Mathematical Explorers: Building Foundations · 2nd Class · Counting and Place Value to 199 · Autumn Term

Tens and Units , Building Numbers

Exploring the concept of numbers below zero in real-world contexts like temperature and debt.

About This Topic

The tens and units concept introduces students to place value in two-digit numbers up to 199. Children identify the tens digit, which represents groups of ten, and the units digit, which counts singles. They build numbers using tens rods and unit cubes, then convert between standard form, such as 46, and expanded form, 40 + 6. This aligns with the NCCA Primary Mathematics Curriculum's Counting and Place Value strand in 2nd class, where partitioning numbers builds number sense.

These skills form the basis for mental strategies in addition and subtraction. Students see how 35 equals three tens and five units, or thirty plus five, which supports flexible thinking about numbers. Real-world links, like grouping pencils in tens or counting euros in tens and ones, make the math relevant to daily life.

Active learning benefits this topic because hands-on work with manipulatives turns abstract place value into concrete experiences. When students physically trade ten unit cubes for a tens rod, they grasp the base-ten structure intuitively. Collaborative building and sharing reinforces understanding through discussion and peer feedback.

Key Questions

1. What are the tens and units in a two-digit number?
2. How can you build a number using tens rods and unit cubes?
3. Can you swap between the expanded form (e.g., 30 + 7) and the standard form (37) of a number?

Learning Objectives

• Identify the tens and units digits in numbers up to 199.
• Construct numbers by combining tens rods and unit cubes, and represent them in expanded form.
• Convert numbers between standard form (e.g., 57) and expanded form (e.g., 50 + 7).
• Explain the value of each digit in a two-digit number based on its position.

Before You Start

Counting to 100

Why: Students need to be able to count reliably to 100 before they can explore numbers beyond this range and understand place value.

Number Recognition to 99

Why: Familiarity with the appearance and names of numbers up to 99 is essential for understanding their composition in tens and units.

Key Vocabulary

Tens	Groups of ten. In a two-digit number, the tens digit tells us how many groups of ten there are.
Units	Singles or ones. In a two-digit number, the units digit tells us how many ones are left over after making groups of ten.
Place Value	The value of a digit based on its position in a number. For example, in 37, the 3 has a value of 30 because it is in the tens place.
Expanded Form	Writing a number as the sum of the value of its digits. For example, 42 in expanded form is 40 + 2.

Watch Out for These Misconceptions

Common Misconception

The number 24 means two ones and four ones.

What to Teach Instead

Students often overlook place value and count all digits as units. Using tens rods and cubes shows the 2 as twenty; small group building lets them trade ten units for a tens rod, visually correcting the error through hands-on repetition.

Common Misconception

Swapping between 30 + 4 and 34 is just rewriting.

What to Teach Instead

Children may not see the numerical equivalence. Pair activities matching forms and building both ways highlight the sameness; peer explanations during verification build confidence in flexible representation.

Common Misconception

Tens always come before units in writing.

What to Teach Instead

Some confuse order in expanded form. Manipulative trades and station recordings clarify structure; group discussions compare builds to standard notation, addressing reversal errors collaboratively.

Active Learning Ideas

Manipulatives: Build the Number

Give each small group tens rods and unit cubes. Call out numbers like 28 or 53; students build them, record the standard form, and write the expanded form. Have groups swap builds to check accuracy.

30 min·Small Groups

Pairs: Standard to Expanded Match

Prepare cards with standard numbers on one set and expanded forms on another. Pairs match them, such as 37 with 30 + 7, then build matches with manipulatives to verify. Discuss any mismatches as a class.

20 min·Pairs

Whole Class: Place Value Line-Up

Students hold number cards and line up to form a class number line from 10 to 99. Call changes like 'add 20' by inserting tens rods; everyone adjusts position and states the new number in expanded form.

35 min·Whole Class

Stations Rotation: Tens and Units Challenges

Set up three stations: build with blocks, draw expanded forms on mats, sort digit cards into tens/units columns. Groups rotate every 10 minutes, recording one fact per station.

45 min·Small Groups

Real-World Connections

• Bank tellers count money in tens and units when handling large sums, like counting out 50 euro notes and then adding individual euro coins to reach a total.
• Grocery store inventory clerks organize items in boxes of ten, then count the remaining individual items to determine stock levels for products like chocolate bars or pencils.

Assessment Ideas

Quick Check

Show students a number on the board, such as 63. Ask them to write down the tens digit and the units digit on a mini-whiteboard. Then, ask them to write the number in expanded form (60 + 3).

Exit Ticket

Give each student a card with a number written on it (e.g., 81). Ask them to draw the number using tens rods and unit cubes, and then write the number in expanded form on the back of the card.

Discussion Prompt

Present students with two numbers, for example, 45 and 54. Ask: 'What is the same about these numbers? What is different? How does the place of the digit 4 or 5 change its value?'

Frequently Asked Questions

How do you teach tens and units in 2nd class?

Start with concrete manipulatives like tens rods and unit cubes to build numbers called out by you. Move to representing in standard and expanded forms, then link to real contexts like money. Daily practice with quick builds reinforces partitioning, ensuring students fluently identify digit values by position within the NCCA place value strand.

What manipulatives work best for place value?

Tens rods and unit cubes are ideal as they mirror the base-ten system directly. Students physically group units into tens, seeing why 15 equals one ten and five units. Combine with place value mats for drawing or writing forms; this progression from concrete to abstract supports all learners in building secure understanding.

How can active learning help students understand tens and units?

Active learning with manipulatives makes place value tangible: students trade ten cubes for a rod, experiencing equivalence firsthand. Small group stations and pair matching encourage talk about 'why this many tens?', deepening insight. Whole-class line-ups show number relationships dynamically. These methods outperform worksheets, as physical interaction and collaboration lead to lasting retention and flexible number sense.

Common place value errors in early primary math?

Pupils frequently treat digits as loose units, like seeing 42 as four plus two ones, or struggle with expanded form equivalence. Address through visual builds and trades. Structured peer checks in pairs correct misconceptions quickly, aligning with NCCA emphasis on concrete-pictorial-abstract progression for solid foundations.