What time does he go to sleep if the night is 8 hours long?
Daily Routine: 14 waking hours, 8 night hours (sleep 4h, awake 4h at night).
Time fractions: Using fractions to describe parts of time periods like days, nights, or hours.
- Identify the total time period
- Determine what fraction is used for sleeping
- Calculate the remaining fraction
- Convert fractions to actual time if needed
From 7 AM to 9 PM is 14 hours of day
Night is 8 hours long
Tom sleeps 1/2 of night = 1/2 × 8 = 4 hours
Awake time = Day (14) + Night awake (4) = 18 hours out of 24
So awake fraction = 18/24 = 3/4
If night is 8 hours and he sleeps 4 hours, he goes to sleep 4 hours before midnight
So he goes to sleep at 8 PM
Tom is awake for 3/4 of the day. He goes to sleep at 8 PM.
• Time conversion: Convert fractions to actual time
• Day calculation: 24 hours in a day
• Fraction simplification: 18/24 = 3/4
What fraction of the carrots does Mom keep?
Family Sharing: 6 carrots, 2 children, equal portions.
Equal sharing: Dividing items equally among people, often using fractions.
Mom has 6 carrots in total
Daughter gets 1/3 of 6 = 1/3 × 6 = 2 carrots
Son gets 1/3 of 6 = 1/3 × 6 = 2 carrots
Given away = 2 + 2 = 4 carrots
Mom keeps = 6 - 4 = 2 carrots
As a fraction = 2/6 = 1/3
Each child gets 2 carrots. Mom keeps 1/3 of the carrots.
• Multiplication: Fraction × total = amount
• Subtraction: Total - given away = kept
• Equal sharing: Same fraction for equal distribution
How many shirts are red?
How many shirts are blue?
What fraction are yellow?
Clothing Organization: 8 shirts sorted by color using fractions.
Fraction of a set: Using fractions to describe parts of a group of items.
Red shirts = 1/2 of 8 = 1/2 × 8 = 4 shirts
Blue shirts = 1/4 of 8 = 1/4 × 8 = 2 shirts
Yellow shirts = Total - red - blue = 8 - 4 - 2 = 2 shirts
Yellow fraction = 2/8 = 1/4
Red (1/2) + Blue (1/4) + Yellow (1/4) = 2/4 + 1/4 + 1/4 = 4/4 = 1 whole ✓
Sarah has 4 red shirts, 2 blue shirts, and 2 yellow shirts. Yellow shirts make up 1/4 of her collection.
• Fraction of set: Fraction × total = count
• Addition: All parts should sum to whole
• Verification: Check that fractions add to 1
Definitions:
Fraction: A number that shows part of a whole. It has a top number (numerator) and bottom number (denominator).
Numerator: The top number showing how many parts we have or take.
Denominator: The bottom number showing how many equal parts there are in total.
Equal parts: All sections must be the same size for valid fractions.
Time fractions: Using fractions to describe parts of time periods.
Fraction of a set: Using fractions to describe parts of a group of items.
Equal sharing: Dividing items equally among people using fractions.
Core Rules:
1. All parts must be equal in size
2. Numerator = parts we have/take
3. Denominator = total parts
4. Fraction = numerator/denominator
5. All parts should add up to whole (1)
6. Fraction × total = actual amount
7. Time can be divided into fractional parts
Step-by-Step Method:
Step 1: Identify the total amount (denominator)
Step 2: Identify the part being described (numerator)
Step 3: Write the fraction as part/total
Step 4: Calculate actual amounts if needed
Step 5: Verify the answer makes sense
Step 6: Check if all parts add to whole
Examples:
Simple: 1/2 of 4 apples = 2 apples
Medium: 1/3 of day = 8 hours
Advanced: 1/4 of 12 toys = 3 toys
Tips:
- Look for fractions in daily routines
- Practice with real objects (food, toys, time)
- Draw pictures to visualize
- Check if parts add to whole
- Remember: equal parts are essential
- Connect fractions to daily activities
Key Notes:
- Fractions are everywhere in daily life
- Understanding fractions helps with sharing and planning
- Time can be divided into fractional parts
- Practice makes fractions natural
Half day = 12 hours
Quarter pizza = 1/4
Third shirts = 1/3
Half chores = 1/2
What fraction of the book has she read?
What fraction is left to read?
Reading Schedule: 12-page book, 2 days of reading.
Progress tracking: Using fractions to track completion of tasks or reading.
Monday: 1/4 of 12 = 1/4 × 12 = 3 pages
Tuesday: 1/4 of 12 = 1/4 × 12 = 3 pages
Total read = 3 + 3 = 6 pages
Fraction read = 6/12 = 1/2
Fraction left = 1 - 1/2 = 1/2
Emma read 6 pages in total. She has read 1/2 of the book. 1/2 of the book is left to read.
• Multiplication: Fraction × total = actual amount
• Addition: Combine fractions with same denominator
• Complement: What's left = 1 - what's done
What fraction of the rolls is left?
Household Planning: 10 rolls, 2 weeks of usage.
Supply management: Using fractions to track usage of household supplies.
First week: 2/5 of 10 = 2/5 × 10 = 4 rolls
Second week: 1/5 of 10 = 1/5 × 10 = 2 rolls
Total used = 4 + 2 = 6 rolls
Fraction used = 6/10 = 3/5
Fraction left = 1 - 3/5 = 2/5
The family used 6 rolls in total. 2/5 of the rolls are left.
• Multiplication: Fraction × total = actual amount
• Addition: Combine fractional parts
• Complement: Remaining = 1 - used fraction
Fraction: A number expressing part of a whole
Numerator: Top number showing parts we have/use
Denominator: Bottom number showing total parts
Equal parts: All sections must be the same size
Everyday life: Applying math concepts to routine activities
- Identify the situation: What activity involves fractions?
- Count total amount: How many items/time units available?
- Identify used amount: How many are used/allocated?
- Write fraction: Used over total
- Calculate remaining: Total - used = left
- Verify: Check if parts make sense
• Equal parts: All parts must be the same size
• Numerator: Number of parts used/allocated
• Denominator: Total number of parts
• Time fractions: Applying fractions to time periods
• Remaining: What's left after use
• Verification: All parts should add to whole