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Authoritative PPT Summary
"Using Letters to Represent Numbers" PPT Courseware 7
The unit price of exercise books is a yuan. How to express the total price of 100 exercise books?
Because the total price of exercise books = number of exercise books x unit price,
Therefore, the total price of 100 exercise books is 100xa yuan, which is 100a yuan.
When numbers are multiplied by letters representing numbers, the multiplication sign can be omitted or replaced with ".". When multiplying numbers and letters, when the multiplication sign is omitted, the numbers should be written in front of the letters. If nx2 is written as 2n, generally do not write it as n2.
Do it
1. The father is 28 years older than his son. If x represents the son's current age, then the father's current age is ______ years.
2. Assume that each can of milk powder costs p yuan and each can of oranges costs q yuan (as shown in the figure), then buy 10 cans of milk powder.
6 cans of oranges cost _______ yuan in total.
3. The area of the large square made of rectangles and squares as shown in the figure is ______.
super walkthrough
1. Xiaoling’s age is c years, and her father’s age is 3 times 1 year younger than hers. What is her father’s age? ______ years.
2. The car drove from point A to point B at a speed of c kilometers per hour. After driving for 2 hours, it traveled another 5 kilometers before reaching its destination. How many kilometers is it from point A to point B?
3. If you buy 1 1/2 kilograms of apples at m yuan per kilogram, you will spend a total of ______ yuan.
Summary: 1. The same letters can represent different quantities in different questions.
2. Mixed numbers should be converted into improper fractions when multiplied by letters.
Can you express the following mathematical rules by using letters to express numbers?
Multiplicative associative law: (ab)c=a(bc)
Distributive law of multiplication: a(b+c)=ab+ac
The absolute value of a negative number is its opposite: if a<0, then �a�= -a
Ask students to review the mathematical rules they have learned and give some examples of using letters to represent numbers.
Thinking expansion:
The sports committee member brought 500 yuan to buy sporting goods. It is known that a football is a yuan, a basketball is b yuan, and a volleyball is c yuan. Please tell me the meaning of each of the following expressions:
⑴a＋b,
⑵500-3b,
⑶2(a＋b＋c)
ability surfing
On Sunday, Liangliang took 50 yuan from her mother and went to the store to buy school supplies.
⑴I met the math teacher half an hour after leaving home, chatted for 5 minutes, and walked for t minutes to the store.
Think: Can you make up a math problem based on this passage?
(2) Liangliang bought w exercise books at 2 yuan each.
Thinking: Can you make up related math problems?
(3) Liangliang also bought h meters of handmade ribbons at 0.7 yuan per meter. When she got home, she divided them into 4 equal sections.
Think: What other math problems can you make up?
Start simple and explore:
It takes 4 small sticks to build a square.
(1) According to the diagram, ___ small sticks are needed to build 2 squares.
It takes ____ small sticks to build 3 squares.
(2) How many small sticks are needed to build 10 such squares?
(3) How many small sticks are needed to build 100 such squares? How did you get it?
(4) If x represents the number of squares to be built, how many small sticks are needed to build x such squares? Communicate with peers.
Summary of this lesson
⑴Using letters to represent numbers can express quantitative relationships concisely and with universal significance;
⑵ Key points to note in writing format.
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