Number and Operations:
* Whole Numbers: Fluency in addition, subtraction, multiplication, and division, including multi-digit numbers. Understanding place value to at least the millions. Estimating sums, differences, products, and quotients.
* Decimals: Understanding place value to the thousandths. Adding, subtracting, multiplying, and dividing decimals. Rounding decimals. Converting between fractions and decimals.
* Fractions: Adding, subtracting, multiplying, and dividing fractions and mixed numbers (with unlike denominators). Simplifying fractions. Understanding equivalent fractions. Comparing and ordering fractions.
* Number Theory: Understanding prime and composite numbers, factors, multiples, and least common multiple (LCM) and greatest common factor (GCF).
Algebraic Thinking:
* Patterns and Relationships: Identifying, describing, and extending numerical and geometric patterns. Representing patterns using tables and graphs. Understanding and using variables (letters representing unknown numbers).
* Equations and Inequalities: Solving simple one-step equations and inequalities. Understanding the meaning of the equal sign.
Measurement:
* Units of Measurement: Converting units of length, weight, capacity, and time within the same system (e.g., inches to feet, liters to milliliters).
* Geometric Measurement: Finding the perimeter, area, and volume of various shapes (rectangles, squares, triangles, cubes, rectangular prisms). Understanding the concept of angles and their measurement in degrees.
Geometry:
* Shapes: Classifying and identifying two-dimensional shapes (triangles, quadrilaterals, polygons) and three-dimensional shapes (cubes, rectangular prisms, pyramids, cones, cylinders, spheres). Understanding properties of shapes (e.g., number of sides, angles).
* Spatial Reasoning: Visualizing and drawing shapes. Understanding transformations (slides, flips, turns).
Data Analysis and Probability:
* Data Representation: Reading and interpreting data from bar graphs, line graphs, and pictographs. Creating line plots and stem-and-leaf plots.
* Data Analysis: Finding the mean, median, mode, and range of a data set.
* Probability: Understanding simple probability (e.g., the likelihood of an event occurring).
Important Considerations:
* Problem Solving: 5th graders should be able to apply their mathematical knowledge to solve real-world problems. This often involves multiple steps and requires them to choose appropriate strategies.
* Mathematical Reasoning: They should be able to explain their thinking, justify their answers, and make connections between different mathematical concepts.
* Fluency: While understanding concepts is crucial, fluency in basic calculations is also important.
This list provides a comprehensive overview. The specific curriculum may vary slightly depending on the school and state standards. It's always best to check with the student's teacher or school for the most accurate and detailed information on what is expected.