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             \ 18-Aug-2025                      Surender Prajapati   Proof-6              Reader’s Sign _______________________ Date __________






                  Features oF the Book
                                                                             GET READY!
                                                                        Sneha and her family are sitting in a living room spending quality time.
                                                                                               Papa! I want to distribute    That's great!
                                                                                              some stationery items to an
                                                                                               orphanage on my birthday.
                  1
                                       Integers

                Learning Objectives
                After studying this chapter, students will be able to...
                                                        Scan to learn
                  recall the concept of integers and addition and subtraction of integers and their properties
                                                                         What is this, and
                  understand the multiplication of integers and their properties
                  understand the division of integers and their properties
                                                                         why are we using
                                                                           ‘x’ in math?
                                                                                                You should buy some notebooks and 8 more
                Learning Objectives—at the                                                     pencils than the double of notebooks. Suppose, if
                    GET READY!
                beginning of each chapter to                                                    you buy ‘x’ notebooks, then you should buy
                                                                                                   (2x + 8) pencils to distribute.
                set the goals of study.              Get Ready—for
                On Environment Day, a school has decided to show the documentary film 'Life Below Water' to its students.
                  Oceans are our planet's life support
                 as they provide water and food and
                  help regulate the weather. So, we   quick and easy
                  should not pollute our oceans.
                                                     recapitulation
                                                     through Maths talk.      Get it Right—
                     Think and Answer—                                        for avoiding the      Get it right!
               Do you know?  interspersed within the                          common errors       (–1) 51  × (–1) 49  = (–1) 51 × 49
               of the ocean? text for checking the   Ruhi! How deep can a     by learners         3 5  × 5 3  = 3 5 + 3
               The deepest part                                               committed           (–1) 51  × (–1) 49  = (–1) 51 + 49  = (–1) 100
                               It is around 36089 ft or 11 km
                     understanding of the       we represent it in an integer?  while doing       3 5  × 2 5  = 2 5 + 5
                                                human go in the ocean? Can
                               deep from the sea level. We can
                               write it in integers as –36089 ft.
                     concept learnt in the                                    calculations.       3 5  × 3 6  = 3 5 + 6
                     class.
                   Yes, my father told me
                   once ‘The Challenger Deep’
                  at the Marina Trench is the
                   deepest part of the ocean.                                Brain Sizzlers
                                                                            (a)     The net given below in the given figure can be used to make a cube.
                         Think and Answer                                                        (ii) Which edge meets DE?
                                                                               (i) Which edge meets AN?    I  H
                      Can you identify the name of related
                                                                                             L  K  J  G
                      angle  formed  between  the  angles
                                   7                                                       N M
                                                        Brain Sizzlers—
                      south-east to south-west and south-                                    B  D  E  F              4  3
                      west to north-west? Name it.                                         A  C                      5  6
                                                        to focus on 21st    (b)     Two dice are placed side by side as shown, can you determine the total of the numbers
                              North                                          opposite to (i) 5 + 6 (ii) 4 + 3
                         North-West
                                 North-East             Century skills in
                         West                           teaching, learning
                                   East
                                                        and assessment.
                         South-West  South-East
                              South
                                                           Knowledge Desk—
                                                           includes additional
                                                           interesting information/      Knowledge Desk
                                                           facts based on the
                     Activity—to engage children in        topics discussed            ‘Statistics’ is a branch of mathematics
                     mathematical discussion and                                       that deals with the collection, presentation,
                     activities to establish a learning                                analysis, and interpretation of data. It helps
                     environment of fun and enjoyment.                                 in understanding and drawing conclusions
                                                                                       from the given data using various methods to
                   activity                                                            summarise and interpret numerical information.
                 Steps of construction:
                 Drawing a perpendicular bisector of a line using a transparent tape, a pair of scissors, and a pencil.
                  1.  Draw a line segment  AB
                                        A
                                                    B
                  2.  Place a strip of transparent tape diagonally across AB as shown in the figure.
                                        A
                                                    B
                  3.     Repeat step 2 by placing another tape over  A  4.
                   and B just diagonally across the previous one.   Join M and N.  MN  is the perpendicular bisector of
                   Both the strips cross at M and N.
                                              AB .  Verify it using a ruler and a protractor.
                              M
                                                            M
                        A
                                    B                A
                              N                                  B
                                                          N
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