Adding and Subtracting Fractions

Active learning works for adding and subtracting fractions because hands-on tools and real-world problems help students see why a common denominator matters. When they physically manipulate fraction strips or move along number lines, they build the mental models needed to move beyond rote rules.

• Year 7
• Mathematics
• 4 activities
• 30 min–45 min

Learning Objectives

1. Calculate the sum and difference of fractions with unlike denominators by finding common multiples.
2. Explain the necessity of a common denominator for adding and subtracting fractions, referencing unit fractions.
3. Analyze and compare at least two different strategies for determining the least common denominator.
4. Create a word problem involving the addition or subtraction of mixed numbers, applicable to a specific real-world context.
5. Evaluate the efficiency of different methods for finding common denominators when adding or subtracting fractions.

Collaborative Problem-Solving

⏱ 35 min·Pairs

Manipulative Sort: Fraction Strip Addition

Provide fraction strips for pairs to build equivalent fractions and add unlike denominators, such as 1/2 + 1/3. Students record steps on mini-whiteboards, then share one solution with the class. Extend to subtraction by removing strips.

Prepare & details

Explain why a common denominator is essential for adding or subtracting fractions.

Facilitation Tip: During Fraction Strip Addition, circulate and ask students to verbalize how the strips show equal parts before combining.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

Collaborative Problem-Solving

⏱ 45 min·Small Groups

Strategy Stations: Finding LCD Methods

Set up three stations: listing multiples, prime factors, and division rule. Small groups spend 10 minutes per station solving problems like LCD of 4 and 6, then vote on the most efficient method. Circulate to prompt explanations.

Prepare & details

Analyze different strategies for finding the least common denominator.

Facilitation Tip: At Strategy Stations, provide a timer for each method so students compare speed and accuracy of listing multiples versus prime factorization.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

Collaborative Problem-Solving

⏱ 40 min·Small Groups

Real-World Build: Mixed Number Problems

In small groups, students create and solve a problem using mixed numbers, such as sharing 2 1/4 meters of fabric among three people. They draw models, compute, and swap problems with another group for verification.

Prepare & details

Construct a real-world problem that requires adding or subtracting mixed numbers.

Facilitation Tip: For Real-World Build, limit materials to encourage creative problem-solving without overcomplicating scenarios.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

Collaborative Problem-Solving

⏱ 30 min·Small Groups

Number Line Relay: Subtracting Fractions

Mark number lines on the floor. Teams send one student at a time to plot and subtract fractions like 7/4 - 5/6 on a shared line, tagging the next teammate. Discuss LCD choices as a class afterward.

Prepare & details

Explain why a common denominator is essential for adding or subtracting fractions.

Facilitation Tip: In Number Line Relay, require teams to mark both the starting and ending fractions to emphasize distance and difference.

Setup: Groups at tables with problem materials

Materials: Problem packet, Role cards (facilitator, recorder, timekeeper, reporter), Problem-solving protocol sheet, Solution evaluation rubric

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

Teaching This Topic

Teach this by alternating concrete and abstract representations. Start with manipulatives like fraction strips to build understanding, then move to written methods. Avoid rushing to algorithms before students can articulate why denominators must match. Research shows that students who explain their reasoning aloud develop stronger retention and fewer misconceptions.

What to Expect

Students will confidently explain why fractions need common denominators and choose efficient methods to find them. They will apply these skills to mixed numbers in real-world contexts without reverting to incorrect shortcuts.

Watch Out for These Misconceptions

Common Misconception

During Fraction Strip Addition, watch for students who place strips end-to-end without aligning their unit fractions or who treat the total length as a new denominator.

What to Teach Instead

Ask them to point to where the unit fractions align and have them label each part before writing the sum. Peer partners check for matching endpoints.

Common Misconception

During Strategy Stations, watch for students who default to multiplying denominators without testing whether a smaller common multiple exists.

What to Teach Instead

Have them list multiples for both denominators on the station card and circle the smallest shared value. Use a timer to encourage efficiency.

Common Misconception

During Number Line Relay, watch for students who subtract numerators without adjusting the starting position to account for borrowing.

What to Teach Instead

Require them to mark the whole number and fraction separately on the line, then cross out and regroup visibly before moving left.

Assessment Ideas

Quick Check

After Strategy Stations, present the quick-check problems on the board. Ask students to write their steps on a sticky note, including the LCD method they chose and one sentence explaining why the common denominator was necessary.

Exit Ticket

After Real-World Build, collect student-generated problems. Evaluate both the scenario and the solution for correct operation labeling and accurate fraction arithmetic.

Discussion Prompt

During Strategy Stations, pose the discussion prompt as a station task. Listen for students to justify their chosen method using efficiency and accuracy, and collect reasoning samples to assess understanding.

Extensions & Scaffolding

• Challenge: Create a three-fraction addition problem with denominators 2, 3, and 5, requiring two steps of renaming.
• Scaffolding: Provide fraction circles pre-divided into halves, thirds, fourths, and sixths for students to physically combine.
• Deeper: Research and present another real-world context involving mixed numbers, such as adjusting a recipe for a larger group.

Key Vocabulary

Common Denominator	A shared multiple of the denominators of two or more fractions, which allows them to be added or subtracted.
Least Common Multiple (LCM)	The smallest positive integer that is a multiple of two or more numbers. It is used to find the least common denominator.
Equivalent Fractions	Fractions that represent the same value or proportion, even though they have different numerators and denominators. They are created by multiplying or dividing the numerator and denominator by the same number.
Mixed Number	A number consisting of a whole number and a proper fraction, such as 2 1/2.