Fraction Bridges

Connecting HOW we solve to WHY it works

5th Grade Parent Workshop

Remember this?

"Ours is not to reason why,
just invert and multiply."

\( \frac{4}{5} \div 3 \rightarrow \frac{4}{5} \times \frac{1}{3} \)

The Problem with Rules:

Hard to remember which number to "flip."
No way to check if the answer "makes sense."
Modern Approach: We build a picture first!

See it in Action

Matholia: Division of Fractions

Let's Pause...

"Each friend receives one-third of four-fifths."

Notice how the video shows that dividing by 3 is the exact same thing as finding 1/3 of a group.

The picture makes the rule clear!

The Bar Model

Step 1: Start with the whole

4/5 Shaded

Step 2: Divide into 3 groups

1/3 of 4/5

The denominator (the bottom number) represents the total number of small pieces in the whole.

5 pieces \(\times\) 3 groups = 15 total pieces

Practice #1: The Model

Building the Concept

\( \frac{1}{2} \div 4 = ? \)

"Imagine half a sandwich shared by 4 people..."

1. Draw 1 whole bar.

2. Shade half of it.

3. Split the shaded half into 4 equal pieces.

4. How much of the whole bar is each piece?

Practice #2: The Algorithm

Checking for Efficiency

\( \frac{2}{3} \div 5 = ? \)

The Steps:

Keep the 1st fraction.
Change \(\div\) to \(\times\).
Use the unit fraction (\(5 \rightarrow 1/5\)).

\( \frac{2}{3} \times \frac{1}{5} = \frac{2}{15} \)

Supporting at Home

Instead of giving the answer, try asking these Guiding Questions from your discussion cards:

"Can you draw a picture of what we're starting with?"

"Are the pieces getting smaller or larger when we divide them?"

"What would this look like if we shared it with one more friend?"

Questions?

We're here to bridge the gap together. No question is too small!

The Math

Homework

Resources

Thank You for Coming!

Check your take-home folder for:

Parent Letter Practice Sheet Discussion Cards

"Understanding the 'why' makes the 'how' stick."

Fraction Bridges Workshop

Parent Workshop Facilitator Guide

Fraction Bridges Presentation Slides

Math Bridge Parent Letter

Math Talk Discussion Cards

Fraction Practice Homework Sheet

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