Constructing and reading algebraic expressions

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Budowanie i odczytywanie wyrażeń algebraicznych

Learning objectives

You will become familiar with the notion of the algebraic expression.

Learning effect

You write down the algebraic expressions on the basis of the task.
You read algebraic expressions including the sum, the subtraction, the product and the quotient.
You describe algebraic expressions in English.

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nagranie abstraktu

Prepare for the lesson a box which contains:

- 4 bananas,
- 2 apples,
- 2 oranges.

Also prepare pieces of paper with letters on them:

- 4 letters „b”,
- 3 letters „j”,
- 3 letters „c”,
- 2 letters „p”,
- 2 letters „d”,
- 2 letters „a”,
- 2 letters „b”.

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nagranie abstraktu

Note that while solving the task algebraic expressionsalgebraic expressionsalgebraic expressions are often written and their values are calculated.

In algebraic expressions we use numbers, signs, brackets e.g.

25 : 5,2 · (18 + 7), (5 + 4)Indeks górny 2

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nagranie abstraktu

Today you are going to construct the expressions in which (apart from numbers and signs) letters are used. Such expressions are called algebraic expressionsalgebraic expressionsalgebraic expressions.

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nagranie abstraktu

Take one fruit out of the box and put it in front of you. Next, choose the card with the first letter of the fruit (in Polish) and put it in front of the fruit.

Repeat the activities described above five times.

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nagranie abstraktu

Answer the following questions:

How many bananas are there in front of you? How many letters “b” are there?
How many apples are there in front of you? How many letters “j” are there?
How many oranges are there in front of you? How many letters “p” are there?

Task 1

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nagranie abstraktu

Using algebraic expressionsalgebraic expressionsalgebraic expressions write the number of fruits which were taken out. Give at least two methods.

Example 1

You drew 2 bananas, 2 apples and 2 oranges. You write the expression:

b + b + j + j + p + p,

2b + 2j + 2p,

2(b + j + p).

Note that the number is always written before the letter and the letters are ordered alphabetically.

The expressions 2 · a, 2 · b, 2 · c mean the same as 2a, 2b, 2c. The letters which are in an algebraic expression are called the variables.

Task 2

Put in front of you two cards with the letter „d” for girls, and three cards with the letter „c” for boys.

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nagranie abstraktu

Write the number of selected students by using an algebraic expression. Use two different methods.

Task 3

Put in front of you two cards with the letter „a”, two cards with the letter „b” and two with the letter „c”.

Using tha algebraic expression write the number of letters put in front of you. Use at least two methods.

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nagranie abstraktu

Answer the following questions:

- How do we call the result of the addition?
- How do we call the result of the subtraction?
- How do we call the result of the multiplication?
- How do we call the result of the division?
- How do we call the number to the power of two?
- How do we call the number to the power of three?

Task 4

Watch the slideshow and on its basis do tasks 5‑7.

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Task 5

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nagranie abstraktu

Mum is m years old. Using an algebraic expression write the age of:

a) Kate who is three times younger than her mum,
b) dad who is three years older than mum,
c) uncle who is three years younger than mum.

Task 6

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nagranie abstraktu

One rose costs r PLN and the tulip t PLN.

Using an algebraic expression write the cost of following:

a) one rose and three tulips,
b) five roses and six tulips,
c) three roses and four times more tulips,
d) six tulips and three times less roses.

Task 7

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nagranie abstraktu

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Wersja alternatywna ćwiczenia: Match the statement to the appropriate algebraic expression. the sum of the numbers a and m Możliwe odpowiedzi: 1.

\frac{a}{m}

, 2.

a + m

, 3.

a^{2}

, 4.

2a

, 5.

a - m

, 6.

am

, 7.

\frac{a}{2}

the subtraction of the numbers a and m Możliwe odpowiedzi: 1.

\frac{a}{m}

, 2.

a + m

, 3.

a^{2}

, 4.

2a

, 5.

a - m

, 6.

am

, 7.

\frac{a}{2}

the product of the numbers a and m Możliwe odpowiedzi: 1.

\frac{a}{m}

, 2.

a + m

, 3.

a^{2}

, 4.

2a

, 5.

a - m

, 6.

am

, 7.

\frac{a}{2}

the quotient of the numbers a and m Możliwe odpowiedzi: 1.

\frac{a}{m}

, 2.

a + m

, 3.

a^{2}

, 4.

2a

, 5.

a - m

, 6.

am

, 7.

\frac{a}{2}

half of the number a Możliwe odpowiedzi: 1.

\frac{a}{m}

, 2.

a + m

, 3.

a^{2}

, 4.

2a

, 5.

a - m

, 6.

am

, 7.

\frac{a}{2}

double value of the number a Możliwe odpowiedzi: 1.

\frac{a}{m}

, 2.

a + m

, 3.

a^{2}

, 4.

2a

, 5.

a - m

, 6.

am

, 7.

\frac{a}{2}

square of the number a Możliwe odpowiedzi: 1.

\frac{a}{m}

, 2.

a + m

, 3.

a^{2}

, 4.

2a

, 5.

a - m

, 6.

am

, 7.

\frac{a}{2}

Match the statement to the appropriate algebraic expression.

the sum of the numbers a and m
the subtraction of the numbers a and m
the product of the numbers a and m
the quotient of the numbers a and m
half of the number a
double value of the number a
square of the number a

Task 8

An extra task:

Two identical coaches were sent for a trip. In each of them there was a driver, x students and 3 teachers. How many people went for the trip?

Answer the question by using an algebraic expression.

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nagranie abstraktu

Remember:

Expressions in which (apart from numbers, signs and brackets and letters are used) are called algebraic expressionsalgebraic expressionsalgebraic expressions.
3 · b means the same as 3b.
The algebraic expression a + b is read as: the sum of the numbers a and b.
The algebraic expression a - b is read as: the subtraction of the numbers a and b.
The algebraic expression ab is read as: the product of the numbers a and b.
The algebraic expression a : b is read as: the quotient of the numbers a and b.

Do the summarising exercises.

Exercises

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Exercise 1

Wersja alternatywna ćwiczenia: Determine which sentence is true. Możliwe odpowiedzi: 1. The sum of the numbers n and s: n + s, 2. Half of the number s: hs, 3. The subtraction of the numbers n and s: s – n, 4. Three times the number n: 3n, 5. The product of n squared and the number s:

n^{2} s

, 6. The product of the numbers n and s squared:

{(n s)}^{2}

, 7. The quotient of s by the number n squared:

s n^{2}

, 8. The subtraction of the half of the number n and number s: 0,5n - s, 9. The half of product of the numbers n and s: 0,5(ns)

Determine which sentence is true.

The sum of the numbers n and s: n + s
Half of the number s: hs
The subtraction of the numbers n and s: s – n
Three times the number n: 3n
The product of n squared and the number s: $n^{2} s$
The product of the numbers n and s squared: ${(n s)}^{2}$
The quotient of s by the number n squared: $s n^{2}$
The subtraction of the half of the number n and number s: 0,5n - s
The half of product of the numbers n and s: 0,5(ns)

zadanie

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Exercise 2

Using the algebraic expression write:

a) the number of legs of k cats and w sparrows,

b) the number of wheels of m motorbikes and s cars,

c) the value of 5 kilos of apples which cost x PLN per kilo and three kilos of oranges which cost PLN per kilo.

Exercise 3

Describe the following algebraic expressions in English:

a) x + y

b) 2w

c) aIndeks górny 2

d) $\frac{m}{p}$

e) ab

f) k – m

g) $\frac{d}{2}$

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Exercise 4

Indicate which pairs of expressions or words are translated correctly.

wyrażenie algebraiczne - algebraic expressions
zmienna - variable
kwadrat liczby - square number
sześcian liczby - cube number
połowa liczby - subtraction of numbers
iloczyn liczb - quotient of numbers

Rzadanie

Source: GroMar, licencja: CC BY 3.0.

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Match Polish terms with their English equivalents.

variable
half a number
square number
zmienna
sześcian liczby
cube number
kwadrat liczby
wyrażenie algebraiczne
algebraic expressions
połowa liczby

Source: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

Glossary

algebraic expressions

wyrażenie algebraiczne

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wymowa w języku angielskim: algebraic expressions

variable

zmienna

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wymowa w języku angielskim: variable

square number

kwadrat liczby

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wymowa w języku angielskim: square number

cube number

sześcian liczby

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wymowa w języku angielskim: cube number

half of number

połowa liczby

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wymowa w języku angielskim: half of number

sum of numbers

suma liczb

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wymowa w języku angielskim: sum of numbers

subtraction of numbers

różnica liczb

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wymowa w języku angielskim: subtraction of numbers

product of numbers

iloczyn liczb

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wymowa w języku angielskim: product of numbers

quotient of numbers

iloraz liczb

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wymowa w języku angielskim: quotient of numbers

twice the number

dwukrotność liczby

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wymowa w języku angielskim: twice the number

Keywords

algebraic expressionsalgebraic expressionsalgebraic expressions

variablevariablevariable

square numbersquare numbersquare number

cube numbercube numbercube number

half a numberhalf of numberhalf a number

Scenariusz

Exercises

Glossary

Keywords