Edit — Intro to algebra - Worksheet Generator

Details

Title *

Subject

Class / Grade

Content

Update content (optional)

Keep existing PDF Upload Camera / Photo Manual Input

Current source: manual-input

18,186 characters of extracted content

===== PAGE 1 =====
“Ss introduction tc
:. £& pra 7
Warm-up ™&" —
Amaya and her mother go to the nearby market to buy some items. *
1, Amaya has a basket of 50 cherries. Her mother gives her 30 more cherries. 7
_ How many cherries does Ananya have itt total? .......0000 a
2. She buys five chocolates. She will give two chocolates to her friends. 7
How many chocolates will be left with her? .......00s06 ; ie
_ 3. Her mother buys 5 pens each costing % 15. iY «BA
The total cost of § pens is... Lae Bg ff
4, Amaya buys 130 sheets of paper for her brother’s project. —— S WS
Her brother has to make $ books with 130 sheets. 14 ‘
How many sheets of paper will each book have? \ V
| , mee Learning Objectives
. In this chapter, you will learn abo id re
0 aaa | © Variables and constants os
: Ax ahs 3 || ¢ Variables in rules
© 3¢=¢ q || ¢ Algebraic expressions ia
a Ya) , [| * Using expressions practically a
, = ; Bre —_ — ~
t “i a
— £ _swonder, why are Yeah, it is | ke
ff weusing letters secret code to fine
4 __ instead of numbers | i s ae numbdels.
' eS i “iy
ee Rit
ao ta
3

===== PAGE 2 =====
m an auditorium, seats are arranged in such a way that the first row kontanis 5 ahh the
ond row has 10 seats, the third row has 15 seats and so on, Amaya is sitting in the
Oth row. How can we find the number of seats in the row where Amaya is seated?
(in algebra, letters (such asx, y, 2,4,
 b...) representing the value of a
| number are known as ‘literals’ or
= can
…[truncated]

===== PAGE 1 =====
“Ss introduction tc
:. £& pra 7
Warm-up ™&" —
Amaya and her mother go to the nearby market to buy some items. *
1, Amaya has a basket of 50 cherries. Her mother gives her 30 more cherries. 7
_ How many cherries does Ananya have itt total? .......0000 a
2. She buys five chocolates. She will give two chocolates to her friends. 7
How many chocolates will be left with her? .......00s06 ; ie
_ 3. Her mother buys 5 pens each costing % 15. iY «BA
The total cost of § pens is... Lae Bg ff
4, Amaya buys 130 sheets of paper for her brother’s project. —— S WS
Her brother has to make $ books with 130 sheets. 14 ‘
How many sheets of paper will each book have? \ V
| , mee Learning Objectives
. In this chapter, you will learn abo id re
0 aaa | © Variables and constants os
: Ax ahs 3 || ¢ Variables in rules
© 3¢=¢ q || ¢ Algebraic expressions ia
a Ya) , [| * Using expressions practically a
, = ; Bre —_ — ~
t “i a
— £ _swonder, why are Yeah, it is | ke
ff weusing letters secret code to fine
4 __ instead of numbers | i s ae numbdels.
' eS i “iy
ee Rit
ao ta
3

===== PAGE 2 =====
m an auditorium, seats are arranged in such a way that the first row kontanis 5 ahh the
ond row has 10 seats, the third row has 15 seats and so on, Amaya is sitting in the
Oth row. How can we find the number of seats in the row where Amaya is seated?
(in algebra, letters (such asx, y, 2,4,
 b...) representing the value of a
| number are known as ‘literals’ or
= can find the answer by making a table.
m you analyse the table? 5
‘The number of seats in the 10th foW iS verses A symbol which can
Do you find any pattern in the number of seats? ,. 5 git ong
Pon you Ala nist (ean called a variable. A symbol
amemnch en 810 AEH WY ~ which has a fixed numerical
uy~sing the table, we find a relationship between the rows and value is called a constant.
Tauimber of seats. ae AR ae :
Rt is, the number of seats is five times the row number, |
&S write the letter ‘x’ to represent the row numbers. eo ich Naat 4 caloh Mi 3
fa. the number of seats = 5 x x or 5x He i = | Coefficients oA
r<>w 1,x= 1, Number ofseas=5X1=5 f =D) i In 5x, 5 is called the numerical
tow 2,.x= CMs sath? AROS i coefficient of x. Similarly, x is called
— x = 2. Number of seats = > 7 \ ie fh ; Perit i the literal coefficient of 5. =
iow 11,x=................ Number of seats F 5x semmerrnine = arenes 4 In Oxy, 10's the numerical
Mw 12,x= Number of seats FSX cccessseseess Ssscssseeseesseeee £ Coefficient of xy and xy is the literal :
f. the x isa variable asx takes different values. But,the = | _ coefficient of 10. i
I<rical value remains the same, Thus, 5 isa constant. i ne nole ee xis * ni et i
S x is considered as a variable as the value of 5x will keep changing when i ee j * ee a ;
value of x changes. A combination of a variable and a constant, iftaken Bal
> Fun) 3 ecco neal ee ; me fal Reet
ER en nS fo CQuvmmansaanniian,
“Take some earbuds and try to make a square, Find out how many earbuds are required to make a square. :
Then, make two squares and find out the number of earbuds used to make them, Similarly, make 3, 4 and S F
squares and complete the following table, Did you recognise any pattern? i
tale SE Tea rel , z
Wi a |

===== PAGE 3 =====
a rae | a —— OES el th d
" ~(@) Exercise 7.1 :
1 1. There are 35 students in each class. How many students are there in the school? (Use the letter x bee

number of classes.) ©
2. Arun bought 20 books. Fach book costs 2 y. What is the total cost of 20 books? vi
3. Naina brought some cookies to school. She gave 10 cookies to her friends. How many cookies are| e!
(Use ‘c’ to show the number of cookies.) i,
4, If Meenu’s age is 10 years more than her sister's age, then write Meenu’s age in terms of her sister’s age. (I
age be y.) a
§. There are 15 students standing in a row in an assembly. If there are n rows, then how many students ¢
6. Rohan increased the temperature of the air conditioner by 5°C. What is the new temperature set for f
conditioner? (Use the letter x to show the increase in temperature.) a
Pui
Maths Connect 4 —— Cy
We often see cartons and packets in a grocery store. We can use algebra there too. For example, P she
sells x packets of milk daily, then how many packets of milk does he sell monthly? This can be expres
algebraically. Can you write down the algebraic expression for this statement? if a
| . ° Scientific : 4
Variables in Rules s
-S2 ” |wanted to decorate
k f es mother's day card using a yarn y
ig 3 & ; a border. The length and breadth of the K 5
we RB: card is 8 cm and 12 cm, respectively. Ni o>)
md My friend says that | would need > >
< 4 os 40cm yarn in total. | wonder how \ >
we does she know that. ak
4 “ HAPPY
2 MOTHERS DAY
Rules from Geometry a
We know how to find the perimeter of a rectangle, a square and a triangle. q
| The perimeter of any closed figure is the sum of all its sides, id
___ Perimeter of a Rectangle A a
Peri eter of a rectangle = Sum of all the sides a
i =AB+BC+CD+AD «
i =b+l+b+] ae
ie 5 : Eee —
Siemens 2 (1+ b) B liga
Lh os

===== PAGE 4 =====
Ls RAPE ay ABS 1 ca, Adee =
Let us take variable P as perimeter, |
: Thus, P = 2 x (1+)
D Here, | and b are also variables. You could take any variables apart from | and b as per your choice.
3 Perimeter of a Square A s D
TP AWe know that a square has foUr sce Sides,
4 So, the perimeter of a square is given by, $ $
BE + BC + CD-+ AD & Ae llsd ae,
Thus, P = 4s. Here, the variable 's’ stands for the sides of the square ABCD, B $ C
_ Perimeter of an Equilateral Triangle A
Now, let us find the perimeter of an equilateral triangle.
We know that in an equilateral triangle, all the sides are equal. a 4
Perimeter of an equilateral triangle = AB + ooo t scsssssssecssserses
Hence, P = 3a.
1 e e
! Cx Explain Your Thinking) i nite
: ‘i of How do you create a rule for the perimeter of a triangle with unequal sides? }
2 we ———™m————<—<—$——— = o
Rules from Arithmetic
Commutative Property “—
__ We have learned the properties of numbers. The commutative property under addition says that we can add
__Sumbers in any order. For example, 4 + 6 = 10 is the same as 6 + 4 = 10. This can be written in terms of
ae variables. Let us take a and b to be any two vari hen a + b = b+ where a and b can take on any values.
- Similarly, in the case of multiplication.a x h=) x a,
i a Bus § tear 2 f
__ Associative Property of Multiplication
___ We know that the associative property of multiplication says that while multiplying three numbers, the
product will always be the same regardless the grouping of the numbers. For example, (5 x 3) x 7 = 5 x
,. (3 x 7). Now, for -any three variables, a, b and.c_(q x b) Xc=ax (bx ¢) where a, b, ¢ can take any values.
Thus, the property satisfied by the numbers is generalised. :
. Distributive Property
_ Let us solve 99 x 8 by the distributive property,
99x 8=(100-1)x8=100x8-1x8
i bee — a — . Sane” %
"nes Wo tis. * ON oY
SS ee eu * £47 6 * CC ee

===== PAGE 5 =====
| : Exercise 7.2 7
| 1. Write the general rule to find the perimeter of: ie
a. an isosceles triangle f 14
b. arhombus | 1 iff C
2. Write the perimeter of the regular pentagon using variable |. a
3, The associative property of addition says that when three numbers are I a
added, the order in which they are added will not change their sum. Bes
Express this property as a general rule and variables. a
4, Generalise the additive identity property and multiplicative identity property using a variable. ce *
5. To find the area of a rectangle, we need to find the product of its length and breadth. Taking | as length an d
breadth, find the general rule for finding the area of a rectangle. es,
6. If the area of a square is side x side, find the general rule to calculate the area of the square taking the side ¢
the square as a. a
ea
> Gre-+* 0 a
Algebra in geometry 4 a
Material required: A pair of scissors, plain sheet of paper, marker, glue BS a
Activity: Cut the paper into square shapes (identical squares). Stick them together to form a cube ( nee
dimensional figure). ag
a. Now, you have a cube whose six faces are identical squares. If the length of an edge of the cube is give
by y, find the formula for the total length of the edges of a cube. ie
b. Place one of the square sheets on the floor and go round the square x times while counting every co 7
twice and no more. How will the counting be expressed algebraically? re
c. To get a value equal to 34, find the number of corners you have to pass through. sia
= ae TON EH NR tail nid a
Al. ah e ° Scientifi — |
Algebraic Expressions (ersiceney{Consptual understanding) ey
" : i E .
ee An express
BUEDE EXPFESSION le 58) formed using
mbersandoneor Seen (71 constants
basic operations. ae NT | J mathematicale
or exaMp @2+3, le y is called an al

===== PAGE 6 =====
— $% Ls Ls aren A eee Ne Oe ee mf i.
Le Me v ; * Xi ~
: { ‘ -
‘ braic Expressi " {
| Eraming an Algebrale Expression
Nee can convert a statement into an algebraic expression. ieee
Sor example, the statement’3 added to a number’ can be converted into an algebraic expression 7) ral gaa eie
Hy taking the unknown number as the variable ‘x’. Reais
Ate Sa 249
Then, the expression will be‘3 +x’, sitnar#!
How will you write'7 multiplied toa number’? cians
Value of an Algebraic Expression
As you know, a variable cannot have a fixed value. So, the value of an algebraic expression can be found by
assigning any value to the variable,
Let us solve the expression 5x-8forx=2. 0
1. The value of xis... alias ee
a i. omo (fy ain Ti ii ae |
> ZN Z << i i ,
; OSS = Material required: ) Colour pencils, grid paper 0
Activ: h | foo. 1. Write an algebraic expression of your own with any chosen variable. q
: ~g ST 2. Now, solve the expression by putting any values for the variable. I
} 3. Colour the grid to shéw the number you get after solving. Q
4, If you get a whole number, colour the squares with red colour. If you get an integer, colour the squares { |
} with yellow colouring, in amr 0
if 5. If you get a fraction or a decimal, try again till you get a whole number or an integer. |
|
9) Exercise 7.3 ——
ort the following as arithmetic expressions or algebraic expressions. S) See
b 7x2+3-2 ob xt c 12y Saag
oat. 3\- 2 e, 10y — 6x f, 2x + Sy
e algebraic expressions for the following statements,
ded fo 6m b. 10 subtracted from a c, 15 mes x
Hiplied with yaddedto} = e. Twice the product of x and y
of y added to th difference of x and 3
,y=2] 1 0 x= 3y+5[x=1,y=2] c 100x+50y[x=ly=1)
4) e xtytz[x=12,y=10,2=3] f 2x+ iy t2[x=ly=3,2=4]
yo reo®

===== PAGE 7 =====
e —  ! 22°, = a a a ——— oe Ps
Using Expressions Practically (ce [Conceptual understanding ) ff
Sui, i
Ihave 10 / Howdowe ™
more pencils ae write this statement
than you. (COR as an algebraic
- a v expression? ag
i) v td
—4 a
<< * w& ¥ i
To help Manu, let us take the variable x for the number of pencils Manu has. 4
Then, we could express the situation as:
Manu’s sister has x + 10 pencils. a
1. Express as an algebraic expression: Anu is 2 years younger than Manu. ; a {
2. Express ‘How old was Anu 3 years ago?’ as an algebraic expression. a ’
Exercise 7.4 a
1. The breadth of a rectangle is 2 m less than thrice its length. What is the breadth of the rectangle if the len th
2. Saran’s age is 30 years less than his mother’s age. What was his age 2 years back? be
3. Asquare has a side 5 cm less than the length of a rectangle. What will be the perimeter of the square if th
. length of the rectangle is y m? ve
4, The cost of a pen is €x and the cost of a pencil is ¥y. What will be the total amount Sarath will have oP
buys 10 pens and 12 pencils? i
§. The weight of two types of cartons are x kg and y kg. What will be the total weight of 15 cartons of each
7. maya thought of a number. She multiplied it by 7 and added 18 to the result. Express it in algebraic fort
considering the number to be y. “ff
# - an!, om
sy oy a ‘i
aber of students trying for a solo part in a chorus concert, Only 6 will be chosen. H
vill not be chosen? ie
n Grade 6, x number of students are performing a group dance and 6 are pert
dents are not performing at all. Express y in an algebraic expression. on.
tem ee . " pictstante soi

===== PAGE 8 =====
446 6 Oe
Introduction to Algebra @ e@ @
{ Algebra is a branch of mathematics that F
i deals with letters and mathematical ‘ \
4 symbols when solving problems. }
: d Variables and Constant 4 @
} Variables are quantities which can take i
: different values. i
q Constants have a fixed numerical value. i
: Expressions formed using variables along : } The value of an algebraic expression i
} with constants and mathematical operations ¥ can be found by assigning any value
4 are called algebraic expressions, } £ to the variable. i
j i
; Algebra Variables Constants Literals é
SU BS SE LTS OSLO SRE ONENESS SPN oe
THINK TAC TOE: Let us explore.
= Write the expressions fordistributive | Write an algebraic expression with Write the same algebraicexpression _| Frame any practical situation for the
< ‘property under addition and subtraction variablex which givesthevalue Owhen | with variable x and solve for x= 3. given algebraic expression.
>) arithmetically and algebraically. solving forx=2.
i
St brie {2949093
Student Self-Assessment Rubric
"can't do it by myself. Ineed help, Ican do it by myselfl I can do it without mistakes.
Ss I don’t understand it yet. Iam starting to understand, I make some mistakes, I can help others
'<
ag Reid <
~<a

===== PAGE 9 =====
| owe " © 0 e%s6
| \ Chapter Review STITT TT LLL LLLLLULUAL LULL LEPC
D)_ MunnEcHorqursion LFuENcY BE) i
1, Letters used along with numbers in algebra are called... a a
a. variables b. variant c. letters d. numerals
Qe oeeseseeseesseesss have a fixed numerical value. a
a. Variables b. Literals c. Literal numbers d. Constants
3. 5 times x can be written as: Be
a. Ue b, S+x c. 5x d 52% »
4. Name the property: (a x b) X c=a X (b XC). ay
a. Commutative property b. Distributive property 3
c. Additive identity d. Associative property a
5. 10 added to a number can be written as... A
a 10-x b. 10x c. 10+x d. 10 ee
a fei
6. The general rule to find the perimeter of a square if one side of the square is ‘a’ is given by: a
a. 3a b. 2a c. 4a d. 4+a ae
7. The general rule to find the perimeter of a rectangle if length and breadth of the rectangle are | and b, Sf %
a. 4(1 +b) b. 2(1+b) c. 3(1+b) d. (+b)
8. The algebraic expression for 8 subtracted from the product of x and y is: re é
| a x8 b. xy +8 c x+y-8 d. 8-x Bt,
ia
9. If each box contains 100 toffees, the number of toffees required to fill n such boxes is: % ss
a. 100 +n b. 100n c, 100+n d. 100-n Rae
10. fx=5, thenx-3 4288s Be
| a. 4 b. 0 cd? d. 1 as
__ SUBJECTIVE QUESTIONS PROBLEM-SOLVING }llibcJe |
3 1. Find the value of the algebraic equation: 20y + 30x —10 for x = 4 and y = 3. My 7
_ 2, Savitha is half the age of her mother. Find the age of both after 10 years. 7
3, Write the algebraic statement for 10 — 2x. aa
the perimeter of a regular heptagon is x m, then write the general rule for the length of each side.
ert these expressions into statements in ordinary language: Cost of 1 kg oranges is &x. Cost of 1k
; Fom pwice a number, Write the algebraic expression and find the value of the express
ic expression for two consecutive odd integers, 4
ion for two consecutive even in ie

===== PAGE 10 =====
. a TTT PT yr iyrm rated specs heat me we oe elt toe hee cent Sie en ten Y Reais tT Te ' de Sat ‘ah ed,
be bet bt bad { i ae
e'e'8 6 0 ad ;
AVRAR Le
-somnnnnannnns))))))))))))))
ie
11. Anil’s monthly salary 1s ‘s’ rupees, Find his salary in one year.
12. Rahul's weight is 30 kg. His weight increases by x kg every year. What will be his weight after 5 years?
13. x students plan a one-day tour, $150 is collected from each student, out of which, 71500 is paid in advance as bus
fare. Find the money left with x students,
14. Justify each of the following situations using one of the rules from arithmetic: commutative property of addition,
commutative property of multiplication, distributive property of multiplication over addition. |
a. Lohitha and Bavya are two sisters. On Monday/Lohitha bought 3 cupcakes and Bavya bought 6 cupcakes as
evening snacks. Next day, Lohitha bought 6 cupcakes and Bavya bought 3 cupcakes as evening snacks. Find out the
total number of cupcakes they bought on each day and identify the rule being justified.
b. Two friends order breakfast from a food court. They order a combo pack of 2 sandwiches and a glass of juice
each. Write an expression using distributivity of numbers for the total quantity of food they purchased.
c. Rema and Seema are friends. Rema has 3 boxes with her and each box carries 8 apples. Seema has a total of
8 boxes which have 3 apples each. Calculate how many apples each has in total and identify the arithmetic rule
applied to find this. ‘
PANALVSIS & CREATING EPRI T=
15. Frame 5 situations and write algebraic expressions to express them.
16. Draw any regular polygon and find the general rule for calculating its perimeter.
|
17. Complete the table by taking 5 different values for x.
18. Look at the following matchstick pattern of the letter E. |
: |
serve th e patterns and find the rule that gives the total number of matchsticks.
e remove mare! stick from the middle, what is the pattern obtained? Find a rule for the new pattern.
At; ar? 54 j
gle path, you need three matchsticks, For a 2-triangle path, you could add 2 more matchsticks attached
mangle, Ina: similar manner, by attaching two more matchsticks to the 2-triangle path, you could create
this same pattern of forming triangle paths, how many extra matchsticks would be needed to
any match: ticks would be required for arranging an 8-triangle path?
ber of matchstick 9 requi red to make an n-triangle path. i
many extra migicbat s would be needed for 4 types of such triangular

Replaces all existing content with what you type here.

Cancel

About editing

Details — changing the title, subject, or class only affects how the material is labelled. Previously generated worksheets are unaffected.

Replacing content — swapping in a new PDF, image, or manual text will be used for any worksheets generated after the update. Existing worksheets are unchanged.

Camera / Photo — the image is stored and GPT-4o Vision reads it each time you generate a worksheet from this material.