Numbers and Operations
40%of exam
Algebraic Thinking
30%of exam
Geometry and Measurement, Data, Statistics, Probability
30%of exam
Quick Facts
- Exam
- Praxis 5003
- Full name
- Elementary Ed Math Subtest
- Part of
- Praxis 5001 battery
- Questions
- 50 (some unscored)
- Time
- 65 minutes
- Formats
- Multiple choice + numeric entry
- Calculator
- On-screen scientific (TI-30XS)
- Score scale
- 100-200
- Passing score
- Set by your state
- Fee
- $64 alone; $180 for 5001
- Retake
- 28-day wait
- Scores valid
- 10 years
Order of Operations
Please Excuse My Dear Aunt Sally
ParenthesesExponentsMultiply/divide left to rightAdd/subtract left to rightM and D tie
Factor vs Multiple
Factor
- Divides into it
- Short finite list
- GCF questions
Multiple
- Number times integer
- Infinite list
- LCM questions
Smaller than vs larger than
Word Problem Operation Picker
- Joining equal groups→Multiply(Repeated addition)
- Sharing into equal groups→Divide(How many each)
- How many fit inside→Divide(How many groups)
- Combining unequal amounts→Add
- Finding the difference→Subtract(Comparison)
- Fraction of an amount→Multiply(of means times)
- Percent of a number→Multiply by decimal
- Cost for one unit→Divide(Unit rate)
- Leftover people still travel→Round quotient up
Place Value
- Place
- Position of the digit
- Value
- Digit times its place
- Standard form
- 234
- Expanded form
- 200 + 30 + 4
- Word form
- Two hundred thirty-four
- Powers of ten
- 2×10² + 3×10¹ + 4×10⁰
- One place left
- Ten times greater
- One place right
- One-tenth as much
- Rounding
- Check the digit right
- Round up when
- That digit is ≥ 5
Dividing Fractions
Keep, Change, Flip
Keep the first fractionChange ÷ to ×Flip the second fractionThen multiply across
Place vs Value
Place
- Name of position
- Tens, hundreds, tenths
- Same for any digit
Value
- Digit times place
- 400 inside 3,472
- Changes per digit
Position vs worth
Fraction Rules
- Add or subtract
- Common denominator first
- Multiply
- Numerators and denominators straight across
- Divide
- Multiply by the reciprocal
- Reciprocal
- Flip numerator and denominator
- Unit fraction
- Numerator equals 1
- Bigger denominator
- Smaller piece
- Mixed to improper
- Whole × denominator + numerator
- Improper to mixed
- Divide; remainder over denominator
- Simplify
- Divide both by GCF
- Compare fractions
- Same whole required
- Benchmarks
- Compare to 0, ½, 1
Percent Setup
Part over whole equals percent over 100
Cross multiply to solvePercent change: change ÷ originalof means multiply
Ratio vs Rate
Ratio
- Same units
- 3 boys to 2 girls
- Part to part
Rate
- Different units
- 60 miles per hour
- Unit rate per one
Same units vs different
Decimals + Percents
- Fraction to decimal
- Divide numerator by denominator
- Decimal to percent
- Multiply by 100
- Percent to decimal
- Divide by 100
- Percent to fraction
- Put over 100, simplify
- 1/4
- 0.25 = 25%
- 1/3
- 0.333... ≈ 33.3%
- 3/8
- 0.375 = 37.5%
- 2/3
- 0.666... ≈ 66.7%
- 1/8
- 0.125 = 12.5%
- Percent of a number
- Multiply by the decimal
- Percent change
- Change ÷ original × 100
- 30% off
- Pay 70% of price
First Primes
2, 3, 5, 7, 11, 13, 17, 19
2 is only even prime1 is not primeComposite: more than two
Ratio and Proportion
- Ratio
- Compares two quantities
- Rate
- Ratio with different units
- Unit rate
- Amount per one unit
- Proportion
- Two equal ratios
- Cross multiply
- ad = bc
- Percent setup
- part/whole = percent/100
- Percent means
- Rate per 100
- Ratio 3:2, total 20
- 12 and 8
- $6.99 per 20 ounces
- About $0.35 per ounce
- Scale factor
- Multiplier between similar figures
Number Theory
- Prime
- Exactly two factors
- Composite
- More than two factors
- 1
- Neither prime nor composite
- 2
- Only even prime
- Factor
- Divides evenly into it
- Multiple
- Number times a whole number
- GCF
- Largest shared factor
- LCM
- Smallest shared multiple
- Prime factorization
- 36 = 2² × 3²
- GCF signal
- Splitting into equal groups
- LCM signal
- Events lining up again
- First primes
- 2, 3, 5, 7, 11
Divisibility Rules
- By 2
- Last digit is even
- By 3
- Digit sum divisible by 3
- By 4
- Last two digits divisible
- By 5
- Ends in 0 or 5
- By 6
- Passes both 2 and 3
- By 8
- Last three digits divisible
- By 9
- Digit sum divisible by 9
- By 10
- Ends in 0
Properties of Operations
- Commutative
- Order changes, result same
- Associative
- Grouping changes, result same
- Distributive
- a(b + c) = ab + ac
- Additive identity
- Adding 0 changes nothing
- Multiplicative identity
- Multiplying by 1
- Additive inverse
- Sums to 0
- Multiplicative inverse
- Product is 1
- Zero property
- Product is always 0
- Not commutative
- Subtraction and division
Estimation Checks
- Front-end
- Use the leading digits
- Compatible numbers
- Round to easy pairs
- Reasonableness
- Does the size fit
- Decimal check
- Estimate catches misplaced point
- Rounded answer choices
- Never round midway
- Remainder up
- Buses, boxes, tables needed
- Remainder down
- Complete groups you make
- Remainder shared
- Answer is a fraction
Expression vs Equation
Expression
- No equal sign
- Simplify or evaluate
- 3x + 5
Equation
- Has equal sign
- Solve for variable
- 3x + 5 = 20
Simplify vs solve
Equation Setup Picker
- Says is or totals→Equation(Equal sign)
- Says at least, at most→Inequality
- Variable on both sides→Collect like terms
- Parentheses in the problem→Distribute first
- Two related quantities→Input-output table
- Same amount added repeatedly→Arithmetic pattern
- Same multiplier each step→Geometric pattern
Algebra Vocabulary
- Expression
- No equal sign
- Equation
- Has an equal sign
- Inequality
- Uses < > ≤ ≥
- Term
- Piece separated by signs
- Coefficient
- Number multiplying the variable
- Constant
- Term with no variable
- Leading coefficient
- Coefficient of highest power
- Like terms
- Same variable, same exponent
- Independent variable
- The input you choose
- Dependent variable
- The output that results
- Evaluate
- Substitute, then compute
Independent vs Dependent
Independent
- Input value
- You control it
- Bottles bought
Dependent
- Output value
- Result of input
- Total cost
Cause vs effect
Words into Algebra
- Sum of
- Add
- Difference of
- Subtract
- Product of
- Multiply
- Quotient of
- Divide
- Twice a number
- 2n
- A number increased by 6
- n + 6
- 6 less than a number
- n − 6
- At least
- ≥
- At most
- ≤
- Is, equals, totals
- Equal sign
- Per, each
- Divide or unit rate
Solving Equations
- Goal
- Isolate the variable
- Step 1
- Distribute, clear parentheses
- Step 2
- Combine like terms
- Step 3
- Undo adding or subtracting
- Step 4
- Undo multiplying or dividing
- Balance rule
- Same operation both sides
- Check
- Substitute back into original
- Flip inequality
- Multiply or divide by negative
- Open circle
- < or >, not included
- Closed circle
- ≤ or ≥, included
Patterns and Sequences
- Arithmetic
- Add a common difference
- Geometric
- Multiply a common ratio
- aₙ = a₁ + (n − 1)d
- Arithmetic term formula
- Common difference
- Term minus previous term
- Function rule
- Output from every input
- Table rule
- Must fit every row
- Shape pattern
- Repeating or growing
- Conjecture
- Prediction from a pattern
Metric Stairs
King Henry Died By Drinking Chocolate Milk
kilo, hecto, dekabase unitdeci, centi, milliEach step is ×10
Area vs Perimeter
Area
- Space inside
- Square units
- Multiply dimensions
Perimeter
- Distance around
- Linear units
- Add all sides
Cover it vs fence it
Formula Picker
- Fencing around a garden→Perimeter(Linear units)
- Carpet covering a floor→Area(Square units)
- Water filling a tank→Volume(Cubic units)
- Paper wrapping a box→Surface area(Add the faces)
- L-shaped figure given→Decompose into rectangles
- Only a net shown→Add every face
- Dimensions all doubled→Volume ×8(Area ×4)
Shapes, Angles, Coordinates
- Acute angle
- Less than 90°
- Right angle
- Exactly 90°
- Obtuse angle
- Between 90° and 180°
- Straight angle
- Exactly 180°
- Triangle angles
- Add to 180°
- Quadrilateral angles
- Add to 360°
- Parallel lines
- Never meet
- Perpendicular lines
- Meet at 90°
- Equilateral
- Three equal sides
- Isosceles
- At least two equal
- Scalene
- No equal sides
- Parallelogram
- Two pairs parallel sides
- Rhombus
- Four equal sides
- Trapezoid
- One pair parallel sides
- Origin
- (0, 0)
- Ordered pair
- (x, y): across then up
- Quadrant I
- x positive, y positive
- Quadrant order
- Counterclockwise from upper right
Center and Spread
Mean average, Median middle, Mode most
Median: order firstMode: appears mostRange: max − min
Volume vs Surface Area
Volume
- Space inside solid
- Cubic units
- length × width × height
Surface area
- Outside covering
- Square units
- Add all faces
Fill it vs wrap it
Measure of Center Picker
- One extreme outlier→Median(Resists extremes)
- Data roughly symmetric→Mean(Uses every value)
- Need most common→Mode(Works for categories)
- Data is categorical→Mode
- Need spread only→Range(Maximum minus minimum)
- Total matters→Mean(Sum drives it)
Area and Perimeter
- Perimeter
- Add all side lengths
- Rectangle area
- length × width
- Rectangle perimeter
- 2l + 2w
- Square area
- side × side
- Square perimeter
- 4 × side
- Triangle area
- ½ × base × height
- Parallelogram area
- base × height
- Trapezoid area
- ½ × (b₁ + b₂) × h
- Height
- Perpendicular to the base
- Composite figure
- Split into rectangles, triangles
- Area units
- Square units
- Perimeter units
- Linear units
- Diameter
- 2 × radius
- Circumference
- π × diameter
- Circle area
- π × radius²
Mean vs Median
Mean
- Sum ÷ count
- Uses every value
- Outliers pull it
Median
- Middle after ordering
- Position based
- Outliers barely matter
Balance point vs middle
Graph Picker
- Compare separate categories→Bar graph
- Show change over time→Line graph
- Show parts of whole→Circle graph(Totals 100%)
- Show numeric frequency ranges→Histogram(Bars touch)
- Show two-variable relationship→Scatterplot(Trend direction)
- Small data set→Line plot(Dot plot)
- Show median and quartiles→Boxplot
Volume and Surface Area
- Rectangular prism volume
- length × width × height
- Cube volume
- side × side × side
- Prism surface area
- 2(lw + lh + wh)
- Net
- Unfolded three-dimensional figure
- Surface area from net
- Add every face area
- Cube faces
- Six equal squares
- Volume units
- Cubic units
- Fractional edge lengths
- Formula still works
- Double every dimension
- Area ×4, volume ×8
Unit Conversions
- 1 foot
- 12 inches
- 1 yard
- 3 feet = 36 inches
- 1 mile
- 5,280 feet
- 1 cup
- 8 fluid ounces
- 1 pint
- 2 cups
- 1 quart
- 2 pints = 4 cups
- 1 gallon
- 4 quarts = 16 cups
- 1 pound
- 16 ounces
- 1 ton
- 2,000 pounds
- 1 kilometer
- 1,000 meters
- 1 meter
- 100 centimeters
- 1 centimeter
- 10 millimeters
- 1 liter
- 1,000 milliliters
- 1 kilogram
- 1,000 grams
- 1 gram
- 1,000 milligrams
- 1 hour
- 60 minutes
- Elapsed time
- Count up in chunks
- Small unit to large
- Divide
- Large unit to small
- Multiply
- Blueprint scope
- Convert within one system
Measures of Center
- Mean
- Sum ÷ number of values
- Median
- Middle of ordered list
- Even-count median
- Average the two middles
- Mode
- Most frequent value
- Range
- Maximum − minimum
- No mode
- Every value appears once
- Outlier
- Value far from others
- Outlier effect
- Mean moves, median resists
- Skewed data
- Median describes center better
- Statistical question
- Expects varying answers
- Add a high value
- Mean rises, range widens
Graphs and Probability
- Bar graph
- Compares separate categories
- Line graph
- Change over time
- Circle graph
- Parts of one whole
- Histogram
- Frequency by numeric interval
- Line plot
- Dots above number line
- Boxplot
- Five-number summary
- Scatterplot
- Two variables, possible trend
- Double bar graph
- Compares two data sets
- Probability
- Favorable ÷ total outcomes
- Impossible event
- Probability 0
- Certain event
- Probability 1
- Complement
- 1 − P(event)
- Independent events
- Multiply the probabilities
- Theoretical probability
- Counted, not experimental
Common Traps
Multiplying does not enlarge
Multiply can shrink ≠ Divide can grow
Area vs perimeter
Area covers inside ≠ Perimeter goes around
Mean vs median
Mean follows outliers ≠ Median resists outliers
Place vs value
Place is position ≠ Value is worth
Triangle height
Height is perpendicular ≠ Slant side is longer
Percent of vs off
30% of is 0.30 ≠ 30% off is 0.70
Doubling every dimension
Area multiplies by four ≠ Volume multiplies by eight
Order of operations
Multiply-divide left to right ≠ Not multiply before divide
Less than wording
6 less than n ≠ Not 6 − n
Adding fractions
Common denominator first ≠ Never add denominators
Converting units
Small to large divides ≠ Large to small multiplies
Inequality sign
Negative multiply flips ≠ Positive multiply keeps
Last Minute
- 1.Numbers 40%, Algebra 30%, Geometry 30%
- 2.50 questions in 65 minutes
- 3.On-screen scientific calculator provided
- 4.Passing score set by state
- 5.Divide fractions: keep, change, flip
- 6.Percent change: change ÷ original
- 7.Area = square units; perimeter = linear
- 8.Volume = length × width × height
- 9.Triangle area = ½ base height
- 10.Triangle angles sum to 180°
- 11.Mean follows outliers; median resists
- 12.1 gallon = 4 quarts = 16 cups
- 13.GCF splits groups; LCM repeats
- 14.Multiplying by fraction can shrink
- 15.Flip inequality when multiplying negative
- 16.Estimate first, then trust calculator
Buy on Amazon
Study guide on MometrixSame family resources
Explore More Praxis Exams
Continue into nearby exams from the same family. Each card keeps practice questions, study guides, flashcards, videos, and articles in one place.
More From This Family
Videos and articles for deeper review.
VideoFREE Praxis 5038 ELA Exam Guide 2026: Pass Content Knowledge First TryVideoFREE Praxis Core Study Guide 2026: Pass Your Teacher Certification ExamVideoFREE Praxis Elementary Education (5001) Exam Guide 2026: All 4 Subtests, Scores & FeesVideoFREE Praxis Elementary Education (5001) Exam Guide 2026: All 4 Subtests, Scores & FeesArticleFREE Praxis ESOL 5362 Exam Guide 2026: Pass with Confidence15 min readArticleFREE Praxis 5038 ELA Exam Guide 2026: Pass Content Knowledge First Try15 min readArticleFREE Praxis Core Study Guide 2026: Pass Your Teacher Certification Exam15 min readArticleTExES Exam 2026: FREE Texas Teacher Certification Guide30 min read