Adding and Subtracting Decimals (Tenths and Hundredths)

Active learning works well for decimal addition and subtraction because students often struggle to see the relationship between whole numbers and decimal fractions. Hands-on and collaborative tasks let learners physically align place values, which builds concrete understanding before moving to abstract problems. This approach also addresses common errors by making misconceptions visible during the activity itself.

• 5th Year
• Mathematical Mastery: Exploring Patterns and Logic
• 4 activities
• 20 min–35 min

Learning Objectives

1. Calculate the sum of two decimal numbers with tenths and hundredths, aligning decimal points correctly.
2. Subtract a decimal number with tenths and hundredths from another, ensuring accurate place value alignment.
3. Identify and explain common errors, such as misaligned decimal points, when adding or subtracting decimals.
4. Justify the necessity of aligning decimal points based on place value principles.
5. Predict the approximate result of adding two decimals that have a different number of decimal places.

Problem-Based Learning

⏱ 25 min·Pairs

Pairs: Decimal Place Value Match-Up

Provide cards with decimals and base-ten visuals. Pairs match 2.5 to its hundredths equivalent 2.50, then add or subtract matched pairs. Switch roles after five rounds and discuss alignments. End with pairs creating their own problems.

Prepare & details

Analyze the common errors made when adding or subtracting decimals and propose solutions.

Facilitation Tip: During Decimal Place Value Match-Up, provide place value mats that separate tenths and hundredths columns to visually reinforce alignment.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 35 min·Small Groups

Small Groups: Shopkeeper Challenge

Set up a class shop with priced items to two decimals. Groups receive budgets, select items, add totals, and subtract costs. Rotate shopkeeper roles every 10 minutes. Groups present final balances and justify calculations.

Prepare & details

Justify the need to align decimal points when performing addition or subtraction.

Facilitation Tip: In the Shopkeeper Challenge, set up stations with labeled price tags so students practice recording transactions with proper decimal placement.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 30 min·Whole Class

Whole Class: Prediction Relay

Write decimal problems on board with varying places. Teams predict answers by writing on mini-whiteboards, then justify as a class. Correct predictions score points. Use results to model annexing zeros.

Prepare & details

Predict the outcome of adding two decimals with different numbers of decimal places.

Facilitation Tip: For the Prediction Relay, use a whiteboard timer to keep the pace brisk and maintain student engagement in quick calculations.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 20 min·Individual

Individual: Error Hunt Worksheet

Distribute worksheets with five flawed calculations. Students circle errors, rewrite correctly, and explain fixes. Follow with pair shares to compare solutions. Collect for quick feedback.

Prepare & details

Analyze the common errors made when adding or subtracting decimals and propose solutions.

Facilitation Tip: With the Error Hunt Worksheet, have students first solve problems individually, then trade papers with partners to discuss corrections in pairs.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Teaching This Topic

Experienced teachers begin by modeling the alignment of decimal points with clear visuals, such as writing numbers on a grid or using base-ten blocks to represent tenths and hundredths. Avoid rushing to abstract steps without first building spatial understanding. Research shows that students who physically manipulate decimal cards or use money manipulatives are less likely to misalign places, so incorporate these tools regularly.

What to Expect

In successful learning, students consistently align decimal points, annex zeros as needed, and explain their steps using place value language. They should also correct peers’ mistakes during group work and articulate why place value alignment matters. By the end of the activities, students will compute accurately and justify their reasoning with confidence.

Watch Out for These Misconceptions

Common Misconception

During Decimal Place Value Match-Up, watch for students who stack numbers without aligning decimal points.

What to Teach Instead

Stop the pair and have them rebuild the numbers on the place value mat, asking them to explain why the decimal points must line up before they continue.

Common Misconception

During Decimal Place Value Match-Up, watch for students who believe annexing zeros changes a decimal's value.

What to Teach Instead

Ask students to cover the same area on the decimal square with 1.2 and 1.20, then discuss what they notice about the total space covered.

Common Misconception

During Shopkeeper Challenge, watch for students who borrow without adjusting the decimal point in subtraction.

What to Teach Instead

Prompt them to model the transaction with play money, showing how regrouping dollars into dimes and pennies keeps the decimal aligned.

Assessment Ideas

Exit Ticket

After Decimal Place Value Match-Up, provide two problems: 1) 7.83 + 2.5 and 2) 9.1 - 3.45. Ask students to solve both, showing their work and explaining in one sentence why they aligned the decimal points as they did.

Quick Check

During Shopkeeper Challenge, present students with a partially solved addition problem: 5.6 + 1.23 = ?. Ask them to write down the next step they would take to solve this problem correctly, focusing on place value alignment and annexing zeros if needed.

Discussion Prompt

After Prediction Relay, pose the question: 'Imagine you are adding 15.7 and 8.42. What might go wrong if you don't align the decimal points? Describe two possible errors and how to avoid them.' Have students share responses with a partner before whole-class discussion.

Extensions & Scaffolding

• Challenge: Create a real-world scenario where adding three decimal prices exceeds $20.00 and requires precise computation.
• Scaffolding: Provide a template with pre-aligned decimal points and blank spaces for students to fill in numbers.
• Deeper Exploration: Ask students to design a menu with prices in tenths and hundredths, then calculate total costs for different orders including tax at 7% (using a calculator for tax only).

Key Vocabulary

Decimal Point	A symbol used to separate the whole number part from the fractional part of a number. In addition and subtraction of decimals, it is crucial for aligning place values.
Place Value	The value of a digit based on its position within a number. For decimals, this includes tenths, hundredths, and so on, which must align for correct computation.
Annexing Zeros	Adding zeros to the right of the last digit in the decimal part of a number without changing its value. This is often done to make the number of decimal places equal in addition and subtraction.
Regrouping	The process of borrowing from a higher place value to a lower place value when subtracting, or carrying over from a lower place value to a higher place value when adding, essential for accurate decimal calculations.