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

Subtracting Multiples of Ten

Students subtract multiples of 10 from multiples of 10 and from two-digit numbers.

• Common Core State Standards
• CCSS.Math.Content.1.NBT.C.6

About This Topic

Subtracting multiples of ten from two-digit numbers builds directly on students' understanding of place value and the structure of the base-ten system. CCSS.Math.Content.1.NBT.C.6 asks students to subtract multiples of ten from multiples of ten and two-digit numbers within 100, using concrete models, drawings, and strategies based on place value. The key insight is that subtracting a multiple of ten affects only the tens digit, leaving the ones digit completely unchanged.

This parallel structure with adding multiples of ten is instructionally valuable. Students who understand that adding 30 increases the tens digit by 3 can reason symmetrically that subtracting 30 decreases it by 3. Base-ten blocks illustrate this directly: removing whole rods from a number never disturbs the unit cubes, so the ones place stays fixed regardless of how many rods are taken away.

Active learning strengthens this topic because students often discover the ones-digit stability pattern more reliably through their own exploration than through direct instruction. When pairs test predictions and share surprising results, the pattern becomes a class-constructed generalization that students are far more likely to remember and transfer.

Key Questions

1. Explain how subtracting a multiple of ten only affects the tens digit.
2. Predict the result of subtracting 10 or 20 from a given two-digit number.
3. Design a mental strategy for subtracting multiples of ten.

Learning Objectives

• Calculate the difference between two multiples of ten within 100.
• Identify the digit that changes when subtracting a multiple of ten from a two-digit number.
• Explain why the ones digit remains constant when subtracting multiples of ten.
• Compare the results of subtracting different multiples of ten from the same two-digit number.

Before You Start

Counting by Tens

Why: Students need to be able to fluently count by tens to recognize and work with multiples of ten.

Understanding Place Value (Tens and Ones)

Why: Students must understand that numbers are composed of tens and ones to see how subtracting tens affects only the tens place.

Key Vocabulary

Multiple of Ten	A number that can be divided by 10 with no remainder. Examples include 10, 20, 30, up to 100.
Tens Digit	The digit in a two-digit number that represents the number of tens. For example, in the number 53, the tens digit is 5.
Ones Digit	The digit in a two-digit number that represents the number of ones. For example, in the number 53, the ones digit is 3.
Place Value	The value of a digit based on its position within a number. This helps us understand that the tens digit represents groups of ten and the ones digit represents individual units.

Watch Out for These Misconceptions

Common Misconception

Subtracting a multiple of ten changes both the tens digit and the ones digit.

What to Teach Instead

Students may reduce both digits. Physically removing only rods from a base-ten block model and watching the unit cubes remain untouched is the most direct correction, especially in a collaborative investigation where peers can observe and confirm what changed.

Common Misconception

You cannot subtract 20 from 23 because the tens digit is not big enough.

What to Teach Instead

Students who try to subtract digit by digit may get confused when the tens digits are equal. Connecting the problem to rods (remove 2 rods from 2 rods, leaving 0 tens plus the 3 unchanged units) resolves this by keeping the place values physically separate.

Active Learning Ideas

Think-Pair-Share: What's Left in the Ones?

Present 63 - 40. Partners individually predict the result and specifically predict what the ones digit will be before solving. They share predictions, then use a hundreds chart or base-ten blocks to verify. The class discusses why every pair got the same ones digit even when their solving strategies differed.

15 min·Pairs

Inquiry Circle: Rod Removal

Groups build a two-digit number with rods and unit cubes. One student removes a specified number of rods (e.g., 3 rods for subtracting 30) while another watches the units and confirms they never change. The group records the before and after numbers and writes the equation.

20 min·Small Groups

Gallery Walk: Hundreds Chart Trails

Post hundreds charts with a start number circled. Students visit each chart, draw arrows moving up the specified number of rows to subtract a given multiple of ten, and write the equation. Pairs compare charts and discuss why moving up on the hundreds chart subtracts tens.

20 min·Pairs

Stations Rotation: Mental Subtraction Ladders

At each station a ladder shows a starting two-digit number. Students subtract a given multiple of ten at each rung and write the result, varying the multiple (10, 20, 30) and starting number across stations. Students explain their mental strategy aloud to a partner before writing the answer.

25 min·Small Groups

Real-World Connections

• A cashier at a grocery store might need to calculate change by subtracting multiples of ten. For example, if a customer pays with a $50 bill for an item costing $20, the cashier subtracts 20 from 50 to determine the $30 change.
• A construction worker might measure materials in lengths of ten feet. If they need 70 feet of wood and have 100 feet, they subtract 70 from 100 to know how much is left.

Assessment Ideas

Exit Ticket

Give students a card with a problem like '60 - 30 = ?' and '75 - 20 = ?'. Ask them to write the answer and circle the digit that changed in the second problem. Then, ask them to write one sentence explaining why the other digit did not change.

Quick Check

Display a number on the board, such as 48. Ask students to hold up fingers to show how many tens they would subtract (e.g., 1, 2, or 3). Then, ask them to write the resulting number on a mini-whiteboard and hold it up. Discuss the ones digit for each result.

Discussion Prompt

Pose the question: 'Imagine you have 50 blocks. You take away 20 blocks. How many are left? Now, imagine you have 58 blocks and you take away 20 blocks. How many are left? What is the same about these two problems?' Facilitate a discussion about the role of the ones digit.

Frequently Asked Questions

How do I teach subtracting multiples of ten without the standard algorithm?

Use base-ten blocks and hundreds charts. For 75 - 30, show 7 rods and 5 units, remove 3 rods, and count what remains: 4 rods and 5 units, or 45. On the hundreds chart, start at 75 and move up 3 rows to land on 45. Both methods highlight that only the tens digit changes.

Why does the ones digit stay the same when subtracting multiples of ten?

Multiples of ten contain zero ones. Subtracting zero ones from the ones digit leaves it unchanged. This is a direct consequence of place value logic: each place is independent, and only the tens are affected when only tens are removed.

What mental math strategies help students subtract multiples of ten?

Teach the tens-only strategy: identify the tens digit, subtract the multiple of ten as a single-digit subtraction, and keep the ones digit unchanged. For 68 - 40, think 6 - 4 = 2, so the result is 28. The hundreds chart supports this until the mental strategy is fully internalized.

How can active learning help students see the pattern in subtracting multiples of ten?

When students predict the ones digit before removing rods from a model, they commit to a hypothesis. Finding that the ones digit is always unchanged across many different examples creates a pattern discovery moment that sticks. Peer collaboration amplifies this because one student's insight about the pattern spreads quickly through discussion in a way it would not in silent independent work.