Estimated Time: 10–15 minutes

Goal: Before your lesson, you should understand how each operation works so that the lesson can focus on solving problems instead of introducing the ideas for the first time.

Flipping Flashcards First:

Flip through the primer’s flashcards before you start and after you finish. These help with context and comprehension.

Step 1 — READ (3–5 minutes)

Part A — Adding & Subtracting Fractions

The Vertical Rule

Whenever you are adding or subtracting fractions or mixed numbers:

✅ Rewrite the problem vertically.

If the top fraction is smaller than the bottom fraction, borrow one whole from the whole number.

Remember:

So

Now subtract normally.

Part B — Multiplication & Division

Mixed Number Rule

🚫 Never multiply or divide mixed numbers.

Always change them to improper fractions first.

The Mathematical Way

A mixed number is really a whole number PLUS a fraction.

Example:

↓

Rewrite the mixed number as addition.

↓

Rewrite the whole number using the same denominator.

↓

Substitute it back into the expression.

↓

Now add like fractions.

The Circle Method (Shortcut)

Instead of writing every intermediate step, we can combine them into one shortcut.

Example:

↓

Multiply the whole number by the denominator.

↓

Add the numerator.

↓

Keep the denominator.

Circle Method Formula

💡 Why does this work?

The Circle Method is simply a shortcut for

It combines all of those intermediate steps into one quick calculation.

The Circle Method (1 more time)

For a mixed number like

Step 1.

Multiply the whole number by the denominator.

Step 2.

Add the numerator.

Step 3.

Keep the denominator.

Cross-Simplify First

Before multiplying fractions,

look for numbers that can cancel diagonally.

Example:

Notice that

9 and 3 divide by 3.

Rewrite as

Now multiply.

Division Rule

Remember:

Keep • Change • Flip

Example:

1. Convert the mixed number.
2. Keep the first fraction.
3. Change ÷ to ×.
4. Flip the second fraction.
5. Cross-simplify.
6. Multiply.

Step 2 — WATCH (5–10 minutes)

Watch ONE of these videos.

• Khan Academy — Multiplying Mixed Numbers
• Math with Mr. J — Multiplying & Dividing Mixed Numbers

Step 3 — TRY IT YOURSELF

1.

2.

Convert to an improper fraction.

3.

Cross-simplify first.

4.

Use Keep • Change • Flip

Come Prepared

⭐ Bring any questions you have.

If something doesn't make sense yet, that's okay—that's exactly what we'll work on together during our session.