PRAXIS 5003 · COURSE
Praxis 5003 Elementary Education: Mathematics Subtest course
17 guided lessons across 3 sections. Read the first chapter free — no account needed.
FREE CHAPTER
Place Value, Expanded Form, and Rounding
Numbers and Operations is 40% of the 5003, the biggest category. Everything starts with place value: knowing what each digit is worth.
Key words
- Place value
- The value a digit has because of its position in a number. — e.g. In 5,309 the 3 is in the hundreds place, so it's worth 300.
- place value and base ten
- Each place to the left is ten times the value of the place to its right — e.g. In 4,305 the 3 represents three hundreds
- evidence
- Information that supports or challenges an explanation of place value and base ten. — e.g. In 4,305 the 3 represents three hundreds
- misconception
- A believable but incorrect understanding of place value and base ten. — e.g. The digit 3 does not always represent three ones
- application
- Using what you know about place value and base ten to solve a new problem. — e.g. Use expanded form to explain regrouping
- Expanded form
- Writing a number as the sum of each digit's value. — e.g. 4,206 = 4,000 + 200 + 6.
- Standard form
- A number written with digits in the usual way. — e.g. 4,206
- Exponent
- A small raised number that tells how many times to multiply the base by itself. — e.g. 10^3 = 10 x 10 x 10 = 1,000.
- Rounding
- Replacing a number with a nearby, simpler number to a given place. — e.g. 3,482 rounded to the nearest hundred is 3,500.
EACH PLACE IS 10 TIMES THE ONE TO ITS RIGHT
Ones, tens, hundreds, thousands... and to the right of the decimal: tenths, hundredths, thousandths. Moving one place LEFT multiplies by 10. Moving one place RIGHT divides by 10 (one-tenth). In 444, the first 4 is worth 400, which is 10 times the middle 4 (40).
DIGIT vs. VALUE
The digit is the symbol (7). The value is what it's worth in its place. In 3,782 the digit 7 is in the hundreds place, so its value is 700. Test questions love to ask for the value, not the place.
THREE WAYS TO WRITE A NUMBER
Standard form: 4,206. Word form: four thousand, two hundred six. Expanded form: 4,000 + 200 + 6, or (4 x 1,000) + (2 x 100) + (6 x 1). Notice the zero in the tens place just disappears in expanded form.
POWERS OF 10
10^1 = 10, 10^2 = 100, 10^3 = 1,000. The exponent tells you how many zeros. Multiplying by 10^3 moves every digit 3 places left: 4.5 x 10^3 = 4,500. Dividing by 10^2 moves digits 2 places right: 36 / 10^2 = 0.36.
ROUNDING
Underline the place you're rounding to. Look at the digit just to its right. 5 or more, round up. 4 or less, keep it the same. Then make everything after it zero. 47,382 to the nearest thousand: underline 7, look at 3, keep 7, answer 47,000.
COMPOSE AND DECOMPOSE
1,350 can be 1 thousand + 3 hundreds + 5 tens, OR 13 hundreds + 5 tens, OR 135 tens. Same number, different groupings. This is the idea behind regrouping (borrowing and carrying).
Remember this
- Each place is 10 times the place to its right.
- Value = digit x its place (the 7 in 3,782 is worth 700).
- 10^n means n zeros; multiplying by 10^n moves digits n places left.
- Rounding: look one place to the right; 5 or more rounds up.
Left is Larger: every step left is x10, every step right is /10.
Every lesson in the course
I. Numbers and Operations
40%- Place Value, Expanded Form, and RoundingFree
- Operations, Order of Operations, and Properties
- Fractions, Decimals, and Percents
- Ratios, Rates, Proportions, and Percent Problems
- Primes, Factors, Multiples, and Estimation
- Factors, multiples, and integers
II. Algebraic Thinking
30%- Expressions: Vocabulary, Evaluating, and Simplifying
- Equations and Formulas
- Inequalities and Linear Relationships
- Patterns and Function Tables
- Equality and student misconceptions
III. Geometry and Measurement, Data, Statistics, and Probability
30%- Lines, Angles, and Classifying Shapes
- Perimeter, Area, Surface Area, and Volume
- The Coordinate Plane and Measurement
- Statistics: Measures of Center and Spread
- Data Displays and Probability
- Probability and sampling