"Using Letters to Represent Numbers" PPT Courseware 6

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"Using Letters to Represent Numbers" PPT Courseware 6

Scenario 1

(1) Xiaojun and Xiaoming travel towards each other from places A and B at the same time. What do A and B mean?

Letters can represent: place names

(2) Ah P and little D are watching "The Story of Ah Q". What do P, D and Q mean?

Letters can represent: person’s name

(3) What do the poker cards "Ace of Spades", "K of Clubs", A and K represent?

Letters can represent: numbers

Scenario 2

We all know that the 2008 Olympic Games will be held in our country. In order to welcome the 2008 Olympic Games, I imagine building 2008 squares from left to right in the following form. Who can tell the teacher how many matchsticks are needed?

Think about it: What formulas or rules have you learned that are represented by letters?

Letters can be used to represent the laws of operation of numbers

Letters can be used to calculate the perimeter, area, and volume of some shapes.

1. Use a, b, c to represent three numbers, then the operating law of numbers can be expressed as

Commutative law of addition a+b=b+a

Associative law of addition (a+b)+c=a+(b+c)

Commutative law of multiplication ab=ba

Associative law of multiplication (ab)c=a(bc)

Distributive law of multiplication (a+b)c=ac+bc

2. Use letters to express formulas

Rectangle L=2(a+b) S=ab

Square L=4a S=a2

Triangle L=a+b+c S=1/2ah

Parallelogram S=ah

Trapezoidal S=1/2(a+b)h

Circle L=πd=2πr S=πr²

1. What are the advantages of using letters to represent numbers?

Answer: Make some quantitative relationships more concise and easier to discover patterns.

2. Give examples of using letters to represent numbers in your daily life or in mathematical knowledge you have learned before, and share them with your classmates.

Practice in class:

(1) Mingming walks to school at a speed of v meters/second, and Liangliang rides a bicycle to school at a speed 3 times that of Mingming. Then Liangliang’s speed can be expressed as ________ meters/second;

(2) The perimeter of a square with side length a cm is _______ and the area is _______;

(3) You spend 166 yuan to buy pens and buy n pens with a unit price of 5 yuan. The remaining money is ________ yuan.

Reflection and Summary

(1) Letters can represent any number

(2) Using letters to represent numbers can make some quantitative relationships more concise and make it easier to discover patterns.

(3) Be able to use letters to represent previously learned operational laws, calculation formulas and simple quantitative relationships

race one race

1. Fill in the blanks:

(1) After the temperature drops by 2 ℃ from t ℃, it is ________ ℃;

(2) Li Hua is m years old this year, Li Hua is ______ years old last year, and Li Hua will be _____ years old in 5 years;

(3) 15% of a minus 70 can be expressed as _______________;

(4) He obviously traveled s meters in t seconds, but his speed is ________ meters/second.

practice

4. Use matchsticks to match the shapes as follows:

(1) Fill in the following form:

(2) How many matchsticks are needed for the nth figure?

7+5(n–1)

n+n+n+(n+1)+(n+1)

2+5n

7n-2(n-1)

(1) Observe the following formulas, what patterns will you find?

3×5=15 and 15=42-1

5×7=35 and 35=62-1

7×9=63 and 63=82-1

… …

If n-1 is used to represent the former factor, the latter factor can be expressed as _______; can you express the above rule with an equation?

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For more information about the PPT courseware "Using Letters to Represent Numbers", please click the Use Letters to Represent Numbers ppt tag.

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Update Time: 2024-09-29

This template belongs to Mathematics courseware Hebei Education Edition Seventh Grade Mathematics Volume 1 industry PPT template

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