Math Grade 4


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Math Grade 4

Step-by-Step Explanations
  • Understanding place value up to 1,000,000: Each digit has a value based on its position. In 345,678, 3 is hundred thousands, 4 is ten thousands, etc.
  • Reading and writing large numbers: Use commas to separate every 3 digits. Example: 1,234,567 is "one million two hundred thirty-four thousand five hundred sixty-seven."
  • Comparing and ordering numbers: Compare digit by digit from left to right. Larger digits in higher places mean a bigger number.
  • Rounding numbers to nearest 10, 100, 1000: Look at the digit to the right of the rounding place. If 5 or more, round up. Otherwise, round down.
  • Understanding and using expanded form: Express the number by breaking it into place values. For example, 452 = 400 + 50 + 2.
  • Even and odd numbers: Even numbers end in 0, 2, 4, 6, 8. Odd numbers end in 1, 3, 5, 7, 9.
Practice Questions (30)
  1. What is the value of the 5 in 452,761?
  2. Write 723,800 in words.
  3. Which is larger: 98,456 or 89,456?
  4. Order these numbers: 345, 354, 435
  5. Round 387 to the nearest 10.
  6. Write 602 in expanded form.
  7. Is 91 an odd number?
  8. What is the value of 3 in 830,245?
  9. Write 1,000,001 in words.
  10. Compare: 760,200 and 760,020
  11. Round 6,425 to the nearest 100.
  12. Expanded form of 7,002?
  13. Is 36 even?
  14. What’s the value of 9 in 900,123?
  15. Write 1,230,004 in words.
  16. Arrange: 12,340; 13,240; 11,340 in ascending order.
  17. Round 888 to nearest 1000.
  18. Expanded form of 809?
  19. Is 55 odd?
  20. Value of 6 in 163,487?
  21. Write 450,050 in words.
  22. Compare 300,000 and 299,999
  23. Round 2,345 to nearest 10
  24. Expanded form of 5,060?
  25. Is 0 even or odd?
  26. Value of 2 in 234,567?
  27. Write 1,001,001 in words.
  28. Order: 999,100; 1,000,000; 998,900
  29. Round 7,777 to nearest 100
  30. Expanded form of 1,234?

Step-by-Step Explanations
  • Adding and subtracting multi-digit numbers (up to 1,000,000): Line up digits by place value. Start from the rightmost digit.
  • Using mental math strategies: Break numbers into parts (e.g., 500 + 300 = 800).
  • Estimating sums and differences: Round numbers to nearest 10 or 100 before adding/subtracting.
  • Solving word problems involving addition and subtraction: Identify key numbers and operation based on context.
  • Understanding properties of addition and subtraction: Addition is commutative and associative; subtraction is not.
  • Understanding multiplication as repeated addition: 3 × 4 = 4 + 4 + 4.
  • Multiplication facts up to 12 × 12: Memorize to improve speed and accuracy.
  • Multiplying multi-digit numbers by one-digit numbers: Multiply each digit starting from right and carry over as needed.
  • Using arrays and area models to visualize multiplication: Break numbers into tens and ones to simplify.
  • Solving multiplication word problems: Identify repeated groups and use multiplication.
  • Properties of multiplication: Commutative (a×b = b×a), Associative ((a×b)×c = a×(b×c)), Distributive (a×(b + c) = a×b + a×c).
Practice Questions (30)
  1. 654 + 238 = ?
  2. Round 749 to the nearest 10, then subtract 200.
  3. Estimate: 1,245 + 3,876
  4. Is addition commutative?
  5. Solve: 9 × 6
  6. Use mental math: 400 + 600 = ?
  7. Subtract: 10,000 - 6,789
  8. Use array for 4 × 3
  9. Solve 3 × (5 + 2)
  10. True or false: 8 + 5 = 5 + 8
  11. Solve: 1,234 + 3,456
  12. Estimate: 6,555 - 2,444
  13. What is 7 × 7?
  14. Subtract 900 from 1,500
  15. Solve: (3 × 2) × 4
  16. Word problem: If a bag has 8 apples and there are 7 bags, how many apples?
  17. Subtract: 5,000 - 4,123
  18. True or false: 6 × 5 = 5 × 6
  19. Solve: 600 + 320
  20. Estimate: 2,901 + 4,002
  21. What is the associative property?
  22. Multiply 321 by 4
  23. Solve: 11 × 12
  24. Write 5 × (6 + 3) using distributive property
  25. Subtract: 100 - 75
  26. Use mental math: 150 + 250
  27. What is 9 × 8?
  28. Solve: 4,321 + 2,789
  29. Subtract: 999 - 333
  30. Solve: 25 × 3

Step-by-Step Explanations
  • Understanding multiplication as repeated addition: Multiplication shows how many times a number is added. For example, 3 × 4 = 4 + 4 + 4 = 12.
  • Multiplication facts up to 12 × 12: Memorizing times tables up to 12 helps speed and accuracy in solving larger problems.
  • Multiplying multi-digit numbers by one-digit numbers: Multiply each digit starting from the right, carrying over if needed.
  • Using arrays and area models: Visual tools like grids and rectangles help understand multiplication.
  • Solving multiplication word problems: Identify repeated groups in the scenario, then multiply.
  • Properties of multiplication:
    • Commutative: a × b = b × a
    • Associative: (a × b) × c = a × (b × c)
    • Distributive: a × (b + c) = a × b + a × c
Practice Questions (30)
  1. What is 6 × 7?
  2. Use repeated addition to show 4 × 3.
  3. Multiply: 123 × 4
  4. What is the product of 12 and 11?
  5. Fill in the blank: 9 × ___ = 81
  6. Is multiplication commutative?
  7. Use area model to represent 6 × 5
  8. Write (3 × 4) × 2 using associative property
  9. Solve: 7 × (3 + 2)
  10. Solve: 100 × 9
  11. Which is larger: 8 × 7 or 9 × 6?
  12. What is 0 × 999?
  13. Is 1 × any number equal to that number?
  14. What’s 3 × 12?
  15. Estimate: 48 × 5
  16. Multiply: 36 × 2
  17. True or false: 5 × 6 = 6 × 5
  18. What is the distributive form of 5 × (6 + 2)?
  19. Solve: 42 × 10
  20. Multiply 73 by 3
  21. What’s 12 squared?
  22. Write a multiplication problem that equals 64
  23. How many groups of 9 in 81?
  24. Solve: 50 × 4
  25. True or false: 7 × (2 + 3) = 7 × 5
  26. What is 11 × 11?
  27. Estimate: 299 × 3
  28. What does repeated addition for 5 × 4 look like?
  29. What is the product of 15 and 2?
  30. Multiply 86 by 0

Step-by-Step Explanations
  • Understanding division as sharing and grouping: Division means splitting a total into equal parts or groups. For example, 12 ÷ 3 = 4 means 12 split into 3 groups gives 4 in each group.
  • Division facts up to 144 ÷ 12: Memorizing division tables helps in quick and accurate calculations. For instance, 144 ÷ 12 = 12.
  • Dividing multi-digit numbers by one-digit numbers: Use long division method starting from the leftmost digit. Divide, multiply, subtract, bring down the next digit, and repeat.
  • Understanding remainders in division: If a number doesn’t divide evenly, the leftover is called a remainder. Example: 10 ÷ 3 = 3 R1.
  • Solving division word problems: Identify the total and how many groups to split it into or how many items in each group.
  • Relationship between multiplication and division: Division is the inverse of multiplication. If 3 × 4 = 12, then 12 ÷ 4 = 3 and 12 ÷ 3 = 4.
Practice Questions (30)
  1. What is 12 ÷ 4?
  2. Divide: 144 ÷ 12
  3. Use long division to solve 75 ÷ 3
  4. What is the quotient of 100 ÷ 5?
  5. Solve: 63 ÷ 9
  6. What’s the remainder of 10 ÷ 3?
  7. Split 48 apples into 6 baskets equally. How many per basket?
  8. Write a related multiplication fact for 56 ÷ 7
  9. Solve: 35 ÷ 6
  10. How many times does 8 go into 72?
  11. Estimate: 253 ÷ 4
  12. What is 0 ÷ 5?
  13. True or False: Division is the reverse of multiplication.
  14. Find the missing number: ___ ÷ 6 = 9
  15. Solve 81 ÷ 9
  16. Divide: 132 ÷ 11
  17. What is the result of 84 ÷ 7?
  18. If 96 marbles are shared among 8 students, how many per student?
  19. What is 45 ÷ 5?
  20. True or False: 7 ÷ 0 = 0
  21. What is 49 ÷ 7?
  22. Divide 108 by 9
  23. Which is greater: 64 ÷ 4 or 72 ÷ 8?
  24. Find the quotient: 200 ÷ 10
  25. Use long division: 123 ÷ 3
  26. Estimate: 314 ÷ 6
  27. What is 36 ÷ 6?
  28. What is 1 ÷ 1?
  29. How many 6s in 36?
  30. Write a real-life division problem for 40 ÷ 5

Step-by-Step Explanations
  • Introduction to decimals to tenths and hundredths: Decimals represent parts of a whole. Tenths have one digit after the decimal point (0.1), hundredths have two (0.01).
  • Reading and writing decimals: Say the number normally and name the place value. Example: 0.25 is "twenty-five hundredths."
  • Comparing and ordering decimals: Line up decimal points. Compare digits left to right. Example: 0.3 > 0.25
  • Relating decimals to fractions: 0.1 = 1/10, 0.25 = 25/100. Move between them by placing over the correct power of 10.
  • Adding and subtracting decimals: Line up decimal points. Add or subtract as with whole numbers, keeping the decimal in the same place.
Practice Questions (30)
  1. What is 0.1 + 0.2?
  2. Subtract: 0.9 - 0.3
  3. Which is greater: 0.75 or 0.8?
  4. Write 0.25 as a fraction
  5. Add: 1.5 + 2.3
  6. Subtract: 5.0 - 4.7
  7. Compare: 0.62 ___ 0.61
  8. Write 3/10 as a decimal
  9. Order: 0.2, 0.25, 0.1
  10. Round 3.678 to the nearest hundredth
  11. Add: 0.4 + 0.6
  12. What’s 0.75 + 0.25?
  13. Is 0.5 = 1/2?
  14. Subtract 1.2 - 0.9
  15. Write 7/100 as a decimal
  16. Compare 0.09 and 0.9
  17. True or False: 0.10 = 0.1
  18. Write 0.2 in words
  19. Round 2.849 to the nearest tenth
  20. Add 3.33 + 2.22
  21. Convert 0.06 to a fraction
  22. What is 0.5 + 0.5?
  23. Subtract 0.5 - 0.2
  24. Write 1/10 as a decimal
  25. Which is smaller: 0.33 or 0.3?
  26. Compare: 0.27 and 0.72
  27. Write 0.01 in words
  28. Add 6.5 + 1.75
  29. Subtract 4.0 - 2.45
  30. Round 9.999 to the nearest whole number

Step-by-Step Explanations
  • Understanding and using customary and metric units: Learn the basic units like inches, feet, meters, grams, and liters. Use rulers and measuring tools to apply them.
  • Measuring length, weight, and volume: Practice with real objects. Measure with rulers (length), scales (weight), and measuring cups (volume).
  • Converting units within the same system: Know that 100 cm = 1 m, 1000 g = 1 kg, and use multiplication or division to convert.
  • Understanding time: Learn to read digital and analog clocks, calculate elapsed time, and distinguish AM/PM.
  • Solving word problems involving measurement: Apply measurement knowledge to everyday scenarios.
Practice Questions (30)
  1. Convert 150 cm to meters
  2. How many grams in 2 kilograms?
  3. How many minutes in 2 hours?
  4. Convert 500 mL to liters
  5. What is the total weight of 3 boxes each weighing 2 kg?
  6. How many feet in 36 inches?
  7. Read a clock showing 3:45 PM
  8. What is the elapsed time from 2:30 to 5:00?
  9. Convert 1.2 kg to grams
  10. Measure the length of a pencil in cm
  11. Compare: 500 mL or 0.6 L?
  12. Estimate the weight of a watermelon
  13. How many seconds in 3 minutes?
  14. True or False: 1 km = 100 m
  15. What is 1/2 hour in minutes?
  16. Convert 2500 mL to L
  17. Convert 0.75 L to mL
  18. How much is 3 yards in feet?
  19. Write the AM/PM time for 14:00
  20. How many millimeters in 2.5 cm?
  21. Read a scale showing 1.5 kg
  22. Estimate: 1 liter or 5 liters for a water bottle?
  23. How many cups in 1 quart?
  24. Convert 1.5 hours to minutes
  25. Compare 2 kg and 1500 g
  26. True or False: 60 seconds = 1 minute
  27. Convert 0.5 L to mL
  28. Find the perimeter of a square with 3 cm sides
  29. Calculate elapsed time from 9:15 to 12:45
  30. Convert 100 cm to meters

Step-by-Step Explanations
  • Identifying and classifying 2D shapes (triangles, quadrilaterals, polygons): Recognize shapes by their number of sides and angles. Triangles have 3 sides, quadrilaterals 4, polygons 5 or more.
  • Understanding properties of shapes (sides, angles, symmetry): Learn how sides relate (equal or not), measure angles, and identify lines of symmetry.
  • Introduction to lines, line segments, rays: A line extends infinitely in both directions, a line segment has two endpoints, and a ray starts at one point and extends infinitely.
  • Understanding parallel and perpendicular lines: Parallel lines never meet and stay the same distance apart; perpendicular lines intersect at right angles.
  • Classifying 3D shapes (cubes, spheres, cylinders, cones): Differentiate solids by faces, edges, and vertices. Cubes have flat faces, spheres are round, cylinders have circular faces and curved surfaces.
  • Understanding faces, edges, and vertices of 3D shapes: Faces are flat surfaces, edges are where two faces meet, vertices are points where edges meet.
Practice Questions (30)
  1. What shape has 3 sides?
  2. How many sides does a quadrilateral have?
  3. Name a polygon with 6 sides.
  4. What is symmetry in shapes?
  5. Define a line segment.
  6. How does a ray differ from a line?
  7. What makes lines parallel?
  8. At what angle do perpendicular lines intersect?
  9. How many faces does a cube have?
  10. Describe a sphere.
  11. What is the difference between an edge and a vertex?
  12. How many vertices does a cube have?
  13. Give an example of a 3D shape with curved surfaces.
  14. How many edges does a rectangular prism have?
  15. What is a polygon?
  16. Identify the number of lines of symmetry in an equilateral triangle.
  17. What shape has 4 equal sides and 4 right angles?
  18. What is the name for a line that divides a shape into two equal parts?
  19. How many sides does a pentagon have?
  20. Can a line segment be measured? Why?
  21. Explain what a vertex is in 2D shapes.
  22. Are all quadrilaterals rectangles? Explain.
  23. How many edges does a cone have?
  24. What shape results from slicing a cylinder parallel to its base?
  25. Is a circle a polygon? Why or why not?
  26. Describe the properties of a square.
  27. What do parallel lines look like on a grid?
  28. How many right angles are in a rectangle?
  29. What is the difference between a prism and a pyramid?
  30. How many faces does a cylinder have?

Step-by-Step Explanations
  • Recognizing and measuring angles using a protractor: Learn how to place a protractor correctly to measure the size of an angle in degrees.
  • Types of angles: right, acute, obtuse, straight: Right angle is exactly 90°, acute less than 90°, obtuse between 90° and 180°, and straight is exactly 180°.
  • Estimating and comparing angles: Practice estimating angle sizes and comparing which are larger or smaller without exact measurement tools.
  • Understanding angle relationships: Learn about complementary, supplementary, adjacent, and vertical angles and how they relate.
Practice Questions (30)
  1. What is the measure of a right angle?
  2. Name an angle less than 90°.
  3. What angle measures exactly 180°?
  4. How do you use a protractor to measure an angle?
  5. Estimate the size of an acute angle.
  6. What is an obtuse angle?
  7. Define supplementary angles.
  8. What are complementary angles?
  9. Describe adjacent angles.
  10. What are vertical angles?
  11. Can two angles be both adjacent and complementary?
  12. What angle is formed by the hands of a clock at 3 o’clock?
  13. How many degrees are in a full rotation?
  14. Is a straight angle larger than a right angle?
  15. What angle do perpendicular lines form?
  16. Estimate the angle between 12 and 1 on a clock.
  17. How do you know if two angles are vertical angles?
  18. What type of angle is less than 90 degrees but more than 45 degrees?
  19. Explain why complementary angles add up to 90 degrees.
  20. How many degrees do supplementary angles add up to?
  21. What is the measure of an acute angle if its complementary angle is 60°?
  22. What type of angle is between 90° and 180°?
  23. Are adjacent angles always supplementary?
  24. Can an angle be both obtuse and adjacent to a right angle?
  25. How do you draw an acute angle?
  26. What tools do you need to measure an angle?
  27. What is the difference between acute and obtuse angles?
  28. What angle measures exactly 90 degrees?
  29. What angle do the hands of a clock make at 6 o’clock?
  30. What angle is formed when two lines meet but do not form a right angle?

Step-by-Step Explanations
  • Collecting and organizing data: Understand how to gather data systematically and arrange it for analysis.
  • Reading and creating bar graphs and pictographs: Learn how to interpret and draw bar graphs and pictographs to represent data visually.
  • Understanding line plots and tally charts: Recognize and use line plots and tally charts to show frequency of data points.
  • Interpreting data from graphs and tables: Learn how to extract information and trends from various types of data displays.
  • Solving problems using data: Use the data presented in graphs or tables to solve real-world problems.
Practice Questions (30)
  1. What is the purpose of collecting data?
  2. How do you organize data for analysis?
  3. What type of graph uses bars to represent data?
  4. What is a pictograph?
  5. How do tally charts help in data collection?
  6. Describe a line plot.
  7. What information can you get from a bar graph?
  8. How do you create a bar graph?
  9. What is the difference between a bar graph and a pictograph?
  10. How can you use data from a graph to solve problems?
  11. What is frequency in data?
  12. What is the use of tally marks?
  13. How do you read data from a table?
  14. What does a line plot show?
  15. Why is it important to organize data?
  16. What type of data is best shown in a pictograph?
  17. How can you tell trends from a graph?
  18. What are the parts of a bar graph?
  19. What is the title of a graph used for?
  20. How do you label the axes on a bar graph?
  21. How do you find the range of data?
  22. What is a histogram?
  23. What is the difference between a histogram and a bar graph?
  24. How do you interpret data from a histogram?
  25. What is a data table?
  26. What is the difference between qualitative and quantitative data?
  27. How do you collect data for a survey?
  28. What is an outlier in data?
  29. How do you use a tally chart to find the mode?
  30. What does the mean of data represent?

Step-by-Step Explanations
  • Recognizing, describing, and extending patterns: Patterns are sequences that repeat or grow according to a rule. By understanding the rule, you can predict future elements.
  • Understanding numeric and geometric patterns: Numeric patterns involve numbers following a rule; geometric patterns involve shapes arranged in a specific order.
  • Introduction to variables and simple expressions: Variables represent unknown or changing numbers. Expressions combine numbers and variables with operations.
  • Solving simple equations and inequalities: Find values of variables that make the equation or inequality true.
  • Using patterns to solve problems: Patterns help simplify complex problems by identifying predictable sequences.
Practice Questions (30)
  1. What is a pattern in math?
  2. Identify the next number in the sequence: 2, 4, 6, 8, ...
  3. What type of pattern is formed by repeating shapes?
  4. Define a variable in algebra.
  5. Solve for x: x + 5 = 12
  6. What does it mean to extend a pattern?
  7. Describe the difference between numeric and geometric patterns.
  8. Write a simple algebraic expression using x.
  9. Solve the inequality: x - 3 > 5
  10. How can patterns help solve math problems?
  11. What is the 5th term in the pattern 3, 6, 9, 12, ...?
  12. Identify the rule for the pattern: 1, 4, 9, 16, 25, ...
  13. What is an equation?
  14. How do you know if a number is a solution to an equation?
  15. Write an expression for "3 more than a number y."
  16. Find x if 2x = 10
  17. What is an inequality?
  18. Give an example of a geometric pattern.
  19. What does the expression 4x mean?
  20. How do you check your solution to an equation?
  21. Identify the pattern: 5, 10, 20, 40, ...
  22. What is the next shape in a pattern of square, triangle, square, triangle?
  23. Solve: x/2 = 8
  24. What is the difference between an equation and an inequality?
  25. Describe how to write a pattern rule.
  26. How does a variable help in solving problems?
  27. Simplify the expression: 3x + 4x
  28. What does it mean if x > 7?
  29. Find the next term in the pattern: 2, 4, 8, 16, ...
  30. Write an inequality for "a number less than 10."

Step-by-Step Explanations
  • Applying math concepts to real-world problems: Use math to understand and solve everyday situations.
  • Multi-step problem solving: Break complex problems into smaller steps to solve them efficiently.
  • Reasoning and explaining math thinking: Justify your methods and solutions clearly.
  • Using estimation to check answers: Approximate calculations to verify if answers are reasonable.
Practice Questions (30)
  1. Why is problem solving important in math?
  2. What is a multi-step problem?
  3. How can you break down a complex problem?
  4. What does it mean to reason in math?
  5. How do you explain your math thinking?
  6. Why use estimation in checking answers?
  7. Give an example of a real-world math problem.
  8. What is the first step in problem solving?
  9. How can you verify your solution?
  10. What strategies help in problem solving?
  11. Describe how to handle multi-step problems.
  12. Why is it important to justify your answer?
  13. How does estimation save time?
  14. What is an example of a problem that needs reasoning?
  15. How do diagrams help in problem solving?
  16. What role does understanding the problem play?
  17. How do you check if an answer makes sense?
  18. What is the benefit of explaining your work?
  19. How can you use math in daily life?
  20. What tools help in problem solving?
  21. How do you organize information in a problem?
  22. What should you do if stuck on a problem?
  23. Why is critical thinking important?
  24. What is the role of logic in math?
  25. How can you develop better problem solving skills?
  26. What does it mean to reflect on your solution?
  27. How can you communicate your math ideas effectively?
  28. Why is it important to consider different approaches?
  29. How can collaboration improve problem solving?
  30. What is the importance of practice in critical thinking?