Topicm80658cf495950c97_1528449000663_0Topic

The numerical value of an algebraic expressionalgebraic expressionalgebraic expression

Levelm80658cf495950c97_1528449084556_0Level

Second

Core curriculumm80658cf495950c97_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 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;

Timingm80658cf495950c97_1528449068082_0Timing

45 minutes

General objectivem80658cf495950c97_1528449523725_0General objective

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

Specific objectivesm80658cf495950c97_1528449552113_0Specific objectives

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

2. Calculating the numerical value of algebraic expressions.

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

Learning outcomesm80658cf495950c97_1528450430307_0Learning outcomes

The student:

- writes algebraic expressions on the basis of the task,

- calculates the numerical value of an algebraic expressionalgebraic expressionalgebraic expression.

Methodsm80658cf495950c97_1528449534267_0Methods

- Situational analysis.

- Method of exposing.

Forms of workm80658cf495950c97_1528449514617_0Forms of work

- Individual work.

- Class work.

Lesson stages

Introductionm80658cf495950c97_1528450127855_0Introduction

The teacher prepares the following items:

- 5 identical checked notebooks,

- 10 pens,

- 2 sets of colourful felt‑tip pens,

- 4 sets containing the ruler, set squares and the protractor.

Alternatively, the teacher prepares the magnets and the photos of the objects listed above. The teacher also prepares a piece of paper and writes SHOP on it and cards with the prices.

- 3,5 PLN
- 5 PLN
- 1.4 PLN
- 2 PLN
- 6,8 PLN
- 10 PLN
- 4,5 PLN
- 7 PLN

The teacher places the desk under the table where he puts all the objects. He puts the prices of 3,5 PLN and 5 PLN next to the notebooks, the prices 1,4 PLN and 2 PLN next to the pens, the prices 6,8 PLN and 10 PLN next to the felt‑tip pens. Then, he puts the note “SHOP” on the board.

Alternatively, the teacher places the photos of the objects and their prices which should not be visible to the students.

The teacher refers to the notion of the algebraic expressionalgebraic expressionalgebraic expression. The expressions in which (apart from the numbers, signs and brackets) letters are used are called algebraic expressions.

Procedurem80658cf495950c97_1528446435040_0Procedure

The teacher informs the students they are going to write algebraic expressions and calculate their numerical values.

Task
The students work individually using their computers. They are going to watch the change of the numerical value of an algebraic expressionalgebraic expressionalgebraic expression depending on the change of the variables.

[Geogebra aplet]

The students answer the following questions:
How do we calculate the numerical value of an algebraic expression?m80658cf495950c97_1527752263647_0How do we calculate the numerical value of an algebraic expression?

Does the numerical value of an algebraic expression remain the same?m80658cf495950c97_1527752263647_0Does the numerical value of an algebraic expression remain the same?

What does the numerical value of an algebraic expression depend on?m80658cf495950c97_1527752263647_0What does the numerical value of an algebraic expression depend on?

The students should come up with the following conclusions:

- While calculating the numerical value of an algebraic expression we substitute the variables with numbers and then carry out the operations.
- The numerical value of an algebraic expression varies each time and it depends on the numbernumbernumber we substitute the variablevariablevariable with.

The teacher selects one student who chooses 5 objects from the “SHOP”. He writes thealgebraic expressionalgebraic expressionalgebraic expression describing the total value of the selected objects. He can use any letters he likes. Then, he draws the prices of the products and finally he calculates the numerical value of the expression.

The teacher chooses two other students who repeat the steps described above. Students work individually calculating the numerical values of the algebraic expressions.

Students work individually calculating the numerical values of the algebraic expressions.

Task
Calculate the numerical values of the following algebraic expressions:
a. $x-6$ for $x=12$

b. $5a$ for $a=100$

c. $3w+4$ for $w=-2$

d. $\frac{m}{4}+5$ for $m=48$

e. $-4s+t$ for $s=-3, t=0,2$

f. $x^2+y^3$ for $x=0,3, y=-2$.

Task
Calculate the numerical value of the algebraic expressionalgebraic expressionalgebraic expression $\frac{1}{2}·(a+b)·h$ for:
a) $a=3, b=5, h=2$
b) $a=4,8, b=7,2, h=4$
c) $a=-\frac{3}{4}, b=2\frac{1}{4}, h=\frac{3}{5}$

Task
Adam has got only t 5‑zloty coins and z 2‑zloty coins in his moneybox.
How much money has Adam got in his moneybox?
Write the appropriate algebraic expression.algebraic expressionalgebraic expression. Calculate its numerical value for $t=15$ and $z=20$.

An extra task
Calculate the numerical value of the expression  $-x^3-(x+1{)}^2$ for $x=4$.

Lesson summarym80658cf495950c97_1528450119332_0Lesson summary

Students do the exercises summarising the class.

Then, they together sum up the classes drawing the conclusions to memorise:
- To calculate the numerical value of an algebraic expressionalgebraic expressionalgebraic expression we substitute all the variables with given numbers and carry out the operations.

- The numerical value of an algebraic expression depends on the numbernumbernumber we substitute the variable with.

Selected words and expressions used in the lesson plan

algebraic expressionalgebraic expressionalgebraic expression

bracketbracketbracket

half a numberhalf a numberhalf a number

numbernumbernumber

numerical value of the algebraic expressionnumerical value of the algebraic expressionnumerical value of the algebraic expression

order of operationsorder of operationsorder of operations

product of numbersproduct of numbersproduct of numbers

sum of the numberssum of the numberssum of the numbers

variablevariablevariable