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Math Grade 7

Step-by-Step Explanations
  • Integers: Addition and Subtraction: Same signs: add values and keep the sign. Different signs: subtract and keep the sign of the bigger number. Example: -5 + 3 = -2.
  • Multiplication and Division of Integers: Multiply/divide normally. Same sign = positive; different sign = negative. Example: (-6) / 2 = -3.
  • Prime Numbers and Factors: Prime = only divisible by 1 and itself. Factors are divisors. Example: 7 is prime, factors of 8 are 1, 2, 4, 8.
  • Greatest Common Factor (GCF): Biggest number that divides both. Example: GCF of 12 and 16 is 4.
  • Least Common Multiple (LCM): Smallest number both divide into. Example: LCM of 4 and 6 is 12.
  • Rational Numbers: Any number as a fraction. Includes integers, decimals, fractions. Example: -2, 0.5, 3/4.
  • Fractions: Simplifying and Comparing: Divide numerator and denominator by GCF. Compare using same denominator or decimal form.
  • Operations with Fractions: Add/subtract with common denominators. Multiply straight across. Divide = multiply by reciprocal.
  • Decimals: Place Value and Rounding: Tenths, hundredths, etc. Round to place by checking next digit.
  • Converting Between Fractions, Decimals, Percents: Fraction → decimal = divide. Decimal → percent = ×100. Percent → decimal = ÷100.
Practice Questions (30)
  1. -5 + 3 = ?
  2. 6 - (-4) = ?
  3. -3 × 2 = ?
  4. -12 ÷ 3 = ?
  5. Is 11 a prime number?
  6. List factors of 20.
  7. GCF of 14 and 21?
  8. LCM of 3 and 5?
  9. Is 0.25 a rational number?
  10. Simplify 6/9.
  11. Compare 3/4 and 2/3.
  12. 1/2 + 1/4 = ?
  13. 2/3 - 1/6 = ?
  14. 3/4 × 1/2 = ?
  15. 5/6 ÷ 1/3 = ?
  16. Round 3.678 to 2 decimal places.
  17. Convert 2/5 to decimal.
  18. Convert 0.6 to percent.
  19. Convert 35% to decimal.
  20. -8 + 5 = ?
  21. 9 - (-3) = ?
  22. -7 × -2 = ?
  23. 15 ÷ (-5) = ?
  24. Is 17 prime?
  25. Factors of 36?
  26. GCF of 18 and 24?
  27. LCM of 4 and 10?
  28. Simplify 9/12.
  29. 3/5 + 2/10 = ?
  30. Convert 0.2 to percent.
  31. Convert 80% to fraction.

Step-by-Step Explanations
  • Algebraic Expressions: Contain variables, numbers, and operations. Example: 3x + 2.
  • Terms and Coefficients: In 5x + 3, 5 is the coefficient, x is the variable, 3 is a constant.
  • Simplifying Expressions: Combine like terms. Example: 2x + 3x = 5x.
  • Evaluating Expressions: Substitute values for variables and solve. If x = 2, then 3x = 6.
  • Properties of Operations: Commutative (a + b = b + a), Associative ((a + b) + c = a + (b + c)), Distributive (a(b + c) = ab + ac).
  • Writing and Interpreting Expressions: Translate phrases like “5 more than a number” into x + 5.
  • Solving One-step Equations: Use inverse operations. x + 3 = 7 → x = 4.
  • Solving Two-step Equations: x/2 + 3 = 7 → subtract 3, then multiply by 2.
  • Using Equations to Solve Word Problems: Translate the problem into an equation and solve.
  • Inequalities: Use symbols like <, >, ≤, ≥ to compare values. Example: x > 3 means x is greater than 3.
  • Writing Inequalities: Turn statements like “a number less than 5” into x < 5.
Practice Questions (30)
  1. Simplify: 4x + 5x
  2. Evaluate: 2x + 3 when x = 4
  3. Distribute: 3(2 + x)
  4. Solve: x + 7 = 10
  5. Solve: x - 5 = 8
  6. Solve: 2x = 12
  7. Solve: x/3 = 6
  8. Solve: x/2 + 4 = 10
  9. Simplify: 5x - 3x + 2
  10. Translate: 6 more than a number
  11. Translate: A number divided by 4
  12. Is x = 2 a solution to 2x + 1 = 5?
  13. Combine: 2a + 3 + 5a - 1
  14. Write inequality for: A number is at most 10
  15. Evaluate: x² + 3x when x = 2
  16. Solve: 5x - 4 = 11
  17. Solve: 3(x - 2) = 6
  18. Simplify: 2x + 4 - x
  19. Evaluate: 4x - 5 when x = 3
  20. Solve: x/5 + 2 = 4
  21. Distribute: 4(x + 1)
  22. Write expression for: Twice a number decreased by 3
  23. Solve: 2x + 3 = 11
  24. Write: A number is greater than or equal to 7
  25. Evaluate: x³ when x = 2
  26. Combine: 7x - 2x + 5
  27. Solve: x/4 - 1 = 2
  28. Simplify: 6x - 3 + 2x + 5
  29. Solve: 3x + 2 = 17
  30. Translate: The sum of a number and 9
  31. Evaluate: 2x² - x when x = 3

Step-by-Step Explanations
  • Understanding Ratios: A ratio compares two quantities. Example: 3:2 means for every 3 of one, there are 2 of the other.
  • Equivalent Ratios: Ratios that express the same relationship. Example: 1:2 is the same as 2:4.
  • Unit Rates: A rate with a denominator of 1. Example: 60 miles in 2 hours = 30 miles/hour.
  • Solving Proportions: Set two ratios equal and solve for the unknown using cross-multiplication.
  • Percent: Concept and Calculations: Percent means per 100. 45% = 45/100 = 0.45.
  • Percent of a Number: Multiply percent (as decimal) by number. 20% of 50 = 0.2 × 50 = 10.
  • Percent Increase and Decrease: Increase = new - original / original × 100%. Decrease is similar.
  • Solving Percent Problems: Use proportion or formula (part = percent × whole).
  • Scale Drawings and Models: Use ratio between drawing and real size. Example: 1 cm = 5 km.
  • Using Ratios in Real Life: Recipes, maps, speed, etc.
Practice Questions (30)
  1. Write the ratio of 8 apples to 12 oranges.
  2. Simplify the ratio 6:9.
  3. Are 3:4 and 6:8 equivalent?
  4. Find the unit rate: 120 miles in 3 hours.
  5. If 5 pens cost $15, how much is 1 pen?
  6. Solve: 2/5 = x/10
  7. Solve: 3/x = 6/8
  8. What is 25% of 80?
  9. 45 is what percent of 90?
  10. Increase 50 by 20%
  11. Decrease 100 by 25%
  12. What percent is 30 out of 120?
  13. If a shirt costs $40 and is on sale for 20% off, what’s the discount?
  14. Total cost if item is $60 and tax is 10%
  15. Use scale 1 cm = 4 m. How long is a 16 m room on the drawing?
  16. Convert 0.75 to percent.
  17. Convert 25% to decimal.
  18. Convert 3/4 to percent.
  19. What is 10% of 500?
  20. If 3 books cost $27, what’s the cost per book?
  21. What is the percent increase from 20 to 25?
  22. Find x: 4/7 = x/14
  23. Is 2:3 equivalent to 6:9?
  24. Find 15% of 200.
  25. What is 60% of 80?
  26. Convert 0.2 to a percent.
  27. Convert 45% to fraction.
  28. If a $50 item has 8% tax, total cost?
  29. Reduce 10:20 to simplest form.
  30. Scale: 1 in = 5 ft. Real length of 4 in?

Step-by-Step Explanations
  • Points, Lines, and Planes: Points are locations, lines are straight with infinite length, planes are flat surfaces.
  • Measuring and Classifying Angles: Use a protractor. Acute (< 90°), right (90°), obtuse (> 90°).
  • Types of Triangles: By sides: equilateral, isosceles, scalene. By angles: acute, right, obtuse.
  • Properties of Quadrilaterals: Trapezoid, parallelogram, rectangle, square, rhombus – each with unique properties.
  • Parallel and Perpendicular Lines: Parallel = never intersect, same slope. Perpendicular = intersect at 90°.
  • Polygons and their Properties: Closed shapes with straight sides. Regular = all sides and angles equal.
  • Circumference and Area of Circles: C = πd or 2πr. A = πr².
  • Area of Triangles and Quadrilaterals: Triangle: ½bh. Rectangle: lw. Parallelogram: bh. Trapezoid: ½(a + b)h.
  • Coordinate Plane: Grid with x (horizontal) and y (vertical) axes to plot points.
  • Distance Between Points: Count spaces or use Pythagorean theorem if diagonal.
Practice Questions (30)
  1. What is a point?
  2. Name a pair of perpendicular lines.
  3. Classify angle: 110°
  4. Measure of right angle?
  5. Triangle with all sides equal?
  6. Shape with 4 equal sides and 4 right angles?
  7. Are opposite sides of a parallelogram equal?
  8. Draw an obtuse triangle.
  9. Is a square a rectangle?
  10. Find circumference of circle with r = 7
  11. Area of circle with d = 10
  12. Area of triangle with b = 6, h = 4
  13. Area of rectangle: l = 8, w = 3
  14. Find area of parallelogram: b = 5, h = 6
  15. Area of trapezoid: a = 3, b = 7, h = 4
  16. Plot (3,2) on grid – which quadrant?
  17. Distance between (2,2) and (2,5)?
  18. Name a regular polygon
  19. Define a plane
  20. What is π approximately?
  21. Area of square with side 5
  22. Draw a polygon with 6 sides
  23. What is the formula for area of triangle?
  24. How many sides in an octagon?
  25. Which angle is smaller: 30° or 60°?
  26. Define scalene triangle
  27. Plot (0,0)
  28. How many degrees in a right angle?
  29. Identify base in triangle
  30. What shape is a stop sign?

Step-by-Step Explanations
  • Nets of 3D Figures: A net is a two-dimensional pattern that can be folded into a 3D figure.
  • Surface Area of Rectangular Prisms: SA = 2lw + 2lh + 2wh
  • Surface Area of Triangular Prisms: Add areas of all sides, including triangular bases and rectangular sides.
  • Surface Area of Cylinders: SA = 2πr² + 2πrh
  • Volume of Rectangular Prisms: V = l × w × h
  • Volume of Triangular Prisms: V = (½ × b × h) × length
  • Volume of Cylinders: V = πr²h
  • Converting Units of Volume: 1 m³ = 1,000,000 cm³
  • Estimating Surface Area and Volume: Round dimensions for easier mental calculation.
  • Solving Real-world Problems: Apply formulas to situations like storage or containers.
Practice Questions (30)
  1. Draw the net of a cube.
  2. Find surface area of 2×3×4 box.
  3. Area of one face of 5×5 cube?
  4. Surface area of cube with side 6?
  5. Volume of 2×3×4 box?
  6. Volume of cube with side 3?
  7. Find SA of triangular prism with base 4, height 3, length 10.
  8. Volume of triangular prism: base 5, height 4, length 6.
  9. Find SA of cylinder: r = 3, h = 7.
  10. Volume of cylinder: r = 4, h = 5.
  11. Estimate volume of box 9.8×10.2×5.1
  12. Find lateral surface area of cylinder r=2, h=5.
  13. Convert 2 m³ to cm³
  14. If SA = 94 cm², what might be the shape?
  15. Estimate SA of can: r = 3.2, h = 11
  16. Compare volumes: cube side 4 vs rectangular prism 2×4×4
  17. Box holds 200 cm³. Dimensions?
  18. Find base area of prism: volume 120, height 10
  19. SA of box: 5×2×3
  20. Volume of triangular prism: base 6, height 3, length 8
  21. SA of cylinder: r = 5, h = 4
  22. Convert 5000 cm³ to liters
  23. Find volume of cube with side 10
  24. What units are used for SA? Volume?
  25. Why round π in volume problems?
  26. Estimate how many 1cm³ cubes fill 1L box
  27. Difference in volume between 6×6×6 and 3×12×3
  28. Does changing height or base affect volume more?
  29. SA vs Volume: which grows faster as size increases?
  30. What is the volume of cylinder with diameter 6, height 10?

Step-by-Step Explanations
  • Collecting Data: Use surveys, observations, experiments, or existing sources.
  • Organizing Data in Tables: Group results in rows and columns for easy reading.
  • Reading and Creating Bar Graphs: Bars show data quantities. Height represents value.
  • Line Graphs and Histograms: Line graphs show trends. Histograms show frequency of ranges.
  • Circle (Pie) Graphs: Show parts of a whole using sectors.
  • Measures of Central Tendency: Mean = average, Median = middle value, Mode = most frequent.
  • Range and Variability: Range = max - min. Variability = how spread out values are.
  • Interpreting Data Sets: Look for trends, clusters, outliers, and gaps.
  • Identifying Outliers: Values far from rest. Can affect mean significantly.
Practice Questions (30)
  1. What is a survey?
  2. List 2 ways to collect data.
  3. Create a tally chart for 5 fruit choices.
  4. Draw a bar graph of test scores.
  5. What is a histogram?
  6. How does a line graph differ from bar graph?
  7. Show pie graph of class vote with 4 choices.
  8. Find mean of 10, 20, 30
  9. Find median of 3, 9, 6
  10. Find mode of 4, 5, 5, 7
  11. Range of 8, 10, 3, 1
  12. Identify outlier: 3, 4, 4, 5, 25
  13. How do outliers affect mean?
  14. What is a data set?
  15. Which graph best for trends?
  16. When use pie chart?
  17. Make frequency table of 20 test scores
  18. Draw histogram from score ranges
  19. Calculate average of 5 numbers
  20. Find median of even set: 4, 6, 8, 10
  21. List pros of using bar graph
  22. What is variability?
  23. Graph favorite sport of class
  24. How many degrees in pie chart total?
  25. Divide 360° among 4 equal groups
  26. Can you have more than one mode?
  27. When do you use range?
  28. Estimate range: 2, 4, 8, 9, 15
  29. Why organize data?
  30. Is a dot plot a graph?

Step-by-Step Explanations
  • Probability Concepts: Likelihood that an event will occur, expressed as a number between 0 and 1.
  • Simple Probability: P = number of favorable outcomes / total outcomes.
  • Experimental vs Theoretical Probability: Experimental is based on trials; theoretical is based on reasoning.
  • Compound Events: Events with more than one outcome.
  • Organized Lists/Tree Diagrams: Visual tools to show all possible outcomes.
  • Independent Events: One event doesn't affect another.
  • Dependent Events: One event affects another.
  • Complementary Events: Events that cover all possible outcomes together.
  • Simulation: Using models to mimic random events.
  • Real-life Probability: Used in games, insurance, weather forecasts.
Practice Questions (30)
  1. What is the probability of rolling a 6 on a die?
  2. Flip a coin. What's the chance of heads?
  3. If 5 out of 20 marbles are red, what is P(red)?
  4. Difference between theoretical and experimental probability?
  5. List outcomes of rolling 2 dice.
  6. Tree diagram for 2 coin flips?
  7. Draw all outcomes of picking A, B from 2 groups.
  8. What does P=0 mean?
  9. What does P=1 mean?
  10. Probability of drawing a heart from a 52-card deck?
  11. Are drawing 2 cards without replacement independent?
  12. What is a compound event?
  13. Example of complementary events?
  14. Simulate dice roll 10 times and record results.
  15. Is weather prediction theoretical or experimental?
  16. Probability of getting 2 heads in 2 coin flips?
  17. Use a spinner with 4 colors. P(red)?
  18. Estimate chance of rain based on past 10 days.
  19. If P(win) = 0.2, what's P(not win)?
  20. When are events dependent?
  21. Use probability in real-life example.
  22. Roll die. Even number outcome?
  23. Bag of 3 blue, 2 red. P(red)?
  24. What tool shows all outcomes?
  25. How do you write probability as a percent?
  26. Are dice and coins fair objects?
  27. Can probability be greater than 1?
  28. Find experimental P(head) from 20 coin flips.
  29. What is the total probability of all outcomes?
  30. Describe use of probability in sports.

Step-by-Step Explanations
  • Add/Subtract Integers: Use number lines and rules of signs (same sign: add, keep; diff: subtract, keep sign of larger).
  • Multiply/Divide Integers: Same signs = positive; different = negative.
  • Rational Numbers on Number Line: Rational = fractions, decimals; plot them as points.
  • Comparing Rational Numbers: Convert to decimals or use common denominators.
  • Absolute Value: Distance from 0; always positive.
  • Operations: Apply integer rules to add/subtract/multiply/divide rational numbers.
  • Problem Solving: Use rational numbers in real-life contexts like banking or temperature.
  • Understanding Opposites: Opposite of 5 is -5; opposites are same distance from 0.
  • Representing in Context: Negative = loss, below zero; positive = gain, above zero.
  • Integer Rules: Memorize basic rules to operate correctly.
Practice Questions (30)
  1. What is -5 + 3?
  2. -4 - 6 = ?
  3. -8 × -2 = ?
  4. -12 ÷ 3 = ?
  5. Plot 1/2 and -0.5 on a number line.
  6. Compare -3 and -5
  7. What is | -7 |?
  8. Add -2 + (-4)
  9. Divide -10 by -2
  10. Is 4/5 rational?
  11. Is 0.333... rational?
  12. Find opposite of 9
  13. Subtract: -8 - (-3)
  14. Multiply: -3 × 5
  15. What does absolute value measure?
  16. Convert 3/4 to decimal
  17. Is 0 a rational number?
  18. What is -3 × -3?
  19. Use a rational number to describe debt.
  20. Use an integer to describe temperature drop.
  21. What’s the rule for + × - ?
  22. Is -7 + 2 positive or negative?
  23. Use opposite of -4 in a problem.
  24. Add: -6 + 8
  25. Divide 18 by -3
  26. Find distance from -4 to 2
  27. Which is greater: 2/3 or 0.6?
  28. Write real-world use of rational numbers
  29. Estimate: -2.5 + 3.2
  30. Is 7/0 rational?

Step-by-Step Explanations
  • Identifying Proportional Relationships: Proportional relationships maintain a constant ratio between values.
  • Graphing: A straight line through the origin on a graph indicates proportionality.
  • Constant of Proportionality: The ratio (k) that relates two proportional quantities (y = kx).
  • Solving Proportions: Use cross-multiplication to find missing values in equivalent ratios.
  • Tables: Use tables to determine constant ratio across rows or columns.
  • Real-world: Recipes, maps, blueprints apply proportions in daily use.
  • Direct Variation: When one variable increases/decreases, the other does too at a constant rate.
  • Percent Proportions: Solve problems involving percent using ratio forms.
  • Scale Factors: Used in resizing figures or models proportionally.
  • Applications: Solve multi-step real-world problems using ratios.
Practice Questions (30)
  1. Is y = 3x proportional?
  2. Graph a table with x: 1, 2, 3; y: 2, 4, 6.
  3. Find constant of proportionality: x=5, y=20.
  4. Solve: 2/3 = x/6
  5. Create a table for y = 4x
  6. Is a 1:2 ratio proportional to 2:4?
  7. Solve recipe: 2 cups flour to 3 eggs. How much flour for 6 eggs?
  8. Direct variation example?
  9. Solve 25% of 160
  10. Map scale: 1cm = 10km. How many km is 5cm?
  11. Is y = x + 5 proportional?
  12. Graph line through origin
  13. Identify proportional table
  14. Write ratio as fraction
  15. Convert 40% to fraction
  16. Use proportion to solve tip
  17. Identify non-proportional relation
  18. Write equation y = kx from table
  19. Proportional or not: x:1,2; y:3,5?
  20. Find scale factor for enlargement
  21. Real-life proportional example?
  22. How does doubling x affect y?
  23. Cross-multiply to solve 4/x = 2/6
  24. Convert 0.5 to percent
  25. Does ratio simplify?
  26. What is 120% of 50?
  27. Solve for unknown using k=y/x
  28. Map: 3in = 15mi. How far is 7 in?
  29. Apply ratio to discount
  30. Graph scale drawing

Step-by-Step Explanations
  • Word Problems: Translate real-life scenarios into algebraic expressions.
  • Parentheses: Group terms to control order of operations.
  • Like Terms: Combine terms with the same variable part.
  • Distributive Property: a(b + c) = ab + ac
  • Factoring: Reverse distributive property to factor expressions.
  • Multi-step Equations: Solve using inverse operations in steps.
  • Formulas: Rearrange known formulas to solve for unknowns.
  • Inequalities: Solve like equations; flip sign if multiplying/dividing by negative.
  • Graphing Inequalities: Use number line with open/closed circle.
  • Checking: Plug answer back into original expression to verify.
Practice Questions (30)
  1. Write expression: 3 more than x
  2. Simplify: 2x + 3x
  3. Distribute: 4(x + 2)
  4. Factor: 6x + 12
  5. Solve: x - 4 = 10
  6. Solve: 3x = 15
  7. Simplify: x + 2 + x + 5
  8. Write inequality: y is less than 5
  9. Graph x > 2
  10. Check solution for x = 4 in x + 3 = 7
  11. Factor: 9x + 3
  12. Solve: x/4 = 3
  13. Write formula for perimeter of square
  14. Distribute: 5(2x - 1)
  15. Evaluate x = 3 in 2x + 5
  16. Simplify: 3x + 2 - x + 4
  17. Write expression for total of x, y, z
  18. Write inequality: x ≥ 7
  19. Graph solution of x ≤ 0
  20. Solve: 2(x - 1) = 6
  21. Solve: x + x + x = 18
  22. Check x = 2 in x² = 4
  23. Use distributive to expand 3(x + 4)
  24. Factor: 10x + 20
  25. Solve: -2x = 10
  26. Write as formula: area of triangle
  27. Compare x = 3, x > 3
  28. Combine: 4a - 2a
  29. Rearrange: a = b + c to solve for b
  30. Graph inequality: x < -1

The Coordinate Plane Basics: Understand x- and y-axes, quadrants, and the origin (0,0).

Plotting Points in All Four Quadrants: Use positive and negative values to place points in all four areas.

Reading Coordinates: Interpret (x, y) pairs from a graph.

Graphing Linear Equations: Make tables of values and connect points for a straight line.

Slope of a Line (Intro): Learn rise/run and what slope means visually and algebraically.

Graphing Inequalities: Shade areas on the graph that satisfy linear inequalities.

Distance Between Two Points (Using Counting): Count units between points when directly aligned.

Midpoint of a Segment (Conceptual): Average the x-values and y-values to find midpoint.

Translations on the Coordinate Plane: Slide a figure without rotating or flipping.

Reflections and Rotations: Flip or turn figures on the coordinate plane.

Explanation: Coordinate geometry involves understanding and using the coordinate plane to represent and analyze geometric figures. The plane is divided into four quadrants by the x-axis and y-axis. Points are plotted using ordered pairs (x, y). You can graph equations, calculate distances, find midpoints, and apply transformations like reflections, translations, and rotations.

30 Practice Questions
  1. Plot the point (3, -2).
  2. In which quadrant is the point (-5, 4)?
  3. Graph the line y = 2x + 1.
  4. What is the slope of a line passing through (0,0) and (4,2)?
  5. Find the distance between (1,2) and (1,5).
  6. Find the midpoint of (2,2) and (4,6).
  7. Reflect point (3,4) over the x-axis.
  8. Rotate point (1,2) 90 degrees counterclockwise.
  9. Translate point (3,-1) by (2,3).
  10. Write the coordinates of a point 4 units to the right of (1,1).
  11. Graph the inequality y < x + 2.
  12. What is the y-intercept of y = -3x + 5?
  13. What does a slope of 0 represent?
  14. Which axis is horizontal?
  15. Which axis is vertical?
  16. What is the origin?
  17. Plot a point in Quadrant II.
  18. Find the slope of a horizontal line.
  19. Reflect (-2,5) over the y-axis.
  20. Rotate (0,1) 180 degrees around the origin.
  21. Translate (-1, -1) by (-3, 2).
  22. Plot the points that create a square with side length 2.
  23. Graph the function y = x.
  24. What quadrant is (0,-3) in?
  25. What is the midpoint between (0,0) and (6,6)?
  26. Distance from (2,3) to (5,3)?
  27. Equation of a line with slope 1 and y-intercept -2?
  28. Graph y = -x.
  29. Reflect (1,-1) over the origin.
  30. Plot a triangle with vertices (0,0), (3,0), (0,4).

Translations: Slide a figure left/right or up/down.

Reflections: Flip shapes across the x-axis or y-axis.

Rotations: Turn shapes around a point, usually 90°, 180°, or 270°.

Identifying Symmetry: Find mirror lines or rotational matches.

Tessellations: Repeat shapes to cover a plane with no gaps.

Dilations and Scale Factor: Enlarge or shrink figures while keeping shape.

Compositions of Transformations: Combine two or more movements.

Coordinates After Transformation: Calculate new locations of points.

Congruence and Similarity: Determine if shapes are identical or proportional.

Real-world Applications: Design, animation, mapping tasks using transformations.

Explanation: Transformations in mathematics are operations that move or change shapes on a coordinate plane. These include translations (slides), reflections (flips), rotations (turns), and dilations (resizing). Each transformation affects the position, size, or orientation of shapes without altering their properties. Understanding how each transformation works is key to solving geometry problems and applying concepts to real-world tasks such as design and animation.

30 Practice Questions
  1. Translate the point (2, 3) up 4 units.
  2. Reflect the point (5, -2) over the x-axis.
  3. Rotate the point (3, 1) 90° clockwise around the origin.
  4. Translate (-3, -3) by (4, 2).
  5. Reflect (-6, 7) over the y-axis.
  6. Rotate (0, 4) 180° around the origin.
  7. Translate (0, 0) by (-2, -5).
  8. Reflect (1, 1) over the origin.
  9. Rotate (2, -3) 270° clockwise.
  10. Translate (6, -1) left 3 units.
  11. Reflect (-4, 0) over the x-axis.
  12. Rotate (5, 0) 90° counterclockwise.
  13. Translate (-2, 5) down 6 units.
  14. Reflect (3, -4) over the y-axis.
  15. Rotate (-1, -1) 180° around the origin.
  16. Translate (2, 2) by (3, -2).
  17. Reflect (0, -7) over the x-axis.
  18. Rotate (4, 3) 90° clockwise.
  19. Translate (-5, 2) right 6 units.
  20. Reflect (6, -6) over the y-axis.
  21. Rotate (1, -2) 270° counterclockwise.
  22. Translate (3, -1) up 5 units.
  23. Reflect (-1, 4) over the origin.
  24. Rotate (0, 6) 90° clockwise.
  25. Translate (-4, -4) down 3 units.
  26. Reflect (2, -5) over the x-axis.
  27. Rotate (7, 2) 180° around the origin.
  28. Translate (1, 1) left 1 and up 2.
  29. Reflect (-3, -2) over the y-axis.
  30. Rotate (-2, 3) 90° counterclockwise.

Understanding Variables and Functions: Match inputs (x) to outputs (y).

Function Notation: Express like f(x) = 2x + 1.

Creating Tables: Use x-values to calculate y-values in functions.

Plotting Linear Functions: Draw lines using coordinate pairs.

Slope as Rate of Change: Change in y over change in x.

Interpreting Slope: Translate slope into meaning, e.g. speed or rate.

Graphing With Slope & Intercept: Start at b, move by slope (rise/run).

Writing Equations of Lines: Use y = mx + b format.

Comparing Graphs: Spot differences between straight and curved lines.

Solving Using Graphs: Use graphs to find values and intersections.

Explanation: Linear functions describe relationships between two variables where the rate of change is constant. These are written in the form y = mx + b, where m is the slope and b is the y-intercept. Graphing these functions involves plotting points from a table of values and understanding slope as a measure of steepness. Interpreting graphs helps in comparing functions, identifying intercepts, and solving real-world problems.

30 Practice Questions
  1. What is the slope in y = 3x + 4?
  2. Identify the y-intercept in y = -2x + 5.
  3. Plot the function y = x.
  4. What is the output of f(x) = 2x when x = 3?
  5. Graph y = -x + 2.
  6. What does a slope of 0 mean?
  7. Find the slope of a line passing through (1,2) and (3,6).
  8. Write a linear function with a slope of 4 and y-intercept -1.
  9. Evaluate y = 5x + 3 for x = -2.
  10. Which graph has a steeper slope: y = 2x or y = 5x?
  11. What does the point (0, b) represent on a graph?
  12. Graph the function y = 0.5x - 1.
  13. Find x when y = 0 in y = 4x - 8.
  14. Create a table of values for y = 3x.
  15. What is the slope between (2,4) and (4,8)?
  16. Compare the slopes: y = 2x vs y = -2x.
  17. Find the y-intercept of y = -x + 6.
  18. Which graph is horizontal: y = 5 or y = 0?
  19. What is the function rule for a slope of 1, y-int of -4?
  20. Plot three points on y = 2x + 1.
  21. Graph the line passing through (0,3) and (2,7).
  22. Determine if the function y = x^2 is linear.
  23. What does the slope represent in a real-world graph?
  24. Which equation represents a vertical line?
  25. Find the slope and y-intercept: y = -3x + 9.
  26. How does increasing the slope affect a line?
  27. Interpret the graph of y = 2x in terms of speed.
  28. Graph y = -0.5x + 4.
  29. What does f(0) mean in a function?
  30. Sketch a function with slope 0 and y-int = 2.

Units of Length: Convert cm to m, in to ft, etc.

Units of Area: Use cm², m²; conversions square units.

Units of Volume: Use cm³, liters; convert between systems.

Using Tools: Measure with accuracy using rulers, protractors.

Precision & Estimation: Use appropriate rounding and approximation.

Perimeter & Circumference: Add all side lengths; for circles use πd.

Area of Composite Figures: Break shapes down into rectangles, triangles, etc.

Volume of Solids: Combine volumes of prisms, cylinders, cubes.

Time and Temperature: Read clocks and thermometers, convert units.

Real-world Problems: Apply concepts to building, cooking, travel, etc.

Explanation: Measurement involves determining the size, length, area, volume, or quantity of an object using specific units. It includes converting between units, measuring with tools, estimating, and applying formulas to calculate perimeter, area, volume, time, and temperature. Accurate measurement skills are essential in real-world contexts like construction, cooking, or science labs.

30 Practice Questions
  1. Convert 5 meters to centimeters.
  2. How many millimeters in 2.5 meters?
  3. Convert 300 cm to meters.
  4. What is the perimeter of a rectangle with sides 4 m and 3 m?
  5. Find the area of a rectangle with length 10 cm and width 6 cm.
  6. Convert 3.5 kg to grams.
  7. What is the volume of a cube with side 5 cm?
  8. Convert 1.2 liters to milliliters.
  9. Convert 1500 mL to liters.
  10. What is the area of a triangle with base 8 cm and height 5 cm?
  11. Convert 120 minutes to hours.
  12. Convert 2.5 hours to minutes.
  13. What is the circumference of a circle with radius 7 cm? (Use 3.14)
  14. Convert 2 km to meters.
  15. Convert 4500 m to kilometers.
  16. Convert 5000 mg to grams.
  17. Estimate the area of a circle with diameter 10 cm.
  18. How much is 1 liter in mL?
  19. What is 0.75 of an hour in minutes?
  20. Convert 90°F to Celsius (approx.).
  21. What is the volume of a rectangular box (10x5x2 cm)?
  22. What is the area of a square with side 12 cm?
  23. How many seconds are there in 1.5 minutes?
  24. Find the perimeter of a triangle with sides 6 cm, 8 cm, and 10 cm.
  25. Convert 0.03 km to meters.
  26. What is the surface area of a cube with side 4 cm?
  27. Estimate the time it takes to walk 1 km at 5 km/h.
  28. Convert 3 hours and 15 minutes into minutes.
  29. How many liters in 2500 mL?
  30. Find the area of a parallelogram with base 9 cm and height 4 cm.

Understand the Problem: Clarify what's known and unknown.

Make a Plan: Choose a method to solve the problem.

Choose the Right Operation: Decide between +, −, ×, ÷.

Use Diagrams: Draw models or number lines.

Work Backwards: Start at the end and reverse steps.

Guess & Check: Try possible answers and test them.

Use Logic: Eliminate wrong options logically.

Use Tables/Lists: Organize info to reveal patterns.

Check & Reflect: Review and verify the solution.

Word Problems: Practice solving real-world scenarios.

Explanation: Problem solving strategies help students tackle mathematical challenges in a structured way. Key strategies include understanding the problem, devising a plan, carrying out the plan, and evaluating the result. Techniques like drawing diagrams, using logical reasoning, making tables, working backward, estimating, and identifying patterns are essential tools for real-world and academic success.

30 Practice Questions
  1. Use guess and check to find a number that doubled then added 3 gives 15.
  2. Work backward: A number was multiplied by 4 then 6 was subtracted, result is 14. What is the number?
  3. Draw a diagram to solve: You have 3 red, 2 blue, and 4 green marbles. How many total?
  4. Make a table: If each candy costs $0.75, how much for 1 to 5 candies?
  5. Estimate the answer: What is approximately 456 ÷ 9?
  6. Identify a pattern: 2, 4, 8, 16... What’s the 6th term?
  7. Logical reasoning: If all squares are rectangles, and this shape is not a rectangle, can it be a square?
  8. Use a model: Draw an area model for 6 × 7.
  9. Choose the right operation: You bought 3 pens at $2.50 each. What’s the cost?
  10. Understand the problem: "A train leaves at 2 PM and arrives at 6 PM." What info is needed to find speed?
  11. Using diagrams: A rectangle is 5 cm longer than it is wide. Total perimeter is 28 cm. Find dimensions.
  12. Trial and error: Guess a number whose square is close to 50.
  13. Use logic: Sam is older than Max, Max is older than Jake. Who is oldest?
  14. Estimate: What’s close to the product of 23 × 48?
  15. Check answer: If 4x = 20, then x = 5. Prove your answer is correct.
  16. Guess and check: Two numbers add to 15 and multiply to 54. Find them.
  17. Work backward: A bag had 20 candies, you ate 5, then doubled what’s left. Now 30. How many at first?
  18. Make a list: Find all even numbers between 10 and 20.
  19. Diagram: A square and circle fit inside a rectangle. What's missing if area = 100 cm²?
  20. Choose strategy: How many ways to arrange 3 books?
  21. Find error: If 6 × 4 = 20 is the answer, what's wrong?
  22. Use table: Track daily savings: $1, $2, $3... How much in 5 days?
  23. Logical thinking: If it rains, the game is canceled. It did not rain. Was game canceled?
  24. Working backward: A number was divided by 5, then 7 was added. Result: 15.
  25. Find the pattern: 5, 10, 20, 40... What's the 7th term?
  26. Check work: Solve 8 + (3 × 2). Then verify.
  27. Use elimination: One number is 7 more than another. Their sum is 27. Find numbers.
  28. Estimate and round: What’s 738 + 497 rounded?
  29. Find strategy: You toss a coin and roll a die. How many outcomes?
  30. Draw and solve: A triangle has base 6 cm, height 4 cm. Find area.

Understanding Money: Learn about coins, bills, and value.

Earning & Income: Understand wages, jobs, allowances.

Budgeting: Plan spending vs savings.

Saving & Interest: Save money to earn more over time.

Simple Interest: Use formula I = Prt for basic savings.

Needs vs Wants: Separate essentials from extras.

Banking Basics: Understand deposits, withdrawals, accounts.

Credit & Debit: Learn the difference and when to use each.

Understanding Taxes: Recognize deductions like sales tax or income tax.

Making Financial Decisions: Practice comparing costs, saving, and planning.

Explanation: Financial literacy involves understanding how money works in everyday life. It covers earning, budgeting, saving, banking, credit, and taxes. Students learn to manage income, make informed spending decisions, calculate simple interest, and understand financial tools like debit and credit cards. These skills are essential for responsible money management and planning for the future.

30 Practice Questions
  1. What is budgeting and why is it important?
  2. Define simple interest.
  3. If you save $100 at 5% interest per year, how much interest will you earn in 1 year?
  4. What is the difference between a debit card and a credit card?
  5. How do taxes affect your income?
  6. Explain the concept of needs vs wants.
  7. What is a bank account?
  8. How can you earn income?
  9. What is the purpose of saving money?
  10. Calculate simple interest on $200 for 3 years at 4% per year.
  11. Why is it important to keep track of expenses?
  12. What is the difference between gross income and net income?
  13. Explain how budgeting helps avoid debt.
  14. What are some common taxes deducted from a paycheck?
  15. How does credit card interest work?
  16. What is an emergency fund?
  17. Describe the difference between saving and investing.
  18. What are the benefits of using a debit card?
  19. How can you create a simple budget?
  20. What should you consider before taking a loan?
  21. Explain the term ‘financial goal.’
  22. What is a credit score and why does it matter?
  23. How can you improve your financial literacy?
  24. Calculate the total amount to be paid on a $500 loan with 6% simple interest over 2 years.
  25. What is the role of banks in financial management?
  26. How can budgeting help with saving for a big purchase?
  27. Explain the impact of taxes on prices of goods and services.
  28. What are some ways to reduce unnecessary spending?
  29. Describe what a paycheck stub shows.
  30. Why is it important to avoid late payments on credit cards?