MINDSETS CHALLENGES BY CBSE - CURRICULUM MAP
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
MINDSETS CHALLENGES BY
CBSE
CURRICULUM MAP
Current as of February 26, 2022
www.mindsets.com
STEAM platform for the classroom hello@mindsets.com
Real-world learning - World ready students
© Mindsets Learning
© Mindsets Learning 2022 1Curriculum Map - Math
Class 6
Standards Mindsets Challenges
Algebra
Introduction to algebra: Introduction to variable through patterns and through
• Theme Park App
appropriate word problems and generalisations (example 5 × 1 = 5 etc.).
Introduction to algebra: Generate such patterns with more examples. • Theme Park App
Introduction to algebra: Introduction to unknowns through examples with
• Save the Elephants
simple contexts (single operations).
Data Handling
• Amazon’s Amazing
Making bar graphs for given data interpreting bar graphs.
Rainforests
Number System
Knowing our Numbers: Consolidating the sense of numberness up to 5 digits,
Size, estimation of numbers, identifying smaller, larger, etc. Place value
(recapitulation and extension), connectives: use of symbols =, and use of
brackets, word problems on number operations involving large numbers up to • Party Planner
a maximum of 5 digits in the answer after all operations. This would include • Save the Elephants
conversions of units of length & mass (from the larger to the smaller units), • Ice Caps
estimation of outcome of number operations. Introduction to a sense of the
largeness of, and initial familiarity with, large numbers up to 8 digits and
approximation of large numbers).
• Piles & Holes 1:
Negative numbers and integers: How negative numbers arise, models of Digging
negative numbers, connection to daily life, ordering of negative numbers, • Piles & Holes 2: It's
representation of negative numbers on number line. Children to see patterns, Raining Opposites
identify and formulate rules. What are integers, identification of integers on • Piles & Holes 3:
the number line, operation of addition and subtraction of integers, showing the Collecting & Sorting
operations on the number line (addition of negative integer reduces the value • Piles & Holes 4:
of the number) comparison of integers, ordering of integers. Evaluating
• Hike Mount Everest
Fractions: Revision of what a fraction is, Fraction as a part of whole,
Representation of fractions (pictorially and on number line), fraction as a
• Party Planner
division, proper, improper & mixed fractions, equivalent fractions, comparison
• Sienna Sauce
of fractions, addition and subtraction of fractions (Avoid large and complicated
• Delicious Dishes
unnecessary tasks). (Moving towards abstraction in fractions) Review of the
• Catchy Clothing
idea of a decimal fraction, place value in the context of decimal fraction, inter
• Stop Food Waste
conversion of fractions and decimal fractions (avoid recurring decimals at this
• Aquarium Vet
stage), word problems involving addition and subtraction of decimals (two
operations together on money, mass, length and temperature).
Class 7
Standards Mindsets Challenges
Algebra
Generate algebraic expressions (simple) involving one or two variables. • Theme Park App
© Mindsets Learning 2022 2Like and unlike terms, degree of expressions e.g., x² y etc. (exponent≤ 3, • Bracelet Business
number of variables) • Theme Park App
Addition, subtraction of algebraic expressions (coefficients should be integers). • Theme Park App
Geometry
• Design a Baseball
Properties of triangles: Pythagoras Theorem (Verification only).
Field
• Design a Logo:
Gourmet
• Eye-Catching
Symmetry: Recalling reflection symmetry.
Advertising
• Design a Logo: Social
Media
• Design a Logo:
Gourmet
Symmetry: Idea of rotational symmetry, observations of rotational symmetry • Eye-Catching
of 2-D objects. (90 degrees, 120 degrees, 180 degrees). Advertising
• Design a Logo: Social
Media
• Design a Logo:
Gourmet
Symmetry: Operation of rotation through 90 and 180 degrees of simple • Eye-Catching
figures. Advertising
• Design a Logo: Social
Media
• Design a Logo:
Gourmet
Symmetry: Examples of figures with both rotation and reflection symmetry • Eye-Catching
(both operations). Advertising
• Design a Logo: Social
Media
• Eye-Catching
Examples of figures that have reflection and rotation symmetry and vice-versa.
Advertising
• Design a Logo:
Gourmet
Congruence: Extend congruence to simple geometrical shapes e.g. triangles, • Eye-Catching
circles. Advertising
• Design a Logo: Social
Media
Mensuration
Revision of perimeter, Circumference of Circle, Idea of Area Concept of
measurement using a basic unit area of a square, rectangle, triangle, • Solar Energy for
parallelogram and circle, area between two rectangles and two concentric Power
circles.
Number System
• Design Your Own Ice
Fractions and rational numbers. Cream Sundae Store
• Stop Food Waste
© Mindsets Learning 2022 3Multiplication of fractions. • Stop Food Waste
Word problems involving mixed fractions. • Stop Food Waste
Operations on rational numbers (all operations). • Making Face Shields
Ratio and Proportion
Unitary method continued, consolidation, general expression. • Pizza Delight
Percentage - an introduction. • Concert T-shirts
Understanding percentage as a fraction with denominator 100. • Concert T-shirts
Converting fractions and decimals into percentage and vice-versa. • Concert T-shirts
Class 8
Standards Mindsets Challenges
Algebra
Identities (a ± b)² = a² ± 2ab + b², a² – b² = (a – b) (a + b), Factorisation
(simple cases only) as examples the following types a(x + y), (x ± y)², a² – b², • Bracelet Business
(x + a).(x + b).
Solving linear equations in one variable in contextual problems involving
• Price for Kicks
multiplication and division (word problems) (avoid complex coefficient in the
• Best Cell Plan
equations).
Data Handling
Consolidating and generalising the notion of chance in events like tossing
coins, dice etc. Relating it to chance in life events. Visual representation of
frequency outcomes of repeated throws of the same kind of coins or dice.
• Sports Stats
Throwing a large number of identical dice/coins together and aggregating the
Prediction
result of the throws to get large number of individual events. Observing the
aggregating numbers over a large number of repeated events. Comparing with
the data for a coin. Observing strings of throws, notion of randomness.
Mensuration
• Packaging Sporting
Goods
Concept of volume, measurement of volume using a basic unit, volume of a • Baseball Bonanza
cube, cuboid and cylinder. • NASA's Hidden
Figures
• Save a Sea Otter
• Packaging Sporting
Goods
Volume and capacity (measurement of capacity)
• Baseball Bonanza
• Save a Sea Otter
Number System
• Famous Company
Powers.
Shares
• Famous Company
Integers as exponents.
Shares
• Famous Company
Laws of exponents with integral powers.
Shares
© Mindsets Learning 2022 4• Perfect Platforms 2
Squares, Square roots, Cubes, Cube roots.
• Perfect Platforms 1
• Perfect Platforms 2
Square and Square roots.
• Perfect Platforms 1
Estimating square roots and cube roots. Learning the process of moving nearer • Perfect Platforms 2
to the required number. • Perfect Platforms 1
Ratio and Proportion
• Price for Kicks
• Become a Real
Slightly advanced problems involving applications on percentages, profit & Estate Expert
loss, overhead expenses, discount, tax. • The Amazing Race
Adventure
• Diligent Deductions
• Solar Energy for
Direct variation – Simple and direct word problems. Power
• Doggy Day Care
Class 9
Standards Mindsets Challenges
Linear Equations in 2 variables
Recall of linear equations in one variable. Introduction to the equation in two
variables. Focus on linear equations of the type ax+by+c=0. Explain that a • Sales Ramp
linear equation in two variables has infinitely many solutions and justify their • Where to Work: Tech
being written as ordered pairs of real numbers, plotting them and showing that Career
they lie on a line. Graph of linear equations in two variables. Examples, • Where to Work: Road
problems from real life with algebraic and graphical solutions being done to College
simultaneously.
Mensuration
Surface areas and volumes of cubes, cuboids, spheres (including hemispheres)
• Space Mission
and right circular cylinders/cones.
Real Numbers
Review of representation of natural numbers, integers, rational numbers on
the number line. Rational numbers as recurring/ terminating decimals. • Perfect Platforms 1
Operations on real numbers.
Examples of non-recurring/non-terminating decimals. Existence of non-rational
numbers (irrational numbers) such as √2, √3, and their representation on the • Perfect Platforms 1
number line.
Statistics and Probability
History, Repeated experiments and observed frequency approach to
probability. Focus is on empirical probability. (A large amount of time to be
devoted to group and to individual activities to motivate the concept; the • Teen Gym
experiments to be drawn from real - life situations, and from examples used in
the chapter on statistics).
Class 10
Standards Mindsets Challenges
Arithmetic Progressions
© Mindsets Learning 2022 5Motivation for studying Arithmetic Progression Derivation of the nth term and • Electric Cars 1
sum of the first n terms of A.P. • Electric Cars 2
Lines
• Where to Work: Tech
Review: Concepts of coordinate geometry, graphs of linear equations. Distance Career
formula. Section formula (internal division). • Where to Work: Road
to College
Pair of linear equations in two variables
• Where to Work: Tech
Career
Pair of linear equations in two variables and graphical method of their solution,
• Where to Work: Road
consistency/inconsistency. Algebraic conditions for number of solutions.
to College
Solution of a pair of linear equations in two variables algebraically - by
• You've Been
substitution, by elimination. Simple situational problems. Simple problems on
Cheated!
equations reducible to linear equations.
• You've Been
Cheated... Again!
Class 11
Standards Mindsets Challenges
Relationships and Functions
Ordered pairs. Cartesian product of sets. Number of elements in the Cartesian
product of two finite sets. Cartesian product of the set of reals with itself ( R x
R only).Definition of relation, pictorial diagrams, domain, co-domain and range
of a relation. Function as a special type of relation. Pictorial representation of a
• Sunset Sales
function, domain, co-domain and range of a function. Real valued functions,
domain and range of these functions, constant, identity, polynomial, rational,
modulus, signum, exponential, logarithmic and greatest integer functions, with
their graphs.
© Mindsets Learning 2022 6Curriculum Map - Science
Class 7
Standards Mindsets Challenges
Materials
What is heat? • Too Hot to Handle!
• Bouncy Balls
How things change/react with one another.
• The Case for Casein
Class 8
Standards Mindsets Challenges
Materials
Materials in daily life. • Reduce, Reuse, Recycle: Shopping Bags
• Bouncy Balls
How things change/react with one another.
• The Case for Casein
© Mindsets Learning 2022 7Mindsets Challenges - Math
Challenge name Description
Amazon’s Amazing Help environmental scientists analyze the changing patterns of rain and how it
Rainforests affects the plants and animals in the Amazon rainforest.
Work with marine biologists at the Georgia Aquarium! Use rounding to check
Aquarium Vet
the weight and height of animals, and medicines they may need.
Puerto Rico is still recovering from hurricane damage. Work with your Little
Baseball Bonanza
League baseball team to help get sports programs running again.
Become a Real Estate On the TV show, House Hunters, you sell the most amazing homes in the
Expert world. Calculate how much money you’ll make as a real estate agent!
As the pricing analyst for Verizon, you've been tasked to create mobile data
Best Cell Plan
plans for the teen market using linear equations.
Your school will be hosting an upcoming International Art Fair! Create and
Bracelet Business
design special patterned bands for sale using a basic design.
Work with a kids clothing brand to design, measure and make a new line of t-
Catchy Clothing
shirts which feature inspiring artists and trailblazers.
Spotify is hosting a school concert and needs help selecting concert T-shirts to
Concert T-shirts
sell! Which will be the most popular in your class?
Use recipes to create small servings of delicious dishes from around the world
Delicious Dishes
to serve at your school’s International Food Night.
Design Your Own Ice Ben & Jerry’s is accepting applications to open new locations and you have an
Cream Sundae Store idea for a “design-your-own” ice creams. Let's get started!
You’re an architect designing a baseball stadium in Tampa Bay, Florida. Use
Design a Baseball Field
Pythagorean Theorem to determine the dimensions of the field.
Design a Logo: It's your big chance to create a new logo for the world famous Kraft Heinz
Gourmet Company using transformations and congruent shapes.
Design a Logo: Social Facebook has asked you to create a new logo for its world-famous company.
Media Develop a logo using rigid transformations and congruent shapes.
Choose a career and see what salary you'll earn each month. We'll learn how
Diligent Deductions
your career choice affects what you decide to spend and buy!
Dog walking is big business! You are inspired by how much other people can
Doggy Day Care
earn from dog walking and decide to start your own company!
You're working for Tesla to create an ad to promote the new Model 3 car! First,
Electric Cars 1
let's analyze data and compare it to a competitor's car.
Now that you're familiar with electric cars, use your data to create a viral ad
Electric Cars 2
for Tesla's new Model 3 and analyze the results.
Eye-Catching Design and create eye-catching images using rigid transformations for a new
Advertising marketing campaign for LeBron James.
Famous Company Apple wants buy growing companies that are popular with teenagers. As the
Shares technical analyst, research and recommend companies to invest in.
National Geographic has hired you to create graphs for a story on the negative
Hike Mount Everest
effects climbing Mount Everest has on your body.
© Mindsets Learning 2022 8Study the changes in glaciers around the world and how these impact animals
Ice Caps
and the environment. Let's help create positive change!
Help support health and medical workers who are fighting the COVID‑19 virus.
Making Face Shields
Use your math skills to make face shields and help save lives!
You’ve been asked to design a memorial at the NASA headquarters to honor
NASA's Hidden Figures
Mary Jackson, the first female African American engineer at NASA.
Packaging Sporting Packaging is expensive! As the Packaging Engineer at Amazon, use surface
Goods area calculations to lower costs by packaging goods effectively.
You’re a party planner hired by a local high school to plan their graduation
Party Planner
party. Keep track of money spent and stay within budget!
The 2028 Summer Olympics in Los Angeles will be here soon! You’ve been
Perfect Platforms 1
hired to design platforms for judo, weightlifting, and gymnastics.
You’ve done such an excellent job designing platforms, that the Olympic
Perfect Platforms 2
Committee has asked you to inspect new platforms. Let's get to work!
Piles & Holes 1: What happens when you combine sand piles with other sand piles. Piles with
Digging holes? Holes with holes? In this challenge we'll find out!
Piles & Holes 2: It's You discovered how to add piles in the first piles and holes Challenge. Now,
Raining Opposites let’s see what else we can learn about piles and holes!
Piles & Holes 3: What happens when you group collections of piles and holes together? Find
Collecting & Sorting out how to use parentheses to communicate with piles and holes!
Piles & Holes 4: Now that you've learned all about piles and holes, let's practice evaluating
Evaluating groups of piles and holes in different ways!
Are you happy with your school lunches? Whole Foods is partnering with your
Pizza Delight
school to test a new pizza dish, and they'd like your help.
Help Nike to relaunch one of its best selling sneakers! You'll pick a retro
Price for Kicks
sneaker, then work out costs and a range of sales and profits.
A competitor is about to overtake Nike's sales! You've got one chance to pick
Sales Ramp
an advertising method that will grow weekly sales the fastest.
Baby sea otters are rescued everyday! Help marine centers design pools to
Save a Sea Otter
help save and care for these sea otters.
You’re partnering with Save the Elephants to raise the profile of African
Save the Elephants
Elephants. Encourage people to donate money to this cause!
Learn how a teenager created her own barbeque sauce business and calculate
Sienna Sauce
the ingredient amounts required for larger barbeque sauce orders.
The University of California aims to be carbon neutral by 2025. Estimate how
Solar Energy for Power
many solar panels you'll need to power one of their buildings.
As an aeronautical engineer, use your understanding of volume and ratio to
Space Mission
design a capsule that can bring expandable modules into space!
As a sports statistician, your job is to record data, determine probabilities and
Sports Stats Prediction
make predictions on games and players using statistics.
Each year, more than $1 trillion in food is wasted around the world. Explore
Stop Food Waste
how you can save food at home, at school and in the community.
You're the head of marketing for McDonald’s and will use functions to track the
Sunset Sales
sales of new Sunset menu items in your San Diego restaurant.
© Mindsets Learning 2022 9After the success of its community programs, Nike would like your help in their
Teen Gym
next project to create teen gyms at school. Let's get fit!
The Amazing Race You’re a producer for the teen version of The Amazing Race. Book flights and
Adventure convert money for the contestants' traveling to 3 cities!
Six Flags needs your help creating a cost calculator app, which supports
Theme Park App
visitors planning and enjoying their theme park visit.
Where to Work: Road College is expensive, so you start working and saving early. You've been
to College offered jobs by Subway and McDonald’s. Which one will you choose?
Where to Work: Tech You've been offered two jobs - one by Google and one by Amazon. Which will
Career you pick? Use salary and company data to make a decision!
You’re a forensic accountant! Analyze clues from receipts and financial records
You've Been Cheated!
to determine if companies are being stolen from.
You've Been Cheated... You’ve perfected your forensic accounting skills! Use financial records to
Again! investigate whether hackers are stealing from online purchases.
© Mindsets Learning 2022 10Mindsets Challenges - Science
Challenge name Description
Use your knowledge of polymers, conservation of mass, and conduct
Bouncy Balls
experiments to create the bounciest ball for the New York Toy Fair!
Reduce, Reuse, Whole Foods is looking for new ideas to reduce plastic bag use in the
Recycle: Shopping Bags community. You’ll help design a new environmentally friendly bag!
Recycle unused milk using the milk's casein to create useful, biodegradable
The Case for Casein
plastic products that McDonald's and the community can use.
Pizzas lose heat during delivery, and no one wants to eat cold, soggy pizza!
Too Hot to Handle!
Design a container to keep your lunch-time pizza piping hot!
© Mindsets Learning 2022 11Math Depth of Knowledge (DOK)
Class 6 Mindsets Challenge
2 - Procedural fluency with arithmetic operations. • Party Planner
• Catchy Clothing
2 - Procedural fluency.
• Delicious Dishes
2 - Application and contextual interpretation of inequalities. • Ice Caps
2 - Interpretation of line plots. • Amazon’s Amazing Rainforests
2 - Application of visual model. • Sienna Sauce
2 - Procedural fluency with inequalities. • Save the Elephants
2 - Routine problem-solving with writing expressions. • Theme Park App
• Piles & Holes 1: Digging
• Stop Food Waste
• Piles & Holes 2: It's Raining
3 - Strategic reasoning about concrete integer representations. Opposites
• Piles & Holes 3: Collecting &
Sorting
• Piles & Holes 4: Evaluating
3 - Strategic reasoning about graphing. • Hike Mount Everest
3 - Strategic reasoning. • Aquarium Vet
Class 7 Mindsets Challenge
• Design Your Own Ice Cream
2 - Procedural fluency with division of fractions by fractions.
Sundae Store
2 - Procedural fluency with fractions and multiplication to solve a
• Making Face Shields
real-world problem.
• Design a Logo: Gourmet
2 - Application of skills and concepts of rigid transformations.
• Design a Logo: Social Media
3 - Strategic reasoning about area, volume, and unit rates. • Solar Energy for Power
3 - Strategic reasoning about expressions. • Bracelet Business
3 - Strategic reasoning about transformations. • Eye-Catching Advertising
3 - Strategic reasoning using proportional relationships. • Pizza Delight
3 - Strategic reasoning about percentages. • Concert T-shirts
3 - Strategic reasoning about the Pythagorean Theorem. • Design a Baseball Field
Class 8 Mindsets Challenge
1 - Recall and Reproduction • Save a Sea Otter
2 - Procedural fluency. Students will use volume concepts (unit
cubes of fractional length) to find the capacity of various sized • Baseball Bonanza
boxes.
2 - Procedural fluency with fractions and multiplication to solve a
• NASA's Hidden Figures
real-world problem.
2 - Procedural fluency in working with positive and negative
• Famous Company Shares
exponents.
© Mindsets Learning 2022 122 - Procedural fluency with square roots of small numbers. • Perfect Platforms 1
2 - Application of math skills and concepts in relation to
• Sports Stats Prediction
probability and predictions.
2 - Procedural fluency with writing and solving linear equations. • Best Cell Plan
3 - Strategic reasoning about percent changes and inequalities. • Price for Kicks
3 - Strategic thinking about unit rates and ratios. • Doggy Day Care
3 - Strategic reasoning using equations and rates. • The Amazing Race Adventure
3 - Strategic reasoning using proportions. • Become a Real Estate Expert
3 - Strategic reasoning using simple financial plans and
• Diligent Deductions
percentages.
3 - Strategic reasoning about volume and surface area. • Packaging Sporting Goods
3 - Strategic thinking about irrational numbers and approximating
• Perfect Platforms 2
them.
Class 9 Mindsets Challenge
2 - Procedural fluency with calculating unit rates and applying
• Sales Ramp
proportional reasoning.
3 - Strategic reasoning using unit rates and the graphs of • Where to Work: Tech Career
proportional relationships. • Where to Work: Road to College
3 - Strategic reasoning about random and representative samples. • Teen Gym
3 - Strategic reasoning about volume. • Space Mission
Class 10 Mindsets Challenge
2 - Procedural fluency in solving systems of 2 linear equations. • You've Been Cheated!
2 - Procedural fluency with solving systems of equations. • You've Been Cheated... Again!
2 - Application of skills and concepts of arithmetic and geometric
• Electric Cars 1
sequences.
3 - Strategic reasoning about arithmetic and geometric
• Electric Cars 2
sequences.
Class 11 Mindsets Challenge
3 - Strategic reasoning about functions. • Sunset Sales
© Mindsets Learning 2022 13Science Depth of Knowledge (DOK)
Class 7 Mindsets Challenge
2 - Procedural fluency in distinguishing between chemical and
• Bouncy Balls
physical changes.
2 - Procedural fluency with distinguishing between a physical and
• The Case for Casein
chemical change.
3 - Strategic thinking through application of the principles of heat
• Too Hot to Handle!
transfer.
Class 8 Mindsets Challenge
3 - Students apply strategic thinking to designing, building, and • Reduce, Reuse, Recycle:
testing shopping bag and then reflecting on improvements. Shopping Bags
© Mindsets Learning 2022 14Math Appendix
Class 6
Algebra
Introduction to algebra: Introduction to variable through patterns and through appropriate word
problems and generalisations (example 5 × 1 = 5 etc.).
Introduction to algebra: Generate such patterns with more examples.
Introduction to algebra: Introduction to unknowns through examples with simple contexts (single
operations).
Data Handling
What is data - choosing data to examine a hypothesis?
Collection and organisation of data - examples of organising it in tally bars and a table.
Pictograph - Need for scaling in pictographs interpretation & construction.
Making bar graphs for given data interpreting bar graphs.
Geometry
Basic Geometric ideas (2D): Introduction to geometry. Its linkage with and reflection in everyday
experience.
Basic Geometric ideas: Line, line segment, ray.
Basic Geometric ideas: Open and closed figures.
Basic Geometric ideas: Interior and exterior of closed figures.
Basic Geometric ideas: Curvilinear and linear boundaries.
Basic Geometric ideas: Angle - Vertex, arm, interior, and exterior.
Basic Geometric ideas: Triangle - vertices, sides, angles, interior and exterior, altitude and median.
Basic Geometric ideas: Quadrilateral — Sides, vertices, angles, diagonals, adjacent sides and opposite
sides (only convex quadrilateral are to be discussed), interior and exterior of a quadrilateral.
Basic Geometric ideas: Circle — Centre, radius, diameter, arc, sector, chord, segment, semicircle,
circumference, interior and exterior.
Understanding Elementary Shapes (2-D and 3-D): Measure of Line segment.
Understanding Elementary Shapes (2-D and 3-D): Measure of angles.
Understanding Elementary Shapes (2-D and 3-D): Pair of lines – Intersecting and perpendicular lines –
Parallel lines
Understanding Elementary Shapes (2-D and 3-D): Types of angles- acute, obtuse, right, straight, reflex,
complete and zero angle.
Understanding Elementary Shapes (2-D and 3-D): Classification of triangles (on the basis of sides, and
of angles).
Understanding Elementary Shapes (2-D and 3-D): Types of quadrilaterals – Trapezium, parallelogram,
rectangle, square, rhombus.
Understanding Elementary Shapes (2-D and 3-D): Simple polygons (introduction) (Up to octagons
regulars as well as non regular).
© Mindsets Learning 2022 15Understanding Elementary Shapes (2-D and 3-D): Identification of 3-D shapes: Cubes, Cuboids, cylinder,
sphere, cone, prism (triangular), pyramid (triangular and square) Identification and locating in the
surroundings.
Understanding Elementary Shapes (2-D and 3-D): Elements of 3-D figures. (Faces, Edges and vertices).
Understanding Elementary Shapes (2-D and 3-D): Nets for cube, cuboids, cylinders, cones and
tetrahedrons.
Symmetry: (reflection) Observation and identification of 2-D symmetrical objects for reflection
symmetry.
Symmetry: (reflection) Operation of reflection (taking mirror images) of simple 2-D objects.
Symmetry: (reflection) Recognising reflection symmetry (identifying axes).
Constructions: Drawing of a line segment.
Constructions: Construction of circle.
Constructions: Perpendicular bisector.
Constructions: Construction of angles (using protractor).
Constructions: Angle 60°, 120° (Using Compasses).
Constructions: Angle bisector- making angles of 30°, 45°, 90° etc. (using compasses).
Constructions: Angle equal to a given angle (using compass).
Constructions: Drawing a line perpendicular to a given line from a point a) on the line b) outside the
line.
Mensuration
Concept of Perimeter and introduction to area: Introduction and general understanding of perimeter
using many shapes. Shapes of different kinds with the same perimeter. Concept of area, Area of a
rectangle and a square Counter examples to different misconcepts related to perimeter and area.
Perimeter of a rectangle – and its special case – a square. Deducing the formula of the perimeter for a
rectangle and then a square through pattern and generalisation.
Number System
Knowing our Numbers: Consolidating the sense of numberness up to 5 digits, Size, estimation of
numbers, identifying smaller, larger, etc. Place value (recapitulation and extension), connectives: use of
symbols =, and use of brackets, word problems on number operations involving large numbers up to a
maximum of 5 digits in the answer after all operations. This would include conversions of units of length
& mass (from the larger to the smaller units), estimation of outcome of number operations. Introduction
to a sense of the largeness of, and initial familiarity with, large numbers up to 8 digits and
approximation of large numbers).
Playing with Numbers: Simplification of brackets, Multiples and factors, divisibility rule of 2, 3, 4, 5, 6, 8,
9, 10, 11. (All these through observing patterns. Children would be helped in deducing some and then
asked to derive some that are a combination of the basic patterns of divisibility.) Even/odd and
prime/composite numbers, Co-prime numbers, prime factorisation, every number can be written as
products of prime factors. HCF and LCM, prime factorization and division method for HCF and LCM, the
property LCM × HCF = product of two numbers. All this is to be embedded in contexts that bring out
the significance and provide motivation to the child for learning these ideas.
Whole numbers: Natural numbers, whole numbers, properties of numbers (commutative, associative,
distributive, additive identity, multiplicative identity), number line. Seeing patterns, identifying and
formulating rules to be done by children. (As familiarity with algebra grows, the child can express the
generic pattern.)
© Mindsets Learning 2022 16Negative numbers and integers: How negative numbers arise, models of negative numbers, connection
to daily life, ordering of negative numbers, representation of negative numbers on number line.
Children to see patterns, identify and formulate rules. What are integers, identification of integers on
the number line, operation of addition and subtraction of integers, showing the operations on the
number line (addition of negative integer reduces the value of the number) comparison of integers,
ordering of integers.
Fractions: Revision of what a fraction is, Fraction as a part of whole, Representation of fractions
(pictorially and on number line), fraction as a division, proper, improper & mixed fractions, equivalent
fractions, comparison of fractions, addition and subtraction of fractions (Avoid large and complicated
unnecessary tasks). (Moving towards abstraction in fractions) Review of the idea of a decimal fraction,
place value in the context of decimal fraction, inter conversion of fractions and decimal fractions (avoid
recurring decimals at this stage), word problems involving addition and subtraction of decimals (two
operations together on money, mass, length and temperature).
Ratio and Proportion
Concept of Ratio.
Proportion as equality of two ratios.
Unitary method (with only direct variation implied).
Word problems.
Class 7
Algebra
Generate algebraic expressions (simple) involving one or two variables.
Identifying constants, coefficient, powers.
Like and unlike terms, degree of expressions e.g., x² y etc. (exponent≤ 3, number of variables)
Addition, subtraction of algebraic expressions (coefficients should be integers).
Simple linear equations in one variable (in contextual problems) with two operations (avoid complicated
coefficients).
Data Handling
Collection and organisation of data – choosing the data to collect for a hypothesis testing.
Mean, median and mode of ungrouped data – understanding what they represent.
Constructing bargraphs.
Feel of probability using data through experiments. Notion of chance in events like tossing coins, dice
etc. Tabulating and counting occurrences of 1 through 6 in a number of throws. Comparing the
observation with that for a coin. Observing strings of throws, notion of randomness.
Geometry
Understanding shapes: Pairs of angles (linear, supplementary, complementary, adjacent, vertically
opposite) (verification and simple proof of vertically opposite angles).
Understanding shapes: Properties of parallel lines with transversal (alternate, corresponding, interior,
exterior angles).
Properties of triangles.
Properties of triangles: Angle sum property (with notions of proof & verification through paper folding,
proofs using property of parallel lines, difference between proof and verification.)
Properties of triangles: Exterior angle property.
Properties of triangles: Sum of two sides of a triangle is greater than the length of the third side.
© Mindsets Learning 2022 17Properties of triangles: Pythagoras Theorem (Verification only).
Symmetry: Recalling reflection symmetry.
Symmetry: Idea of rotational symmetry, observations of rotational symmetry of 2-D objects. (90
degrees, 120 degrees, 180 degrees).
Symmetry: Operation of rotation through 90 and 180 degrees of simple figures.
Symmetry: Examples of figures with both rotation and reflection symmetry (both operations).
Examples of figures that have reflection and rotation symmetry and vice-versa.
Representing 3-D in 2-D: Drawing 3-D figures in 2-D showing hidden faces.
Representing 3-D in 2-D: Identification and counting of vertices, edges, faces, nets (for cubes cuboids,
and cylinders, cones).
Representing 3-D in 2-D: Matching pictures with objects (Identifying names).
Representing 3-D in 2-D: Mapping the space around approximately through visual estimation.
Congruence: Congruence through superposition (examples: blades, stamps, etc.).
Congruence: Extend congruence to simple geometrical shapes e.g. triangles, circles.
Congruence: Criteria of congruence (by verification) SSS, SAS, ASA, RHS.
Construction (Using scale, protractor, compass).
Construction of a line parallel to a given line from a point outside it.(Simple proof as remark with the
reasoning of alternate angles).
Construction of simple triangles. Like given three sides, given a side and two angles on it, given two
sides and the angle between them.
Mensuration
Revision of perimeter, Circumference of Circle, Idea of Area Concept of measurement using a basic unit
area of a square, rectangle, triangle, parallelogram and circle, area between two rectangles and two
concentric circles.
Number System
Knowing our Numbers: Integers.
Multiplication and division of integers (through patterns). Division by zero is meaningless.
Properties of integers (including identities for addition & multiplication, commutative, associative,
distributive) (through patterns). These would include examples from whole numbers as well. Involve
expressing commutative and associative properties in a general form. Construction of
counterexamples, including some by children. Counter examples like subtraction is not commutative.
Word problems including integers (all operations).
Fractions and rational numbers.
Multiplication of fractions.
Fraction as an operator.
Reciprocal of a fraction.
Division of fractions.
Word problems involving mixed fractions.
Introduction to rational numbers (with representation on number line).
Operations on rational numbers (all operations).
Representation of rational number as a decimal.
© Mindsets Learning 2022 18Word problems on rational numbers (all operations).
Multiplication and division of decimal fractions.
Conversion of units (length & mass).
Word problems (including all operations).
Powers.
Exponents only natural numbers.
Laws of exponents (through observing patterns to arrive at generalisation.)
Ratio and Proportion
Ratio and proportion (revision).
Unitary method continued, consolidation, general expression.
Percentage - an introduction.
Understanding percentage as a fraction with denominator 100.
Converting fractions and decimals into percentage and vice-versa.
Application to profit and loss (single transaction only).
Application to simple interest (time period in complete years).
Class 8
Algebra
Algebraic Expressions: Multiplication and division of algebraic exp.(Coefficient should be integers).
Some common errors (e.g. 2 + x ≠ 2x, 7x + y ≠ 7xy )
Identities (a ± b)² = a² ± 2ab + b², a² – b² = (a – b) (a + b), Factorisation (simple cases only) as
examples the following types a(x + y), (x ± y)², a² – b², (x + a).(x + b).
Solving linear equations in one variable in contextual problems involving multiplication and division
(word problems) (avoid complex coefficient in the equations).
Data Handling
Reading bar-graphs, ungrouped data, arranging it into groups, representation of grouped data through
bar-graphs, constructing and interpreting bar-graphs.
Simple Pie charts with reasonable data numbers.
Consolidating and generalising the notion of chance in events like tossing coins, dice etc. Relating it to
chance in life events. Visual representation of frequency outcomes of repeated throws of the same kind
of coins or dice. Throwing a large number of identical dice/coins together and aggregating the result of
the throws to get large number of individual events. Observing the aggregating numbers over a large
number of repeated events. Comparing with the data for a coin. Observing strings of throws, notion of
randomness.
Geometry
Understanding shapes: Properties of quadrilaterals – Sum of angles of a quadrilateral is equal to 360
degrees (By verification).
Understanding shapes: Properties of parallelogram (By verification) (i) Opposite sides of a parallelogram
are equal, (ii) Opposite angles of a parallelogram are equal, (iii) Diagonals of a parallelogram bisect
each other. [Why (iv), (v) and (vi) follow from (ii)] (iv) Diagonals of a rectangle are equal and bisect
each other. (v) Diagonals of a rhombus bisect each other at right angles. (vi) Diagonals of a square are
equal and bisect each other at right angles.
© Mindsets Learning 2022 19Represent 3-D in 2-D: Identify and Match pictures with objects [more complicated e.g. nested, joint 2-D
and 3-D shapes (not more than 2)].
Represent 3-D in 2-D: Drawing 2-D representation of 3-D objects (Continued and extended).
Represent 3-D in 2-D: Counting vertices, edges & faces & verifying Euler’s relation for 3-D figures with
flat faces (cubes, cuboids, tetrahedrons, prisms and pyramids).
Construction of quadrilaterals: Given 4 sides and 1 diagonal.
Construction of quadrilaterals: Given 3 sides and 2 diagonals.
Construction of quadrilaterals: Three sides and two included angles.
Construction of quadrilaterals: Two adjacent sides and three angles.
Graphs
Preliminaries: Axes (Same units), Cartesian Plane.
Preliminaries: Plotting points for different kind of situations (perimeter vs length for squares, area as a
function of side of a square, plotting of multiples of different numbers, simple interest vs number of
years etc.)
Preliminaries: Reading off from the graphs - Reading of linear graphs - Reading of distance vs time
graph
Mensuration
Area of a trapezium and a polygon.
Concept of volume, measurement of volume using a basic unit, volume of a cube, cuboid and cylinder.
Volume and capacity (measurement of capacity)
Surface area of a cube, cuboid, cylinder.
Number System
Rational numbers.
Properties of rational numbers. (including identities). Using general form of expression to describe
properties.
Consolidation of operations on rational numbers.
Representation of rational numbers on the number line.
Between any two rational numbers there lies another rational number (Making children see that if we
take two rational numbers then unlike for whole numbers, in this case you can keep finding more and
more numbers that lie between them.)
Word problem (higher logic, two operations, including ideas like area).
Powers.
Integers as exponents.
Laws of exponents with integral powers.
Squares, Square roots, Cubes, Cube roots.
Square and Square roots.
Square roots using factor method and division method for numbers containing (a) no more than total 4
digits and (b) no more than 2 decimal places.
Cubes and cubes roots (only factor method for numbers containing at most 3 digits).
Estimating square roots and cube roots. Learning the process of moving nearer to the required number.
Playing with numbers.
© Mindsets Learning 2022 20Writing and understanding a 2 and 3 digit number in generalized form (100a + 10b + c , where a, b, c
can be only digit 0-9) and engaging with various puzzles concerning this. (Like finding the missing
numerals represented by alphabets in sums involving any of the four operations.) Children to solve and
create problems and puzzles.
Number puzzles and games.
Deducing the divisibility test rules of 2, 3, 5, 9, 10 for a two or three-digit number expressed in the
general form.
Ratio and Proportion
Slightly advanced problems involving applications on percentages, profit & loss, overhead expenses,
discount, tax.
Difference between simple and compound interest (compounded yearly up to 3 years or half-yearly up
to 3 steps only), Arriving at the formula for compound interest through patterns and using it for simple
problems.
Direct variation – Simple and direct word problems.
Inverse variation – Simple and direct word problems.
Time & work problems– Simple and direct word problems.
Class 9
Coordinate Geometry
The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane,
notations, plotting points in the plane.
Geometry
Lines and angles: 1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so
formed is 180 degrees and the converse. 2. (Prove) If two lines intersect, vertically opposite angles are
equal. 3. (Motivate) Results on corresponding angles, alternate angles, interior angles when a
transversal intersects two parallel lines. 4. (Motivate) Lines which are parallel to a given line are
parallel. 5. (Prove) The sum of the angles of a triangle is 180 degrees. 6. (Motivate) If a side of a
triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite
angles.
Triangles: 1. (Motivate) Two triangles are congruent if any two sides and the included angle of one
triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence). 2.
(Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the
other triangle (SSS Congruence). 3. (Motivate) Two right triangles are congruent if the hypotenuse and
a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS
Congruence) 4. (Prove) The angles opposite to equal sides of a triangle are equal. 5. (Motivate) The
sides opposite to equal angles of a triangle are equal.
Quadrilaterals: 1. (Prove) The diagonal divides a parallelogram into two congruent triangles. 2.
(Motivate) In a parallelogram opposite sides are equal, and conversely. 3. (Motivate) In a parallelogram
opposite angles are equal, and conversely. 4. (Motivate) A quadrilateral is a parallelogram if a pair of its
opposite sides is parallel and equal. 5. (Motivate) In a parallelogram, the diagonals bisect each other
and conversely. 6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is
parallel to the third side and in half of it and (motivate) its converse.
© Mindsets Learning 2022 21Circles: Through examples, arrive at definition of circle and related concepts-radius, circumference,
diameter, chord, arc, secant, sector, segment, subtended angle. 1. (Prove) Equal chords of a circle
subtend equal angles at the center and (motivate) its converse. 2. (Motivate) The perpendicular from
the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of
a circle to bisect a chord is perpendicular to the chord. 3. (Motivate) Equal chords of a circle (or of
congruent circles) are equidistant from the center (or their respective centers) and conversely. 4.
(Prove) The angle subtended by an arc at the center is double the angle subtended by it at any point on
the remaining part of the circle. 5. (Motivate) Angles in the same segment of a circle are equal. 6.
(Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its
converse.
Constructions: 1. Construction of bisectors of line segments and angles of measure 60 degrees, 90
degrees, 45 degrees etc., equilateral triangles. 2. Construction of a triangle given its base,
sum/difference of the other two sides and one base angle.
Linear Equations in 2 variables
Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear
equations of the type ax+by+c=0. Explain that a linear equation in two variables has infinitely many
solutions and justify their being written as ordered pairs of real numbers, plotting them and showing
that they lie on a line. Graph of linear equations in two variables. Examples, problems from real life with
algebraic and graphical solutions being done simultaneously.
Mensuration
Area of a triangle using Heron's formula (without proof)
Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular
cylinders/cones.
Polynomials
Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a
polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear,
quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a
polynomial. Factorization of ax² + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic
polynomials using the Factor Theorem.
Real Numbers
Review of representation of natural numbers, integers, rational numbers on the number line. Rational
numbers as recurring/ terminating decimals. Operations on real numbers.
Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational
numbers) such as √2, √3, and their representation on the number line.
Rationalization (with precise meaning) of real numbers of the type 1/(a+b*√x) and 1/(√x+√y) (and their
combinations) where x and y are natural number and a and b are integers.
Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be
done by particular cases, allowing learner to arrive at the general laws.)
Statistics
Introduction to Statistics: Collection of data, presentation of data — tabular form, ungrouped / grouped,
bar graphs
Statistics and Probability
History, Repeated experiments and observed frequency approach to probability. Focus is on empirical
probability. (A large amount of time to be devoted to group and to individual activities to motivate the
concept; the experiments to be drawn from real - life situations, and from examples used in the chapter
on statistics).
© Mindsets Learning 2022 22Class 10
Arithmetic Progressions
Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of
A.P.
Lines
Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section
formula (internal division).
Pair of linear equations in two variables
Pair of linear equations in two variables and graphical method of their solution,
consistency/inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear
equations in two variables algebraically - by substitution, by elimination. Simple situational problems.
Simple problems on equations reducible to linear equations.
Class 11
Relationships and Functions
Ordered pairs. Cartesian product of sets. Number of elements in the Cartesian product of two finite
sets. Cartesian product of the set of reals with itself ( R x R only).Definition of relation, pictorial
diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Pictorial
representation of a function, domain, co-domain and range of a function. Real valued functions, domain
and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential,
logarithmic and greatest integer functions, with their graphs.
© Mindsets Learning 2022 23Science Appendix
Class 7
Materials
What is heat?
How things change/react with one another.
Class 8
Materials
Materials in daily life.
How things change/react with one another.
© Mindsets Learning 2022 24You can also read
