SOL Math Spiral Review Slides
VIRGINIA STANDARDS OF LEARNING (SOL)
Grade 4 Mathematics
COMPREHENSIVE SPIRAL REVIEW
4th Grade Math SOL
Mastery Spiral Review
20 multi-strand test-prep challenges covering Number Sense, Computation, Geometry, Measurement, Data, and Algebraic Patterns.
Challenge Set
20 Rigorous Questions
Standards Mix
All 5 Major SOL Strands
Detailed Review
Full Solutions & Tips
Review Blueprint & Strands
Virginia Standards of Learning Overview
Overview Guide
Strand 1
Number & Number Sense
SOL 4.1 • 4.2 • 4.3
Q1 – Q4
Strand 2
Computation & Estimation
SOL 4.4 • 4.5 • 4.6
Q5 – Q9
Strand 3
Measurement & Geometry
SOL 4.7 • 4.8 • 4.9 • 4.10 • 4.11
Q10 – Q14
Strand 4
Probability & Statistics
SOL 4.13 • 4.14
Q15 – Q17
Strand 5
Patterns & Algebra
SOL 4.15 • 4.16
Q18 – Q20
Student Strategy: Read each question carefully, show your step-by-step thinking on scratch paper, and eliminate unreasonable answers.
SOL 4.1b Number & Number Sense • Rounding Whole Numbers
Question 01 of 20
A Virginia state park recorded 748,329 visitors during the past year. What is 748,329 rounded to the nearest ten thousand?
A
700,000
B
740,000
C
750,000
D
748,000
Identify the digit in the ten thousands place and look to the right. SOL Spiral Challenge
SOL 4.2a Number & Number Sense • Comparing Fractions
Question 02 of 20
Which statement correctly compares \( \frac{3}{5} \) and \( \frac{5}{8} \) using a common denominator or benchmark?
A
\( \frac{3}{5} > \frac{5}{8} \) because \( 3 > 5 \)
B
\( \frac{3}{5} < \frac{5}{8} \) because \( \frac{24}{40} < \frac{25}{40} \)
C
\( \frac{3}{5} = \frac{5}{8} \) because both equal \( \frac{1}{2} \)
D
\( \frac{3}{5} > \frac{5}{8} \) because 5ths are smaller pieces
Find a common denominator of 40 to compare accurately. SOL Spiral Challenge
SOL 4.3a/b Number & Number Sense • Decimal Place Value & Rounding
Question 03 of 20
The mass of a mineral specimen found in Blue Ridge is 4.872 grams. What is the value of the 7, and what is 4.872 rounded to the nearest tenth?
A
Value: 0.07 ; Rounds to 4.9
B
Value: 0.7 ; Rounds to 4.8
C
Value: 0.007 ; Rounds to 5.0
D
Value: 0.07 ; Rounds to 4.8
Tenths is 1 place after decimal; hundredths is 2 places after. SOL Spiral Challenge
SOL 4.3d Number & Number Sense • Decimal & Fraction Equivalence
Question 04 of 20
A model is divided into 100 equal squares, and exactly 75 squares are shaded. Which fraction in simplest form and decimal are equivalent to this model?
A
\( \frac{3}{4} \) and \( 0.75 \)
B
\( \frac{7}{10} \) and \( 0.70 \)
C
\( \frac{75}{10} \) and \( 7.5 \)
D
\( \frac{1}{4} \) and \( 0.25 \)
Simplify 75/100 by dividing numerator and denominator by 25. SOL Spiral Challenge
SOL 4.4b Computation & Estimation • Whole Number Multiplication
Question 05 of 20
An elementary school library in Chesterfield received 36 boxes of books. Each box contained exactly 24 books. What is the total number of books the library received?
A
216 books
B
764 books
C
864 books
D
924 books
Use standard algorithm or area model: (30 + 6) × (20 + 4). SOL Spiral Challenge
SOL 4.4c Computation & Estimation • Interpreting Remainders in Division
Question 06 of 20
Coach Evans has 115 tennis balls. He stores them in canisters that hold 4 balls each. What is the least number of canisters Coach Evans needs to hold ALL of the tennis balls?
A
28 canisters
B
29 canisters
C
30 canisters
D
3 canisters
Think: What must happen to the remaining 3 balls so none are left behind? SOL Spiral Challenge
SOL 4.4d Computation & Estimation • Multi-Step Problem Solving
Question 07 of 20
Tyler earned $145 lawn mowing and $85 raking leaves. He then bought a jacket for $48 and 3 shirts that cost $18 each. How much money does Tyler have left?
A
$128
B
$146
C
$164
D
$182
Find total earned first, calculate total spent (jacket + 3 shirts), then subtract. SOL Spiral Challenge
SOL 4.5a Computation & Estimation • Adding Unlike Fractions
Question 08 of 20
At a class picnic, students ate \( \frac{3}{8} \) of a sheet pan of cornbread for lunch and \( \frac{1}{4} \) of the pan for an afternoon snack. What total fraction of the pan of cornbread was eaten?
A
\( \frac{4}{12} \) (or \( \frac{1}{3} \))
B
\( \frac{5}{8} \)
C
\( \frac{4}{8} \) (or \( \frac{1}{2} \))
D
\( \frac{7}{8} \)
Remember to find a common denominator before adding numerators. SOL Spiral Challenge
SOL 4.6a Computation & Estimation • Decimal Addition & Subtraction
Question 09 of 20
Brooke went to the school store with a $20.00 bill. She bought a binder for $4.65, colored pencils for $7.89, and an eraser for $1.25. How much change should Brooke receive?
A
$6.21
B
$7.21
C
$13.79
D
$6.31
Line up decimal points carefully when adding and subtracting. SOL Spiral Challenge
SOL 4.7 Measurement & Geometry • Perimeter & Area of Rectangles
Question 10 of 20
A rectangular garden plot has a length of 14 yards and a width of 8 yards. What are the perimeter and the area of the garden plot?
Length = 14 yd
8 yd Garden 8 yd
14 yd
A
Perimeter = 22 yd ; Area = 112 sq yd
B
Perimeter = 44 yd ; Area = 112 sq yd
C
Perimeter = 44 yd ; Area = 56 sq yd
D
Perimeter = 28 yd ; Area = 112 sq yd
Perimeter = 2L + 2W ; Area = Length × Width. SOL Spiral Challenge
SOL 4.8 Measurement & Geometry • Customary Liquid Volume
Question 11 of 20
The sports cooler for the soccer team holds 5 gallons of water. Knowing that 1 gallon = 4 quarts, how many total quarts of water does the cooler hold?
A
10 quarts
B
15 quarts
C
20 quarts
D
24 quarts
Convert larger unit to smaller unit: multiply by 4. SOL Spiral Challenge
SOL 4.9 Measurement & Geometry • Elapsed Time
Question 12 of 20
A field trip to the Science Museum of Virginia began at 10:45 A.M. and concluded at 2:15 P.M. on the same day. What was the total amount of elapsed time?
A
3 hours 15 minutes
B
3 hours 30 minutes
C
4 hours 30 minutes
D
3 hours 45 minutes
Count forward: 10:45 AM to 1:45 PM is 3 hours; then count the remaining minutes. SOL Spiral Challenge
SOL 4.10b Measurement & Geometry • Line Relationships
Question 13 of 20
Two streets on a map intersect to form four square corners (90° right angles). Which geometric term best describes these lines?
A
Parallel lines
B
Perpendicular lines
C
Acute line segments
D
Ray endpoints
Perpendicular lines meet at exact 90-degree right angles. SOL Spiral Challenge
SOL 4.11 Measurement & Geometry • Quadrilateral Properties
Question 14 of 20
Which geometric property is true for ALL rhombi?
A
They must have 4 right angles.
B
They have 4 congruent sides & opposite sides parallel.
C
They have exactly one pair of parallel sides.
D
All four sides are always different lengths.
A rhombus is an equilateral parallelogram. SOL Spiral Challenge
SOL 4.13 Probability & Statistics • Probability as a Fraction
Question 15 of 20
A bag contains 5 red marbles, 3 blue marbles, 2 green marbles, and 6 yellow marbles. If Mia pulls one marble out without looking, what is the probability that she selects a blue marble?
A
\( \frac{3}{13} \)
B
\( \frac{3}{16} \)
C
\( \frac{1}{3} \)
D
\( \frac{3}{10} \)
Probability = (Favorable outcomes) ÷ (Total possible outcomes). SOL Spiral Challenge
SOL 4.14 Probability & Statistics • Interpreting Bar Graphs
Question 16 of 20
The bar graph shows the number of 4th graders enrolled in after-school clubs. How many more students chose STEM Club than Drama Club?
Art (18)
STEM (26)
Drama (14)
Chess (22)
A
8 students
B
12 students
C
14 students
D
40 students
Look at the difference: 26 students minus 14 students. SOL Spiral Challenge
SOL 4.14 Probability & Statistics • Analyzing Line Graphs
Question 17 of 20
A science class tracked noon outdoor temperatures in Richmond:
Mon
58°F
Tue
62°F
Wed
67°F
Thu
61°F
Fri
70°F
Between which two consecutive days did the temperature decrease?
A
Monday to Tuesday
B
Tuesday to Wednesday
C
Wednesday to Thursday
D
Thursday to Friday
Decrease means the temperature went down from the previous day. SOL Spiral Challenge
SOL 4.15 Patterns & Algebra • Input-Output Function Rules
Question 18 of 20
Examine the input-output function table. Which mathematical rule describes how each Input (\(x\)) is changed into its Output (\(y\))?
Input (\(x\))
Output (\(y\))
3 15
5 23
8 35
10 43
A
Multiply by 5
B
Multiply by 4, then add 3
C
Add 12
D
Multiply by 3, then add 6
Test the rule on more than one row to ensure it works for all pairs. SOL Spiral Challenge
SOL 4.15 Patterns & Algebra • Numerical Sequences
Question 19 of 20
Consider the numerical sequence below:
4 → 11 → 25 → 53 → 109
Which rule was used to determine each subsequent number in the pattern?
A
Add 7 each time
B
Multiply by 2, then add 3
C
Multiply by 3, then subtract 1
D
Double the number each time
Check: (4 × 2) + 3 = 11; (11 × 2) + 3 = 25. SOL Spiral Challenge
SOL 4.16 Patterns & Algebra • Properties of Operations
Question 20 of 20
Which mathematical equation demonstrates the Associative Property of Multiplication?
A
\( 7 \times (4 \times 9) = (7 \times 4) \times 9 \)
B
\( 8 \times 6 = 6 \times 8 \)
C
\( 15 \times 1 = 15 \)
D
\( 5 \times (10 + 2) = (5 \times 10) + (5 \times 2) \)
Associative Property relates to grouping factors using parentheses without changing the product. SOL Spiral Challenge
SOL MASTER ANSWER KEY & STRATEGIES
Questions 01 – 20
TEACHER & STUDENT REVIEW SECTION
Detailed Solutions &
Misconception Walkthroughs
Step-by-step mathematical reasoning, visual models, and Virginia SOL test-taking tips for every problem.
Identifies key SOL traps & error patterns
Reinforces standard vocabulary & notation
Builds SOL test-taking confidence
SOL 4.1b Solution Guide • Rounding Whole Numbers
Question 01 Solution
C
CORRECT ANSWER
750,000
Nearest Ten Thousand
Step-by-Step Reasoning:
1. Find the rounding place: In 748,329, the digit in the ten thousands place is 4 (representing 40,000).
2. Look to the immediate right: The digit in the thousands place is 8.
3. Apply the rounding rule: Since 8 ≥ 5, round the ten thousands digit up from 4 to 5.
4. Replace all digits to the right with zeros: 750,000.
Common SOL Trap: Choosing B (740,000) occurs if a student truncates without looking at the 8 in the thousands place. Choosing A (700,000) rounds to the nearest hundred thousand instead.
SOL Review Key • Question 01
SOL 4.2a Solution Guide • Comparing Fractions
Question 02 Solution
B
CORRECT ANSWER
\( \frac{3}{5} < \frac{5}{8} \) because \( \frac{24}{40} < \frac{25}{40} \)
Step-by-Step Reasoning:
1. Find a common denominator for denominators 5 and 8: \( \text{LCM}(5, 8) = 40 \).
2. Convert \( \frac{3}{5} \): Multiply numerator and denominator by 8: \( \frac{3 \times 8}{5 \times 8} = \frac{24}{40} \).
3. Convert \( \frac{5}{8} \): Multiply numerator and denominator by 5: \( \frac{5 \times 5}{8 \times 5} = \frac{25}{40} \).
4. Compare the equivalent numerators: \( 24 < 25 \), so \( \frac{24}{40} < \frac{25}{40} \), meaning \( \frac{3}{5} < \frac{5}{8} \).
Common SOL Trap: Choosing A is a common error where students compare numerators without common denominators.
SOL Review Key • Question 02
SOL 4.3a/b Solution Guide • Decimal Place Value & Rounding
Question 03 Solution
A
CORRECT ANSWER
Value: 0.07 (7 hundredths) ; Rounds to 4.9
Step-by-Step Reasoning:
1. Place Value: In 4.872, 4 is ones, 8 is tenths (0.8), 7 is hundredths (0.07), and 2 is thousandths (0.002).
2. Rounding to the nearest tenth: Identify the tenths place (8). Look right to hundredths place (7).
3. Because 7 ≥ 5, round 8 tenths up to 9 tenths (4.9).
Common SOL Trap: Confusing "tenths" (one digit after the decimal) with "hundredths" (two digits after).
SOL Review Key • Question 03
SOL 4.3d Solution Guide • Fraction & Decimal Equivalence
Question 04 Solution
A
CORRECT ANSWER
\( \frac{3}{4} \) and \( 0.75 \)
Step-by-Step Reasoning:
1. 75 shaded squares out of 100 total squares represents \( \frac{75}{100} \).
2. In decimal form, 75 hundredths is written as 0.75.
3. Simplify the fraction by dividing both numerator and denominator by 25: \( \frac{75 \div 25}{100 \div 25} = \frac{3}{4} \).
Key SOL Benchmark: 4th graders must know the benchmark conversions by memory: \( \frac{1}{4} = 0.25 \), \( \frac{1}{2} = 0.50 \), and \( \frac{3}{4} = 0.75 \).
SOL Review Key • Question 04
SOL 4.4b Solution Guide • Multiplication Algorithm
Question 05 Solution
C
CORRECT ANSWER
864 books
Partial Products Strategy:
Break down \( 36 \times 24 \):
• \( 36 \times 4 = 144 \)
• \( 36 \times 20 = 720 \)
• Sum the partial products: \( 144 + 720 = \mathbf{864} \text{ books} \).
Common SOL Trap: Forgetting the placeholder zero when multiplying by the tens digit (20), which produces the incorrect answer 216 (144 + 72).
SOL Review Key • Question 05
SOL 4.4c Solution Guide • Interpreting Remainders
Question 06 Solution
B
CORRECT ANSWER
29 canisters
Step-by-Step Division & Context:
1. Divide total balls by capacity: \( 115 \div 4 \).
2. \( 115 \div 4 = 28 \text{ with a remainder of } 3 \).
3. 28 canisters will hold \( 28 \times 4 = 112 \) balls, leaving 3 balls with no canister.
4. Since ALL balls must be stored, an additional canister is needed: \( 28 + 1 = \mathbf{29} \text{ canisters} \).
SOL Remainder Rule: In real-life storage or bus trip problems, remainders require rounding up to the next whole container/vehicle.
SOL Review Key • Question 06
SOL 4.4d Solution Guide • Multi-Step Problem Solving
Question 07 Solution
A
CORRECT ANSWER
$128
Multi-Step Plan:
• Step 1 (Total Earned): \( \$145 + \$85 = \$230 \)
• Step 2 (Cost of Shirts): \( 3 \times \$18 = \$54 \)
• Step 3 (Total Spent): \( \$48 \text{ (jacket)} + \$54 \text{ (shirts)} = \$102 \)
• Step 4 (Money Left): \( \$230 - \$102 = \mathbf{\$128} \)
Common SOL Trap: Forgetting to multiply $18 by 3 and only subtracting $18 once. Always annotate each purchase!
SOL Review Key • Question 07
SOL 4.5a Solution Guide • Adding Fractions (Unlike Denominators)
Question 08 Solution
B
CORRECT ANSWER
\( \frac{5}{8} \) of the pan
Step-by-Step Fraction Addition:
1. Problem: \( \frac{3}{8} + \frac{1}{4} \)
2. Find common denominator for 8 and 4: Least common denominator is 8.
3. Convert \( \frac{1}{4} \) to eighths: \( \frac{1 \times 2}{4 \times 2} = \frac{2}{8} \).
4. Add the numerators: \( \frac{3}{8} + \frac{2}{8} = \mathbf{\frac{5}{8}} \).
Common SOL Trap: Adding straight across \( \frac{3+1}{8+4} = \frac{4}{12} \). Denominators must NEVER be added together!
SOL Review Key • Question 08
SOL 4.6a Solution Guide • Decimal Operations
Question 09 Solution
A
CORRECT ANSWER
$6.21
Calculation Steps:
• Step 1 (Total Cost): \( \$4.65 + \$7.89 + \$1.25 = \mathbf{\$13.79} \)
• Step 2 (Change from $20.00): \( \$20.00 - \$13.79 = \mathbf{\$6.21} \)
Remember to regroup across zeros: \( 20.00 - 13.79 = 6.21 \).
Common SOL Trap: Choosing C ($13.79) means finding the cost but forgetting to subtract from $20 to find the change!
SOL Review Key • Question 09
SOL 4.7 Solution Guide • Perimeter & Area
Question 10 Solution
B
CORRECT ANSWER
Perimeter = 44 yd ; Area = 112 sq yd
Formulas & Solutions:
• Perimeter (Distance Around): \( P = 14 + 8 + 14 + 8 = 2(14) + 2(8) = 28 + 16 = \mathbf{44} \text{ yards} \).
• Area (Surface Inside): \( A = \text{length} \times \text{width} = 14 \times 8 = \mathbf{112} \text{ square yards} \).
Common SOL Trap: Adding only two sides for perimeter (14 + 8 = 22, Option A). A rectangle has FOUR sides!
SOL Review Key • Question 10
SOL 4.8 Solution Guide • Liquid Volume Conversion
Question 11 Solution
C
CORRECT ANSWER
20 quarts
Conversion Reasoning:
1. Identify the relationship: 1 gallon = 4 quarts.
2. We have 5 gallons total.
3. To convert from gallons to quarts, multiply by 4: \( 5 \times 4 = \mathbf{20} \text{ quarts} \).
Helpful Visual: Remember "Gallon Man" or the big "G": inside 1 big G are 4 Qs (quarts). 5 big Gs means 5 × 4 = 20 Qs!
SOL Review Key • Question 11
SOL 4.9 Solution Guide • Elapsed Time
Question 12 Solution
B
CORRECT ANSWER
3 hours 30 minutes
Number Line / Jump Strategy:
• Jump 1: 10:45 A.M. to 11:00 A.M. = 15 minutes
• Jump 2: 11:00 A.M. to 2:00 P.M. = 3 hours
• Jump 3: 2:00 P.M. to 2:15 P.M. = 15 minutes
• Total: 3 hours + (15 min + 15 min) = 3 hours 30 minutes
Common SOL Trap: Subtractive borrowing with time base 60 instead of base 10. Always use an open number line for time!
SOL Review Key • Question 12
SOL 4.10b Solution Guide • Line Relationships
Question 13 Solution
B
CORRECT ANSWER
Perpendicular lines
Key Vocabulary Definitions:
• Perpendicular lines: Lines that intersect to create 90° right angles.
• Parallel lines: Lines in the same plane that never intersect and are always equidistant.
• Intersecting lines: Lines that cross at any angle.
Memory Tip: The capital letter "T" and the corner of a piece of paper show perpendicular lines with right angles.
SOL Review Key • Question 13
SOL 4.11 Solution Guide • Quadrilateral Classification
Question 14 Solution
B
CORRECT ANSWER
4 congruent sides & opposite sides parallel
Properties of Rhombi:
1. A rhombus is defined as a parallelogram with 4 congruent (equal length) sides.
2. Because it is a parallelogram, opposite sides are always parallel and opposite angles are congruent.
3. Right angles are only required if the rhombus is also a square.
Common SOL Trap: Believing a rhombus MUST have right angles (Option A). Only squares have 4 right angles and 4 equal sides!
SOL Review Key • Question 14
SOL 4.13 Solution Guide • Probability as a Fraction
Question 15 Solution
B
CORRECT ANSWER
\( \frac{3}{16} \)
Probability Formula:
• Step 1 (Total Outcomes): Add all marbles: \( 5 + 3 + 2 + 6 = \mathbf{16} \text{ marbles in total} \).
• Step 2 (Favorable Outcomes): There are 3 blue marbles.
• Step 3 (Probability Fraction): \( P(\text{blue}) = \frac{\text{favorable}}{\text{total}} = \mathbf{\frac{3}{16}} \).
Common SOL Trap: Finding odds instead of probability (comparing blue to non-blue, 3/13). Denominator must always be TOTAL items!
SOL Review Key • Question 15
SOL 4.14 Solution Guide • Reading Bar Graphs
Question 16 Solution
B
CORRECT ANSWER
12 students
Data Extraction & Comparison:
1. Find STEM Club frequency: 26 students.
2. Find Drama Club frequency: 14 students.
3. "How many more" signals finding the difference: \( 26 - 14 = \mathbf{12} \text{ students} \).
Common SOL Trap: Adding the two values (26 + 14 = 40) or reading the wrong club row. Double-check labels!
SOL Review Key • Question 16
SOL 4.14 Solution Guide • Line Graph Trends
Question 17 Solution
C
CORRECT ANSWER
Wednesday to Thursday
Day-by-Day Analysis:
• Mon (58°F) to Tue (62°F): +4°F (Increase)
• Tue (62°F) to Wed (67°F): +5°F (Increase)
• Wed (67°F) to Thu (61°F): -6°F (DECREASE)
• Thu (61°F) to Fri (70°F): +9°F (Increase)
Key Concept: A decrease on a line graph shows a line segment sloping downwards from left to right.
SOL Review Key • Question 17
SOL 4.15 Solution Guide • Function Rules
Question 18 Solution
B
CORRECT ANSWER
Multiply by 4, then add 3 (\(4x + 3\))
Testing the Rule Across All Rows:
• Row 1: \( (3 \times 4) + 3 = 12 + 3 = \mathbf{15} \) (Match!)
• Row 2: \( (5 \times 4) + 3 = 20 + 3 = \mathbf{23} \) (Match!)
• Row 3: \( (8 \times 4) + 3 = 32 + 3 = \mathbf{35} \) (Match!)
• Row 4: \( (10 \times 4) + 3 = 40 + 3 = \mathbf{43} \) (Match!)
Common SOL Trap: Rule A (multiply by 5) works only for row 1 (\(3 \times 5 = 15\)), but fails row 2 (\(5 \times 5 = 25 \neq 23\)). Always test multiple rows!
SOL Review Key • Question 18
SOL 4.15 Solution Guide • Sequence Rules
Question 19 Solution
B
CORRECT ANSWER
Multiply by 2, then add 3
Analyzing Term-to-Term Changes:
• Term 1 to 2: \( (4 \times 2) + 3 = 8 + 3 = \mathbf{11} \)
• Term 2 to 3: \( (11 \times 2) + 3 = 22 + 3 = \mathbf{25} \)
• Term 3 to 4: \( (25 \times 2) + 3 = 50 + 3 = \mathbf{53} \)
• Term 4 to 5: \( (53 \times 2) + 3 = 106 + 3 = \mathbf{109} \)
SOL Pattern Tip: If the difference between consecutive terms grows rapidly (+7, +14, +28, +56), the rule involves multiplication!
SOL Review Key • Question 19
SOL 4.16 Solution Guide • Properties of Operations
Question 20 Solution
A
CORRECT ANSWER
\( 7 \times (4 \times 9) = (7 \times 4) \times 9 \)
Review of Virginia SOL Properties:
• Option A (Associative): Regrouping numbers with parentheses does not alter product.
• Option B (Commutative): Changing order of factors: \( 8 \times 6 = 6 \times 8 \).
• Option C (Identity Property): Multiplying by 1 maintains the number's identity.
• Option D (Distributive): Multiplying a sum by multiplying each addend separately.
Easy Memory Trick: Associative property = who you "associate" with in groups (parentheses change groups, but the order of numbers stays 7, 4, 9).
SOL Review Key • Question 20
