Topicm7bbf3701b12a0e00_1528449000663_0Topic

Addition and subtraction of algebraic sums

Levelm7bbf3701b12a0e00_1528449084556_0Level

Second

Core curriculumm7bbf3701b12a0e00_1528449076687_0Core curriculum

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

1) arranges monomials and adds similar monomialssimilar monomialssimilar monomials (which differ only by the numerical coefficient);

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

Timingm7bbf3701b12a0e00_1528449068082_0Timing

45 minutes

General objectivem7bbf3701b12a0e00_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm7bbf3701b12a0e00_1528449552113_0Specific objectives

1. Adding and subtracting algebraic sums.

2. Reducing similar expressions.

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

Learning outcomesm7bbf3701b12a0e00_1528450430307_0Learning outcomes

The student:

- adds and subtracts algebraic sums,

- reduces similar expressions.

Methodsm7bbf3701b12a0e00_1528449534267_0Methods

1. Discussion.

2. The idea rug.

Forms of workm7bbf3701b12a0e00_1528449514617_0Forms of work

1. Work in pairs.

2. Group work.

Lesson stages

Introductionm7bbf3701b12a0e00_1528450127855_0Introduction

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

Students revise their knowledge about how to add 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.

Procedurem7bbf3701b12a0e00_1528446435040_0Procedure

The teacher gives 4 examples of basic addition and basic subtraction of algebraic sumssubtracting algebraic sumssubtraction of algebraic sums. The teacher asks the students to do the sample tasks using the reduction of similar terms.

Students work in groups, using the method of the idea rug. They can use different resources while looking for the information they need. They write down the solutions on the pieces of paper of the ‘rug’. Together they choose the best solution and present it to other groups.

Task
Students work individually, using their computers. Their task is to notice what the easiest way of adding or subtracting algebraic sums of many elements is. After completing the exercise, they order and verify their observations.

[Geogebra applet]

Conclusions:

- If the parentheses in an algebraic expression are preceded by the 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 the minus sign, we can eliminate the parentheses by changing every sign inside it into the opposite sign.m7bbf3701b12a0e00_1527712094602_0- If the parentheses in an algebraic expression are preceded by the minus sign, we can eliminate the parentheses by changing every sign inside it into the opposite sign.

- 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).m7bbf3701b12a0e00_1527752256679_0- 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).

Students use the information they obtained to do the exercises.

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

a) 3x – (-5x + 6y – 3z) + (x – 3y + 5z) =

b) –(2ab – 7a + 0,3b – 2) + (-1,2ab – 3,4b + a + 4) =

c) -5xIndeks górny 2² – (-5xIndeks górny 2² + 4y + 2zIndeks górny 2²) – (1,5y – 5xIndeks górny 2² + 6z) =

d) xyIndeks górny 2² + (-3xIndeks górny 2²y – 4yIndeks górny 2² + 7xIndeks górny 2²) – (-xIndeks górny 2² + 2xIndeks górny 2²y – xyIndeks górny 2²) =

Task 
Check if the following equations are true.

a) (xIndeks górny 2² + 2yIndeks górny 2²) - (-xIndeks górny 2² - (2y)Indeks górny 2²) = 0

b) 1 - (-a + 3b) + (a + 3b) = 1

c) (xIndeks górny 2² + yIndeks górny 2²) - (-xIndeks górny 2² - yIndeks górny 2²) = 0

d) 1 - (x - (x - 1) + 1) = -1

e) -(aIndeks górny 3  Indeks górny koniec³ + aIndeks górny 2²) + (4aIndeks górny 2  Indeks górny koniec² + aIndeks górny 3³) - 2aIndeks górny 2² = aIndeks górny 2²

An extra task: 
A certain algebraic sum was subtracted from the expression -6xIndeks górny 2² - 2xy + 2xyIndeks górny 2² and as a result the expression 5xIndeks górny 2²y - 6xy + xyIndeks górny 2² was obtained. Find the correct sum.

Lesson summarym7bbf3701b12a0e00_1528450119332_0Lesson summary

Students do the revision exercises.

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

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

- 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).m7bbf3701b12a0e00_1527752256679_0- 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).

Selected words and expressions used in the lesson plan

algebraic sumalgebraic sumalgebraic sum

adding algebraic sumsadding algebraic sumsadding algebraic sums

subtracting algebraic sumssubtracting algebraic sumssubtracting algebraic sums

similar monomialssimilar monomialssimilar monomials

terms of the sumterms of the sumterms of the sum

reduction of similar expressionsreduction of similar expressionsreduction of similar expressions