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Math for Grade 5
1 Number Sense
1-1 Place Value
1-1 1 Understanding place value up to millions
1-1 2 Reading and writing numbers in standard and expanded form
1-1 3 Comparing and ordering numbers
1-2 Rounding
1-2 1 Rounding numbers to the nearest 10, 100, and 1000
1-2 2 Estimating sums and differences
1-3 Number Patterns
1-3 1 Identifying and extending number patterns
1-3 2 Using patterns to solve problems
2 Operations
2-1 Addition and Subtraction
2-1 1 Adding and subtracting multi-digit numbers
2-1 2 Solving word problems involving addition and subtraction
2-2 Multiplication
2-2 1 Multiplication facts up to 12x12
2-2 2 Multiplying multi-digit numbers by one-digit numbers
2-2 3 Multiplying multi-digit numbers by two-digit numbers
2-2 4 Solving word problems involving multiplication
2-3 Division
2-3 1 Division facts up to 12x12
2-3 2 Dividing multi-digit numbers by one-digit numbers
2-3 3 Dividing multi-digit numbers by two-digit numbers
2-3 4 Solving word problems involving division
2-4 Order of Operations
2-4 1 Understanding and applying the order of operations (PEMDAS)
2-4 2 Solving problems with multiple operations
3 Fractions
3-1 Understanding Fractions
3-1 1 Identifying parts of a whole and parts of a set
3-1 2 Equivalent fractions
3-1 3 Comparing and ordering fractions
3-2 Operations with Fractions
3-2 1 Adding and subtracting fractions with like denominators
3-2 2 Adding and subtracting fractions with unlike denominators
3-2 3 Multiplying fractions by whole numbers
3-2 4 Solving word problems involving fractions
4 Decimals
4-1 Understanding Decimals
4-1 1 Reading and writing decimals
4-1 2 Comparing and ordering decimals
4-1 3 Converting between fractions and decimals
4-2 Operations with Decimals
4-2 1 Adding and subtracting decimals
4-2 2 Multiplying decimals
4-2 3 Dividing decimals
4-2 4 Solving word problems involving decimals
5 Measurement
5-1 Units of Measurement
5-1 1 Understanding customary and metric units of length, weight, and capacity
5-1 2 Converting between units of measurement
5-2 Time
5-2 1 Telling time to the minute
5-2 2 Calculating elapsed time
5-2 3 Solving word problems involving time
5-3 Area and Perimeter
5-3 1 Finding the area and perimeter of rectangles and squares
5-3 2 Solving word problems involving area and perimeter
6 Geometry
6-1 Shapes
6-1 1 Identifying and classifying 2D shapes (triangles, quadrilaterals, etc )
6-1 2 Identifying and classifying 3D shapes (cubes, pyramids, etc )
6-2 Angles
6-2 1 Identifying and measuring angles
6-2 2 Classifying angles as acute, obtuse, right, or straight
6-3 Symmetry
6-3 1 Identifying lines of symmetry
6-3 2 Creating symmetrical shapes
7 Data and Probability
7-1 Data Representation
7-1 1 Reading and interpreting bar graphs, line graphs, and pie charts
7-1 2 Creating graphs to represent data
7-2 Probability
7-2 1 Understanding probability as a measure of likelihood
7-2 2 Predicting outcomes based on probability
7-2 3 Solving simple probability problems
Calculating Elapsed Time

Calculating Elapsed Time

Key Concepts

1. **Understanding Time Units**: Time is measured in hours, minutes, and seconds. Understanding these units is crucial for calculating elapsed time.

2. **Starting and Ending Times**: To calculate elapsed time, you need to know both the starting time and the ending time.

3. **Converting Between Time Units**: Sometimes, you need to convert minutes to hours or seconds to minutes to simplify calculations.

4. **Adding and Subtracting Time**: Elapsed time can be found by subtracting the starting time from the ending time.

5. **Handling Time Spans Over Multiple Days**: When calculating elapsed time over multiple days, you need to account for the number of days and the time within each day.

Detailed Explanation

Understanding Time Units

Time is typically measured in hours (h), minutes (min), and seconds (s). For example, 1 hour is equal to 60 minutes, and 1 minute is equal to 60 seconds.

Example: Time Units

1 hour = 60 minutes

1 minute = 60 seconds

Starting and Ending Times

To calculate elapsed time, you need to know when an event starts and when it ends. For example, if a movie starts at 7:00 PM and ends at 9:30 PM, the starting time is 7:00 PM and the ending time is 9:30 PM.

Example: Starting and Ending Times

Movie starts at 7:00 PM and ends at 9:30 PM.

Converting Between Time Units

Sometimes, you need to convert between hours and minutes to simplify calculations. For example, 90 minutes can be converted to 1 hour and 30 minutes.

Example: Converting Time Units

90 minutes = 1 hour and 30 minutes

Adding and Subtracting Time

Elapsed time can be found by subtracting the starting time from the ending time. For example, if a movie starts at 7:00 PM and ends at 9:30 PM, the elapsed time is 2 hours and 30 minutes.

Example: Adding and Subtracting Time

Ending time: 9:30 PM

Starting time: 7:00 PM

Elapsed time: 9:30 PM - 7:00 PM = 2 hours and 30 minutes

Handling Time Spans Over Multiple Days

When calculating elapsed time over multiple days, you need to account for the number of days and the time within each day. For example, if an event starts at 10:00 PM on Monday and ends at 2:00 AM on Wednesday, you need to calculate the time for each day and then add them together.

Example: Time Spans Over Multiple Days

Start: 10:00 PM on Monday

End: 2:00 AM on Wednesday

Elapsed time: (12 hours on Monday) + (24 hours on Tuesday) + (2 hours on Wednesday) = 38 hours

Examples and Analogies

Think of calculating elapsed time as counting the hours on a clock. Just as you count the hours from one time to another, you can calculate the elapsed time by subtracting the starting time from the ending time.

Practical Application

Understanding how to calculate elapsed time is essential for various real-life tasks such as:

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