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K01 • Lesson 13 of 105

Place Value: Tens and Ones

Students explore how two-digit numbers are built from groups of ten and leftover ones using base-10 blocks and place value charts. They learn to decompose numbers like 47 into 4 tens and 7 ones, read and write two-digit numbers in expanded form, and understand that the position of a digit determines its value.

K-2 Foundations • K-2

Prerequisites: E01

Key Concepts

  • tens and ones places
  • grouping by ten
  • expanded form of two-digit numbers
  • base-10 block representations

Place Value: Tens and Ones

Every number has a special place for each digit. When we write a two-digit number like 34, each digit tells us something different. The 3 tells us how many groups of ten we have. The 4 tells us how many ones are left over.

Big Idea

We group things by ten because it makes counting easier. Instead of counting 34 things one by one, we can make 3 groups of ten and have 4 left over.

Base-10 Blocks

We use special blocks to show numbers:

BlockWhat It Looks LikeValue
Ones cubeA tiny single cube1
Tens rodA long stick made of 10 cubes10

To show the number 27, we use:

2 tens rods + 7 ones cubes = 27

The Place Value Chart

A place value chart has two columns for two-digit numbers:

TensOnes
27

Read this as: 2 tens and 7 ones, which equals twenty-seven.

Worked Example 1: Breaking Apart a Number

Show 53 using base-10 blocks and a place value chart.

  1. Ask: How many tens are in 53? The tens digit is 5, so we need 5 tens rods.
  2. Ask: How many ones? The ones digit is 3, so we need 3 ones cubes.
  3. Place value chart:
TensOnes
53
53 = 50 + 3

Expanded Form

Expanded form shows a number as the sum of the value of each digit:

46 = 40 + 6
81 = 80 + 1
70 = 70 + 0

Worked Example 2: Writing Expanded Form

Write 95 in expanded form.

  1. The 9 is in the tens place. Its value is 90.
  2. The 5 is in the ones place. Its value is 5.
  3. Write the sum: 95 = 90 + 5

Worked Example 3: From Blocks to Numbers

You have 6 tens rods and 2 ones cubes. What number is this?

  1. 6 tens = 60
  2. 2 ones = 2
  3. 60 + 2 = 62

Watch Out!

Do not mix up tens and ones! In the number 38, the 3 does not mean three -- it means thirty (3 groups of ten). The 8 means eight ones.

Real-World Connection

Think of egg cartons that hold 10 eggs each. If you have 4 full cartons and 7 extra eggs, you have 47 eggs total!

Practice Problems

1. How many tens and ones are in the number 74?

Show Answer

7 tens and 4 ones. The value of the tens digit is 70, and the value of the ones digit is 4.

2. Write 58 in expanded form.

Show Answer

58 = 50 + 8

3. You have 3 tens rods and 9 ones cubes. What number do you have?

Show Answer

39. Three tens is 30, plus 9 ones is 39.

4. What is the value of the digit 6 in the number 63?

Show Answer

60. The 6 is in the tens place, so it stands for 6 tens, which is 60.

5. A number has 0 tens and 5 ones. What is the number?

Show Answer

5. When there are 0 tens, the number is just the ones digit.

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