notice that most teen numbers have "teen" at the end of their name, and the first part tells you how many ones to add to ten:
- Thirteen: "thir" comes from "three" → 10 + 3 = 13
- Fourteen: "four" + "teen" → 10 + 4 = 14
- Fifteen: "fif" comes from "five" → 10 + 5 = 15
- Sixteen: "six" + "teen" → 10 + 6 = 16
- Seventeen: "seven" + "teen" → 10 + 7 = 17
- Eighteen: "eight" + "teen" → 10 + 8 = 18
- Nineteen: "nine" + "teen" → 10 + 9 = 19
The exceptions are eleven and twelve, which have unique names, but they still follow the pattern: 10 + 1 = 11 and 10 + 2 = 12.
Using Your Fingers and Hands
Your hands are perfect tools for learning ten plus facts:
Method 1: Two Hands - Hold up all ten fingers (this represents one ten) - Now think of adding more: if you could show 3 more fingers, you'd have 13 - This helps you visualize 10 + 3 = 13
Method 2: Counting On - Close your fists to represent ten - Now count on from ten using your fingers: "10" (fists closed), "11" (one finger up), "12" (two fingers up), etc.
Ten Frame Plus Some
A ten frame is a 2×5 grid that holds exactly ten items. To show ten plus facts: - Fill the entire ten frame (that's your ten) - Put additional items next to the ten frame (those are your ones) - Count the total to see your teen number
For example, to show 10 + 4 = 14: - Ten frame completely filled = 10 - Four items next to it = 4 - Total = 14
Number Line Strategy
A number line makes ten plus facts visual: - Mark 10 on your number line - Count forward the number of ones you're adding - Where you land is your teen number
For 10 + 6: - Start at 10 - Jump forward 6 spaces - Land on 16
The "Start at Ten" Strategy
Instead of counting from one, start at ten and count on: - 10 + 5: Start at ten, count "11, 12, 13, 14, 15" - You only need to count five more numbers, not fifteen numbers!
This strategy is much faster and helps build the understanding that teen numbers are built from ten.
Practice Activities
Make learning ten plus facts engaging and fun with these activities:
Teen Number Building
Materials: Base-ten blocks or drawing tools
Activity: 1. Choose a teen number (13-19) 2. Build it with one tens rod and the correct number of unit cubes 3. Write the equation: 10 + ___ = ___ 4. Try all the teen numbers!
Flash Card Fun
Materials: Index cards
Create cards with: - Front: "10 + 7 = ?" - Back: "17" - Make a complete set for 10 + 0 through 10 + 9 - Practice until you can answer instantly!
Teen Number Hunt
Activity: - Look for teen numbers around your home or classroom - Page numbers in books - Addresses - Prices - Sports scores - For each teen number you find, say the ten plus fact (like "17 is 10 + 7")
Partner Practice
Activity: - Partner says a teen number: "Fifteen!" - You respond with the ten plus fact: "10 + 5!" - Switch roles - Try to get faster each time
Dice Game: Make a Teen
Materials: Two dice (one standard, one labeled with 0-5 twice)
How to play: 1. Roll both dice 2. Add the numbers to 10 3. Say the complete equation (e.g., if you roll 4 and 3, say "10 + 7 = 17") 4. Challenge: How many different teen numbers can you make in 5 minutes?
Real-World Connections
Ten plus facts appear constantly in everyday life. Recognizing them helps you see math as useful and relevant.
Money
- A ten-dollar bill plus some one-dollar bills
- Ten dollars + four dollars = fourteen dollars ($14)
- This is literally 10 + 4 = 14!
Sports
- A basketball team scores 10 points, then 8 more points
- 10 + 8 = 18 points total
- Keeping score uses ten plus facts constantly!
Cooking and Recipes
- A recipe needs 10 tablespoons of flour plus 3 more
- 10 + 3 = 13 tablespoons total
- Cooking involves math all the time!
Age
- When you turn 13, 14, 15, or older, you're ten years old plus some more years!
- "I'm 12 years old" means "I've lived 10 years + 2 years"
Collections
- "I have 10 baseball cards in one binder and 6 in another"
- 10 + 6 = 16 total cards
- Organizing collections uses teen numbers!
Building Fluency
Fluency means you can recall and use ten plus facts quickly and accurately without struggling. Here's how to build it:
Daily Quick Practice
Spend just 3-5 minutes each day: - Morning: Review five ten plus facts - Afternoon: Test yourself on random facts - Evening: Quick review of any tricky ones
Gradual Progression
Week 1: Focus on 10 + 1 through 10 + 3 Week 2: Add 10 + 4 through 10 + 6 Week 3: Add 10 + 7 through 10 + 9 Week 4: Mix them all together!
Timed Challenges
- Set a timer for one minute
- Write as many teen plus facts as you can
- Check your answers
- Try to beat your record tomorrow!
- Celebrate improvement!
Multiple Representations
Practice in different ways: - Write equations (10 + 5 = 15) - Say equations out loud ("Ten plus five equals fifteen") - Draw pictures (ten frame + 5 dots) - Use physical objects (10 blocks + 5 blocks)
Different ways of practicing strengthen different connections in your brain!
Common Challenges and Solutions
Challenge: "I keep forgetting eleven and twelve"
Solution: These are special! Practice them separately first. Remember: - Eleven = 10 + 1 (sounds like "el-ev-en" - one more than ten) - Twelve = 10 + 2 (comes from "two left" after ten) Create a special flashcard just for these two.
Challenge: "I still count on my fingers from one"
Solution: This is okay at first! But try to transition: - Put ten in your mind (or show ten fingers closed) - Count just the extra ones - Gradually, you'll stop needing to count at all
Challenge: "I mix up the order"
Solution: Practice saying "ten plus [number]" every time: - Always start with "ten plus..." - This reminds you that ten comes first - The pattern becomes automatic
Connecting to Other Math Concepts
Understanding ten plus facts connects to many other important mathematical ideas:
Addition Within 20
Ten plus facts help with harder addition: - 7 + 8: I can think "7 + 3 = 10, then 10 + 5 = 15" - You used your knowledge of 10 + 5!
Subtraction from Teen Numbers
If you know 10 + 6 = 16, then you also know: - 16 - 6 = 10 (take away the ones, keep the ten) - 16 - 10 = 6 (take away the ten, keep the ones) - One addition fact teaches you two subtraction facts!
Understanding Larger Numbers
The same pattern continues with bigger numbers: - 20 + 5 = 25 (two tens plus five ones) - 30 + 7 = 37 (three tens plus seven ones) - 100 + 8 = 108 (one hundred plus eight ones)
Measurement
Teen numbers appear in measurement: - 14 inches, 16 cups, 18 centimeters - Understanding these as "10 plus something" helps with estimation and comparison
Assessment: Know You're Ready When...
You've mastered ten plus facts when you can: - ✓ Instantly say any teen number as a ten plus fact - ✓ Quickly find what to add to 10 to make any teen number - ✓ Explain why 14 is the same as 10 + 4 - ✓ Use ten plus facts to help with other addition problems - ✓ Recognize teen numbers in real-world situations - ✓ Build teen numbers with blocks or drawings
Looking Ahead
Mastering ten plus facts is a stepping stone to:
Two-Digit Addition
Understanding that 15 = 10 + 5 helps when adding: - 25 + 13: Think of this as (20 + 10) + (5 + 3) = 30 + 8 = 38
Understanding Hundreds
The same pattern continues: - 100 + 20 + 5 = 125 - It's still about combining groups (hundreds, tens, ones)
Algebra Preview
Writing 10 + 6 = 16 is actually an algebraic equation: - Later you'll write things like x + 6 = 16, and solve for x - You're building that foundation now!
Conclusion
Ten plus facts are simple but powerful. They help you understand how our number system works, build your confidence with teen numbers, and prepare you for more advanced mathematics. By seeing teen numbers as "ten plus some ones," you're not just memorizing—you're understanding structure and pattern, which is what mathematics is all about. Practice regularly, use visual tools when helpful, and celebrate your growing fluency. You're building a foundation that will support your mathematical learning for years to come!
Ten Plus Facts
Understanding Teen Numbers
The numbers from 11 to 19 have a special name—we call them teen numbers. These numbers are unique because they're the first numbers we encounter that have two digits, and they all share something important: they all contain one ten plus some extra ones. Understanding "ten plus facts" is about recognizing this structure and using it to work with teen numbers confidently and efficiently.
What Are Ten Plus Facts?
Ten plus facts are addition equations where we start with ten and add a single-digit number (0 through 9). These facts create all the teen numbers:
- 10 + 0 = 10
- 10 + 1 = 11
- 10 + 2 = 12
- 10 + 3 = 13
- 10 + 4 = 14
- 10 + 5 = 15
- 10 + 6 = 16
- 10 + 7 = 17
- 10 + 8 = 18
- 10 + 9 = 19
Each teen number is simply ten plus some ones. This simple pattern is the foundation for understanding our entire number system!
The Structure of Teen Numbers
Every teen number can be broken down into two parts: one ten and some ones. Let's explore what this means.
Place Value Foundation
Understanding teen numbers helps you learn about place value—the idea that where a digit appears in a number determines its value:
- In the number 13, the 1 is in the tens place (representing 1 ten = 10)
- The 3 is in the ones place (representing 3 ones = 3)
- Together: 10 + 3 = 13
This pattern works for every teen number. The first digit always represents one ten (10), and the second digit represents the ones.
Visualizing with Base-Ten Blocks
Base-ten blocks help us see the structure of teen numbers: - A tens rod represents 10 (ten unit cubes stuck together) - Unit cubes represent ones - For 15: you'd have 1 tens rod + 5 unit cubes
This visual representation makes it crystal clear that teen numbers are composed of one ten plus some ones.
Why Ten Plus Facts Matter
Understanding ten plus facts is not just about knowing addition—it's about understanding how our number system works and developing mathematical thinking that will help you for years to come.
Building Number Sense
When you understand teen numbers as "10 plus something," you develop strong number sense: - You can quickly compose and decompose numbers - You see patterns in how numbers work - You can estimate and compare more easily - You understand the structure of larger numbers
Foundation for Place Value
Ten plus facts are your first introduction to place value, which is one of the most important concepts in all of mathematics: - Understanding that 15 = 10 + 5 prepares you for understanding that 150 = 100 + 50 - The same pattern continues: 1,500 = 1,000 + 500 - This pattern is the foundation of our entire number system!
Mental Math Speed
When you know ten plus facts automatically, you can: - Add and subtract teen numbers quickly in your head - Use strategies like "make ten" efficiently - Work with larger numbers more confidently - See shortcuts in calculations that others might miss
Strategies for Learning Ten Plus Facts
There are several effective strategies to help you master ten plus facts. Let's explore each one.
The "Teen" Name Pattern
Notice that most teen numbers have "teen" at the end of their name, and the first part tells you how many ones to add to ten:
- Thirteen: "thir" comes from "three" → 10 + 3 = 13
- Fourteen: "four" + "teen" → 10 + 4 = 14
- Fifteen: "fif" comes from "five" → 10 + 5 = 15
- Sixteen: "six" + "teen" → 10 + 6 = 16
- Seventeen: "seven" + "teen" → 10 + 7 = 17
- Eighteen: "eight" + "teen" → 10 + 8 = 18
- Nineteen: "nine" + "teen" → 10 + 9 = 19
The exceptions are eleven and twelve, which have unique names, but they still follow the pattern: 10 + 1 = 11 and 10 + 2 = 12.
Using Your Fingers and Hands
Your hands are perfect tools for learning ten plus facts:
Method 1: Two Hands - Hold up all ten fingers (this represents one ten) - Now think of adding more: if you could show 3 more fingers, you'd have 13 - This helps you visualize 10 + 3 = 13
Method 2: Counting On - Close your fists to represent ten - Now count on from ten using your fingers: "10" (fists closed), "11" (one finger up), "12" (two fingers up), etc.
Ten Frame Plus Some
A ten frame is a 2×5 grid that holds exactly ten items. To show ten plus facts: - Fill the entire ten frame (that's your ten) - Put additional items next to the ten frame (those are your ones) - Count the total to see your teen number
For example, to show 10 + 4 = 14: - Ten frame completely filled = 10 - Four items next to it = 4 - Total = 14
Number Line Strategy
A number line makes ten plus facts visual: - Mark 10 on your number line - Count forward the number of ones you're adding - Where you land is your teen number
For 10 + 6: - Start at 10 - Jump forward 6 spaces - Land on 16
The "Start at Ten" Strategy
Instead of counting from one, start at ten and count on: - 10 + 5: Start at ten, count "11, 12, 13, 14, 15" - You only need to count five more numbers, not fifteen numbers!
This strategy is much faster and helps build the understanding that teen numbers are built from ten.
Practice Activities
Make learning ten plus facts engaging and fun with these activities:
Teen Number Building
Materials: Base-ten blocks or drawing tools
Activity: 1. Choose a teen number (13-19) 2. Build it with one tens rod and the correct number of unit cubes 3. Write the equation: 10 + ___ = ___ 4. Try all the teen numbers!
Flash Card Fun
Materials: Index cards
Create cards with: - Front: "10 + 7 = ?" - Back: "17" - Make a complete set for 10 + 0 through 10 + 9 - Practice until you can answer instantly!
Teen Number Hunt
Activity: - Look for teen numbers around your home or classroom - Page numbers in books - Addresses - Prices - Sports scores - For each teen number you find, say the ten plus fact (like "17 is 10 + 7")
Partner Practice
Activity: - Partner says a teen number: "Fifteen!" - You respond with the ten plus fact: "10 + 5!" - Switch roles - Try to get faster each time
Dice Game: Make a Teen
Materials: Two dice (one standard, one labeled with 0-5 twice)
How to play: 1. Roll both dice 2. Add the numbers to 10 3. Say the complete equation (e.g., if you roll 4 and 3, say "10 + 7 = 17") 4. Challenge: How many different teen numbers can you make in 5 minutes?
Real-World Connections
Ten plus facts appear constantly in everyday life. Recognizing them helps you see math as useful and relevant.
Money
- A ten-dollar bill plus some one-dollar bills
- Ten dollars + four dollars = fourteen dollars ($14)
- This is literally 10 + 4 = 14!
Sports
- A basketball team scores 10 points, then 8 more points
- 10 + 8 = 18 points total
- Keeping score uses ten plus facts constantly!
Cooking and Recipes
- A recipe needs 10 tablespoons of flour plus 3 more
- 10 + 3 = 13 tablespoons total
- Cooking involves math all the time!
Age
- When you turn 13, 14, 15, or older, you're ten years old plus some more years!
- "I'm 12 years old" means "I've lived 10 years + 2 years"
Collections
- "I have 10 baseball cards in one binder and 6 in another"
- 10 + 6 = 16 total cards
- Organizing collections uses teen numbers!
Building Fluency
Fluency means you can recall and use ten plus facts quickly and accurately without struggling. Here's how to build it:
Daily Quick Practice
Spend just 3-5 minutes each day: - Morning: Review five ten plus facts - Afternoon: Test yourself on random facts - Evening: Quick review of any tricky ones
Gradual Progression
Week 1: Focus on 10 + 1 through 10 + 3 Week 2: Add 10 + 4 through 10 + 6 Week 3: Add 10 + 7 through 10 + 9 Week 4: Mix them all together!
Timed Challenges
- Set a timer for one minute
- Write as many teen plus facts as you can
- Check your answers
- Try to beat your record tomorrow!
- Celebrate improvement!
Multiple Representations
Practice in different ways: - Write equations (10 + 5 = 15) - Say equations out loud ("Ten plus five equals fifteen") - Draw pictures (ten frame + 5 dots) - Use physical objects (10 blocks + 5 blocks)
Different ways of practicing strengthen different connections in your brain!
Common Challenges and Solutions
Challenge: "I keep forgetting eleven and twelve"
Solution: These are special! Practice them separately first. Remember: - Eleven = 10 + 1 (sounds like "el-ev-en" - one more than ten) - Twelve = 10 + 2 (comes from "two left" after ten) Create a special flashcard just for these two.
Challenge: "I still count on my fingers from one"
Solution: This is okay at first! But try to transition: - Put ten in your mind (or show ten fingers closed) - Count just the extra ones - Gradually, you'll stop needing to count at all
Challenge: "I mix up the order"
Solution: Practice saying "ten plus [number]" every time: - Always start with "ten plus..." - This reminds you that ten comes first - The pattern becomes automatic
Connecting to Other Math Concepts
Understanding ten plus facts connects to many other important mathematical ideas:
Addition Within 20
Ten plus facts help with harder addition: - 7 + 8: I can think "7 + 3 = 10, then 10 + 5 = 15" - You used your knowledge of 10 + 5!
Subtraction from Teen Numbers
If you know 10 + 6 = 16, then you also know: - 16 - 6 = 10 (take away the ones, keep the ten) - 16 - 10 = 6 (take away the ten, keep the ones) - One addition fact teaches you two subtraction facts!
Understanding Larger Numbers
The same pattern continues with bigger numbers: - 20 + 5 = 25 (two tens plus five ones) - 30 + 7 = 37 (three tens plus seven ones) - 100 + 8 = 108 (one hundred plus eight ones)
Measurement
Teen numbers appear in measurement: - 14 inches, 16 cups, 18 centimeters - Understanding these as "10 plus something" helps with estimation and comparison
Assessment: Know You're Ready When...
You've mastered ten plus facts when you can: - ✓ Instantly say any teen number as a ten plus fact - ✓ Quickly find what to add to 10 to make any teen number - ✓ Explain why 14 is the same as 10 + 4 - ✓ Use ten plus facts to help with other addition problems - ✓ Recognize teen numbers in real-world situations - ✓ Build teen numbers with blocks or drawings
Looking Ahead
Mastering ten plus facts is a stepping stone to:
Two-Digit Addition
Understanding that 15 = 10 + 5 helps when adding: - 25 + 13: Think of this as (20 + 10) + (5 + 3) = 30 + 8 = 38
Understanding Hundreds
The same pattern continues: - 100 + 20 + 5 = 125 - It's still about combining groups (hundreds, tens, ones)
Algebra Preview
Writing 10 + 6 = 16 is actually an algebraic equation: - Later you'll write things like x + 6 = 16, and solve for x - You're building that foundation now!
Conclusion
Ten plus facts are simple but powerful. They help you understand how our number system works, build your confidence with teen numbers, and prepare you for more advanced mathematics. By seeing teen numbers as "ten plus some ones," you're not just memorizing—you're understanding structure and pattern, which is what mathematics is all about. Practice regularly, use visual tools when helpful, and celebrate your growing fluency. You're building a foundation that will support your mathematical learning for years to come!
