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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
Critical Thinking and Reasoning

Critical Thinking and Reasoning

Key Concepts

Critical thinking and reasoning are essential skills that involve analyzing information, making judgments, and solving problems logically. Key concepts include:

Analyzing Information

Analyzing information involves breaking down data into smaller parts to understand its components and relationships. This helps in identifying patterns and making informed decisions.

Example: When solving a word problem, analyze the given information to identify the key numbers and operations needed to find the solution.

Making Judgments

Making judgments involves evaluating information to form opinions or decisions. This requires considering the evidence and reasoning through the pros and cons of different options.

Example: If you have two math problems to solve, and one requires more steps but is straightforward, while the other is simpler but involves tricky calculations, you need to judge which one to tackle first based on your strengths.

Logical Problem Solving

Logical problem solving involves using systematic thinking to find solutions. This includes breaking down the problem, applying logical rules, and verifying the solution.

Example: When solving a geometry problem, use logical reasoning to apply the properties of shapes and the principles of geometry to find the correct answer.

Evaluating Arguments

Evaluating arguments involves assessing the validity and strength of different points of view. This requires understanding the reasoning behind each argument and identifying any flaws or biases.

Example: In a debate about whether to use a calculator for math problems, evaluate the arguments for and against by considering the benefits of accuracy versus the importance of mental calculation skills.

Drawing Conclusions

Drawing conclusions involves synthesizing information to form a final judgment or decision. This requires integrating all the analyzed information and reasoning through the logical steps.

Example: After analyzing a set of data and evaluating different interpretations, draw a conclusion about the average score of students in a math test based on the evidence.

Examples and Analogies

Think of critical thinking and reasoning as solving a mystery. Analyzing information is like gathering clues, making judgments is like weighing the evidence, logical problem solving is like piecing together the clues, evaluating arguments is like considering different theories, and drawing conclusions is like solving the mystery.

Example: If you are trying to determine the best route to school, analyze the available routes, judge which one is the quickest and safest, use logical reasoning to consider traffic patterns, evaluate arguments about walking versus biking, and draw a conclusion about the best route.

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