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NCERT · Ganita Prakash · Volume 1 · Chapter 1

Large Numbers Around Us

19 videosSee all ›

Chapter 1Build One Lakh from Familiar Groups2:51Build One Lakh from Familiar GroupsYou'll learn: Build one lakh step by step from groups learners know, such as hundreds and thousands, and anchor it with familiar benchmarks.Chapter 1How Big Is One Lakh Compared with Everyday Quantities?3:05How Big Is One Lakh Compared with Everyday Quantities?You'll learn: Compare one lakh with everyday quantities to feel how big it really is.Chapter 1Read Indian Number Names from Lakh to Arab3:03Read Indian Number Names from Lakh to ArabYou'll learn: Indian commas group digits as thousands, then lakhs, crores and arabs every two places.Chapter 1Read Million and Billion in the American or International System3:01Read Million and Billion in the American or International SystemYou'll learn: International commas group digits in threes: thousands, millions and billions.Chapter 1Match Indian and International Names for the Same Number3:02Match Indian and International Names for the Same NumberYou'll learn: Read the same number in both systems and match the names, e.g. 10 lakh = 1 million.Chapter 1Make the Same Number with Different Button Presses3:29Make the Same Number with Different Button PressesYou'll learn: The same number can be made with different combinations of +1, +10, +100 … presses by regrouping tens.Chapter 1Why Do the Fewest Clicks Equal the Digit Sum on Place-Value Buttons?3:16Why Do the Fewest Clicks Equal the Digit Sum on Place-Value Buttons?You'll learn: With place-value buttons, the fewest presses use each digit as a count of its button, so the minimum equals the digit sum.Chapter 1When Do We Need an Exact Number?3:13When Do We Need an Exact Number?You'll learn: Some situations need an exact number and others only a sensible approximation; the purpose decides.Chapter 1Use Nearest Place-Value Neighbours to Round a Number3:19Use Nearest Place-Value Neighbours to Round a NumberYou'll learn: Round by finding the nearest place-value neighbours and choosing the closer one.Chapter 1Estimate a Population Change with Sums and Differences3:19Estimate a Population Change with Sums and DifferencesYou'll learn: Estimate sums and differences of large numbers to judge a change such as population growth.Chapter 1Compare Large Quantities Using How Many Times3:12Compare Large Quantities Using How Many TimesYou'll learn: Compare large quantities by asking 'how many times as much?', not only 'how much more?'.Chapter 1Multiply by 5, 25 or 125 Using 10, 100 or 10003:10Multiply by 5, 25 or 125 Using 10, 100 or 1000You'll learn: 5 = 10 ÷ 2, 25 = 100 ÷ 4 and 125 = 1000 ÷ 8, so multiply by a power of ten and divide: one shortcut, three cases.Chapter 1Regroup Factors to Make a Large Product Easier3:15Regroup Factors to Make a Large Product EasierYou'll learn: Reorder and regroup factors so that pairs like 4 × 25 or 8 × 125 make a long product easy.Chapter 1What Patterns Appear in Repeated-Digit Products?3:14What Patterns Appear in Repeated-Digit Products?You'll learn: Products of repeated-digit numbers such as 11 × 11 or 111 × 111 form patterns worth predicting.Chapter 1Predict a Product's Digit Count Using Smallest and Largest Cases3:21Predict a Product's Digit Count Using Smallest and Largest CasesYou'll learn: Bound a product between the smallest and largest numbers with the given digit counts to predict its number of digits.Chapter 1What Does a Large Calculation Tell Us About a Real Quantity?3:17What Does a Large Calculation Tell Us About a Real Quantity?You'll learn: Turn the result of a large calculation back into a real quantity with sensible units and judge its size.Chapter 1Could a Lakh Buses Hold a City's Population?3:16Could a Lakh Buses Hold a City's Population?You'll learn: Use stated assumptions about bus capacity to estimate whether a lakh buses could carry a city's population.Chapter 1Could You Reach the Moon in Ten Years?3:29Could You Reach the Moon in Ten Years?You'll learn: Estimate in stages, distance then speed then time, to test whether the Moon is reachable in ten years.Chapter 1Make the Largest and Smallest Numbers with Fixed Toothpicks3:10Make the Largest and Smallest Numbers with Fixed ToothpicksYou'll learn: Moving a fixed number of toothpicks changes digits; plan moves to make the largest and smallest numbers.

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NCERT · Ganita Prakash · Volume 1 · Chapter 2

Arithmetic Expressions

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Chapter 2Turn a Calculation Story into an Arithmetic Expression3:28Turn a Calculation Story into an Arithmetic ExpressionYou'll learn: Write a story's calculation as an arithmetic expression and read what each operation means.Chapter 2Find the Value of an Arithmetic Expression3:11Find the Value of an Arithmetic ExpressionYou'll learn: Evaluate an expression term by term to find its value.Chapter 2Compare Two Expressions Without Calculating Everything3:16Compare Two Expressions Without Calculating EverythingYou'll learn: Compare two expressions by tracking how their parts differ, without calculating everything.Chapter 2Change an Expression While Keeping Its Value3:17Change an Expression While Keeping Its ValueYou'll learn: Change parts of an expression in balancing ways so its value stays the same.Chapter 2How Do Brackets Change a Calculation's Meaning?3:09How Do Brackets Change a Calculation's Meaning?You'll learn: Brackets group quantities, so the same numbers with different brackets can mean different calculations.Chapter 2Evaluate a Bracketed Expression One Group at a Time3:15Evaluate a Bracketed Expression One Group at a TimeYou'll learn: Evaluate the bracketed groups first, then combine the results.Chapter 2Rewrite Subtraction as Addition of an Opposite3:25Rewrite Subtraction as Addition of an OppositeYou'll learn: Subtracting a number is the same as adding its opposite, which turns expressions into sums of terms.Chapter 2Identify Whole Terms Before Evaluating an Expression3:28Identify Whole Terms Before Evaluating an ExpressionYou'll learn: Products and quotients form single terms; identify the terms first, then add them.Chapter 2Reorder Signed Terms Without Changing Their Value3:29Reorder Signed Terms Without Changing Their ValueYou'll learn: Signed terms can be added in any order and grouping without changing the value.Chapter 2When Does Swapping Numbers Change an Expression?3:14When Does Swapping Numbers Change an Expression?You'll learn: Swapping numbers inside a subtraction or division changes the value; swapping whole signed terms does not.Chapter 2Remove Brackets Without Losing the Signs3:21Remove Brackets Without Losing the SignsYou'll learn: A minus sign before a bracket flips the sign of every term inside when the bracket is removed.Chapter 2Subtract 9 by Subtracting 10 and Adding 13:26Subtract 9 by Subtracting 10 and Adding 1You'll learn: Changing one term changes the total by the same amount, so subtract 10 and add 1 to subtract 9.Chapter 2Why Can Multiplication Spread Across a Sum or Difference?3:22Why Can Multiplication Spread Across a Sum or Difference?You'll learn: A number times a sum equals the sum of the separate products, shown with a grid of objects.Chapter 2Use a Common Factor to Put Terms Back into Brackets3:18Use a Common Factor to Put Terms Back into BracketsYou'll learn: Take out a common factor to put terms back into brackets.Chapter 2Adjust a Product Without Changing Its Value3:15Adjust a Product Without Changing Its ValueYou'll learn: Multiply one factor and divide another by the same number to keep a product unchanged.Chapter 2Build Different Expressions for the Same Target Number3:15Build Different Expressions for the Same Target NumberYou'll learn: Build several different expressions that hit the same target using restricted numbers and operations.Chapter 2What Is an Arithmetic Expression?3:54What Is an Arithmetic Expression?You'll learn: What Is an Arithmetic Expression?Chapter 2Different Expressions Can Have the Same Value3:58Different Expressions Can Have the Same ValueYou'll learn: Different Expressions Can Have the Same Value Chapter 2Comparing and Ordering Arithmetic Expressions4:06Comparing and Ordering Arithmetic ExpressionsYou'll learn: Comparing and Ordering Arithmetic Expressions Chapter 2Comparing Sums Without Calculating Them Fully3:49Comparing Sums Without Calculating Them FullyYou'll learn: Comparing Sums Without Calculating Them Fully Chapter 2Comparing Differences Without Calculating Them Fully3:59Comparing Differences Without Calculating Them FullyYou'll learn: Comparing Differences Without Calculating Them Fully Chapter 2Completing Expressions to Make Both Sides Equal3:50Completing Expressions to Make Both Sides EqualYou'll learn: Completing Expressions to Make Both Sides Equal Chapter 2Why the Order of Operations Matters: The Marble Story3:56Why the Order of Operations Matters: The Marble StoryYou'll learn: Why the Order of Operations Matters: The Marble Story Chapter 2Using Brackets to Show What Happens First3:51Using Brackets to Show What Happens FirstYou'll learn: Using Brackets to Show What Happens First Chapter 2Finding Change: Why Brackets Matter in Subtraction3:55Finding Change: Why Brackets Matter in SubtractionYou'll learn: Finding Change: Why Brackets Matter in Subtraction Chapter 2Identifying Terms and Keeping Their Signs3:58Identifying Terms and Keeping Their SignsYou'll learn: Identifying Terms and Keeping Their Signs Chapter 2Why a Product or Quotient Can Be One Term3:59Why a Product or Quotient Can Be One TermYou'll learn: Why a Product or Quotient Can Be One Term Chapter 2Swapping Terms: The Commutative Property of Addition3:54Swapping Terms: The Commutative Property of AdditionYou'll learn: Swapping Terms: The Commutative Property of Addition Chapter 2Grouping Terms: The Associative Property of Addition4:02Grouping Terms: The Associative Property of AdditionYou'll learn: Grouping Terms: The Associative Property of Addition Chapter 2Evaluating an Expression by Finding Its Terms First4:11Evaluating an Expression by Finding Its Terms FirstYou'll learn: Evaluating an Expression by Finding Its Terms First Chapter 2Writing Expressions for a Restaurant Bill3:45Writing Expressions for a Restaurant BillYou'll learn: Writing Expressions for a Restaurant Bill Chapter 2Writing Expressions for Groups and Leftovers3:56Writing Expressions for Groups and LeftoversYou'll learn: Writing Expressions for Groups and Leftovers Chapter 2Writing Expressions for Rice Packets and Money Payments4:03Writing Expressions for Rice Packets and Money PaymentsYou'll learn: Writing Expressions for Rice Packets and Money Payments Chapter 2Matching Tile Arrangements with Expressions3:48Matching Tile Arrangements with ExpressionsYou'll learn: Matching Tile Arrangements with Expressions Chapter 2Turning Stories, Ticket Costs and Window Measurements into Expressions3:51Turning Stories, Ticket Costs and Window Measurements into ExpressionsYou'll learn: Turning Stories, Ticket Costs and Window Measurements into Expressions Chapter 2Removing Brackets After a Minus Sign: Subtracting a Sum3:51Removing Brackets After a Minus Sign: Subtracting a SumYou'll learn: Removing Brackets After a Minus Sign: Subtracting a Sum Chapter 2Removing Brackets After a Minus Sign: Subtracting a Difference3:55Removing Brackets After a Minus Sign: Subtracting a DifferenceYou'll learn: Removing Brackets After a Minus Sign: Subtracting a Difference Chapter 2Removing Brackets After a Plus Sign3:57Removing Brackets After a Plus SignYou'll learn: Removing Brackets After a Plus Sign Chapter 2Tinker the Terms: Predicting How a Sum Changes4:05Tinker the Terms: Predicting How a Sum ChangesYou'll learn: Tinker the Terms: Predicting How a Sum Changes Chapter 2Matching Equivalent Expressions and Placing Brackets4:25Matching Equivalent Expressions and Placing BracketsYou'll learn: Matching Equivalent Expressions and Placing Brackets Chapter 2Making Different Values Using Two, Three and Five3:51Making Different Values Using Two, Three and FiveYou'll learn: Making Different Values Using Two, Three and Five Chapter 2Subtract Ten and Add One: Explaining Mental Subtraction3:51Subtract Ten and Add One: Explaining Mental SubtractionYou'll learn: Subtract Ten and Add One: Explaining Mental Subtraction Chapter 2Multiplying a Sum: Understanding the Distributive Property4:00Multiplying a Sum: Understanding the Distributive PropertyYou'll learn: Multiplying a Sum: Understanding the Distributive Property Chapter 2Multiplying a Difference: Understanding the Distributive Property3:53Multiplying a Difference: Understanding the Distributive PropertyYou'll learn: Multiplying a Difference: Understanding the Distributive Property Chapter 2Tinker the Terms: Predicting How a Product Changes3:44Tinker the Terms: Predicting How a Product ChangesYou'll learn: Tinker the Terms: Predicting How a Product Changes Chapter 2Using Nearby Round Numbers to Multiply Mentally3:50Using Nearby Round Numbers to Multiply MentallyYou'll learn: Using Nearby Round Numbers to Multiply Mentally Chapter 2Completing and Comparing Distributive Expressions4:04Completing and Comparing Distributive ExpressionsYou'll learn: Completing and Comparing Distributive Expressions Chapter 2Making Fourteen and Counting Picture Totals in Different Ways3:49Making Fourteen and Counting Picture Totals in Different WaysYou'll learn: Making Fourteen and Counting Picture Totals in Different Ways Chapter 2Expressions for Weekly Supplies and Yearly Savings4:02Expressions for Weekly Supplies and Yearly SavingsYou'll learn: Expressions for Weekly Supplies and Yearly Savings Chapter 2The Climbing Snail: Why the Final Day Is Different3:40The Climbing Snail: Why the Final Day Is DifferentYou'll learn: The Climbing Snail: Why the Final Day Is Different Chapter 2Counting Stories Read: Choosing the Correct Expression3:54Counting Stories Read: Choosing the Correct ExpressionYou'll learn: Counting Stories Read: Choosing the Correct Expression Chapter 2Finding Efficient Ways to Add Alternating Positive and Negative Terms3:47Finding Efficient Ways to Add Alternating Positive and Negative TermsYou'll learn: Finding Efficient Ways to Add Alternating Positive and Negative Terms Chapter 2Comparing Expressions and Recognising Equivalent Forms4:28Comparing Expressions and Recognising Equivalent FormsYou'll learn: Comparing Expressions and Recognising Equivalent Forms Chapter 2Creating Ten Different Expressions for One Number3:58Creating Ten Different Expressions for One NumberYou'll learn: Creating Ten Different Expressions for One Number Chapter 2Expression Engineer: Making Numbers with Four Fours3:53Expression Engineer: Making Numbers with Four FoursYou'll learn: Expression Engineer: Making Numbers with Four Fours Chapter 2Expression Engineer: Using Each Given Number Exactly Once3:53Expression Engineer: Using Each Given Number Exactly OnceYou'll learn: Expression Engineer: Using Each Given Number Exactly Once

NCERT · Ganita Prakash · Volume 1 · Chapter 3

A Peek Beyond the Point

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Chapter 3Why Do Measurements Need Units Smaller Than One?3:10Why Do Measurements Need Units Smaller Than One?You'll learn: Measurements rarely come out in whole units, so we subdivide units to measure more precisely.Chapter 3Build Tenths by Dividing One Whole3:04Build Tenths by Dividing One WholeYou'll learn: Divide one whole into ten equal parts to make tenths, written as fractions.Chapter 3Regroup Ten Tenths as One Whole3:04Regroup Ten Tenths as One WholeYou'll learn: Ten tenths regroup into one whole, just as ten ones make a ten.Chapter 3Make Hundredths by Dividing Tenths3:06Make Hundredths by Dividing TenthsYou'll learn: Dividing each tenth into ten equal parts makes hundredths.Chapter 3Regroup Hundredths Before Writing Decimals3:02Regroup Hundredths Before Writing DecimalsYou'll learn: Regroup hundredths into tenths and wholes before writing the decimal.Chapter 3Why Does Decimal Place Value Keep Dividing by Ten?3:08Why Does Decimal Place Value Keep Dividing by Ten?You'll learn: Each place is one-tenth of the place to its left, so place value keeps dividing by ten, giving thousandths and beyond.Chapter 3Read and Write Decimals Using Expanded Form3:02Read and Write Decimals Using Expanded FormYou'll learn: Write a decimal in expanded form to read and write it correctly.Chapter 3Convert Lengths and Masses Using Decimal Units3:22Convert Lengths and Masses Using Decimal UnitsYou'll learn: Metric length and mass units step by tens, hundreds and thousands, so one decimal-shift method converts both.Chapter 3Connect Rupees and Paise with Decimals3:07Connect Rupees and Paise with DecimalsYou'll learn: Paise are hundredths of a rupee, so money amounts are two-place decimals.Chapter 3Why Does Adding a Trailing Zero Leave a Decimal Unchanged?3:27Why Does Adding a Trailing Zero Leave a Decimal Unchanged?You'll learn: A trailing zero after the last decimal digit adds zero tenths or hundredths, so the value is unchanged.Chapter 3Compare and Order Decimals by Place Value3:18Compare and Order Decimals by Place ValueYou'll learn: Compare decimals place by place from the left to order them.Chapter 3Zoom into a Number Line to Locate a Decimal3:17Zoom into a Number Line to Locate a DecimalYou'll learn: Zoom into an interval of the number line again and again to locate a decimal precisely.Chapter 3Find the Distance Between Two Decimals3:19Find the Distance Between Two DecimalsYou'll learn: The distance between two decimals is their difference, found on the number line.Chapter 3Can You Always Find a Decimal Closer to a Target?3:24Can You Always Find a Decimal Closer to a Target?You'll learn: Between any two decimals there is always another, so we can get as close to a target as we like.Chapter 3Regroup to Add and Subtract Decimals3:15Regroup to Add and Subtract DecimalsYou'll learn: Line up places and regroup across the point to add and subtract decimals.Chapter 3Find the Next Terms in a Decimal Sequence3:17Find the Next Terms in a Decimal SequenceYou'll learn: Find the constant change in a decimal sequence to continue it.Chapter 3Estimate a Decimal Sum or Difference Before Calculating3:20Estimate a Decimal Sum or Difference Before CalculatingYou'll learn: Round to whole numbers first to estimate a decimal sum or difference.Chapter 3Spot Decimal-Point and Unit Errors3:24Spot Decimal-Point and Unit ErrorsYou'll learn: A misplaced point or a mixed unit changes a value by a factor of ten or more; check both.Chapter 3Why 1.5 Hours, 5.6 Feet and 4.3 Overs Can Mislead3:19Why 1.5 Hours, 5.6 Feet and 4.3 Overs Can MisleadYou'll learn: Clock time, feet and inches, and cricket overs group by 60, 12 and 6, not 10, so writing them with a dot like a decimal misleads.Chapter 3Write Halves, Quarters and Fifths as Decimals3:19Write Halves, Quarters and Fifths as DecimalsYou'll learn: Rewrite halves, quarters and fifths with denominators 10 or 100 to get their decimals.Chapter 3Separate a Decimal's Whole and Fractional Parts3:29Separate a Decimal's Whole and Fractional PartsYou'll learn: Every decimal has a whole part and a fractional part separated by the point.

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NCERT · Ganita Prakash · Volume 1 · Chapter 4

Expressions using Letter-Numbers

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Chapter 4How Can a Letter Stand for a Changing or Unknown Number?3:04How Can a Letter Stand for a Changing or Unknown Number?You'll learn: A letter can stand for a quantity that changes or for one we don't know yet.Chapter 4Describe a Number Relationship with Letters3:10Describe a Number Relationship with LettersYou'll learn: Translate a number relationship described in words into an expression with letters.Chapter 4Write a Formula for a Total Cost3:09Write a Formula for a Total CostYou'll learn: Write a formula for total cost as price times quantity.Chapter 4Express an Age Relationship with a Letter3:04Express an Age Relationship with a LetterYou'll learn: Write one person's age in terms of another's using a letter.Chapter 4Write Perimeter Formulas for Regular Shapes3:09Write Perimeter Formulas for Regular ShapesYou'll learn: The perimeter of a regular shape is the number of sides times the side length.Chapter 4Write Relative Values in a Calendar or Number Grid3:03Write Relative Values in a Calendar or Number GridYou'll learn: Write every cell of a calendar or grid block relative to one cell, using row and column rules.Chapter 4Why Do the Diagonal Sums Match in a Number Grid?3:17Why Do the Diagonal Sums Match in a Number Grid?You'll learn: Using a letter for one corner shows both diagonal sums are always equal.Chapter 4Substitute a Number Without Changing the Expression's Structure3:03Substitute a Number Without Changing the Expression's StructureYou'll learn: Replace the letter with a number but keep every operation of the expression unchanged.Chapter 4How Does an Expression's Value Change with Its Input?3:17How Does an Expression's Value Change with Its Input?You'll learn: Substitute different inputs to see how the value of an expression changes.

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NCERT · Ganita Prakash · Volume 1 · Chapter 5

Parallel and Intersecting Lines

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Chapter 5Why Do Adjacent Angles on a Line Add to 180°?3:04Why Do Adjacent Angles on a Line Add to 180°?You'll learn: Adjacent angles that form a straight line together make 180°.Chapter 5Why Are Vertically Opposite Angles Equal?3:10Why Are Vertically Opposite Angles Equal?You'll learn: A single equality proof needs the linear-pair deductions to remain visible.Chapter 5Why Does Measuring a Diagram Not Prove a Geometric Fact?3:38Why Does Measuring a Diagram Not Prove a Geometric Fact?You'll learn: Measuring a drawing can suggest a fact, but drawings are imperfect, so a proof is needed.Chapter 5Why Do Four Equal Intersection Angles Make Perpendicular Lines?3:22Why Do Four Equal Intersection Angles Make Perpendicular Lines?You'll learn: If four angles at an intersection are equal, each is 90°, so the lines are perpendicular.Chapter 5When Do Segments Meet—and What Happens If We Extend Them?3:22When Do Segments Meet—and What Happens If We Extend Them?You'll learn: Segments can meet at endpoints, midpoints or interior points, and extending them can create new meeting points.Chapter 5Why Must Parallel Lines Lie in the Same Plane?3:15Why Must Parallel Lines Lie in the Same Plane?You'll learn: Lines that never meet but lie in different planes are not parallel; parallel lines must share a plane.Chapter 5Make Parallel and Perpendicular Creases by Folding3:27Make Parallel and Perpendicular Creases by FoldingYou'll learn: Fold paper to make parallel and perpendicular creases and spot the repeating pattern.Chapter 5Read Parallel-Line Arrows and Right-Angle Squares3:37Read Parallel-Line Arrows and Right-Angle SquaresYou'll learn: Arrows mark parallel lines and a small square marks a right angle in diagrams.Chapter 5Why Do Eight Transversal Angles Have at Most Four Measures?3:27Why Do Eight Transversal Angles Have at Most Four Measures?You'll learn: A transversal makes eight angles from two vertically opposite pairs at each crossing, so at most four different measures.Chapter 5Find Corresponding Angles on Parallel Lines3:32Find Corresponding Angles on Parallel LinesYou'll learn: When lines are parallel, angles in matching positions at the two crossings are equal.Chapter 5Use Corresponding Angles to Test Whether Lines Are Parallel3:26Use Corresponding Angles to Test Whether Lines Are ParallelYou'll learn: If corresponding angles are equal the lines are parallel; if they differ, the lines meet somewhere.Chapter 5Draw a Parallel Line with a Ruler and Set Square3:21Draw a Parallel Line with a Ruler and Set SquareYou'll learn: Slide a set square along a ruler to draw a line parallel to a given line.Chapter 5Create Parallel Lines by Paper Folding3:24Create Parallel Lines by Paper FoldingYou'll learn: Fold paper twice at right angles to create parallel lines.Chapter 5Why Are Alternate Interior Angles Equal on Parallel Lines?3:13Why Are Alternate Interior Angles Equal on Parallel Lines?You'll learn: Alternate interior angles are equal because each equals the same corresponding angle.Chapter 5Why Do Same-Side Interior Angles Add to 180°?3:21Why Do Same-Side Interior Angles Add to 180°?You'll learn: One same-side interior angle equals the angle forming a linear pair with the other, so the two add to 180°.Chapter 5Find Missing Angles in a Parallel-Line Diagram3:08Find Missing Angles in a Parallel-Line DiagramYou'll learn: Chain corresponding, alternate and linear-pair facts to find missing angles.Chapter 5Draw an Extra Parallel Line to Unlock an Angle Problem3:08Draw an Extra Parallel Line to Unlock an Angle ProblemYou'll learn: Drawing an extra parallel line through a corner turns a hard angle problem into known angle pairs.Chapter 5Are These Lines Really Parallel—or Is It an Illusion?3:22Are These Lines Really Parallel—or Is It an Illusion?You'll learn: Optical illusions can make parallel lines look bent; check with measurements and angle facts.Chapter 5Will These Lines Meet If We Extend Them?3:36Will These Lines Meet If We Extend Them?You'll learn: Will These Lines Meet If We Extend Them?Chapter 5Four Angles at an Intersection: Measure and Look for Patterns3:38Four Angles at an Intersection: Measure and Look for PatternsYou'll learn: Four Angles at an Intersection: Measure and Look for Patterns Chapter 5Linear Pairs: Why Adjacent Angles Add to 180 Degrees3:29Linear Pairs: Why Adjacent Angles Add to 180 DegreesYou'll learn: Linear Pairs: Why Adjacent Angles Add to 180 Degrees Chapter 5Why Vertically Opposite Angles Are Equal3:25Why Vertically Opposite Angles Are EqualYou'll learn: Why Vertically Opposite Angles Are Equal Chapter 5Why Measurements May Differ from Geometric Predictions3:44Why Measurements May Differ from Geometric PredictionsYou'll learn: Why Measurements May Differ from Geometric Predictions Chapter 5Four Equal Angles: Recognising Perpendicular Lines3:26Four Equal Angles: Recognising Perpendicular LinesYou'll learn: Four Equal Angles: Recognising Perpendicular Lines Chapter 5Describing How Line Segments Meet3:43Describing How Line Segments MeetYou'll learn: Describing How Line Segments Meet Chapter 5What Makes Two Lines Parallel?3:36What Makes Two Lines Parallel?You'll learn: What Makes Two Lines Parallel?Chapter 5Finding Sets of Parallel Lines in a Drawing3:28Finding Sets of Parallel Lines in a DrawingYou'll learn: Finding Sets of Parallel Lines in a Drawing Chapter 5Repeated Paper Folds: Parallel Creases and a Counting Pattern3:38Repeated Paper Folds: Parallel Creases and a Counting PatternYou'll learn: Repeated Paper Folds: Parallel Creases and a Counting Pattern Chapter 5Making Parallel Diagonal Folds and Folded Triangles3:39Making Parallel Diagonal Folds and Folded TrianglesYou'll learn: Making Parallel Diagonal Folds and Folded Triangles Chapter 5Marking Parallel and Perpendicular Lines Correctly3:43Marking Parallel and Perpendicular Lines CorrectlyYou'll learn: Marking Parallel and Perpendicular Lines Correctly Chapter 5Drawing Perpendicular Lines on Dot Paper3:29Drawing Perpendicular Lines on Dot PaperYou'll learn: Drawing Perpendicular Lines on Dot Paper Chapter 5Drawing Parallel Lines on Dot Paper3:31Drawing Parallel Lines on Dot PaperYou'll learn: Drawing Parallel Lines on Dot Paper Chapter 5Which Slanted Line Is Really Parallel?3:32Which Slanted Line Is Really Parallel?You'll learn: Which Slanted Line Is Really Parallel?Chapter 5A Transversal Makes Eight Angles: How Many Can Be Different?3:34A Transversal Makes Eight Angles: How Many Can Be Different?You'll learn: A Transversal Makes Eight Angles: How Many Can Be Different?Chapter 5Finding All Four Pairs of Corresponding Angles3:39Finding All Four Pairs of Corresponding AnglesYou'll learn: Finding All Four Pairs of Corresponding Angles Chapter 5Copying an Angle to Create Parallel Lines3:29Copying an Angle to Create Parallel LinesYou'll learn: Copying an Angle to Create Parallel Lines Chapter 5Why Parallel Lines Have Equal Corresponding Angles3:32Why Parallel Lines Have Equal Corresponding AnglesYou'll learn: Why Parallel Lines Have Equal Corresponding Angles Chapter 5Can Nonparallel Lines Have Equal Corresponding Angles?3:50Can Nonparallel Lines Have Equal Corresponding Angles?You'll learn: Can Nonparallel Lines Have Equal Corresponding Angles?Chapter 5Drawing Parallel Lines with a Ruler and Set Square3:29Drawing Parallel Lines with a Ruler and Set SquareYou'll learn: Drawing Parallel Lines with a Ruler and Set Square Chapter 5Using the Long Edge of a Set Square to Draw Parallels3:30Using the Long Edge of a Set Square to Draw ParallelsYou'll learn: Using the Long Edge of a Set Square to Draw Parallels Chapter 5Drawing a Parallel Through a Given Point3:32Drawing a Parallel Through a Given PointYou'll learn: Drawing a Parallel Through a Given Point Chapter 5Making a Parallel Through a Point by Paper Folding3:17Making a Parallel Through a Point by Paper FoldingYou'll learn: Making a Parallel Through a Point by Paper Folding Chapter 5Finding Alternate Angles Across a Transversal3:28Finding Alternate Angles Across a TransversalYou'll learn: Finding Alternate Angles Across a Transversal Chapter 5Proving Equal Alternate Angles on Parallel Lines3:28Proving Equal Alternate Angles on Parallel LinesYou'll learn: Proving Equal Alternate Angles on Parallel Lines Chapter 5Finding All Eight Angles When One Angle Is 135 Degrees3:26Finding All Eight Angles When One Angle Is 135 DegreesYou'll learn: Finding All Eight Angles When One Angle Is 135 Degrees Chapter 5Using Unequal Corresponding Angles to Reject Parallelism3:32Using Unequal Corresponding Angles to Reject ParallelismYou'll learn: Using Unequal Corresponding Angles to Reject Parallelism Chapter 5Why Same-Side Interior Angles Add to 180 Degrees3:21Why Same-Side Interior Angles Add to 180 DegreesYou'll learn: Why Same-Side Interior Angles Add to 180 Degrees Chapter 5Following Angle Relationships in a Shape with Two Parallel Pairs3:07Following Angle Relationships in a Shape with Two Parallel PairsYou'll learn: Following Angle Relationships in a Shape with Two Parallel Pairs Chapter 5Angle Practice: Straight Lines and Crossing Lines3:34Angle Practice: Straight Lines and Crossing LinesYou'll learn: Angle Practice: Straight Lines and Crossing Lines Chapter 5Angle Practice: Connected Crossings and Parallel Lines3:26Angle Practice: Connected Crossings and Parallel LinesYou'll learn: Angle Practice: Connected Crossings and Parallel Lines Chapter 5Angle Practice: Combining Several Angles Around a Point3:34Angle Practice: Combining Several Angles Around a PointYou'll learn: Angle Practice: Combining Several Angles Around a Point Chapter 5Finding the Unknown Angle in Four New Configurations3:40Finding the Unknown Angle in Four New ConfigurationsYou'll learn: Finding the Unknown Angle in Four New Configurations Chapter 5Finding X and Y from Parallel-Line Angle Relationships3:39Finding X and Y from Parallel-Line Angle RelationshipsYou'll learn: Finding X and Y from Parallel-Line Angle Relationships Chapter 5Transferring Angles Through a Network of Lines3:12Transferring Angles Through a Network of LinesYou'll learn: Transferring Angles Through a Network of Lines Chapter 5Three Parallel Lines and a Perpendicular: Find Both Angles3:30Three Parallel Lines and a Perpendicular: Find Both AnglesYou'll learn: Three Parallel Lines and a Perpendicular: Find Both Angles Chapter 5Solving a Bent-Line Angle Problem by Adding Parallels3:24Solving a Bent-Line Angle Problem by Adding ParallelsYou'll learn: Solving a Bent-Line Angle Problem by Adding Parallels Chapter 5Are Those Lines Really Parallel? Exploring Visual Illusions3:44Are Those Lines Really Parallel? Exploring Visual IllusionsYou'll learn: Are Those Lines Really Parallel? Exploring Visual Illusions Chapter 5Parallel and Intersecting Lines: Chapter Recap3:47Parallel and Intersecting Lines: Chapter RecapYou'll learn: Parallel and Intersecting Lines: Chapter Recap

NCERT · Ganita Prakash · Volume 1 · Chapter 6

Number Play

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Chapter 6Record How Many Taller People Stand Before Each Person3:05Record How Many Taller People Stand Before Each PersonYou'll learn: Record, for each person in a line, how many taller people stand before them.Chapter 6Rebuild a Height Order from Its Number Clues3:08Rebuild a Height Order from Its Number CluesYou'll learn: Use the taller-before counts to rebuild the height order and test claims about it.Chapter 6Predict Whether a Sum or Difference Is Odd or Even3:01Predict Whether a Sum or Difference Is Odd or EvenYou'll learn: Even ± even and odd ± odd give even; even ± odd gives odd.Chapter 6Use Odd and Even Counts to Track Bulb Toggles3:03Use Odd and Even Counts to Track Bulb TogglesYou'll learn: A bulb toggled an even number of times returns to its start; an odd number flips it.Chapter 6Predict the Parity of a Sum of Page Numbers3:07Predict the Parity of a Sum of Page NumbersYou'll learn: Predict whether a sum of page numbers is odd or even from how many odd numbers it contains.Chapter 6Why Does One Even Factor Make a Product Even?2:57Why Does One Even Factor Make a Product Even?You'll learn: Counting grid squares shows that one even factor makes the whole product even.Chapter 6Why Is a Product of Odd Numbers Always Odd?3:13Why Is a Product of Odd Numbers Always Odd?You'll learn: A product of odd numbers is always odd, because no factor of 2 appears.Chapter 6Use 2n and 2n + 1 to Explain an Expression's Parity2:59Use 2n and 2n + 1 to Explain an Expression's ParityYou'll learn: Write numbers as 2n or 2n + 1 to see when an expression is even or odd for every input.Chapter 6Can an Incomplete Sequence Support a Parity Claim?3:15Can an Incomplete Sequence Support a Parity Claim?You'll learn: Checking a few cases is not enough; a parity claim needs the complete sequence or a general argument.Chapter 6Use Grid Totals and Bounds to Find Missing Numbers3:05Use Grid Totals and Bounds to Find Missing NumbersYou'll learn: Use row and column totals and the possible ranges of values to fill a grid's missing numbers.Chapter 6Check Whether a Number Grid's Clues Can All Be True3:10Check Whether a Number Grid's Clues Can All Be TrueYou'll learn: Check whether all of a grid's clues can be true at once before solving.Chapter 6What Do the Magic Sum and Centre Tell Us About a Magic Square?3:08What Do the Magic Sum and Centre Tell Us About a Magic Square?You'll learn: The magic sum and the centre place strong limits on which numbers can go in the corners.Chapter 6Complete a Magic Square Systematically and Compare Arrangements3:14Complete a Magic Square Systematically and Compare ArrangementsYou'll learn: One complete magic-square construction needs time for the constraints and completion steps.Chapter 6Why Is a 3×3 Magic Square's Sum 3 Times Its Centre?2:58Why Is a 3×3 Magic Square's Sum 3 Times Its Centre?You'll learn: One general magic-square relationship needs a labelled algebraic grid.Chapter 6Transform a Magic Square by Adding or Scaling Its Entries3:08Transform a Magic Square by Adding or Scaling Its EntriesYou'll learn: Adding the same number to every entry, or multiplying every entry, keeps a magic square magic.Chapter 6Build a Magic Square with Sum Zero Using Negative Numbers3:16Build a Magic Square with Sum Zero Using Negative NumbersYou'll learn: Use negative numbers to build a magic square whose rows, columns and diagonals all sum to zero.

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NCERT · Ganita Prakash · Volume 1 · Chapter 8

Working with Fractions

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Chapter 8Multiply a Fraction by a Whole Number Using Repeated Groups4:01Multiply a Fraction by a Whole Number Using Repeated GroupsYou'll learn: A whole number times a fraction is repeated groups of that fraction.Chapter 8Multiplying a Fraction by a Whole Number: Repeated Equal Quantities4:01Multiplying a Fraction by a Whole Number: Repeated Equal QuantitiesYou'll learn: Multiplying a Fraction by a Whole Number: Repeated Equal Quantities Chapter 8Taking One-Fifth of a Whole-Number Quantity4:01Taking One-Fifth of a Whole-Number QuantityYou'll learn: Taking One-Fifth of a Whole-Number Quantity Chapter 8Taking Two-Fifths: Divide First, Then Take the Required Parts3:56Taking Two-Fifths: Divide First, Then Take the Required PartsYou'll learn: Taking Two-Fifths: Divide First, Then Take the Required Parts Chapter 8Multiplication with Mixed Fractions in Sharing and Cost Problems4:02Multiplication with Mixed Fractions in Sharing and Cost ProblemsYou'll learn: Multiplication with Mixed Fractions in Sharing and Cost Problems Chapter 8Fraction Applications: Daily Milk, Canal Work and Shared Oil3:59Fraction Applications: Daily Milk, Canal Work and Shared OilYou'll learn: Fraction Applications: Daily Milk, Canal Work and Shared Oil Chapter 8Fractional Time Changes and Whole-Number Product Practice4:11Fractional Time Changes and Whole-Number Product PracticeYou'll learn: Fractional Time Changes and Whole-Number Product Practice Chapter 8What Is Half of a Quarter?4:02What Is Half of a Quarter?You'll learn: What Is Half of a Quarter?Chapter 8Finding Three-Quarters of Two-Fifths3:59Finding Three-Quarters of Two-FifthsYou'll learn: Finding Three-Quarters of Two-Fifths Chapter 8Multiplying Fractions Greater Than One with a Visual Model4:03Multiplying Fractions Greater Than One with a Visual ModelYou'll learn: Multiplying Fractions Greater Than One with a Visual Model Chapter 8Why Fraction Multiplication Gives the Area of a Rectangle3:54Why Fraction Multiplication Gives the Area of a RectangleYou'll learn: Why Fraction Multiplication Gives the Area of a Rectangle Chapter 8Multiplying Unit Fractions Through Rows and Columns4:00Multiplying Unit Fractions Through Rows and ColumnsYou'll learn: Multiplying Unit Fractions Through Rows and Columns Chapter 8Unit-Square Practice with Non-Unit Fractions3:57Unit-Square Practice with Non-Unit FractionsYou'll learn: Unit-Square Practice with Non-Unit Fractions Chapter 8Deriving the Rule for Multiplying Numerators and Denominators3:53Deriving the Rule for Multiplying Numerators and DenominatorsYou'll learn: Deriving the Rule for Multiplying Numerators and Denominators Chapter 8Cancelling Common Factors Before Multiplying Fractions4:20Cancelling Common Factors Before Multiplying FractionsYou'll learn: Cancelling Common Factors Before Multiplying Fractions Chapter 8Reducing Fractions to Lowest Terms: The Apavartana Connection4:05Reducing Fractions to Lowest Terms: The Apavartana ConnectionYou'll learn: Reducing Fractions to Lowest Terms: The Apavartana Connection Chapter 8A Filling Tank: Finding Fractional Amounts and the Time to Fill It3:57A Filling Tank: Finding Fractional Amounts and the Time to Fill ItYou'll learn: A Filling Tank: Finding Fractional Amounts and the Time to Fill It Chapter 8Sharing the Land That Remains3:59Sharing the Land That RemainsYou'll learn: Sharing the Land That Remains Chapter 8Finding a Rectangle’s Area with Mixed-Number Sides4:06Finding a Rectangle’s Area with Mixed-Number SidesYou'll learn: Finding a Rectangle’s Area with Mixed-Number Sides Chapter 8Four Saplings: Why There Are Only Three Gaps3:54Four Saplings: Why There Are Only Three GapsYou'll learn: Four Saplings: Why There Are Only Three Gaps Chapter 8Which Fractional Quantity Is Heavier?3:58Which Fractional Quantity Is Heavier?You'll learn: Which Fractional Quantity Is Heavier?Chapter 8Does Multiplication Always Make a Number Larger?4:01Does Multiplication Always Make a Number Larger?You'll learn: Does Multiplication Always Make a Number Larger?Chapter 8Why the Order of Fraction Multiplication Does Not Matter4:08Why the Order of Fraction Multiplication Does Not MatterYou'll learn: Why the Order of Fraction Multiplication Does Not Matter Chapter 8Division as a Missing Multiplication4:09Division as a Missing MultiplicationYou'll learn: Division as a Missing Multiplication Chapter 8What Is a Reciprocal and Why Does Its Product Give One?4:07What Is a Reciprocal and Why Does Its Product Give One?You'll learn: What Is a Reciprocal and Why Does Its Product Give One?Chapter 8Dividing a Whole Number by a Fraction4:00Dividing a Whole Number by a FractionYou'll learn: Dividing a Whole Number by a Fraction Chapter 8Dividing One Fraction by Another3:59Dividing One Fraction by AnotherYou'll learn: Dividing One Fraction by Another Chapter 8Deriving the Rule for Fraction Division4:12Deriving the Rule for Fraction DivisionYou'll learn: Deriving the Rule for Fraction Division Chapter 8Can Division Make the Answer Larger?4:10Can Division Make the Answer Larger?You'll learn: Can Division Make the Answer Larger?Chapter 8Sharing a Quarter Litre of Milk Among Five Cups4:00Sharing a Quarter Litre of Milk Among Five CupsYou'll learn: Sharing a Quarter Litre of Milk Among Five Cups Chapter 8How Many Fractional-Area Bricks Cover a Given Area?4:00How Many Fractional-Area Bricks Cover a Given Area?You'll learn: How Many Fractional-Area Bricks Cover a Given Area?Chapter 8Four Fountains Filling One Cistern Together4:05Four Fountains Filling One Cistern TogetherYou'll learn: Four Fountains Filling One Cistern Together Chapter 8Finding a Fraction of a Fraction in a Nested Diagram4:09Finding a Fraction of a Fraction in a Nested DiagramYou'll learn: Finding a Fraction of a Fraction in a Nested Diagram Chapter 8Shaded-Region Practice: Keep Track of the Original Square4:07Shaded-Region Practice: Keep Track of the Original SquareYou'll learn: Shaded-Region Practice: Keep Track of the Original Square Chapter 8A Dramma-tic Donation: Multiplying a Chain of Fractions4:09A Dramma-tic Donation: Multiplying a Chain of FractionsYou'll learn: A Dramma-tic Donation: Multiplying a Chain of Fractions Chapter 8Converting Between the Story’s Historical Coin Units4:13Converting Between the Story’s Historical Coin UnitsYou'll learn: Converting Between the Story’s Historical Coin Units Chapter 8Fraction Arithmetic in the Textbook’s Historical Account4:20Fraction Arithmetic in the Textbook’s Historical AccountYou'll learn: Fraction Arithmetic in the Textbook’s Historical Account Chapter 8Fraction Division Practice: Whole, Proper, Improper and Mixed Numbers4:14Fraction Division Practice: Whole, Proper, Improper and Mixed NumbersYou'll learn: Fraction Division Practice: Whole, Proper, Improper and Mixed Numbers Chapter 8Choosing Division Expressions for Lace, Ribbon and Bread4:02Choosing Division Expressions for Lace, Ribbon and BreadYou'll learn: Choosing Division Expressions for Lace, Ribbon and Bread Chapter 8How Much Flour Is Needed for Half as Many Rotis?4:04How Much Flour Is Needed for Half as Many Rotis?You'll learn: How Much Flour Is Needed for Half as Many Rotis?Chapter 8A Historical Challenge: Adding Reciprocals of Unit Fractions4:02A Historical Challenge: Adding Reciprocals of Unit FractionsYou'll learn: A Historical Challenge: Adding Reciprocals of Unit Fractions Chapter 8Finding the Pages Still Unread in a Novel4:07Finding the Pages Still Unread in a NovelYou'll learn: Finding the Pages Still Unread in a Novel Chapter 8Finding Travel Distance from a Mixed Fraction of Fuel4:19Finding Travel Distance from a Mixed Fraction of FuelYou'll learn: Finding Travel Distance from a Mixed Fraction of Fuel Chapter 8How Much Time Does the Plane Save?4:03How Much Time Does the Plane Save?You'll learn: How Much Time Does the Plane Save?Chapter 8Sharing the Cake That Is Left3:56Sharing the Cake That Is LeftYou'll learn: Sharing the Cake That Is Left Chapter 8Comparing a Fraction Product Without Multiplying It Out4:10Comparing a Fraction Product Without Multiplying It OutYou'll learn: Comparing a Fraction Product Without Multiplying It Out Chapter 8Finding the Shaded Fraction in the Final Square Diagram4:09Finding the Shaded Fraction in the Final Square DiagramYou'll learn: Finding the Shaded Fraction in the Final Square Diagram Chapter 8Ants at Branching Paths: Multiplying Shares and Adding Routes4:16Ants at Branching Paths: Multiplying Shares and Adding RoutesYou'll learn: Ants at Branching Paths: Multiplying Shares and Adding Routes Chapter 8A Product Pattern That Cancels Almost Everything4:20A Product Pattern That Cancels Almost EverythingYou'll learn: A Product Pattern That Cancels Almost Everything Chapter 8Placing Four Queens So None Attack Each Other4:02Placing Four Queens So None Attack Each OtherYou'll learn: Placing Four Queens So None Attack Each Other Chapter 8The Eight-Queens Challenge4:04The Eight-Queens ChallengeYou'll learn: The Eight-Queens Challenge Chapter 8Working with Fractions: Chapter Recap4:14Working with Fractions: Chapter RecapYou'll learn: Working with Fractions: Chapter Recap

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Coming soon

Volume 1 · Chapter 7 · A Tale of Three Intersecting Lines · Volume 2 · Chapter 1 · Geometric Twins · Volume 2 · Chapter 2 · Operations with Integers and 5 more

Volume 1 · Chapter 7 · A Tale of Three Intersecting Lines61 videos coming
Volume 2 · Chapter 1 · Geometric Twins13 videos coming
Volume 2 · Chapter 2 · Operations with Integers22 videos coming
Volume 2 · Chapter 3 · Finding Common Ground18 videos coming
Volume 2 · Chapter 4 · Another Peek Beyond the Point20 videos coming
Volume 2 · Chapter 5 · Connecting the Dots...23 videos coming
Volume 2 · Chapter 6 · Constructions and Tilings26 videos coming
Volume 2 · Chapter 7 · Finding the Unknown28 videos coming