Step-by-step math

Comparing 1

• Ordering numbersOrder: 13, 2, 0, 17

Addition 2

• Number bonds and make ten3 and ? make 10
• Picture addition6 + 3

Subtraction 1

• Picture subtraction10 − 5

Fractions 12

• Adding like fractions2/6 + 4/6
• Adding mixed numbers3 1/7 + 3 1/2
• Adding unlike fractions3/8 + 2/6
• Comparing fractions4/8 ? 4/7
• Equivalent fractions1/4 = ?/8
• Fractions and decimals1/3 as a decimal
• Improper fractions to mixed numbers10/7 = ?
• Mixed numbers to improper fractions1 3/7 = ?
• Simplifying fractions3/9 = ?
• Subtracting fractions4/8 − 1/5
• Subtracting mixed numbers2 1/2 − 2 1/7
• Tenths and hundredths6/10 + 33/100

Addition 7

• Adding three numbers95 + 61 + 21
• Addition with regrouping12 + 38
• Addition within 208 + 4
• Addition without regrouping84 + 12
• Make ten2 + ? = 10
• Missing addends15 + ? = 16
• Vertical addition44 + 2

Mixed 4

• Addition and subtraction within 10087 − 19
• Addition and subtraction within 2019 − 11
• All four operations21 × 10
• Multiplication and division facts50 ÷ 10

Exponents 3

• Cube numbers12³
• Powers of a number5²
• Squares and powers7²

Number patterns 3

• Decreasing number patterns11, ?, 7, 5, 3
• Multiplying number patterns1, ?, 9, 27
• Number patterns5, 17, ?, 41, 53

Division 13

• Dividing by 1080 ÷ 10
• Dividing by 11121 ÷ 11
• Dividing by 12132 ÷ 12
• Dividing by 216 ÷ 2
• Dividing by 324 ÷ 3
• Dividing by 432 ÷ 4
• Dividing by 540 ÷ 5
• Dividing by 648 ÷ 6
• Dividing by 756 ÷ 7
• Dividing by 864 ÷ 8
• Dividing by 972 ÷ 9
• Division facts18 ÷ 2
• Missing number division55 ÷ ? = 11

Remainders 1

• Division with remainders59 ÷ 5

Real life 3

• Elapsed time4:05 to 4:30
• Finding the start time4:30 − 25 min
• What time will it be4:05 + 25 min

Place value 8

• Estimating differences371 − 103
• Estimating products98 × 67
• Estimating sums and products161 + 708
• Expanded form105 in expanded form
• Identifying place value digitsWhich digit is in the ones of 647?
• Naming the placeWhich place is the 5 in, in 501?
• Rounding numbers867 to the nearest ten
• Whole-number place valueWhat is the 5 worth in 501?

Mental math 1

• Mental math strategies55 × 7 + 45 × 7

Multiplication 16

• Missing factors11 × ? = 55
• Multiplication9 × 2
• Multiplication as scalingBigger or smaller?
• Multiplication by 108 × 10
• Multiplication by 1111 × 11
• Multiplication by 1211 × 12
• Multiplication by 28 × 2
• Multiplication by 48 × 4
• Multiplication by 58 × 5
• Multiplication by 68 × 6
• Multiplication by 78 × 7
• Multiplication by 88 × 8
• Multiplication by 98 × 9
• Multiplication facts9 × 2
• Times as many
• Times tables to 121 × 1

Subtraction 6

• Missing number subtraction6 − ? = 1
• Subtraction with borrowing40 − 14
• Subtraction within 1010 − 9
• Subtraction within 2015 − 6
• Subtraction without borrowing78 − 45
• Vertical subtraction30 − 3

Percents 3

• Percent decrease20% less than 115
• Percent increase and decrease50% more than 58
• Simple interest$4725 earns 12% simple interest a year.

Ratios 4

• Ratios and proportions2 : 6 = 1 : 3
• Sharing in a ratio65 in 5 : 8 → larger 40
• Solving proportions1 : 5 = 7 : 35
• Writing a ratio as a percent19 : 25 = 76%

Roman numerals 2

• Reading Roman numeralsXLVII
• Roman numeral conversion98 in Roman numerals

• Equation word problemsHow many spare parts does Sato have? Write an equation using x, then solve it.
• Fraction word problemsHow much juice does Ana need in all?
• Geometry word problemsWhat is the distance all the way around it, in meters?
• Mass and capacity word problemsHow many grams are left?
• Median, mode, and range word problemsFind the median.
• Mixed word problemsBetween the two of them, how many cupcakes are there?
• Mixture word problemsWhat is the price per kg of the blend?
• Multiplication word problemsHow many ration packs does Sato have in all?
• Multiplying and dividing fraction word problemsHow many portions are there?
• Positive and negative number word problemsWhat is the difference between the two elevation readings, in meters?
• Probability word problemsWhat is the probability that it is NOT green? Write your answer in simplest form.
• Quadratic equation word problemsFind the two numbers.
• Ratio and proportion word problemsAt the same rate, how many hours would it take to pack 140 boxes?
• Speed, distance and time word problemsWhat is its speed in km per hour?
• Subtraction word problemsHow many pencils does Zoe have left?
• Systems of equations word problemsFind the price of one muffin and one peach.
• Three-step word problemsHow many strawberries does Ines have now?
• Two-step equation word problemsHow many swims was that?
• Two-step word problemsHow many tomatoes does Nadia have now?
• Unlike denominator word problemsHow much more did Omar use than Kwame?
• Value word problems (coins and notes)How many points is that in total?
• Word problems with extra informationWhat is the difference in water bottles between Courtney and Farah?
• Work and pipes word problemsHow long until the tank is full?

Algebra mistakes 9

• Algebraic fractionsCheck this line: (x² − 36) ÷ (x − 6) − x = 6. Which is correct?
• DistributingMia wrote 6(x + 4) + 5(x + 4) = 11x + 24. Which is correct?
• Dividing and signsNoor wrote 3(x + 7) − (x − 9) = 2x + 30. Which is correct?
• Exponent lawsOn Priya's paper: x³ · x³ ÷ x⁴ = x⁴. Which line should replace it?
• Logarithm lawsCheck this line: log(x²) + log(x⁵) = 7 log x. Which is correct?
• Multiplying two bracketsSpot the mistake: (x + 2)(x + 8) − x² = x² + 10x + 16. Which answer is right?
• Negative powersMia wrote x⁷ · x⁻³ = x²¹. Which is correct?
• Simplifying rootsCheck this line: √(96x²) + √(6x²) = 5x. Which is correct?
• Squaring a binomialAna wrote (x + 5)² − 25 = x² + 10x + 25. Which is correct?

Reasoning 8

• Always, sometimes, neverAn odd number times an even number is odd.
• Is it always true?The sum of four consecutive numbers is a multiple of 4.
• Number sequencesHere are the first four terms of a number sequence. 7 12 17 22
• Odd one outWhich number is the odd one out?
• Spot the errorPriya wrote 24 − 6 = 28. Write the correct answer.
• Statistical questionsIs it a statistical question?
• Symbol puzzles◆ + ◆ + ◆ = 12 and ◆ + ■ = 6. What is ■?
• The quadrilateral hierarchyEvery parallelogram is a rectangle.

Real life 5

• Read Fahrenheit thermometersRead the thermometer
• Read thermometersRead the thermometer
• Tell time to five minutesRead the clock
• Tell time to the minuteRead the clock
• Tell time to the quarter hourRead the clock

Measurement 7

• Customary capacity conversion30 c = ? pt
• Customary unit conversion39 ft = ? yd
• Customary weight conversion20 lb = ? oz
• Metric capacity conversion19 L = ? mL
• Metric length conversion11 m = ? mm
• Metric mass conversion7.5 kg = ? g
• Unit conversion150 mm = ? cm

• Column addition & subtraction678 − 339
• Combining like terms2x + 4x + 20
• Distributive property3(4 + 4x)
• Equivalent expressionsWhich is the same as 3x + 8 + x?
• Evaluating expressions2x − 8, x = 5
• Greatest common factorGCF of 18 and 24
• Least common multipleLCM of 6 and 9
• List the factorsFactors of 16
• Long division837 ÷ 3
• Multi-digit multiplication158 × 33
• Multiplication and division inequalities−3x < −9
• One-step multiplication and division equationsx ÷ 6 = 3
• Order of operations5 × ( 18 − 18 )
• Percent change as one multiplierRead it in order, then say which way around
• Prime or compositeIs 24 prime?
• Solving equationsx − 7 = 20
• Solving inequalitiesx + 8 ≤ 20
• Two-step equations11x + 3 = 14
• Two-step inequalities−6x + 2 ≥ 38
• Variables on both sides10x + 13 = 12x + 3
• Which value makes it true?Try each value and see which one works
• Writing algebraic expressionsRead it in order, then say which way around
• Writing numerical expressionsRead it in order, then say which way around

Decimals 4

• Adding and subtracting uneven decimals15.0 − 14.95
• Dividing decimals19.24 ÷ 2
• Multiplying and dividing decimals1.2 ÷ 4
• Multiplying decimals3.29 × 8.04

Ratios 3

• Constant of proportionalityx: 3, 6, 7, 9 y: 24, 48, 56, 72
• Finding k from a tablex: 2, 4, 7, 9 y: 12, 24, 42, 54
• Writing y = kxx: 4, 6, 7, 9 y: 24, 36, 42, 54

Fractions 3

• Dividing fractions4/5 ÷ 3/8
• Multiplying fractions4/5 × 3/8
• Whole number × fraction3 × 2/5

Integers 2

• Integer operations(-7) + 19
• Multiplying and dividing integers(-96) ÷ 8

Remainders 1

• Long division with remainders143 ÷ 5

• Comparing rates in wordsA y = 11x, y liters and x minutes B 65 liters in 5 minutes
• Composing functionsf(x) = −2x − 5, g(x) = −4x − 5; f(g(5))
• Difference of squares with coefficients100x² − 81
• Difference of two squaresx² − 900
• Discriminant with a leading coefficient8x² − 16x − 90 = 0
• Dividing in scientific notation(3 × 10²) ÷ (7.5 × 10⁻⁵)
• Evaluating exponential functionsEvaluate f(x) = 10 · 4ˣ at x = 2
• Evaluating functionsf(x) = −3x + 10; f(−6)
• Exponential functionsEvaluate f(x) = 2 · 8ˣ at x = 3
• Factor a difference of squaresx² − 225
• Factoring x² + bx + cx² + 12x + 11
• Factoring x² + bx − cx² + 8x − 345
• Factoring x² − bx + cx² − 29x + 138
• Finding the rate of changex: 4, 7, 10, 13 y: 109, 82, 55, 28
• Finding the x-interceptthe x-intercept of 3x + 5y = −15
• Finding the y-interceptthe y-intercept of 5x + y = 5
• Function notationf(x) = 2x + 11; f(−4)
• Geometric sequence nth term3, 6, 12, … — the 9th term
• How many real solutions?x² + 13x + 105 = 0
• Initial value from a tablex: 9, 14, 19, 24 y: 73, 108, 143, 178
• Line equation from two pointsWrite the equation of the line through (1, 4) and (2, 6)
• Multiply a sum by a difference(x + 10)(x − 10) − 10
• Multiplying and dividing in scientific notation(6 × 10⁸) ÷ (1.5 × 10⁻²)
• Multiplying in scientific notation(1.2 × 10⁻³) × (8 × 10²)
• Point-slope equation of a lineWrite the equation of the line with slope 2 through (3, 8)
• Rate of change from a tablex: 7, 12, 17, 22 y: 90, 65, 40, 15
• Rearranging formulasSolve V = ⅓Bh for B
• Solving (x − h)² = k by square rootsSolve (x + 5)² = 9
• Solving absolute value equationsSolve |x − 5| = 7
• Solving quadratics by square rootsSolve (x − 1)² = 25
• Solving x² + bx + c = 0(x + 9)(x + 8) = 0
• Solving x² = p by square rootsSolve 7x² = 28
• Taking out a common factor24x² + 120x + 168
• The discriminantx² + 35x + 44 = 0
• Transformations of a functionWhat happens to the graph?
• What the numbers in a rule meanWhat does the rule start at?
• Which rate is greater?A 42 dollars in 7 weeks B y = 11x, y dollars and x weeks
• Write the rule from a situationFind the start and the rate, then write the rule
• Writing linear equationsWrite the equation of the line through (1, −7) and (3, −15)
• x- and y-intercepts of a linethe x-intercept of x + 9y = −9

Exponents 11

• Cube roots∛1331
• Laws of exponents(4²)⁸
• Power of a power(12⁶)⁵
• Product rule for exponents3¹ × 3²
• Quotient rule for exponents4⁹ ÷ 4⁹
• Scientific notation3.8 × 10²
• Scientific notation: coefficient7300000
• Scientific notation: power of ten700000
• Scientific notation: small numbers3.6 × 10⁻³
• Square roots√289
• Square roots and cube roots√784

Pre algebra 21

• Estimating square roots√431
• Function from a tablex: 19, 5, 5, 8 y: 20, 3, 34, 56
• Function from ordered pairs(14, 34) (8, 5) (14, 6) (9, 12)
• How many solutions?2(−x + 6) = −2x + 12
• Is it a function?x: 0, 24, 7, 10 y: 31, 50, 7, 9
• Linear from a tablex: 0, 3, 6, 9 y: 5, 23, 77, 167
• Linear from an equationy = 10x² + 37
• Linear or nonlineary = x/5 + 20
• Number of solutions17x + 25 = 25 + 17x
• Rational or irrational0.1
• Rational or irrational numbers0.222…
• Rational or irrational roots√50
• Slope and y-intercepty = 8x
• Slope from an equationy = 11x
• Slope from two points(−1, 6) and (4, 6)
• Solutions after expanding3(3x + 1) = 9x + 3
• Square roots between integers√446
• Square roots to one decimal place√483
• Systems by elimination−6x + y = 23 12x − y = −47
• Systems by substitutiony = 4x − 1 −6x − y = 1
• Systems of equations6x + 12y = 18 2x − 12y = 22

Geometry 3

• Parallel and perpendicular linesWrite the equation of the line (−2, −2), // y = 3x + 3
• The equation of a circleFind the center and radius of x² + y² − 8x + 7 = 0
• The equation of a parabola

Graphs 1

• Reading a graphUp, down or level

• Rational exponents8^(4/3)
• Rational expressions(x² + 12x − 160) / (x² − 15x + 56)
• Simplifying radicals√75

• Angles on a straight lineAngles on a line: x, 45°, 90°
• Arc lengthArc: 270° of a circle, radius 6
• Arc length and sector areaSector: 270° of a circle, radius 8
• Area by counting squaresArea of an L-shape by counting
• Area of a circleArea of a circle marked 8 cm
• Area of a circle from the diameterArea of a circle marked 16 cm
• Area of a parallelogramArea of a 6 by 17 parallelogram
• Area of a trapezoidArea of a trapezium, 3 and 4 by 4
• Area of a triangleArea of a 17 by 16 triangle
• Area of composite figuresArea of a 19 by 19 L-shape
• Area of irregular shapesArea of an L-shape by counting
• Area of triangles and quadrilateralsArea of a trapezium, 8 and 14 by 16
• BearingsReading a bearing
• Bisect an angleBisect angle ABC.
• Circumference from the diameterCircumference: circle marked 9 cm
• Circumference of a circleCircumference: circle marked 4 cm
• Circumscribed circle of a triangleThe circle through a 27-36-45 triangle's corners
• Classify triangles by anglesName this triangle
• Classify triangles by sidesName this triangle
• Classifying trianglesName this triangle
• Complementary and supplementary anglesAngles in a right angle, one is 27°
• Complementary anglesAngles in a right angle, one is 33°
• Copy a segmentCopy AB onto the ray from C.
• Copy an angleCopy angle ABC onto the ray from D.
• Corresponding angles40° and x
• CPCTC proofsWhich reason completes the proof?
• Density from area and volumePeople per square mile
• Dilations(2, 0) by scale factor ½
• Distance between two points(5, 7) to (9, 4)
• Distance formula(0, −5) to (4, −2)
• Drawing angles with a protractorDraw an angle
• Exterior angle of a triangleThe exterior angle
• Faces, edges and verticespentagonal prism: how many edges?
• Find a side from the areaMissing side: area 126, one side 18
• Find a side from the perimeterMissing side: perimeter 50, one side 18
• Inscribe a regular polygonInscribe a regular hexagon.
• Inscribed angle in a circleCenter angle 40°, find the angle on the circle
• Inscribed circle of a triangleThe circle inside a 27-36-45 triangle
• Lines of symmetryLines of symmetry: kite
• Measuring angles with a protractorMeasure an angle
• Midpoint formulaMidpoint of (-5, -5) and (1, 3)
• Midpoint of a segmentMidpoint of (0, 0) and (6, 8)
• Midsegment of a triangleThe midsegment
• Missing edge from the volumeMissing edge of a box, volume 175
• Missing side lengthMissing side: area 50, one side 10
• Naming 2D shapesName this shape
• Naming quadrilateralsName this shape
• Parallel through a pointConstruct the parallel through P.
• Parallelogram proofsProve the property
• Perimeter of a parallelogramPerimeter of a 15 by 8 parallelogram
• Perimeter of a rectanglePerimeter of a 15 by 8 rectangle
• Perimeter of a trapezoidPerimeter of a 9-9-17-10 trapezoid
• Perimeter of a trianglePerimeter of a 13-13-20 triangle
• Perimeter of triangles and quadrilateralsPerimeter of a 4 by 4 rectangle
• Perpendicular bisectorConstruct the bisector of AB.
• Perpendicular through a pointConstruct the perpendicular through P.
• Pythagorean theoremRight triangle, 3 and 4
• Pythagorean theorem: find a legRight triangle, 34 and 16
• Pythagorean theorem: find the hypotenuseRight triangle, 16 and 30
• Reflections(5, 3) in the x-axis
• Rotational symmetryHow many times does it land on itself?
• Rotations(2, −2) 90° counterclockwise about O
• Sector areaSector: 45° of a circle, radius 6
• Similar figuresSimilar figures: 8 and 16
• Similar triangle proofsWhich reason completes the proof?
• Supplementary anglesAngles on a straight line, one is 25°
• Surface area and netsSurface area of a 7 × 10 × 13 box
• Surface area from a netSurface area of a 5 × 5 × 13 box
• Surface area of a rectangular prismSurface area of a 5 × 5 × 13 box
• Surface area of a sphereSurface area of a sphere, diameter 12 cm
• Transformations on a grid(0, −3) 90° counterclockwise about O
• Translations(−2, 0) 4 right and 4 up
• Triangle congruence proofsWhich reason completes the proof?
• Triangle congruence rulesWhich congruence rule?
• Triangle inequalityCan it be a triangle?
• Types of anglesName this angle
• Vertical angles
• Volume by counting unit cubesCounting unit cubes
• Volume of a coneA cone marked 3 cm, 2 cm tall
• Volume of a cylinderA cylinder marked 14 cm, 5 cm tall
• Volume of a rectangular prismVolume of a 9 × 7 × 9 stepped solid
• Volume of a sphereVolume of a sphere, diameter 12 cm
• Volume of composite solidsVolume of a 5 × 9 × 9 stepped solid
• Write a similarity proofProve △ADE ~ △ABC
• Write a triangle proofProve △PQR ≅ △PSR

Trigonometry 8

• Area of a triangle with sineFind the area
• Finding a missing angleFind the angle: opposite 13, adjacent 4
• Finding a missing sideFind the opposite, angle 65°
• Law of cosinesFind c by the law of cosines
• Law of sinesFind b by the law of sines
• Right-triangle trigonometryFind the angle: opposite 11, adjacent 6
• The six trig ratiosWrite tan A as a fraction
• Trigonometric ratiosWrite tan A as a fraction

Graphs 33

• Conditional probabilityP(blue, given it is square) from red 5 round, 3 square · blue 2 round, 2 square
• Correlation and causationTry the cause both ways round
• Does the data fit the claim?Work out what the claim predicts, then compare
• Finding the meanMean of 39, 41, 46, 18, 46
• Finding the medianMedian of 20, 2, 26, 46, 46
• Four-quadrant coordinatesPoint C
• HistogramsStanding long jump (cm)
• Independent eventsAre the two events independent?
• Interquartile rangeIQR of 34, 48, 44, 21, 43, 20, 31
• Is this sample fair?Ask who could never have been asked
• Line plotsLength of our pencils (inches)
• Margin of errorOne over the square root of how many were asked
• Mean absolute deviationMAD of 7, 43, 33, 43, 4
• Mean, median, mode, and rangeMedian of 17, 41, 22, 17, 18
• Missing number from the meanMissing number for a mean of 12
• Picture graphsOur favorite sport
• Plotting pointsPoint A
• Points on a coordinate gridPoint A
• Probability3 red, 6 blue, 3 green — P(green)
• Reading box plotsScores on the spelling test (points)
• Relating two number patternsTwo rules, two patterns
• Relative frequencyOf the 25 Grade 7 students, what percent have a pet?
• Scatter plotsIs the pattern linear or nonlinear?
• Simple probability4 red, 4 blue, 4 green — P(blue)
• Stem-and-leaf plotsHow many values does the plot show?
• Survey, experiment or study?Ask first whether anything was assigned
• Tally chartsOur favorite sport
• The addition ruleWhat percent are one or the other?
• The counting principle3 frames, 2 wheels and 4 colors. How many different bikes can you make?
• The line of best fitIn y = 0.25x + 4, what does 4 mean?
• Three-stage counting principle9 mains, 3 sides and 7 drinks. How many different meals can you make?
• Two rules, two patterns
• Two-way tablesThe Large and Sold number is missing

• Counting rectangles in a gridCount the rectangles without drawing them
• Counting triangles in a gridCount the triangles without drawing them
• Domino tilingsCount the tilings by the last column
• Fewest coinsThe obvious way to pay is not the fewest
• Integer trianglesOrder the sides, then keep only the ones that close up
• Lattice pathsCount the routes without drawing them
• Numbers too big to computeOnly the leftover moves the day
• One equation, two unknownsOne total, two unknowns, and only whole things
• Regions of a circleCount the chords and their crossings, do not just double
• Socks in the darkThe worst that can happen, then one more
• Sum and difference puzzlesTwo numbers from their total and their gap
• The fake coinA balance answers three ways, not two
• The gap between two squaresTwo squares apart, and the identity that makes it a list
• The hundred lockersOpen only where the count of divisors is odd
• The lazy catererCount cuts and their crossings, do not just double
• The number that cannot changeSomething does not change, whatever you pick
• The painted cubeWhere a cube sits decides how many faces are painted
• The smudged sumThe ten the ones column sends across
• The spider and the flyUnfold the box, then go straight
• The taking gameSometimes going first is the losing seat
• Things and the gaps between themThe things, or the gaps between them
• Three shares from one totalCount in parts, and take the extra off first
• Truth-tellers and liarsAnchor one islander, then follow the chain
• Two jugs and a tapMap every move to find the shortest route
• What the leftover meansThe division is not the answer
• What two facts settleSubtract the facts, not the prices
• Who am I? number puzzlesCross out everything the clues rule out
• Write your own questionThis one has more than one right answer

Geometry 1

• Area & perimeter puzzlesTwo facts, and only one pair fits both

Pre algebra 1

• GCF & LCM puzzlesBoth numbers are the GCF times something