Mathematics · Grade 1 · Number Sense and Quantity · Term 1

Place Value: Tens and Ones

Understanding that two-digit numbers are composed of tens and ones using concrete models.

• Ontario Curriculum Expectations
• 1.NBT.B.2

About This Topic

Place value for tens and ones forms the foundation of number sense in Grade 1, as students learn that two-digit numbers consist of tens groups and individual ones. Using concrete models like base-ten blocks or bundled straws, they represent 23 as two rods of ten and three single units. This highlights how digit position affects value: the 2 in 23 equals twenty, but in 32 it contributes to thirty-two alongside two ones. These ideas align with Ontario curriculum expectations for composing numbers to 50 and beyond.

Students address key questions by constructing numbers with materials and explaining their structure, which supports partitioning for early addition and subtraction. This topic connects to counting by tens and reading numerals fluently, building skills for multi-digit work in later grades. Hands-on practice reinforces the base-ten system central to mathematics.

Active learning excels with this topic because students manipulate blocks to bundle ten ones into a tens rod, experiencing grouping directly. Pair trades and group builds reveal positional shifts visually, correct errors immediately, and make abstract values tangible for lasting understanding.

Key Questions

1. Explain how the position of a digit changes its value in a two-digit number.
2. Construct a two-digit number using tens and ones blocks, then explain its value.
3. Differentiate between the value of the digit '2' in the number 23 and the number 32.

Learning Objectives

• Represent two-digit numbers using concrete models of tens and ones.
• Explain the value of a two-digit number based on the quantity of tens and ones.
• Differentiate the value of a digit based on its position in a two-digit number.
• Construct a two-digit number given a specific quantity of tens and ones.

Before You Start

Counting to 20

Why: Students need to be able to count reliably to recognize quantities and understand number sequence before composing tens and ones.

One-to-One Correspondence

Why: This fundamental skill allows students to accurately count individual objects (ones) and groups of objects (tens).

Key Vocabulary

Tens	A group of ten ones. In a two-digit number, the tens digit tells us how many groups of ten we have.
Ones	Individual units. In a two-digit number, the ones digit tells us how many individual units are left after making as many tens as possible.
Place Value	The value of a digit based on its position within a number. For example, in 23, the '2' is in the tens place and has a value of 20.
Two-digit number	A number that has two digits, such as 10, 25, or 48. These numbers are made up of tens and ones.

Watch Out for These Misconceptions

Common Misconception

The digit 2 always means two, no matter its position.

What to Teach Instead

Show 23 and 32 with blocks: two tens rods plus three ones versus three tens rods plus two ones. Active building in pairs lets students see and count the difference, adjusting their thinking through peer explanation and repeated trials.

Common Misconception

Tens rods are worth more than ten ones without reason.

What to Teach Instead

Start with ten loose ones, then bundle into a rod; value stays the same. Group trading activities demonstrate efficiency of grouping, helping students internalize base-ten logic through hands-on equivalence checks.

Common Misconception

Two-digit numbers are read from right to left like words.

What to Teach Instead

Use mats to place and read digits correctly, swapping to compare 23 and 32. Collaborative mat work with verbal checks reinforces left-to-right reading, catching reversals early via group feedback.

Active Learning Ideas

Block Build: Two-Digit Numbers

Pairs draw a card with a two-digit number from 11 to 29. They build it using base-ten blocks, count aloud the tens and ones, and write the number with its breakdown (e.g., 2 tens + 3 ones = 23). Partners verify each other's work before drawing a new card.

25 min·Pairs

Trading Station: Ones for Tens

In small groups, students receive 15-25 unit cubes. They trade every ten cubes for a tens rod and record the total before and after trades. Groups compare final representations and discuss how trading keeps the value the same.

30 min·Small Groups

Place Value Mats: Digit Swap

Individuals or pairs use mats divided into tens and ones columns. Place given digits on the mat, build with blocks, and swap digits to form a new number. Explain the value change in writing.

20 min·Individual

Number Line Skip: Tens Count

Whole class lines up and uses blocks to mark tens on a large number line. Students add ones by stepping forward, then regroup by trading for tens. Discuss patterns observed.

35 min·Whole Class

Real-World Connections

• Grocery store cashiers often count out change using bills and coins, grouping them into tens and ones to quickly make amounts like $23 or $32.
• Construction workers building a fence might count posts in groups of ten, then add individual posts for the remaining length, totaling 23 posts for a section.

Assessment Ideas

Exit Ticket

Provide students with base-ten blocks. Ask them to build the number 34. On the back of the ticket, they should write how many tens and how many ones they used.

Discussion Prompt

Show students two numbers, 25 and 52. Ask: 'What is the same about these numbers? What is different? How does the position of the '2' change its value in each number?'

Quick Check

Hold up a card with a two-digit number, for example, 17. Ask students to show you with their fingers how many tens and how many ones are in the number. Then, ask them to build it with drawn tens rods and ones cubes on a whiteboard.

Frequently Asked Questions

How do you introduce place value tens and ones in grade 1?

Begin with concrete models like base-ten blocks or bundled popsicle sticks. Students build numbers from 10 to 29, naming tens and ones parts. Progress to drawing or writing the breakdown, then unbundling to verify totals. This sequence builds from concrete to representational understanding over 3-4 lessons.

What are common place value errors for grade 1 students?

Students often ignore position, treating 23 as two plus three equals five, or fail to group ten ones into tens. They may read 32 as thirty-two ones. Address with daily block builds and trading games that provide immediate visual feedback and repetition.

How does active learning help with place value tens and ones?

Active approaches like block manipulation and partner trading make positional value visible and kinesthetic. Students feel the weight of ten ones versus one tens rod, trade to regroup, and explain to peers, which solidifies concepts better than worksheets. This reduces abstraction, boosts retention, and allows real-time misconception correction in collaborative settings.

How to differentiate place value activities for grade 1?

Provide varied materials: blocks for visual learners, drawings for others. Extend challenge with numbers to 50 or decomposition tasks. Support strugglers with one-on-one trading prompts. Use success criteria checklists for all to track tens and ones identification independently.