Teacher Guide: Adding & Subtracting Fractions

@ Learning Objective 5-10 min lesson

Students will: Add and subtract fractions and mixed numbers with like denominators using visual models, decomposition, and standard algorithms to solve mathematical and real-world problems.

Why this matters for FAST: Fraction operations appear frequently on FAST. Students must add/subtract fractions with like denominators, work with mixed numbers, and solve word problems involving fractional quantities.

% Materials Needed

Whiteboard/projector
Student Concept Worksheet
Fraction strips or tiles
Colored pencils
Number line printout
Fraction bars template

! Common Misconceptions to Address

Misconception #1: Adding the Denominators

Students think 1/4 + 2/4 = 3/8 (adding both numerators AND denominators).

How to Address:

"The denominator tells us the SIZE of the pieces - it doesn't change when we add! If I have 1 fourth and add 2 more fourths, I have 3 fourths. The pieces are still fourths! 1/4 + 2/4 = 3/4"

Misconception #2: Not Regrouping Mixed Numbers

When subtracting 2 1/4 - 1 3/4, students struggle because they can't take 3/4 from 1/4.

How to Address:

"Sometimes we need to regroup! 2 1/4 is the same as 1 5/4 (we borrow 1 whole = 4/4). Now we can subtract: 1 5/4 - 1 3/4 = 2/4 = 1/2"

$ Lesson Steps

1

Activate Prior Knowledge (1 min)

Draw a fraction bar divided into 8 parts. Shade 3 parts. Ask: "What fraction is shaded?" (3/8) "If I shade 2 more parts, how many eighths will be shaded?" (5/8) Connect to the equation 3/8 + 2/8 = 5/8.

2

Introduce the Concept (2 min)

SAY THIS:

"When we add or subtract fractions with the SAME denominator, we only add or subtract the NUMERATORS. The denominator stays the same because it tells us the size of the pieces!"

2/6 + 3/6 = ?

26 + 36 = 56

Add the numerators (2+3=5). Keep the denominator (6).

3

Teach Subtraction (2 min)

Show: "7/8 - 3/8 = ?" Draw 8 parts, shade 7, then cross out 3. Ask: "How many eighths remain?" (4/8 = 1/2)

SAY THIS:

"Subtraction works the same way! Subtract the numerators, keep the denominator. Then simplify if you can."

4

Mixed Numbers (2 min)

Demonstrate: 1 2/5 + 2 1/5

Add whole numbers: 1 + 2 = 3
Add fractions: 2/5 + 1/5 = 3/5
Answer: 3 3/5

For subtraction with regrouping: 3 1/4 - 1 3/4

Regroup: 3 1/4 = 2 5/4 (borrow 1 whole = 4/4)
Subtract: 2 5/4 - 1 3/4 = 1 2/4 = 1 1/2

5

Word Problems (2-3 min)

Model a word problem: "Maria ate 2/8 of a pizza. Her brother ate 3/8 of the same pizza. What fraction did they eat together?"

Identify: Same denominator (8)
Operation: Adding (ate together = combine)
Calculate: 2/8 + 3/8 = 5/8

? Check for Understanding

Quick Exit Ticket (Ask the whole class):

"What is 5/6 - 2/6?"

Correct answer: 3/6 = 1/2 (Subtract numerators: 5-2=3. Keep denominator: 6. Simplify: 3/6=1/2)

& IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Add fractions with like denominators Subtract fractions with like denominators Add mixed numbers with like denominators Subtract mixed numbers with like denominators Add and subtract fractions: word problems

^ Differentiation & Extension

For struggling students: Use physical fraction tiles. Focus on visual models before moving to abstract. Start with unit fractions only (1/4 + 1/4, etc.).

For advanced students: Introduce improper fractions as answers (3/4 + 3/4 = 6/4 = 1 2/4 = 1 1/2). Challenge with multi-step word problems.

For home: Send Parent Activity sheet. Families can use recipes (doubling or halving ingredients) to practice fraction operations.