Foundations of Mathematical Thinking · 1st Class · Counting and Numbers to 100 · Autumn Term

Tens and Units

Investigate how the position of a digit determines its value in multi-digit numbers.

• NCCA Curriculum Specifications
• NCCA: Primary - Number
• NCCA: Primary - Understanding Place Value

About This Topic

Understanding tens and units is fundamental for building number sense and preparing students for more complex mathematical operations. At this stage, children explore how the position of a digit dictates its value, distinguishing between the quantity represented by a '2' in '20' versus '2'. This concept is often introduced using concrete materials like base-ten blocks or bundles of sticks, allowing students to physically group items into sets of ten. They learn to decompose numbers, seeing 34 as three groups of ten and four individual units, which directly supports addition and subtraction strategies later on.

This foundational understanding of place value is crucial for comprehending numbers beyond 20 and for developing efficient calculation methods. When students can confidently identify the number of tens and units in a given number, they are better equipped to compare numbers, order them, and perform mental arithmetic. The NCCA curriculum emphasizes this by framing key questions around the meaning of the tens digit and the composition of numbers using these units. This topic directly supports the 'Number' strand and the 'Understanding Place Value' standard within the primary mathematics framework.

Active learning is particularly beneficial for grasping tens and units because it transforms abstract numerical concepts into tangible experiences. Manipulating objects, building numbers with physical representations, and engaging in games that require grouping and regrouping allow students to internalize the relationship between digits and their values. This hands-on approach solidifies understanding far more effectively than rote memorization.

Key Questions

1. What does the tens digit tell us about a number?
2. How many tens and units are in numbers like 23 or 47?
3. Can you make a number using bundles of tens and single units?

Watch Out for These Misconceptions

Common Misconception

The digit '2' in 23 means two things, not twenty.

What to Teach Instead

Students often confuse the digit itself with the quantity it represents. Using base-ten blocks to show two 'tens' rods and three 'ones' cubes helps them see that the '2' stands for two groups of ten, not just two items.

Common Misconception

Numbers are just a string of digits without inherent value.

What to Teach Instead

Children may not grasp that the position of a digit is critical. Activities where students physically build numbers with tens and units, or sort number cards based on their tens value, highlight the importance of place.

Active Learning Ideas

Tens and Units Tower Building

Provide students with bundles of ten craft sticks and individual craft sticks. Ask them to build towers representing given numbers, such as 23 (two bundles of ten and three individual sticks). They can then count their towers to check.

20 min·Pairs

Place Value Card Game

Create two sets of cards: one with numbers (e.g., 10, 20, 30) and another with quantities (e.g., 1, 2, 3). Students draw a number card and then select the correct quantity cards to represent the tens, then add individual unit cards to form a target number.

15 min·Small Groups

Number Line Jump

Use a large number line marked in tens. Students start at zero and 'jump' by tens, then add individual unit jumps to reach a target number. This visually reinforces the concept of tens as jumps of ten.

15 min·Whole Class

Frequently Asked Questions

Why is understanding tens and units important for first graders?

Grasping tens and units is a cornerstone of number sense. It allows children to understand larger numbers, develop strategies for addition and subtraction, and build a solid foundation for future mathematical concepts like multiplication and division. It moves them beyond simple counting to understanding number composition.

How can I help students who struggle with place value?

Provide ample opportunities for hands-on manipulation with base-ten blocks, unifix cubes, or even drawings of tens and units. Use games and real-world examples, like counting money or grouping objects, to make the abstract concept more concrete and relatable for them.

What is the difference between tens and units?

Units, also called ones, represent individual items. Tens represent groups of ten individual items. In a number like 34, the '4' represents four individual units, while the '3' represents three groups of ten, totaling thirty.

How does active learning benefit the understanding of tens and units?

Active learning, through manipulating physical objects like base-ten blocks or engaging in place value games, allows students to physically build and deconstruct numbers. This hands-on experience makes the abstract concept of place value tangible, reinforcing the idea that a digit's value depends on its position.