Mathematics · 1st Grade · The Power of Ten and Place Value · Quarter 2

Tens and Ones: Grouping Objects

Students use manipulatives to group objects into tens and ones, representing two-digit numbers.

• Common Core State Standards
• CCSS.Math.Content.1.NBT.B.2

About This Topic

Students group manipulatives such as straws, popsicle sticks, or base-10 blocks into bundles of ten and loose ones to represent two-digit numbers. For example, they build 23 with two bundles of ten and three single units. This approach shows why grouping by tens counts large quantities faster than one-by-one and lets students construct numbers while comparing the value of digits by place.

This topic anchors the place value unit by revealing our base-10 system's logic. A digit like 3 means three ones in the ones place but thirty in the tens place. Students connect this to skip-counting by tens and prepare for addition with carrying. Concrete grouping develops number sense and flexible thinking for multi-digit work ahead.

Active learning fits perfectly because students handle materials to bundle and trade, making place value visible and intuitive. Pair shares uncover errors in grouping, while whole-class builds reinforce comparisons. These methods build confidence and retention through repeated, physical practice.

Key Questions

1. Why is grouping by tens an efficient way to count large quantities?
2. Construct a two-digit number using bundles of ten and single units.
3. Compare the value of a digit in the tens place versus the ones place.

Learning Objectives

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

Before You Start

Counting to 100 by Ones

Why: Students need a solid foundation in counting individual objects before they can begin grouping them.

Recognizing Numbers 0-20

Why: Students must be able to identify and read numbers within this range to connect them to the quantities they are building.

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.

Watch Out for These Misconceptions

Common Misconception

23 means twenty-three separate single objects.

What to Teach Instead

Manipulatives let students bundle ten ones into a ten, showing 23 as two tens and three ones for efficient counting. Small group rotations help peers question and correct loose counting through shared builds.

Common Misconception

A digit like 4 always means four items, no matter the place.

What to Teach Instead

Students trade ones for tens bundles and observe value jumps from 4 to 40. Pair challenges with digit swaps clarify position's role, as partners verbalize changes during comparisons.

Common Misconception

Tens bundles contain bigger or different objects than ones.

What to Teach Instead

All items stay identical; bundling creates tens. Whole-class mat builds with uniform sticks reinforce this, as students trade and discuss during choral checks.

Active Learning Ideas

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.

45 min·Small Groups

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.

25 min·Pairs

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.

30 min·Whole Class

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.

20 min·Individual

Real-World Connections

• Grocery store cashiers count money by grouping bills into tens and twenties to quickly calculate the total cost of items.
• Construction workers might count nails or screws by making bundles of ten to estimate how many they have on a job site, saving time compared to counting each one individually.

Assessment Ideas

Exit Ticket

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

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

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?'

Frequently Asked Questions

How to teach tens and ones grouping in 1st grade?

Start with concrete manipulatives like straws or blocks for hands-on bundling. Guide students to build and label two-digit numbers, emphasizing trades from ten ones to one ten. Follow with partner talks to compare place values, building from familiar counting to place value logic. This sequence scaffolds understanding over several lessons.

What manipulatives work best for tens and ones?

Straws, popsicle sticks, or base-10 blocks allow easy bundling and trading. Straws mimic flexible grouping, while blocks provide visual rectangles for tens. Rotate types across activities to show consistency across tools, helping students focus on the math concept rather than the material.

How can active learning help students understand tens and ones?

Active tasks like station rotations and pair builds let students physically group and trade, turning abstract place value concrete. Peer discussions during comparisons reveal and fix errors, while whole-class syncs build collective understanding. These approaches boost engagement and retention, as kids experience efficiency of tens firsthand over weeks of practice.

Why group by tens for counting large numbers?

Grouping by tens skips rote one-by-one counting, matching our base-10 system for quick mental math. Students see this efficiency when building 35 as three tens and five ones versus 35 singles. Activities reinforce it through timed challenges, showing faster results and preparing for addition strategies.