Math Drills
Grade 6 Elementary School
This is the year that closes out primary maths. Multiplication of Fractions and Division of Fractions complete the four operations, and the work goes as far as Mixed Operations with Fractions and Decimals. Replacing a division with a multiplication by the reciprocal is handled here for the first time.
Expressions Using Letters, Ratio and Its Uses, and Proportion and Inverse Proportion deal not with numbers themselves but with the relationships between them, and lead straight into secondary school mathematics. Area of a Circle and Volume of Prisms and Cylinders extend the use of formulas into geometry.
Symmetric Figures
Symmetric Figures
Observation
- Number of Lines of Symmetry1 question
- Identifying Line-Symmetric Figures1 question
- Identifying Point-Symmetric Figures1 question
Expressions Using Letters
Relational Expressions and Substitution
Word Problems (Weight and Distance)
- Total Weight1 question
- Distance and Time (Line Diagram)1 question
Word Problems (Perimeter)
- Perimeter of an Equilateral Triangle1 question
- Perimeter of a Square1 question
Expressing the Area of a Shape with a Letter
Word Problems (Square and Rectangle)
- Square1 question
- Rectangle1 question
Word Problems (Triangle and Trapezoid)
- Triangles1 question
- Trapezoid1 question
Word Problems (Rhombus, Parallelogram)
- Rhombus1 question
- Parallelogram1 question
Multiplication of Fractions
Fraction × Whole Number and Whole Number × Fraction
Calculation
- Fraction × Whole Number and Whole Number × Fraction12 questions
Calculation (Mixed Numbers)
- Mixed Number×Whole Number, Whole Number×Mixed Number8 questions
Fill in the Blank
- Fill in the Blank18 questions
Word Problems
- Word Problems5 questions
Fraction × Fraction
Calculation
- Simplifying Along the Way12 questions
Calculation (Mixed Numbers)
- Including Mixed Numbers8 questions
Fill in the Blank
- Fill in the Blank18 questions
Multiplication of Fractions Word Problems
Word Problems
- Area (Length×Width)1 question
- Compared Quantity, Ratio > 11 question
- Compared Quantity, Ratio < 11 question
- Compared Quantity, Ratio < 1 (Two Steps)1 question
- Per-Unit Quantity (Fraction×Fraction)1 question
Multiplying 3 Fractions
Calculation
- 3 Terms (Calculation)12 questions
Word Problems (Consecutive Percentages)
- 3 Terms, Successive Ratios3 questions
- 3 Terms, Applying Ratios in Stages (Whole-Number Answer)2 questions
Word Problems (Amount per Unit)
- 3 Terms, Per-Unit Quantity (Sum and Difference)5 questions
Summary Prints
Calculation
- Fraction × Whole Number and Whole Number × Fraction · Fraction × Whole Number and Whole Number × Fraction4 questions
- Fraction × Fraction · Simplifying Along the Way4 questions
- Multiplying 3 Fractions · 3 Terms (Calculation)4 questions
Calculation (Mixed Numbers)
- Fraction × Whole Number and Whole Number × Fraction · Mixed Number×Whole Number, Whole Number×Mixed Number4 questions
- Fraction × Fraction · Including Mixed Numbers4 questions
Fill in the Blank
- Fraction × Whole Number and Whole Number × Fraction · Fill in the Blank8 questions
- Fraction × Fraction · Fill in the Blank8 questions
Division of Fractions
Fraction ÷ Whole Number and Whole Number ÷ Fraction
Calculation
- Fraction÷Whole Number6 questions
- Whole Number÷Fraction6 questions
Calculation (Mixed Numbers)
- Mixed Number÷Whole Number12 questions
Fill in the Blank
- Fill in the Blank10 questions
Fraction ÷ Fraction
Calculation
- Proper Fraction÷Proper Fraction4 questions
- Including Mixed Numbers4 questions
Calculation (Decimals, 3 Terms)
- Division Mixing Fractions and Decimals4 questions
- Dividing Three Fractions4 questions
Fill in the Blank
- Fill in the Blank18 questions
Division of Fractions Word Problems
Word Problems (Fraction ÷ Integer, etc.)
- Per-Unit Quantity2 questions
- Fraction÷Whole Number2 questions
- The Base Amount1 question
Word Problems (Integer ÷ Fraction, etc.)
- Per-Unit Quantity2 questions
- Applications (Working Backwards with Ratios)2 questions
- Whole Number÷Fraction1 question
Summary Prints
Calculation
- Fraction ÷ Whole Number and Whole Number ÷ Fraction · Fraction÷Whole Number2 questions
- Fraction ÷ Whole Number and Whole Number ÷ Fraction · Whole Number÷Fraction2 questions
- Fraction ÷ Whole Number and Whole Number ÷ Fraction · Mixed Number÷Whole Number4 questions
- Fraction ÷ Fraction · Proper Fraction÷Proper Fraction4 questions
Calculation (Mixed Numbers and Decimals)
- Fraction ÷ Whole Number and Whole Number ÷ Fraction · Mixed Number÷Whole Number2 questions
- Fraction ÷ Fraction · Including Mixed Numbers3 questions
- Fraction ÷ Fraction · Division Mixing Fractions and Decimals3 questions
Fill in the Blank
- Fraction ÷ Whole Number and Whole Number ÷ Fraction · Fill in the Blank9 questions
- Fraction ÷ Fraction · Fill in the Blank9 questions
Word Problems
- Division of Fractions Word Problems · Per-Unit Quantity1 question
- Division of Fractions Word Problems · Fraction÷Whole Number1 question
- Division of Fractions Word Problems · The Base Amount1 question
- Division of Fractions Word Problems · Applications (Working Backwards with Ratios)1 question
- Division of Fractions Word Problems · Whole Number÷Fraction1 question
Mixed Operations with Fractions and Decimals
Mixed Operations with Fractions
Calculation (Parentheses or Not)
- Without Parentheses4 questions
- With Parentheses4 questions
Calculation (3 Terms, × and ÷)
- Multiplying and Dividing Three Fractions8 questions
Mixed Operations with Fractions and Decimals
Calculation (Multiplication)
- Multiplication8 questions
Calculation (Parentheses or Not)
- Mixed Multiplication and Division (Without Parentheses)4 questions
- With Parentheses4 questions
Summary Prints
Calculation
- Mixed Operations with Fractions · Without Parentheses1 question
- Mixed Operations with Fractions · With Parentheses1 question
- Mixed Operations with Fractions · Multiplying and Dividing Three Fractions2 questions
- Mixed Operations with Fractions and Decimals · Multiplication1 question
- Mixed Operations with Fractions and Decimals · Mixed Multiplication and Division (Without Parentheses)1 question
- Mixed Operations with Fractions and Decimals · With Parentheses2 questions
Ratio and Its Uses
Ratio Values and Simplifying Ratios
Calculation
- Ratio Value (Calculation)20 questions
Calculation (Decimal-Fraction Ratios)
- Simplifying Ratios (Calculation)10 questions
- Converting Decimal and Fraction Ratios to Whole-Number Ratios (Calculation)10 questions
Word Problems
- Ratio Value (Word Problems)2 questions
- Finding and Simplifying Ratios (Word Problems)2 questions
- Converting Decimal and Fraction Ratios to Whole-Number Ratios (Word Problems)2 questions
Equal Ratios and Their Uses
Calculation (Dividing in a Ratio)
- Sharing Using a Ratio (Calculation)8 questions
Fill in the Blank
- Equal Ratios (Fill in the Blank)20 questions
Word Problems
- Using Equal Ratios (Word Problems)3 questions
- Sharing Using a Ratio (Word Problems)3 questions
Summary Prints
Calculation
- Ratio Values and Simplifying Ratios · Ratio Value (Calculation)6 questions
- Ratio Values and Simplifying Ratios · Simplifying Ratios (Calculation)3 questions
- Ratio Values and Simplifying Ratios · Converting Decimal and Fraction Ratios to Whole-Number Ratios (Calculation)3 questions
- Equal Ratios and Their Uses · Equal Ratios (Fill in the Blank)6 questions
Word Problems
- Ratio Values and Simplifying Ratios · Ratio Value (Word Problems)1 question
- Ratio Values and Simplifying Ratios · Finding and Simplifying Ratios (Word Problems)1 question
- Ratio Values and Simplifying Ratios · Converting Decimal and Fraction Ratios to Whole-Number Ratios (Word Problems)1 question
- Equal Ratios and Their Uses · Sharing Using a Ratio (Calculation)1 question
- Equal Ratios and Their Uses · Using Equal Ratios (Word Problems)1 question
- Equal Ratios and Their Uses · Sharing Using a Ratio (Word Problems)1 question
Enlargement and Reduction
Enlargement and Reduction
Calculation
- Properties of Enlargements and Reductions2 questions
Scale
Word Problems
- Converting Actual Length to the Scale Drawing2 questions
- Finding the Scale2 questions
- Actual Length from a Scale Drawing2 questions
Investigating Data
Representative Values
Word Problems (Average)
- Mean of the Data3 questions
Word Problems (Comparing Central Values)
- Various Representative Values1 question
- Comparing Representative Values of Two Groups1 question
Frequency Distribution Tables and Histograms
Word Problems (Analysis)
- Analyzing Frequency Tables and Representative Values1 question
Word Problems (Frequency Table)
- Frequency Distribution Table1 question
Reading
- Histogram1 question
Area of a Circle
Area of a Circle Basics
Finding the Area
- From the Radius (Calculation)3 questions
- From the Diameter (Calculation)3 questions
Word Problems
- From the Radius (Word Problems)3 questions
- From the Diameter (Word Problems)3 questions
Area of Semicircles and Sectors
Finding the Area
- Semicircle (Calculation)3 questions
- Quarter Circle (Calculation)3 questions
Finding the Area (Various Angles)
- Sector (Calculation)6 questions
Word Problems
- Semicircle (Word Problems)2 questions
- Quarter Circle (Word Problems)2 questions
- Sector (Word Problems)2 questions
Composite Figures Addition and Subtraction
Finding the Area (Rectangle − Semicircle and More)
Shuffled questions
- Large Semicircle − Small Semicircles1 question
- Rectangle − Quarter Circle1 question
- Rectangle − Semicircle1 question
- Square − Quarter Circle1 question
Finding the Area (Donut Shape and More)
Shuffled questions
- Donut Shape1 question
- Roof Shape1 question
- Stadium Shape1 question
- Rectangle − Diagonal Quarter Circles (2 Corners)1 question
Composite Figures Overlap and Difference
Finding the Area (Leaf and Clover Shapes)
- Leaf and Lens Shapes1 question
- Two-Wing Shape1 question
- Four-Leaf Space1 question
- Clover Shape1 question
Finding the Area (Crescent and Inscribed Shapes)
- Crescent Shape1 question
- Large Circle − Inscribed Small Circle1 question
- Circle − Inscribed Square and Rhombus1 question
- Square − Inscribed Circle1 question
Finding the Area (Petal and Teardrop Shapes)
- Quarter Circle + Semicircle (Outside the Overlap)1 question
- Four-Petal Shape1 question
- Lune of Hippocrates1 question
- Comma Shape1 question
Volume of Prisms and Cylinders
Volume of Prisms and Cylinders
Finding the Volume (Prism ①)
- Rectangular Prism and Cube1 question
- Triangular Prism1 question
- Trapezoidal Prism1 question
- Pentagonal Prism1 question
Finding the Volume (Prism ②)
- Prism with an Irregular Base1 question
- Parallelogram Prism1 question
- Rhombic Prism1 question
- Hexagonal Prism1 question
Finding the Volume (Cylinder)
- Cylinder (Lying Down)1 question
- Cylinder (Upright)1 question
- Half Cylinder (Lying Down)1 question
- Half Cylinder (Upright)1 question
Word Problems
- Word Problems6 questions
Volume of Composite Solids
Finding the Volume (Prism − Cylinder and More)
- Rectangular Prism − Cylinder1 question
- Prism on Top of a Cylinder1 question
- Concentric Pipe1 question
- Cylinder with a C-Shaped Slit1 question
Finding the Volume (2-Tier Cylinders and More)
- Two Stacked Cylinders1 question
- Half Cylinder + Rectangular Prism1 question
- Prism with Rounded Corners1 question
- Quarter Cylinder1 question
Word Problems
- Word Problems5 questions
Surface Area of Solids
Surface Area of Prisms and Cylinders
Finding the Surface Area (Prism)
- Rectangular Prism and Cube2 questions
- Triangular Prism1 question
- Trapezoidal Prism1 question
Finding the Surface Area (Prisms and Cylinders)
Shuffled questions
- Pentagonal Prism1 question
- Prism with an Irregular Base1 question
- Cylinder1 question
- Half Cylinder1 question
Surface Area of Composite Solids
Finding the Surface Area (Prism − Cylinder and More)
- Rectangular Prism − Cylinder1 question
- Prism on Top of a Cylinder1 question
- Concentric Pipe1 question
- Cylinder with a C-Shaped Slit1 question
Finding the Surface Area (2-Tier Cylinders and More)
- Two Stacked Cylinders1 question
- Half Cylinder + Rectangular Prism1 question
- Prism with Rounded Corners1 question
- Quarter Cylinder1 question
Summary Prints
Finding the Surface Area
- Surface Area of Prisms and Cylinders · Rectangular Prism and Cube1 question
- Surface Area of Prisms and Cylinders · Cylinder1 question
- Surface Area of Composite Solids · Rectangular Prism − Cylinder1 question
- Surface Area of Composite Solids · Prism on Top of a Cylinder1 question
Proportion and Inverse Proportion
Proportion
Word Problems
- Deriving the Table and Expression3 questions
Word Problems (Application)
- Applications6 questions
Inverse Proportion
Word Problems
- Deriving the Table and Expression3 questions
Word Problems (Application)
- Applications (Two Steps)6 questions
Number of Cases
Number of Cases
Word Problems (Combinations)
- Combinations (With Repetition)3 questions
- Combinations (Ways to Choose)2 questions
Word Problems (Arrangements)
- Permutations (Ways to Arrange)2 questions
- Multiplication Principle2 questions
- Counting Routes1 question
The Structure of Measurement Units
Units of Volume
Conversion
- cm³⇔L, dL, kL6 questions
- kL⇔L6 questions
- m³⇔cm³, kL, L, dL6 questions
Word Problems
- Volume Word Problems10 questions
Units of Weight
Conversion
- g⇔mg6 questions
- mg, g, kg, t (Compound)14 questions
Word Problems
- Weight Word Problems10 questions
Units of Time
Conversion (Fraction → Minutes, Seconds)
- Fractional Hours→Minutes6 questions
- Fractional Minutes→Seconds6 questions
Conversion (Minutes, Seconds → Fraction)
- Hours and Minutes→Mixed-Number Hours6 questions
- Minutes and Seconds→Mixed-Number Minutes6 questions
Word Problems
- Fractional Hours→Minutes (Word Problems)3 questions
- Minutes→Fractional Hours (Word Problems)3 questions
Word Problems with Various Quantities
Word Problems
- Word Problems with Various Quantities10 questions
Traveler Problems
Traveler Problems
Word Problems (Meeting)
- Meeting (With a Hint)1 question
- Meeting1 question
- Meeting (Where They Meet)1 question
- Meeting (Finding the Speed)1 question
Word Problems (Catching Up)
- Catching Up (With a Hint)1 question
- Catching Up1 question
- Catching Up (Time Difference)1 question
- Catching Up (Around a Pond)1 question
Word Problems (Walking and Running)
- Ratio of Walking and Running (With a Hint)1 question
- Ratio of Walking and Running1 question
- Distance Walked and Run1 question
- Average Speed of Walking and Running1 question
Various Word Problems
Patterns and Regularity
Word Problems
- The Color at a Given Position1 question
- Counting the Colors1 question
- Repeating Numbers1 question
- Days of the Week1 question
- Arithmetic Sequences1 question
How Savings Grow
Word Problems
- Savings (Basics)1 question
- Starting Savings1 question
- Catching Up1 question
- Spending Over Time1 question
- The Gap Widens1 question
Work-Rate Problems
Word Problems
- Two People Working Together1 question
- The Remaining Work1 question
- Three People Working Together1 question
- Water Tank1 question
- Total Person-Days1 question
Crane and Turtle Problems
Word Problems
- Shopping Problems1 question
- Cranes and Turtles1 question
- Adults and Children1 question
- Correct and Incorrect Answers1 question
- Speed Version1 question
Elimination Problems
Word Problems
- Subtracting Directly to Eliminate1 question
- Multiplying Then Eliminating1 question
- Using the Difference1 question
- Buying in Sets1 question
- Three Items1 question
Age Problems
Word Problems
- Years Later1 question
- Years Before1 question
- Sum of Ages1 question
- Older and Younger Brother1 question
- Current Age1 question
Summary Prints
Word Problems (Work Rate, etc.)
- Work-Rate Problems · Two People Working Together1 question
- Work-Rate Problems · The Remaining Work1 question
- Crane and Turtle Problems · Shopping Problems2 questions
- Elimination Problems · Subtracting Directly to Eliminate1 question
Word Problems (Age Problems, etc.)
- Patterns and Regularity · The Color at a Given Position2 questions
- How Savings Grow · Savings (Basics)1 question
- How Savings Grow · Catching Up1 question
- Age Problems · Years Later1 question