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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
Order of Operations Explained

Order of Operations Explained

Key Concepts

The Order of Operations is a set of rules that dictate the sequence in which mathematical operations should be performed to ensure consistent and accurate results. The acronym PEMDAS is often used to remember these rules: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

1. Parentheses (P)

Operations inside parentheses are performed first. If there are nested parentheses, the innermost ones are solved first.

2. Exponents (E)

Exponents are calculated next. This includes powers and roots.

3. Multiplication and Division (MD)

Multiplication and division are performed from left to right. They are of equal precedence, so the operation that appears first in the expression is performed first.

4. Addition and Subtraction (AS)

Addition and subtraction are performed last, also from left to right. They are of equal precedence, so the operation that appears first is performed first.

Detailed Explanation

Parentheses (P)

Parentheses are used to group parts of an expression that need to be evaluated first. For example, in the expression 3 + (4 * 2), the operation inside the parentheses (4 * 2) is performed first, resulting in 3 + 8 = 11.

Exponents (E)

Exponents indicate how many times a number should be multiplied by itself. For example, in the expression 2^3 + 5, the exponent (2^3) is calculated first, resulting in 8 + 5 = 13.

Multiplication and Division (MD)

Multiplication and division are performed from left to right. For example, in the expression 6 / 2 * 3, the division (6 / 2) is performed first, resulting in 3 * 3 = 9.

Addition and Subtraction (AS)

Addition and subtraction are performed last, also from left to right. For example, in the expression 10 - 4 + 2, the subtraction (10 - 4) is performed first, resulting in 6 + 2 = 8.

Examples and Analogies

Example 1: Using PEMDAS

Solve the expression 3 + 6 * (5 + 4) / 3^2.

Step 1: Parentheses: (5 + 4) = 9.

Step 2: Exponents: 3^2 = 9.

Step 3: Multiplication and Division: 6 * 9 / 9 = 54 / 9 = 6.

Step 4: Addition and Subtraction: 3 + 6 = 9.

Final Answer: 9.

Example 2: Real-Life Analogy

Think of the Order of Operations as following a recipe. Just as you follow the steps in a recipe to bake a cake, you follow the steps in PEMDAS to solve a mathematical expression. For instance, mixing ingredients (parentheses) comes before baking (exponents), which comes before decorating (multiplication and division), and finally serving (addition and subtraction).

Practical Application

Understanding the Order of Operations is essential for solving complex mathematical problems accurately. It ensures that everyone follows the same steps to arrive at the correct answer, making communication and collaboration in mathematics more effective.

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