Understanding Tens for Grade 1 Students

Master the fundamentals of tens: grouping, counting, and number decomposition for 1st grade math.

Complete Summary: Understanding Tens
Core Concepts Explained
Tens Place
The left digit in 2-digit numbers shows groups of 10
Grouping
Organizing 10 ones into 1 ten
Base-10 System
We count in groups of 10
Number Value
Each digit's position determines its value
Key Definitions:

Tens Place: The leftmost digit in a 2-digit number that represents groups of 10 (3 in 34 means 3 tens = 30)

Group of Ten: 10 individual items bundled together as 1 unit

Place Value: The value of a digit based on its position in a number

Base-10: Our number system based on groups of 10

Decompose: Breaking a number into its tens and ones parts

Compose: Putting together tens and ones to make a number

Regroup: Changing 10 ones into 1 ten (or vice versa)

Core Rules and Laws:

• Rule 1: 1 ten = 10 ones (10 individual units = 1 group of 10)

• Rule 2: The position of a digit determines its value

• Rule 3: Tens place value is 10 times the ones place value

• Rule 4: Every 10 ones can be regrouped as 1 ten

• Rule 5: Numbers can be decomposed into tens + ones

• Law: Position matters: left digit = tens, right digit = ones

Step-by-Step Method:
  1. Step 1: Identify the number you want to analyze
  2. Step 2: Look at the left digit (tens place)
  3. Step 3: Look at the right digit (ones place)
  4. Step 4: Count the groups of 10 (tens)
  5. Step 5: Count the individual units (ones)
  6. Step 6: Express as: number = tens + ones
Tip 1: Remember: 1 ten stick = 10 individual ones!
Tip 2: Count by tens first, then add the ones.
Tip 3: Draw groups of 10 and leftover ones to visualize.
Tip 4: Say the number aloud: "thirty" means 3 tens.
Common Pitfalls: Forgetting that 1 ten = 10 ones, confusing positions, miscounting groups.
Memory Aids: "10 ones make 1 ten", "Position tells the value", "Tens are bigger groups".
Key Takeaways:

• Every 2-digit number has tens and ones

• Tens place value is always 10 times the ones place

• 10 individual units can be grouped as 1 ten

• Understanding tens helps with all math operations

• Practice with physical objects like blocks or counters

Exercises 1 to 3 Solutions
1 Identifying tens
Exercise 1
How many tens are in the number 40?
Show the grouping of tens.
Step 1: Identify the number
4
0

Number: 40

Step 2: Identify tens and ones
Tens Place
4
Ones Place
0

40 has 4 tens and 0 ones

Step 3: Visual representation of tens
Ten 1
Ten 2
Ten 3
Ten 4

4 tens = 4 × 10 = 40

Step 4: Write the result

40 = 4 tens + 0 ones

40 = 4 tens
Explanation:

40 has 4 tens because 4 tens equal 40 (4 × 10 = 40). There are 0 ones in 40.

2 Making tens
Exercise 2
You have 30 individual items. How many groups of 10 can you make?
What number does this represent?
Step 1: Start with 30 individual items

Total: 30 individual items

Step 2: Group into tens

Every 10 individual items = 1 group of 10

30 ÷ 10 = 3 groups of 10

Step 3: Visual after grouping
Group 1
Group 2
Group 3

3 groups of 10 = 3 tens

Step 4: Write the number

3 tens = 30

30 individual items = 3 tens = 30
Explanation:

30 individual items can be grouped into 3 groups of 10, which equals 3 tens. The number 30 represents 3 tens and 0 ones.

3 Adding tens
Exercise 3
If you have 2 tens and add 3 more tens, how many tens do you have?
What number does this represent?
Step 1: Identify the starting tens
Ten 1
Ten 2

You have 2 tens

Step 2: Add more tens
Ten 3
Ten 4
Ten 5

You add 3 more tens

Step 3: Count total tens

2 tens + 3 tens = 5 tens

Step 4: Calculate the total value

5 tens = 5 × 10 = 50

2 tens + 3 tens = 5 tens = 50
Explanation:

When you add 2 tens (20) and 3 tens (30), you get 5 tens (50). Adding tens is just like adding regular numbers, but each represents a group of 10.

Exercises 4 to 5 Solutions
4 Subtracting tens
Exercise 4
You have 6 tens (60). If you take away 2 tens, how many tens are left?
What number does this represent?
Step 1: Start with 6 tens
Ten 1
Ten 2
Ten 3
Ten 4
Ten 5
Ten 6

You have 6 tens = 60

Step 2: Take away 2 tens
Take Away 1
Take Away 2

You take away 2 tens

Step 3: Count remaining tens

6 tens - 2 tens = 4 tens

Step 4: Calculate the remaining value

4 tens = 4 × 10 = 40

6 tens - 2 tens = 4 tens = 40
Explanation:

When you subtract 2 tens (20) from 6 tens (60), you get 4 tens (40). Subtracting tens works just like regular subtraction, but each ten represents a group of 10.

5 Comparing tens
Exercise 5
Compare 5 tens and 3 tens. Which is greater?
Use place value to explain.
Step 1: Identify both amounts
5 tens
50
3 tens
30
Step 2: Visual comparison
5 tens
3 tens
Step 3: Compare the tens

5 tens = 50

3 tens = 30

Since 5 > 3, then 5 tens > 3 tens

Step 4: Write the comparison

5 tens > 3 tens

50 > 30

5 tens > 3 tens
Explanation:

5 tens (50) is greater than 3 tens (30) because 5 groups of 10 (50) is more than 3 groups of 10 (30). When comparing tens, the number of tens determines which is greater.

Questions & Answers

Question: I don't understand why 1 ten equals 10 ones. Can you explain?

Answer: Great question! Think of it like this:

  • Counting groups: If you have 10 individual items, you can put them together in a group. That group counts as 1 "ten"
  • Like money: 10 pennies = 1 dime. Both are worth the same amount, just organized differently
  • Real example: 10 pencils tied together = 1 bundle of pencils = 1 ten
  • Math fact: 10 ones = 1 ten = 10

We do this to make counting easier! Instead of counting 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, we say "1 ten" and start over with ones.

Try this: Get 10 small objects and put them in a group. Now you have 1 group (1 ten) instead of 10 separate items (10 ones). They're the same amount, just organized differently!

Question: My child doesn't understand why we group things in tens. Why not 5 or 12?

Answer: The base-10 system (groups of 10) is used worldwide because:

  • Human anatomy: We have 10 fingers, making 10 a natural counting base
  • Historical tradition: Ancient civilizations developed this system
  • Mathematical simplicity: Powers of 10 (10, 100, 1000) are easy to work with
  • Pattern consistency: Same rules apply for all place values

While other systems exist (like base-12 for clocks), the decimal system is standard. We could count by 5s or 12s, but 10s make math operations much simpler and consistent.

To help your child: Use their fingers to count to 10, then bundle groups of 10 objects together.

Question: Why do we need to learn about tens? It seems complicated.

Answer: Learning about tens is super important! Here's why:

  • Real-world connections: Money (tens of dollars, ones of dollars), ages, house numbers
  • Easier counting: Instead of counting 1, 2, 3... up to 30, you can think "3 tens"
  • Future math: Addition, subtraction, multiplication, and division all use place value
  • Understanding numbers: You'll know that 40 isn't just "forty" but "4 tens"

Think of tens like organizing your toys - if you group them in sets of 10, it's easier to know how many you have!

Practice with everyday items: count your fingers (10 ones = 1 ten), group crayons in tens, or count coins in groups of 10.

Once you master tens, all other math becomes much easier!