Tens and Ones: Grouping Objects

Active learning helps students see that grouping by tens is a faster way to count large quantities. When children physically bundle objects, they experience why our number system uses place value, moving beyond abstract symbols to concrete understanding.

• 1st Grade
• Mathematics
• 4 activities
• 20 min–45 min

Learning Objectives

1. Demonstrate the value of a two-digit number by creating it with bundles of tens and single ones.
2. Compare the quantity represented by a digit in the tens place versus the ones place within a two-digit number.
3. Construct two-digit numbers using concrete manipulatives representing tens and ones.
4. Explain why grouping objects by tens is an efficient strategy for counting larger quantities.

Stations Rotation

⏱ 45 min·Small Groups

Stations Rotation: Grouping Stations

Prepare four stations: bundle straws into tens, build numbers with base-10 blocks, match numeral cards to groups, compare two built numbers. Small groups spend 8 minutes per station, recording their constructions on worksheets. End with a share-out of comparisons.

Prepare & details

Why is grouping by tens an efficient way to count large quantities?

Facilitation Tip: At the Grouping Stations, circulate and ask each pair to verbalize how many tens and ones they counted before moving on to the next station.

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

Experiential Learning

⏱ 25 min·Pairs

Pairs: Number Builder Challenge

Partners take turns calling a two-digit number for the other to build with manipulatives. They check accuracy, then trade places and compare values by discussing tens versus ones. Extend by adding one more to cause a trade to tens.

Prepare & details

Construct a two-digit number using bundles of ten and single units.

Facilitation Tip: During the Number Builder Challenge, prompt partners to trade ten ones for one ten bundle and describe what happens to the total count.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Experiential Learning

⏱ 30 min·Whole Class

Whole Class: Place Value Mats

Distribute mats with tens and ones columns. Call numbers for all students to build simultaneously with shared manipulatives. Pause for choral responses on digit values, then have volunteers explain their groups.

Prepare & details

Compare the value of a digit in the tens place versus the ones place.

Facilitation Tip: Use the Place Value Mats during whole-class discussion to model bundling with clear pauses for choral counting of tens and ones.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Experiential Learning

⏱ 20 min·Individual

Individual: Bundle and Draw

Students select manipulatives to build three teacher-chosen numbers, then draw and label their groups. They write the numeral and note tens and ones counts. Collect for a class display.

Prepare & details

Why is grouping by tens an efficient way to count large quantities?

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Teaching This Topic

Teach this concept by letting students struggle slightly with loose counting first, then guiding them to invent bundling as a better way. Avoid rushing to the abstract; instead, let the materials anchor their understanding. Research shows that when children physically trade ones for tens, their brain forms stronger connections between the quantity and the symbol.

What to Expect

Students will confidently bundle ten ones into a ten and count two-digit numbers accurately. They will explain why 34 is three tens and four ones, not thirty-four separate items, and compare place values with clear reasoning.

Watch Out for These Misconceptions

Common Misconception

During Grouping Stations, watch for students who count each stick one-by-one and do not attempt to bundle ten.

What to Teach Instead

Ask them to pause and consider: 'How could you group these sticks to count faster?' Model bundling ten sticks together and ask them to try bundling their own.

Common Misconception

During the Number Builder Challenge, watch for students who treat the digit 4 as always meaning four items, regardless of place value.

What to Teach Instead

Have partners swap digits and rebuild the number, then ask them to explain how the value changes from 4 to 40 using their bundles.

Common Misconception

During Place Value Mats, watch for students who believe tens bundles contain different or larger objects than ones.

What to Teach Instead

Use identical sticks for both tens and ones, and have students trade ten single sticks for a pre-made bundle while discussing that the objects are the same, only the grouping changes.

Assessment Ideas

Exit Ticket

After Bundle and Draw, provide students with 25 counters. Ask them to group the counters into as many tens as possible and then identify the number of ones left over. Have them write the number they created and draw a picture showing their bundles of ten and single ones.

Quick Check

After Place Value Mats, hold up a number of bundles of ten (e.g., 3 bundles) and a number of single ones (e.g., 4 ones). Ask students to write the two-digit number represented. Then ask: 'What is the value of the digit in the tens place? What is the value of the digit in the ones place?'

Discussion Prompt

During Grouping Stations, present students with two numbers built using manipulatives, for example, 32 (three tens, two ones) and 23 (two tens, three ones). Ask: 'Which number has more tens? Which number has more ones? Which number is larger and why?'

Extensions & Scaffolding

• Challenge: Ask students to build numbers greater than 100 using the same bundling system and explain their process to a partner.
• Scaffolding: Provide pre-bundled tens for students who need support, but have them count and verify the bundles themselves.
• Deeper exploration: Introduce a recording sheet where students draw their bundles and write the expanded form of the number they built.

Key Vocabulary

Tens	A group of ten ones. In a two-digit number, the digit in the tens place tells us how many groups of ten we have.
Ones	Individual objects. In a two-digit number, the digit in the ones place tells us how many individual objects we have left after making as many groups of ten as possible.
Bundle	To group objects together, such as ten straws tied with a rubber band, to represent a ten.
Place Value	The value of a digit based on its position within a number. For example, the digit 2 in 23 means 2 tens, or 20, while the digit 3 means 3 ones.