Place Value: Tens and Ones

Active learning helps students grasp place value by making abstract ideas concrete. When children physically group objects into tens and ones, they see why two-digit numbers have special meaning. This hands-on work builds a mental model that counting by groups of ten is faster and more efficient than counting by ones.

• Year 1
• Mathematics
• 4 activities
• 20 min–35 min

Learning Objectives

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

Stations Rotation

⏱ 30 min·Pairs

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.

Prepare & details

Justify why counting large groups by tens is more efficient than by ones.

Facilitation Tip: During Grouping Challenge: Bundle the Beans, circulate and ask students to count aloud as they bundle to reinforce the count of ten in each group.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Stations Rotation

⏱ 25 min·Small Groups

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.

Prepare & details

Compare different ways to represent the same number using base-ten blocks.

Facilitation Tip: During Base-Ten Build-Off: Race to Represent, set a timer so students feel urgency to work quickly, reinforcing the efficiency of counting by tens.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Stations Rotation

⏱ 35 min·Whole Class

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.

Prepare & details

Predict the change in a number's value when a digit moves from the ones to the tens place.

Facilitation Tip: During Number Line Leap: Tens Jumps, have students whisper-count their jumps aloud to internalize the sound of ten as a unit.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Stations Rotation

⏱ 20 min·Pairs

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.

Prepare & details

Justify why counting large groups by tens is more efficient than by ones.

Facilitation Tip: During Digit Switch Prediction: Place Value Flip, pause after each flip to ask students to share their predictions before revealing the new number.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Teaching This Topic

Teach place value through repeated, structured exploration rather than explanation alone. Use consistent materials like beans and pipe cleaners so students build mental images that transfer across tasks. Avoid rushing to symbolic notation; let students verbalize their thinking before writing digits. Research shows that movement and physical grouping strengthen memory for place value concepts in young learners.

What to Expect

By the end of these activities, students will confidently bundle groups of ten, compare two-digit numbers, and explain how changing a digit affects the total value. They will use base-ten materials to justify their reasoning and solve simple place value problems independently.

Watch Out for These Misconceptions

Common Misconception

During Grouping Challenge: Bundle the Beans, watch for students who count each bean in a bundle instead of recognizing it as a single unit of ten.

What to Teach Instead

Ask the student to recount the bundle as ten without touching each bean, then have them count on from ten to show how bundling speeds the count. Ask, 'Which way was faster, counting all the beans or counting by tens?'.

Common Misconception

During Digit Switch Prediction: Place Value Flip, watch for students who think 12 becomes 21 by simply swapping digits, expecting little change in value.

What to Teach Instead

Use base-ten blocks to model 12 as one ten and two ones, then physically swap the blocks to make 21 as two tens and one one. Ask them to compare the total blocks before and after, highlighting the tenfold increase.

Common Misconception

During Number Line Leap: Tens Jumps, watch for students who count each jump as one instead of recognizing each jump as ten.

What to Teach Instead

Have the student stand on the number line and leap while whisper-counting, 'ten, twenty, thirty.' Stop after each leap to ask, 'How many ones is that jump? How many tens?'.

Assessment Ideas

Quick Check

After Grouping Challenge: Bundle the Beans, present students with a collection of 37 counters and 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

After Base-Ten Build-Off: Race to Represent, 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

During Digit Switch Prediction: Place Value Flip, 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?'.

Extensions & Scaffolding

• Challenge: Ask students to represent numbers up to 99 using the fewest possible base-ten blocks, then write the number in expanded form.
• Scaffolding: Provide pre-bundled sets of ten beans for students who struggle with grouping, so they can focus on counting groups rather than bundling.
• Deeper exploration: Introduce the concept of zero as a placeholder by asking students to represent numbers like 50 or 70 and explain why the zero matters.

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.