Topicm76ed77aab5fdd7d2_1528449000663_0Topic

Constructing and reading algebraic expressions

Levelm76ed77aab5fdd7d2_1528449084556_0Level

Second

Core curriculumm76ed77aab5fdd7d2_1528449076687_0Core curriculum

VI. The elements of algebra. The student:

1) uses simple formulas with the letter marking, describes the formulas verbally;

2) uses the letter marking of unknown figures and writes down simple algebraic expressionsalgebraic expressionsalgebraic expressions on the basis of the information filled in with a practical contents, e.g. writes the perimeter of the triangle with the sides: a, a + 2, b.

Timingm76ed77aab5fdd7d2_1528449068082_0Timing

45 minutes

General objectivem76ed77aab5fdd7d2_1528449523725_0General objective

Using mathematical language to describe the reasoning and the obtained results.

Specific objectivesm76ed77aab5fdd7d2_1528449552113_0Specific objectives

1. Writing the text of the task by using algebraic expressions.

2. Reading algebraic expressions.

3. Communicating in English; developing mathematical and basic scientific, technical and digital competences; developing learning skills.

Learning outcomesm76ed77aab5fdd7d2_1528450430307_0Learning outcomes

The student:

- writes algebraic expressions on the basis of the task,

- reads algebraic expressions including the sum, the difference, the product and the quotient.

Methodsm76ed77aab5fdd7d2_1528449534267_0Methods

1. Active method (the box).

2. Situational analysis.

Forms of workm76ed77aab5fdd7d2_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm76ed77aab5fdd7d2_1528450127855_0Introduction

The teacher brings to class a big box which contains:

- 4 bananas,
- 2 apples,
- 2 oranges

He also prepares the pieces of paper with tasks 7‑9, magnets and sheets with letters written on them:

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

The teacher places the box with the fruits on the desk near the board.

The teacher reminds the students that they often write algebraic expressionsalgebraic expressionsalgebraic expressions and calculate their values while doing different tasks.

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

25 : 5,2 · (18 + 7), (5 + 4)Indeks górny 2²

Procedurem76ed77aab5fdd7d2_1528446435040_0Procedure

The teacher informs the students they are going to construct the expressions in which (apart from numbers and signs) letters are used. Such expressions are called algebraic expressions.

A volunteer draws one fruit from the box and says what fruit he has got. Next, he chooses the card with the first letter of the fruit (in Polish) and using the magnet he places it on the board.

The teacher chooses five other students, each of whom repeats the activities described above.

The students answer the following questions:

How many bananas were drawn? How many letters “b” are there on the board?

How many apples were drawn? How many letters “j” are there on the board?

How many oranges were drawn? How many letters “p” are there on the board?

Example:

The teacher uses algebraic expressions and writes:

2 bananas, 2 apples, 2 oranges were drawn.

We write the expressions:

b + b + j + j + p + p

2b + 2j + 2p

2(b + j + p)

Task 1

Using 2 different algebraic expressionsalgebraic expressionsalgebraic expressions the students write the number of the fruit which was drawn.

The teacher notes 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.

The teacher chooses two girls and three boys. The girls get the cards with letter „d”, the boys get the letter „c”.

Task 2

The students write the number of the selected students by using an algebraic expression. They use two different methods.

The teacher chooses six students: two get the card with the letter „a”, two get the card with the letter „b” and remaining two with the letter „c”.

Task 3

The students write the numbers of the letters held by the students using an algebraic expression. They should use at least two methods.

The students 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

The students work in groups, they watch the slideshow and on its basis they do tasks 5‑7. Then the leaders of the groups present the solutions on the board. The rest of the students check their answers.

[Slideshow]

Task 5

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.m76ed77aab5fdd7d2_1527752256679_0Mum 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

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.m76ed77aab5fdd7d2_1527752263647_0One 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

Match the statement to the appropriate algebraic expression:

1. the sum of the numbers a and m A. a : m

2. the subtraction of the numbers a and m B. $\frac{a}{2}$

3. the product of the numbers a and m  C. a + m

4. the quotient of the numbers a and m D. a - m

5. half of the number a  E. aIndeks górny 2²

6. double value of the number a F. am

7. square of the number a  G. 2a

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.

Lesson summarym76ed77aab5fdd7d2_1528450119332_0Lesson summary

Students do the exercises summarising the class.

Then, they together sum up the classes drawing the conclusions to memorise:

- Expressions in which (apart from numbers, signs and brackets and letters are used) are called algebraic 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.

Selected words and expressions used in the lesson plan

algebraic expressionsalgebraic expressionsalgebraic expressions

variablevariablevariable

square numbersquare numbersquare number

cube numbercube numbercube number

half of numberhalf of numberhalf of number

sum of numberssum of numberssum of numbers

subtraction of numberssubtraction of numberssubtraction of numbers

product of numbersproduct of numbersproduct of numbers

quotient of numbersquotient of numbersquotient of numbers

twice the numbertwice the numbertwice the number