Understanding Tens and Ones for Grade 1 Students

Master the fundamentals of place value: tens and ones, number decomposition, and visual representations for 1st grade math.

Complete Summary: Tens and Ones
Core Concepts Explained
Tens Place
The left digit in 2-digit numbers shows groups of 10
Ones Place
The right digit shows individual units
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)

Ones Place: The rightmost digit in a 2-digit number that represents individual units (4 in 34 means 4 ones = 4)

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 break down
  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-four" has 3 tens and 4 ones.
Common Pitfalls: Forgetting that 1 ten = 10 ones, confusing positions, miscounting groups.
Memory Aids: "Tens on the left, ones on the right", "10 ones make 1 ten", "Position tells the value".
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 and ones helps with all math operations

• Practice with physical objects like blocks or counters

Exercises 1 to 3 Solutions
1 Number decomposition
Exercise 1
Break down the number 27 into tens and ones.
Show how many tens and how many ones.
Step 1: Identify the number
2
7

Number: 27

Step 2: Identify tens and ones
Tens Place
2
Ones Place
7

27 has 2 tens and 7 ones

Step 3: Visual representation
27 =
2 tens + 7 ones = 20 + 7 = 27
Step 4: Write the breakdown

27 = 20 + 7

27 = 2 tens + 7 ones

27 = 2 tens + 7 ones
Explanation:

27 has 2 tens (which equals 20) and 7 ones (which equals 7). Together, 20 + 7 = 27.

2 Base-10 model
Exercise 2
Show the number 43 using tens and ones.
How many tens and how many ones?
Step 1: Identify the number
4
3

Number: 43

Step 2: Identify tens and ones
Tens Place
4
Ones Place
3

43 has 4 tens and 3 ones

Step 3: Visual representation
43 =
4 tens + 3 ones = 40 + 3 = 43
Step 4: Write the breakdown

43 = 40 + 3

43 = 4 tens + 3 ones

43 = 4 tens + 3 ones
Explanation:

43 has 4 tens (which equals 40) and 3 ones (which equals 3). Together, 40 + 3 = 43.

3 Composing numbers
Exercise 3
If you have 5 tens and 8 ones, what number do you get?
Combine tens and ones to make the number.
Step 1: Identify tens and ones
Tens
5
Ones
8

5 tens and 8 ones

Step 2: Convert to values

5 tens = 5 × 10 = 50

8 ones = 8 × 1 = 8

Step 3: Add together

50 + 8 = 58

Step 4: Visual representation
58 =
5 tens + 8 ones = 50 + 8 = 58
5 tens + 8 ones = 58
Explanation:

5 tens equal 50 and 8 ones equal 8. Combined, 50 + 8 = 58.

Exercises 4 to 5 Solutions
4 Regrouping concept
Exercise 4
You have 13 ones. How can you regroup them?
Change 10 ones into tens.
Step 1: Start with 13 ones
13 ones:
13 individual ones
Step 2: Regroup 10 ones as 1 ten

Every 10 ones can be grouped as 1 ten

13 ones = 10 ones + 3 ones

10 ones = 1 ten

So: 13 ones = 1 ten + 3 ones

Step 3: Visual after regrouping
1 ten + 3 ones:
1 ten + 3 ones = 13
Step 4: Write the result

13 ones = 1 ten + 3 ones

13 ones = 13

13 ones = 1 ten + 3 ones
Explanation:

When you have 13 ones, you can regroup 10 of them as 1 ten, leaving 3 ones. So 13 ones becomes 1 ten and 3 ones, which still equals 13.

5 Comparing with tens and ones
Exercise 5
Compare 35 and 42 by looking at their tens and ones.
Which number is greater and why?
Step 1: Break down both numbers
3
5
vs
4
2
35 =
3 tens + 5 ones
42 =
4 tens + 2 ones
Step 2: Compare tens first

35 has 3 tens

42 has 4 tens

Since 4 > 3, then 42 > 35

Step 3: Visual comparison
35:
3 tens + 5 ones = 35
42:
4 tens + 2 ones = 42
Step 4: Write the comparison

42 > 35 because 4 tens (40) is greater than 3 tens (30)

42 > 35
Explanation:

42 is greater than 35 because 42 has 4 tens while 35 has only 3 tens. Even though 35 has more ones (5 vs 2), the tens determine the comparison since 4 tens (40) is greater than 3 tens (30).

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 confuses the tens and ones places. How can I help them remember which is which?

Answer: Here are effective strategies to help with place value positions:

  • Left-Right Rule: "Tens on the LEFT, ones on the RIGHT" - always point to the left digit first
  • Size Matters: Tens are bigger (worth more) so they sit on the left, like adults sitting on the left side of a bench
  • Memory Phrase: "Tens are TALL, Ones are ON the right" (both start with "T" and "O")
  • Physical Activity: Have your child touch their LEFT shoulder for tens and RIGHT shoulder for ones

Practice tip: Write numbers with arrows pointing to each place: 45 → (↑) 4 tens, (↑) 5 ones. Repeat this pattern daily until it becomes automatic.

Use visual aids like color-coding: write tens in blue and ones in red to make the positions distinct.

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

Answer: Learning tens and ones 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 24, you can think "2 tens and 4 ones"
  • Future math: Addition, subtraction, multiplication, and division all use place value
  • Understanding numbers: You'll know that 57 isn't just "fifty-seven" but "5 tens and 7 ones"

Think of tens and ones 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 and ones, all other math becomes much easier!