Mathematics · Year 1 · Number Sense and Counting Systems · Term 1

Place Value: Tens and Ones

Developing an understanding of place value by grouping objects into tens and ones, representing numbers up to 100.

• ACARA Content Descriptions
• AC9M1N02

About This Topic

Place value with tens and ones introduces Year 1 students to the structure of two-digit numbers up to 100. Students group objects, such as counters or straws, into bundles of ten and single ones to represent numbers like 23 as two tens and three ones. This hands-on grouping shows why counting by tens is faster than by ones, as they justify through comparison activities. They also compare representations using base-ten blocks and predict how a number changes when a one becomes a ten, such as seeing that adding a ten increases value by ten.

Aligned with AC9M1N02, this topic strengthens number sense within the Number and Algebra strand. Students order numbers on lines and recognise patterns in place value, which supports later work in addition and subtraction. Collaborative tasks encourage them to explain their groupings, building mathematical language and reasoning skills essential for the Australian Curriculum.

Active learning shines here because manipulatives turn abstract positions into concrete quantities students can see, touch, and rearrange. When they build and break apart numbers in pairs or small groups, misconceptions fade quickly, and they gain confidence in flexible representations that stick for future units.

Key Questions

1. Justify why counting large groups by tens is more efficient than by ones.
2. Compare different ways to represent the same number using base-ten blocks.
3. Predict the change in a number's value when a digit moves from the ones to the tens place.

Learning Objectives

• Represent two-digit numbers up to 100 using concrete materials, grouping tens and ones.
• Compare and order numbers up to 100 based on their tens and ones composition.
• Explain the value of a digit based on its position in a two-digit number.
• Justify why grouping by tens is an efficient strategy for counting larger quantities.
• Construct different representations of the same two-digit number using base-ten blocks.

Before You Start

Counting to 20

Why: Students need a solid foundation in counting to at least 20 to build upon when extending to larger numbers and grouping by tens.

One-to-One Correspondence

Why: This foundational skill is necessary for accurately counting individual objects before they can be grouped into 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, such as the tens place or the ones place.
Base-Ten Blocks	Manipulatives used to represent numbers, where a rod represents a ten and a small cube represents a one.

Watch Out for These Misconceptions

Common Misconception

Tens are just ten separate ones with no special value.

What to Teach Instead

Students often see 20 as twenty loose items. Using bundling activities with pipe cleaners or ten-frames shows the group as a single unit worth ten. Group discussions reveal how this efficiency speeds counting, correcting the view through shared models.

Common Misconception

Moving a digit from ones to tens adds only one.

What to Teach Instead

Children predict small changes, like 12 becoming 21 adds little. Manipulatives demonstrate the tenfold shift clearly. Hands-on regrouping in stations lets them experiment and compare predictions to actual values, building accurate mental models.

Common Misconception

All numbers are counted only by ones.

What to Teach Instead

Some insist on one-by-one counting. Races comparing ones versus tens grouping prove efficiency. Whole-class timelines of their counts visualise the time saved, reinforcing the strategy through evidence.

Active Learning Ideas

Grouping Challenge: Bundle the Beans

Provide 20-50 dried beans per pair. Students count by ones first, then regroup into tens and ones, recording the number on place value mats. Discuss which method is quicker and why. Extend by trading 10 ones for a ten bundle.

30 min·Pairs

Base-Ten Build-Off: Race to Represent

In small groups, call out numbers like 45. Students race to build with base-ten blocks on mats, then swap and verify each other's models. Rotate roles to explain the tens and ones.

25 min·Small Groups

Number Line Leap: Tens Jumps

Mark a floor number line to 100. Students hold ten-frames or blocks and leap tens to reach target numbers, naming the tens and ones at each stop. Record jumps on individual sheets.

35 min·Whole Class

Digit Switch Prediction: Place Value Flip

Give cards with numbers like 19. Students predict and build what happens if the 1 moves to tens place (91), using blocks to check value change. Pairs justify the difference.

20 min·Pairs

Real-World Connections

• Cashiers at a supermarket use place value to count money. For example, they might count a $20 bill as two tens, or count out 35 cents as three dimes (tens) and five pennies (ones).
• Construction workers use place value when measuring materials. A length of 42 meters could be thought of as four 10-meter lengths and two 1-meter lengths, making it easier to manage and cut.

Assessment Ideas

Quick Check

Present students with a collection of 37 counters. Ask them to physically group the counters into tens and ones. Observe if they correctly form three groups of ten and have seven individual ones remaining.

Exit Ticket

Give each student a card showing a number, for example, 52. Ask them to draw the number using base-ten blocks (rods for tens, squares for ones) and write a sentence explaining how many tens and ones are in the number.

Discussion Prompt

Show two different representations of the same number, such as 4 tens and 6 ones versus 3 tens and 16 ones. Ask students: 'Are these numbers the same? How do you know? Which representation is easier to count and why?'

Frequently Asked Questions

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

Start with concrete materials like beans or blocks for grouping into tens and ones. Use place value charts to label parts, then link to numerals. Daily number talks compare representations, such as 34 as three tens-four ones or thirty-four, ensuring students connect symbols to quantities over several lessons.

What activities build place value understanding up to 100?

Hands-on tasks with base-ten blocks, ten-frames, and bundling objects work best. Students represent, decompose, and compose numbers in varied ways. Include games like rolling dice to build two-digit numbers, promoting repeated practice and peer teaching for retention.

How can active learning help students grasp place value?

Active approaches with manipulatives make positions tangible, as students physically group and trade ones for tens. Pair work and rotations encourage talk about values, correcting errors in real time. This beats worksheets, as building numbers themselves reveals patterns like ten ones equal one ten, fostering deep, lasting comprehension.

Common errors in tens and ones for beginners?

Mistakes include ignoring place value, treating 23 as twenty-three singles, or misunderstanding digit shifts. Address with visual aids and predictions using blocks. Regular regrouping practice in small groups clarifies these, as students verbalise and test ideas collaboratively.