# Algebraic Expressions

Philosophy of Mathematics |

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## Contents

- 1 Concept Map
- 2 Textbook
- 3 Additional Information
- 4 Teaching Outlines
- 4.1 Concept 1 - Solution for the Problems of Chapter 8-Polynomials 10 STD
- 4.2 Concept 2: Generalization; and stating in algebraic terms
- 4.3 Concept 3: Combining algebraic terms – commutative and distributive properties
- 4.4 Concept 4: Making simple expressions (addition, subtraction of multiple algebraic terms)
- 4.5 Concept 5 : Introduction to terminology called monomial, binomial, etc.

- 5 Hints for difficult problems
- 6 Project Ideas
- 7 Math Fun

# Concept Map

# Textbook

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# Additional Information

This video is related to writing and evaluating algebraic expression and translate the algebraic expression into word

## Useful websites

- videos related to algebraic expressionclick here

## Reference Books

- NCERT textbook for class 7- Chapter 12: Algebraic Expressions

2. Different approaches to teaching algebraic expressions by using and developing contexts such that students see the purpose in algebraic expressions. Click here

# Teaching Outlines

## Concept 1 - Solution for the Problems of Chapter 8-Polynomials 10 STD

### Learning objectives

### Notes for teachers

*These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.*

### Activity No #

**Estimated Time****Materials/ Resources needed****Prerequisites/Instructions, if any****Multimedia resources****Website interactives/ links/ Geogebra Applets****Process (How to do the activity)****Developmental Questions (What discussion questions)****Evaluation (Questions for assessment of the child)****Question Corner**

### Activity No #

**Estimated Time****Materials/ Resources needed****Prerequisites/Instructions, if any****Multimedia resources****Website interactives/ links/ Geogebra Applets****Process (How to do the activity)****Developmental Questions (What discussion questions)****Evaluation (Questions for assessment of the child)****Question Corner**

## Concept 2: Generalization; and stating in algebraic terms

The students must complete the table like the following:

No of squares

No of match sticks Write match sticks (as a number expression) Write algebraically

### Algebraic variables can be “x” or “y” or “a” of “b”

- Practice with generalization
- Commutative and distributive properties
- Work with Ex 11.1 (from the textbook referred). Different children can be given different problems. The important thing is they know variables can be in different letters.They should also know that different phenomena can be generalized. Mangoes, students, pencils.
- Ask children to talk about (I) did they add (ii) did they multiply?
- For example, when they made “Z” they added three match sticks. When they made 10 “Z” they added 3 +3+3+..... 10 times This is also multiplying by 10. And we simply wrote this as if “n” sticks are needed for a “Z”, then 10n sticks are needed for 10 “Z”. Multiplication is repeated addition.
- Work with the patterns and let children see generalization is not only addition but subtraction and multiplication.

## Concept 3: Combining algebraic terms – commutative and distributive properties

### Lesson 1

- Give students simple addition (with carry forward).
- In a group students add in different order and verify
- They should multiply in different order and verify
- Also do the distributive property like this
- Go back to the number of squares and triangles and activities and introduce Expressions.
- Give Ex-11.2 different problems as homework/ classwork practice problems.

### Lesson 2

- Numbers and generalizations – Use the spreadsheet to work with addition and subtraction and multiplication generalization
- Students must make word problems in groups to describe a given expression
- Students can work in groups for this number pyramid also - check file
- See page 232 of NCERT book used. That verbal/ mathematical expression important to build.
- Exercise 11.3 for all students (Do 11.3 with the spreadsheet – discuss some problems)
- In groups have children write out expressions for given situations in Page 234 of the book chapter.
- Exercise 11.4 based on student level
- Introduce equation (based on perimeter of an object) – Show Geogebra file

## Concept 4: Making simple expressions (addition, subtraction of multiple algebraic terms)

### Learning objectives

- Revisit forming an expression; take the same square example they did above. Extend by making it like this

- See this link very useful - http://nrich.maths.org/8111
- How may different ways can you draw?
- How many down (vertical) lines and how many inverted C?
- How many along (horizontal lines) and and how any downs?
- How many squares and inverted C?
- How many match sticks?
- Exercise 11.4 based on student level
- Exercise 11.5 based on student level

### Notes for teachers

*These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.*

### Activity No #

**Estimated Time****Materials/ Resources needed****Prerequisites/Instructions, if any****Multimedia resources****Website interactives/ links/ Geogebra Applets****Process (How to do the activity)****Developmental Questions (What discussion questions)****Evaluation (Questions for assessment of the child)****Question Corner**

### Activity No #

**Estimated Time****Materials/ Resources needed****Prerequisites/Instructions, if any****Multimedia resources****Website interactives/ links/ Geogebra Applets****Process (How to do the activity)****Developmental Questions (What discussion questions)****Evaluation (Questions for assessment of the child)****Question Corner**

## Concept 5 : Introduction to terminology called monomial, binomial, etc.

- Expressions involving square
- The objectives of this lesson is to show the difference between 5x2 and (5x)2
- Use the attached Geogebra file and use following questions.
- What is the side of small square?
- What is the side of large square? Explain in terms of small square
- What is the area? Of small square? Of large square? Express in variables

(x)² and (factor*x)². How is this different from factor*x²

- For the (5x)2 you should keep drawing squares using polygon tool.
- Use the following second NCERT textbook

http://ncert.nic.in/NCERTS/textbook/textbook.htm?gemh1=12-15 - Exercise 12.1

# Hints for difficult problems

# Project Ideas

# Math Fun

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