Topicm37f4bc1a48ded96f_1528449000663_0Topic

Addition and subtraction of algebraic sums

Levelm37f4bc1a48ded96f_1528449084556_0Level

Second

Core curriculumm37f4bc1a48ded96f_1528449076687_0Core curriculum

IV. Transformation of algebraic expressions. Algebraic sums and operations done on them. The student:

1) adds and subtracts algebraic sums, while doing the reduction of similar expressionsreduction of similar expressionsreduction of similar expressions.

Timingm37f4bc1a48ded96f_1528449068082_0Timing

45 minutes

General objectivem37f4bc1a48ded96f_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm37f4bc1a48ded96f_1528449552113_0Specific objectives

1. Adding and subtracting algebraic sumssubtracting algebraic sumssubtracting algebraic sums.

2. Reducing similar expressions.

3. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesm37f4bc1a48ded96f_1528450430307_0Learning outcomes

The student:

- adds and subtracts algebraic sums,

- reduces similar expressions.

Methodsm37f4bc1a48ded96f_1528449534267_0Methods

1. Discussion.

2. Thematic contest.

Forms of workm37f4bc1a48ded96f_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm37f4bc1a48ded96f_1528450127855_0Introduction

The teacher informs students that during this class they will add and subtract algebraic sums.

Students revise their knowledge related to adding arithmetic expressions with parentheses – without doing the calculations in parentheses. They give examples of the application of the distributive property of multiplication over addition in arithmetic calculations.

Procedurem37f4bc1a48ded96f_1528446435040_0Procedure

Task

Students work individually, using computers. Their task is to observe the easiest way of adding and subtracting algebraic sumssubtracting algebraic sumssubtracting algebraic sums. After completing the exercise, students order and verify their observations.

[Geogebra applet]

[Gallery]

Conclusions:

- If the parentheses in an algebraic expression are preceded by a plus sign or no sign, then we can eliminate the parentheses without changing the signs inside it.
- If the parentheses in an algebraic expression are preceded by a minus sign, then we can eliminate the parentheses by changing every sign inside it into the opposite sign.
- In order to add (or subtract) two algebraic sums, we need to eliminate the parentheses (if they exist) and then do the reduction of similar terms (add them).m37f4bc1a48ded96f_1527752263647_0- If the parentheses in an algebraic expression are preceded by a plus sign or no sign, then we can eliminate the parentheses without changing the signs inside it.
- If the parentheses in an algebraic expression are preceded by a minus sign, then we can eliminate the parentheses by changing every sign inside it into the opposite sign.
- In order to add (or subtract) two algebraic sums, we need to eliminate the parentheses (if they exist) and then do the reduction of similar terms (add them).

Task contest – students work in groups of 4‑5. Each group does the same set of exercises prepared by the teacher. The prize for the contest is getting a grade for the correct solution.

Task
Eliminate the parentheses and do the reduction of similar terms.

a) (c + b) - c

b) 2a + (-a + b)

c) (-3x - z) + (z - 1)

d) - (6a + 2b - 3c)

e) - (2a - 5b) + (-2a - b)

f) 2 - (-c + 2b) + 4c

g) 18x - (-x + 5y - 10)

Task

Let A = xIndeks górny 2² - 2x, B = -5xIndeks górny 2² + 3, C = 4x - 7, D = -2xIndeks górny 2² - 2x + 5.

Write the expressions in their simplest form.

a) A + B + C

b) B - D - A

c) A - C + D

d) D - A - B

Task
Rewrite the following statements in the form of algebraic expressions. Do the reduction of similar terms.

a) To the sum of numbers x, y and z add the difference of the numbers x and z.

b) From the difference of the numbers b and c subtract the sum of the numbers a and c.

c) To the difference of the numbers a and c add the difference of the numbers c and b.

d) From the sum of the numbers x and y subtract the sum of the numbers x and z.

An extra task:
There are algebraic expressions: A = aIndeks górny 3³ + 3aIndeks górny 2² + 3a, B = -2aIndeks górny 2² + 4a, C = -2aIndeks górny 3³ + 4a - 3, D = aIndeks górny 3³ - a. Insert the parentheses in the expressions on the left so that the equation below is true.

A + B - C - D = 3aIndeks górny 3³ + 2aIndeks górny 2² + 2a + 3.

After completing the exercises, the fastest group presents the solutions. If the group did all obligatory tasks and the extra task, they would obtain the highest grade.

Lesson summarym37f4bc1a48ded96f_1528450119332_0Lesson summary

Students do the revision exercises.

Then together they sum‑up the classes, by formulating the conclusions to memorise.

- In order to add (or subtract) two algebraic sums, we need to eliminate the parentheses (if they exist) and then do the reduction of similar terms (add them).

- If the parentheses in an algebraic expression are preceded by a plus sign or no sign, then we can eliminate the parentheses without changing the signs inside it.

- If the parentheses in an algebraic expression are preceded by a minus sign, then we can eliminate the parentheses by changing every sign inside it into the opposite sign.

Selected words and expressions used in the lesson plan

adding algebraic sumsadding algebraic sumsadding algebraic sums

algebraic sumalgebraic sumalgebraic sum

reduction of similar expressionsreduction of similar expressionsreduction of similar expressions

similar monomialssimilar monomialssimilar monomials

subtracting algebraic sumssubtracting algebraic sumssubtracting algebraic sums

terms of the sumterms of the sumterms of the sum