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

Adding Multiples of Ten

Students add multiples of 10 to two-digit numbers using concrete models and mental math strategies.

• Common Core State Standards
• CCSS.Math.Content.1.NBT.C.4
• CCSS.Math.Content.1.NBT.C.5

About This Topic

Adding multiples of ten to two-digit numbers is both a foundational computational skill and a window into the structure of the base-ten number system. CCSS.Math.Content.1.NBT.C.4 and C.5 ask students to add within 100 using models or strategies based on place value, and to mentally find 10 more or 10 less than a given number. The key insight is that adding a multiple of ten changes only the tens digit while leaving the ones digit completely unchanged.

This pattern is visually compelling with base-ten materials. When a student holds a rod (ten) and adds more rods, the unit cubes sitting beside them stay exactly as they are. The ones place is stable; only the tens place grows. Building this observation into a reliable mental strategy, changing just the tens digit, is the goal of the lesson.

Active learning is well-suited here because the pattern is best discovered through repeated, varied examples. When students generate predictions, test them with materials, and report results to the group, they construct the rule themselves. This inductive approach produces a stronger and more transferable understanding than being told the pattern and practicing it procedurally.

Key Questions

1. Explain how adding a multiple of ten only changes the tens digit.
2. Predict the outcome when adding 10, 20, or 30 to a given number.
3. Design a mental strategy for quickly adding multiples of ten.

Learning Objectives

• Calculate the sum of a two-digit number and a multiple of ten (10, 20, 30) using base-ten blocks.
• Explain how adding a multiple of ten to a two-digit number affects the tens digit and the ones digit.
• Predict the result of adding 10, 20, or 30 to a given two-digit number without using manipulatives.
• Design a personal strategy for mentally adding multiples of ten to two-digit numbers.
• Compare the sums of different two-digit numbers when adding the same multiple of ten.

Before You Start

Understanding Place Value to 100

Why: Students need to understand that numbers are composed of tens and ones to grasp how adding multiples of ten affects the tens digit.

Counting by Tens

Why: Familiarity with counting by tens is essential for recognizing and adding multiples of ten efficiently.

Key Vocabulary

Multiple of Ten	A number that can be divided by 10 with no remainder, such as 10, 20, 30, 40, and so on.
Two-Digit Number	A whole number greater than or equal to 10 and less than or equal to 99, consisting of a tens digit and a ones digit.
Tens Digit	The digit in a two-digit number that represents the number of tens.
Ones Digit	The digit in a two-digit number that represents the number of ones.
Base-Ten Blocks	Manipulatives used to represent numbers, where rods represent tens and small cubes represent ones.

Watch Out for These Misconceptions

Common Misconception

Adding a multiple of ten changes both digits.

What to Teach Instead

Students sometimes increment the ones digit when adding tens, perhaps treating it as single-digit addition across the whole number. Placing base-ten units beside rods and physically adding only rods while the units remain untouched makes the ones-place stability concrete and observable.

Common Misconception

You have to count by ones to add a multiple of ten.

What to Teach Instead

Students who lack mental strategies fall back on counting all from one. Explicitly connecting the skip-count-by-tens sequence (10, 20, 30...) to the act of adding rods builds the mental framework for efficient computation and removes the need for exhaustive counting.

Active Learning Ideas

Inquiry Circle: What Changed?

Partners build a two-digit number with base-ten blocks, then add one rod (ten) at a time. After each addition, they record the new number and circle what changed. Groups compile results and share their pattern discovery with the class.

20 min·Pairs

Think-Pair-Share: Predict the New Number

Announce a starting number (e.g., 34). Ask partners to predict what 34 + 20 will be before any calculation. Each partner shares their prediction and reasoning. The class tests predictions with a hundreds chart or base-ten blocks and discusses why the ones digit never moved.

15 min·Pairs

Gallery Walk: Hundreds Chart Hop

Post large hundreds charts around the room with a starting number circled. Students rotate and draw an arrow showing the result of adding a given multiple of ten (10, 20, or 30). They record the equation and explain in one sentence why the ones digit stayed the same.

20 min·Small Groups

Stations Rotation: Mental Math Challenge

Each station provides a starting number and a multiple of ten to add (presented with blocks, a hundreds chart, and numerals only). Students solve mentally at the numeral station and explain their strategy, building toward fluent mental addition of multiples of ten.

25 min·Small Groups

Real-World Connections

• Cashiers at a grocery store often add multiples of ten when calculating the total cost of items, especially when dealing with bulk purchases or discounts. For example, adding the cost of two 10-pound bags of potatoes.
• Construction workers use multiples of ten when measuring materials. A carpenter might need to add 20 feet to an existing 30-foot beam for a specific project, changing only the total length measurement.

Assessment Ideas

Quick Check

Present students with a number line from 10 to 100. Ask them to mark where 45 would be, then circle 55, 65, and 75. Ask: 'What do you notice about the numbers you circled?'

Exit Ticket

Give each student a card with a problem like '32 + 20 = ?'. After they solve it using drawings or mental math, ask them to write one sentence explaining how adding 20 changed the number 32.

Discussion Prompt

Pose the question: 'If you have 57 cents and you find 3 more dimes, how much money do you have now? Explain your thinking.' Encourage students to share different strategies they used to solve the problem.

Frequently Asked Questions

How do you explain adding multiples of ten to a first grader?

Use base-ten rods and unit cubes. Show a two-digit number, then add whole rods one at a time. Each time a rod is added, only the tens digit in the written number grows; the unit cubes and the ones digit stay the same. Repeat with a hundreds chart: moving down one row adds ten while staying in the same column keeps the ones digit unchanged.

Why does adding a multiple of ten only change the tens digit?

Multiples of ten have no ones component (10, 20, 30 each have zero ones). When you add zero ones to a number, the ones digit cannot change. This is a direct consequence of how place value organizes numbers, and it is one of the clearest demonstrations of the base-ten system's structure available at grade one.

What mental math strategies help with adding multiples of ten?

The most direct strategy is to identify the tens digit, add the multiple of ten to it as if it were a single-digit addition, and keep the ones digit unchanged. For example, 45 + 30: think 4 + 3 = 7, so the answer is 75. A hundreds chart supports this by making the row-jump pattern visual until the mental strategy is internalized.

How does active learning support the teaching of adding multiples of ten?

When students predict a result before testing it with blocks or a hundreds chart, they invest in finding out whether their reasoning is correct. This prediction-and-verify cycle makes the stability of the ones digit a genuine discovery rather than a fact to be memorized. Sharing findings in small groups also builds the vocabulary students need to articulate place value relationships clearly.