Overview
This lecture reviews a 5th grade math practice test, covering key concepts such as number forms, place value, operations with decimals and fractions, measurement conversions, geometry, prime factorization, and interpreting data displays.
Number Forms and Place Value
- The word "and" in a number represents the decimal point (e.g., 550 and 306 thousandths = 550.306).
- When dividing by 10^n, move the decimal n places to the left; when multiplying by 10^n, move it n places to the right.
- 10^n means 10 multiplied by itself n times (e.g., 10^3 = 1,000).
- Place values after the decimal: tenths, hundredths, thousandths.
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Rounding, Comparisons, and Operations
- To round, look at the digit to the right of the target place: 5 or higher rounds up; 4 or lower rounds down.
- When comparing decimals or fractions, align digits or use common denominators.
- Multiply and divide fractions by multiplying numerators and denominators directly.
- Inequality symbols: '>' means greater than, '<' means less than; use the Pac-Man analogy to remember.
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Fractions, Decimals, and Mixed Numbers
- Multiplying by a fraction greater than 1 increases the product; less than 1 decreases it.
- For subtracting mixed numbers, borrow if the fractional part is too small.
- Convert fractions to decimals by dividing the numerator by the denominator.
- Simplify fractions by dividing by common factors.
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Expanded Form, Exponents, and Models
- Expanded form can use powers of 10 (e.g., 7,042 = 7×10^3 + 4×10^1 + 2).
- Visual models for multiplication show area or overlap for decimals and fractions.
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Measurement and Unit Conversion
- 1 pint = 2 cups; 1 quart = 2 pints; 1 gallon = 4 quarts.
- Convert units by multiplying or dividing by the correct conversion factor.
- For perimeter, add all sides; for area, multiply length × width; for volume, multiply length × width × height.
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Data, Graphs, and Patterns
- Use line plots, bar graphs, and tables to find totals, fractions, or recognize arithmetic/multiplicative patterns.
- For ordered pairs (x, y), plot x (horizontal) first, then y (vertical).
- Additive patterns: add the same number each time; multiplicative patterns: multiply by the same number.
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Geometry and Shapes
- Quadrilaterals have 4 sides (e.g., square, trapezoid, rhombus).
- Prime numbers have exactly two factors: 1 and itself; 1 is not prime.
- When dividing by a fraction, use "keep, change, flip" (invert the divisor and multiply).
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Key Terms & Definitions
- Standard Form — Writing numbers using only numerals.
- Expanded Form — Writing numbers to show the value of each digit.
- Prime Number — A number greater than 1 with only two factors: 1 and itself.
- Improper Fraction — Numerator is larger than the denominator.
- Mixed Number — A whole number combined with a fraction.
- Perimeter — The distance around a shape.
- Area — The amount of surface covered; for rectangles, length × width.
- Volume — The amount of space inside a 3D object.
- Order of Operations — PEMDAS (Parentheses, Exponents, Multiply/Divide, Add/Subtract).
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Action Items / Next Steps
- Review times tables, place value, and fraction/decimal conversions.
- Practice unit conversions for cups, pints, quarts, and gallons.
- Complete any additional homework or practice extra word problems.
General Math Practice Video: