In the fifth grade, the second volume of mathematics, the addition and subtraction of fractions with the same denominator, is the first teaching goal;
1. Make students understand that the meaning of fractional addition and subtraction is the same as that of integer addition and subtraction, master the calculation rules of fractional addition and subtraction with the same denominator, and calculate related exercises correctly and quickly.
2. Use what you have learned to solve problems in real life and cultivate students' knowledge application ability.
3. Through students' independent exploration and cooperative communication, cultivate students' cooperative consciousness and enhance their desire and confidence to learn mathematics well.
Teaching emphasis: Understand the meaning of the addition and subtraction of fractions and correctly calculate the addition and subtraction of simple fractions with the same denominator.
Teaching difficulties: correct addition and subtraction of fractions with the same denominator.
Teaching process:
(a), basic training courseware:
1, review and fill in the blanks 1: 3/8 means that the unit "1" is divided into () shares on average, that is to say (). Its decimal unit is (), and 3/8 has ().
2. Review and fill in the blanks 2: (1) The score unit of 7/8 is (). (2)5/9 has () 1/9. (3)4/7 is 4 (). (4) Three 1/5 is (). (5) 1 contains () 1/5, which is ().
3. Review and fill in the blank 3:1= ()/8 = ()/2 = ()/7 = ()/a (a ≠ 0) Approximate score: 6/8 = 5/10 = 3/9 = 6/65438.
(2) New course introducer: Students, in grade three, we learned simple addition and subtraction of fractions. Can you write the addition and subtraction formulas of fractions with the same denominator respectively? Please write one for each draft and make a bold guess at the result. Students write formulas. Teacher's blackboard writing project "addition and subtraction of fractions with the same denominator"
(3) Try to practice: Who wants to tell you what kind of formula you have written? Students report the formulas they wrote.
Teacher: Is the formula written by the students correct? I believe you can find the answer through this lesson.
(d), learning exchange, exploring new knowledge 1, teaching examples 1: (show courseware)
Mother baked a big cake at home. Dad divided the cake into eight pieces on average. Dad ate 3 pieces and mom ate 1 piece.
Q: Can you talk about your understanding of scores? How many cakes did dad eat? )
Q: Can you put forward a math problem based on the fractional knowledge you just thought of and tell me how to solve it?
What do you mean by 1/8+3/8? How many cakes did mom and dad eat? ) How much is it?
Are the students' guesses right? Students think and explore independently.
(1) View the results from the chart.
(2) Reasoning: 1/8 is1/8, 3/8 is 3 1/8,1/8 plus 3 1/8 is 4/.
Key point: How much can 4/8 write? (1/2) Teacher: Associating the meaning of integer addition, can you tell the meaning of decimal addition? The meaning of fractional addition is the same as that of integer addition, which is the operation of combining two numbers into one number. )
Oral arithmetic exercises:
1/5+2/5 = 5/9+2/9 = 2/7+4/7 =1/3+/kloc-0 = q: What do you find about the addition of fractions with the same denominator? (Add denominator fraction, denominator unchanged, add numerator)
2. Learn to subtract fractions with the same denominator.
(1) Courseware Example 2
Students give feedback after independent thinking and pay attention to the standardization of writing format.
(2) Associating the meaning of integer subtraction, can you tell the meaning of decimal subtraction?
The significance of fractional subtraction is the same as that of integer subtraction. It is an operation to find the other addend by knowing the sum of two addends and one of them. )
Oral arithmetic exercises:
3/5-1/5 = 7/9-5/9 = 6/7-2/7 = 2/3-1/3 = q: Observing these formulas, what do you find about the subtraction of fractions with the same denominator? (Subtract denominator fraction, denominator unchanged, subtract numerator)
(5) Inspiration induction
Teacher: What are the characteristics of these fractional addition and subtraction formulas?
What do you find by observing the formulas and results of adding and subtracting these fractions?
Blackboard writing: add and subtract fractions with the same denominator, the denominator remains the same, and only add and subtract molecules.
Follow-up: What if the calculation result is not the simplest score?
(The result of calculation is not that the quotation with the simplest score becomes the simplest score. )
(6) Consolidate exercises
1. Complete the textbook page 105. Do it yourself and answer by name.
2. Complete the textbook page 106.
Teaching plan 2 1 teaching content of "addition and subtraction of fractions with the same denominator" in the second volume of fifth grade mathematics
Addition and subtraction of fractions with the same denominator
(1) The contents of the textbook 104- 106 and exercise 2 1 and 2 questions on page 1.
Second, the teaching objectives
1. Through teaching, students can initially understand the addition and subtraction of fractions with the same denominator and master the rules of addition and subtraction of fractions with the same denominator.
2. Cultivate students' mathematical thinking ability of combining numbers with shapes. Improve students' analogical transfer and calculation ability.
3. Cultivate students' good habits of standardized writing and careful calculation.
Three key points and difficulties
Understand the addition and subtraction operation and calculation method of fractions with the same denominator.
Preparation of teaching AIDS
Multimedia courseware.
teaching process
(1) import
The decimal unit of (1) is (), and it has () such decimal units.
Yes, there are in the room.
(3) Three are () and four are ().
2. Talk: In the third grade, we learned the addition and subtraction of the same fractions. Today, we will continue to learn this knowledge.
(B) Teaching implementation
1. Give an example of 1.
Question: What mathematical information do you know by observing the pictures?
Divide a cake into eight equal parts. My father ate a cake and my mother ate a cake. Ask my parents how many cakes they ate.
Question: How many cakes did Mom and Dad eat? How to list them? Why?
Students think and answer:+,which means to add up the two scores, so add them up.
Question: Can you work out the result? what do you think?
Students can think like this: yes 1, yes 3, together it is.
Question: The sum of+is, why hasn't the denominator changed, and how did the numerator get it?
(Because and have the same denominator, that is, their fractional units are the same, you can add them directly with two molecules, and the denominator remains the same. ) Question: Can you write down the calculation process?
Blackboard:+= =
Use multimedia courseware to demonstrate the above calculation process:
Looking at the picture, we can see that the result is, that is. Note: As a result of calculation, it can be converted into the quotation with the simplest score.
2. Question: Think about the significance of fractional addition by answering the above questions. How to calculate the fractional addition with the same denominator?
Summary: The meaning of fractional addition is the same as that of integer addition, which refers to the operation of combining two numbers into one number. When calculating the addition of fractions with the same denominator, the denominator is unchanged and only the numerator is added.
3. Give an example 2.
Let the students look at the questions, try to make formulas and calculate.
Ask students to report the calculation process:-= = =
Question: Why use subtraction? Do fractional subtraction have the same meaning as integer subtraction?
Because the sum of two numbers in this problem is known, one of which is what the other number is, so we use subtraction to calculate it. Fractional subtraction and integer subtraction have the same meaning. )
Question: Why does the denominator remain the same in the calculation process? Can you talk about the calculation method of fractional subtraction with the same denominator?
4. Summary: What are the similarities between observation example 1 and example 2? How to calculate the addition and subtraction of fractions with the same denominator (students discuss in groups. )
5. Complete "Doing" on page 105 and "Doing" on page 107 of the textbook.
Students finish independently and revise collectively.
6. Complete Exercise 2 1 on page 109 of the textbook.
Students do it independently. Choose two or three questions and let the students talk about the calculation process and the problems that need attention.
7. Complete the second question of Exercise 2 109 on page1of the textbook.
Let the students talk about the relationship on which the calculation is based.
The third teaching goal of the addition and subtraction of the same denominator fraction in the fifth grade mathematics volume;
1, master the basic addition and subtraction of fractions with the same denominator, and be able to correctly perform related calculations;
2. Understand the operation of fractional addition and subtraction with the same denominator, and get through the internal relationship among integer, decimal and fractional addition and subtraction, so as to prepare for further learning addition and subtraction with different denominators;
3. Cultivate students' mathematical consciousness and the ability to transfer analogy and induction.
Emphasis and difficulty in teaching:
Know arithmetic, master algorithm and be good at calculation.
Prepare teaching AIDS and learning tools:
Courseware, rectangular, square and round pieces of paper.
Teaching process:
First of all, mathematical bedding.
1. Will you add it? Give it a try. Courseware demonstration: 25+3=
How did 28 come from? But there is a first-grade child who always likes to add the first number (courseware). Right? Who can reason with him?
Health 1: 3 is in the unit, and it should be aligned with the unit.
Health 2: The numbers on the same number are aligned.
Teacher's summary: When adding and subtracting integers, only two numbers with the same unit can be added directly. (blackboard writing: addition and subtraction of numbers with the same unit)
2. Integer addition is like this. What about decimal addition? Demonstration: 0.25+0.3=0.28 (courseware)
Teacher: Is that right? (The courseware shows vertical error). Why?
Health: the decimal points should be aligned, and the same digits should be aligned.
Teacher's summary: When calculating decimal addition, two numbers with the same unit should also be added directly.
Second, explore new knowledge.
1, students write their own questions.
Teacher: Besides integers and decimals, what other numbers have we learned?
Health: scores.
Teacher: According to the existing knowledge and experience, can you try to work out several formulas for adding and subtracting fractions? (The teacher is writing on the blackboard)
Teacher: Can you classify these formulas according to certain standards?
Student: Fractional addition and subtraction with the same denominator and fractional addition and subtraction with different denominator.
Teacher: In this class, we will learn the addition and subtraction of fractions with the same denominator. (blackboard writing topic)
2. Explore the addition of fractions with the same denominator
(1) try
Teacher: Please try to calculate this 2/5+3/5 first.
Health: 2+3=5, so it is1;
Teacher: It's that simple? Just use 1+3 to get 4? Just write 4, why should you bring the denominator?
I found that some students calculated this way:+=, do you think it's right? Why is it wrong?
Health: ...
Teacher: It seems that behind the simple topic, there are reasons worthy of our study. In order to better understand these reasons, please use the rectangular, square or circular pieces of paper in your hand to fold and draw to show the process of addition, and then talk about the reasons for this calculation.
Origami, coloring, exploring arithmetic.
(3) communication.
Raw 1: represents rectangular paper; Health 2: square pieces of paper; ……
Teacher: What these students just said is the same meaning, that is, three plus two equals five, that is. (Courseware demonstration) Correct calculation process of blackboard writing.
Teacher: (pointing to three on the blackboard) What does it mean here? What does this mean?
Student: In the calculation process, the unit of the score is the same. (blackboard writing)
Teacher: But after listening to so many explanations when Mr. Wang was in another class, one of his classmates still thought it was right. He also drew a picture:
I know he is wrong, but I can't convince him. Can you help me? Where is he wrong?
Health: Mom and Dad eat the same whole, a whole. We can't draw another one.
Teacher: You mean that three books and two books are in the same eight books, and you can't draw another eight books. In other words, the total number of copies here has not changed.
Watch this three times together, or not? so this is it？
By the same token, these two copies are not? It became, so it combined.
(4) Try to do the questions given by the students themselves:
Show students' calculations and results. Tell me how you worked it out.
3. Explore the same fraction subtraction.
Teacher: We can calculate the addition of fractions, but can you calculate the subtraction? Please contact the fractional addition operator and try to calculate-
Teacher: Next, please sit at the same table and explain to each other in your favorite way:
Student: Explain in composition, and subtract (2) from (3) () to get (1) (), that is.
Teacher: Who knows? Who will say?
Teacher: Let's look at the picture again: (Courseware)-Student: Retell.
Name the board of directors. Tell me why this calculation is done.
Teacher: Who can try to come up with several such fractional subtraction methods for everyone to do?
Students give each other questions, and everyone counts. A complete calculation process is needed. )
4. Summary algorithm, communication algorithm.
Teacher: Looking back at the problem we just calculated, what can you find? Think about the addition and subtraction of fractions with the same denominator. (Group communication)
Student: Fractions with the same denominator are added and subtracted, but the denominator remains the same, and the numerator is added and subtracted. (Teacher writes on the blackboard)
Teacher: Why is the denominator the same?
Student: Only when the units of scores are the same can we add and subtract.
Teacher: This sentence is really familiar. Please contact the addition and subtraction of integers and decimals you have learned to see if they are similar in calculation methods.
Student: All numbers with the same unit can be added or subtracted directly.
The fourth teaching goal of fifth grade mathematics "addition and subtraction of fractions with the same denominator"
1. Experience the formation process of knowledge and understand the significance of reduction.
2. Explore and master the method of reduction, and make reduction correctly.
Emphasis and difficulty in teaching
Understand the significance and methods of simplest fraction and simplification, and master the methods of simplification.
teaching process
First, set the situation and introduce the topic (card display, group study)
Review of old knowledge: (Students train on the answer sheet)
1, can you quickly find the greatest common factor of each of the following group numbers?
9 and 18 7 and 9 20 and 28 1 1 and 13.
3. Answer: How did you find the greatest common factor of two numbers? How many special cases are there to find the greatest common factor of two numbers?
Find the greatest common factor of two numbers through enumeration and decomposition of prime factors. But there are two special cases: one is that two numbers are multiples.
(2) Exploring new knowledge
Analysis and exploration 1:
(Students train on the answer sheet)
1, card out the scene diagram of Example 3 for students to observe.
Teacher: What should I do if I want to become the simplest score? Let the students try to turn it into the simplest score first, and guide them to come up with all kinds of tangent methods, then communicate, and the teacher will summarize and write it on the blackboard.
Method 1: Use the common factor of numerator and denominator to remove numerator and denominator one by one, and finally wait until the simplest score. (Teacher's blackboard writing: successive reduction method)
Method 2: Using the greatest common factor of numerator and denominator, the numerator and denominator are removed respectively to get the simplest score. (Teacher's blackboard writing: one-time reduction method)
2. Guide students to summarize methods:
Second, consolidate the practice.
Students complete the answer sheet independently. (Ask several students to answer and act)
Third, the class summary:
1. What have we learned today? (the simplest score; About integration)
2. Do you have any questions?
Fourth, homework
1, class assignment: exercise 16, question 1 and 4.
2. Homework: Exercise 16, questions 2, 3 and 5.