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Math for Grade 4
1 Number Sense and Operations
1-1 Place Value
1-1 1 Understanding place value through millions
1-1 2 Reading and writing numbers in standard, word, and expanded form
1-1 3 Comparing and ordering numbers
1-2 Rounding and Estimating
1-2 1 Rounding numbers to the nearest 10, 100, and 1000
1-2 2 Estimating sums, differences, products, and quotients
1-3 Addition and Subtraction
1-3 1 Adding and subtracting multi-digit numbers
1-3 2 Solving word problems involving addition and subtraction
1-4 Multiplication and Division
1-4 1 Multiplication tables up to 12
1-4 2 Multiplying multi-digit numbers by one-digit numbers
1-4 3 Dividing multi-digit numbers by one-digit numbers
1-4 4 Solving word problems involving multiplication and division
1-5 Factors and Multiples
1-5 1 Identifying factors and multiples of a number
1-5 2 Finding the greatest common factor (GCF)
1-5 3 Finding the least common multiple (LCM)
2 Fractions and Decimals
2-1 Understanding Fractions
2-1 1 Identifying and naming fractions
2-1 2 Comparing and ordering fractions with like and unlike denominators
2-1 3 Equivalent fractions
2-2 Operations with Fractions
2-2 1 Adding and subtracting fractions with like denominators
2-2 2 Solving word problems involving fractions
2-3 Understanding Decimals
2-3 1 Reading and writing decimals to the hundredths place
2-3 2 Comparing and ordering decimals
2-4 Operations with Decimals
2-4 1 Adding and subtracting decimals
2-4 2 Solving word problems involving decimals
3 Geometry and Measurement
3-1 Basic Shapes and Properties
3-1 1 Identifying and classifying 2D shapes (triangles, quadrilaterals, etc )
3-1 2 Identifying and classifying 3D shapes (cubes, pyramids, etc )
3-2 Perimeter and Area
3-2 1 Finding the perimeter of polygons
3-2 2 Finding the area of rectangles and squares
3-3 Lines and Angles
3-3 1 Identifying and measuring angles using a protractor
3-3 2 Classifying angles (acute, obtuse, right, straight)
3-4 Time and Measurement
3-4 1 Telling time to the nearest minute
3-4 2 Solving word problems involving time
3-4 3 Measuring length, weight, and capacity using standard units
4 Data Handling and Probability
4-1 Collecting and Organizing Data
4-1 1 Creating and interpreting bar graphs, line plots, and pictographs
4-1 2 Collecting and organizing data in tables
4-2 Analyzing Data
4-2 1 Finding the mode, median, and range of a set of data
4-2 2 Interpreting data from graphs and tables
4-3 Introduction to Probability
4-3 1 Understanding the concept of probability
4-3 2 Predicting outcomes based on data
5 Problem Solving and Critical Thinking
5-1 Strategies for Problem Solving
5-1 1 Using logical reasoning to solve problems
5-1 2 Applying the four operations to solve multi-step problems
5-2 Patterns and Relationships
5-2 1 Identifying and extending number patterns
5-2 2 Understanding and using simple algebraic expressions
5-3 Critical Thinking and Reasoning
5-3 1 Evaluating and justifying solutions to problems
5-3 2 Making connections between different mathematical concepts
Factors and Multiples

Factors and Multiples

Key Concepts

Factors and multiples are fundamental concepts in mathematics. Factors are numbers that divide another number exactly without leaving a remainder, while multiples are the result of multiplying a number by an integer.

Factors

Factors of a number are all the numbers that divide it exactly. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers divides 12 without leaving a remainder.

Example: Find the factors of 20.

Step 1: Start with 1 and 20 (since 1 and the number itself are always factors).

Step 2: Check 2: 20 ÷ 2 = 10 (no remainder), so 2 and 10 are factors.

Step 3: Check 3: 20 ÷ 3 = 6.67 (remainder), so 3 is not a factor.

Step 4: Check 4: 20 ÷ 4 = 5 (no remainder), so 4 and 5 are factors.

Step 5: Check 5: 20 ÷ 5 = 4 (already listed).

Factors of 20: 1, 2, 4, 5, 10, 20.

Multiples

Multiples of a number are the products obtained when that number is multiplied by integers. For example, the multiples of 3 are 3, 6, 9, 12, 15, etc., because these are the results of multiplying 3 by 1, 2, 3, 4, 5, etc.

Example: Find the first five multiples of 7.

Step 1: Multiply 7 by 1: 7 × 1 = 7.

Step 2: Multiply 7 by 2: 7 × 2 = 14.

Step 3: Multiply 7 by 3: 7 × 3 = 21.

Step 4: Multiply 7 by 4: 7 × 4 = 28.

Step 5: Multiply 7 by 5: 7 × 5 = 35.

First five multiples of 7: 7, 14, 21, 28, 35.

Examples and Analogies

Think of factors as the building blocks of a number. Just as a building is made up of smaller bricks, a number is made up of its factors. Multiples, on the other hand, are like the steps on a staircase. Each step is a multiple of the height of one step.

Practical Application

Understanding factors and multiples helps in various real-life situations. For example, when dividing a pizza into equal slices, you are dealing with factors. When counting items in groups, such as the number of students in a class, you are dealing with multiples.

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