Additive commutative law and Multiplication method of substitution Teaching Plan 1 Design Description
1. Focus on cultivating students' ability of independent cooperation and inquiry.
Mathematics Curriculum Standard points out that independent inquiry and cooperative communication are important ways for students to learn mathematics. Exploring the significance of additive commutative law and Multiplicative Commutation Law in cooperative communication, so that students can draw a conclusion in communication, which not only respects the main position of students' learning, but also enhances the cultivation of students' cooperative inquiry ability. Students not only learned to use the learned algorithms to solve problems, but also infiltrated the mathematical ideas of analogy and transfer at random, which further deepened their understanding of the significance of additive commutative law and multiplicative commutative law in the process of exploration.
2. Pay attention to the application of knowledge.
Mathematics curriculum standards emphasize that everyone can get the necessary mathematics. On the basis of students' mastery of additive commutative law and multiplicative commutative law, exercises are designed from different angles and levels. Students have experienced the whole process of solving problems, fully experienced the close relationship between mathematics and life, and felt the role and value of mathematics.
Preparation before class
Teachers prepare PPT courseware
teaching process
Review old knowledge and introduce new lessons.
Display theme:
→4+6=6+4
→3×5=5×3
Teacher: Observe two groups of formulas respectively. Please write another group according to the pattern.
Design Intention: additive commutative law and multiplicative commutative law are presented and studied at the same time, which fully respects students' cognitive laws, creates an innovative and practical learning environment for students, not only stimulates students' interest in learning and desire to explore, but also enables students to gain a successful experience.
Explore activities and gain new knowledge.
1. additive commutative law.
(1) Observe the formula and find the law.
Observe the first set of formulas and say what you find.
preinstall
Health: two numbers are added, the position of the addend is exchanged, and the sum is unchanged.
(2) Verify the summary rule.
Teacher: In the formula of 4+6 = 6+4, the position of the addend is reversed and the sum is unchanged. Is it true that in all addition formulas, the position of the sum of exchange addends will not change? Now let's verify it together. Please write several addition formulas and try to exchange the positions of the two addends, calculate their results and verify our conjecture.
Students verify, report, communicate, and the teacher summarizes: two numbers are added, the addend positions are exchanged, and the sum is unchanged. This is additive commutative law.
(3) additive commutative law is represented by letters.
Teacher: Who can represent additive commutative law by letters?
(a + b = b + a)
(4) feedback exercises.
20+30=( )+( )
524+678=( )+524
□+( )=○+( )
3+( )= Y +()
2. Multiplicative commutative law.
(1) Observe the formula and find the law.
Teacher: Observe the second set of formulas and say what you find.
preinstall
Student: Multiply two numbers, exchange the position of the multiplier, and the product remains unchanged.
(2) Verify the summary rule.
Teacher: Let each student work out the multiplication formula and try to exchange the positions of the two multipliers to see if their results have changed.
Students verify, report, communicate, and the teacher summarizes: two numbers are multiplied and the position of the multiplier is exchanged, and the product remains unchanged. This is the multiplicative commutative law.
(3) Use letters to express the multiplicative commutative law.
Teacher: How are multiplication and method of substitution expressed in letters?
(a × b = b × a)
Teacher: What numbers can A and B stand for here?
(Students discuss in groups first, and then report)
(4) feedback exercises.
10×5=( )×( )
( )×△=( )×☆
C ×( )= F ×()
Additive commutative law and Multiplicative Commutation Law Teaching Plan 2: additive commutative law and Multiplicative Commutation Law.
Teaching objectives:
1. Through the teaching exploration process of exchange law and multiplication exchange law, additive commutative law and multiplication exchange law are expressed in letters, so as to cultivate the ability to find and ask questions and accumulate experience in mathematical activities.
2. Explain the process of additive commutative law and multiplicative commutative law by enumerating life examples, understand the rich realistic background of the algorithm, understand the use of additive commutative law and multiplicative commutative law, and discover the application consciousness.
Teaching emphasis: cultivate students' observation ability and generalization ability through the process of observation, induction, conjecture and verification.
Mathematical thinking method of penetrating inductive conjecture.
Teaching difficulty: the infiltration of mathematical thinking method of inductive conjecture.
Teaching process:
First, the import stage:
Show the theme map and introduce the "Love Education Movement" to students. A store held a charity sale to help students in poor mountainous areas and donated all its turnover to Hope Primary School. Look, Xiao Pang and Xiao Ya have come to help.
Q: What mathematical information can you get from the picture?
What other math questions do you ask?
Second, the inquiry stage:
1. Projection demonstration: (Juice) Teacher: How many cans of juice do Xiaoya and Xiao Pang have? How many cans of juice are there on the table? Who can calculate with a column chart?
Teacher: Who can tell some of the two addition formulas?
Question: Look carefully, what are the similarities and differences between these two formulas?
(The same point is that the two addends are 8 and 18 respectively, and the sum is 26. The difference is that the positions of the two addends are different. )
Teacher: Because 8+ 18 = 26 18 = 26, 8+ 18 = 18+8.
Teacher: Who can imitate the form of this topic and give a similar example? The two groups at the same table communicate with each other.
(1) According to our example, what did you find? (Group communication)
Tip: These examples are the addition of several numbers. What has changed between the two? What was the result?
Induction: two numbers are added, and the addend positions are exchanged, and the sum is unchanged. This is called additive commutative law.
(2) Let students express additive commutative law in their favorite way (inspire students to use symbols or letters).
Example: ◆ +● = ● +◆ A number +B number = B number +A number A+B = B+A What numbers can A and B be here?
Additive commutative law is represented by letters: a+b = b+a.
(3) Vertical calculation 74+64 1
Teacher: With additive commutative law, you can also check whether the calculation result of addition is correct.
74 Checking calculation: 64 1
+64 1+74
7 157 15
Summary: When checking, you can exchange positions and then add the two addends. You can also use the original vertical style to repeat the numbers on each number from bottom to top.
2. Projection demonstration:
(1) How many cans of juice are there in the small box in the picture? 6×3= 183×6= 18
Teacher: Please read the above two formulas separately. Because the results of these two formulas are equal, we can connect them with an equal sign.
(2) According to our example, what did you find? Question: What are the similarities on the left side of the equation?
What is the connection between the left and right sides of each set of equations?
Teacher: This is what we are going to learn in this class. Just now the students have summed it up in their own words, so what is the multiplicative commutative law? (Show conclusion)
Summary: When two numbers are multiplied, the position of the exchange factor remains unchanged. This is the so-called multiplication commutative law.
(3) If two numbers are represented by letters A and B respectively, how can multiplication and method of substitution be represented by letters? Give a similar example in the form of this question? The two groups at the same table communicate with each other.
(4) If two numbers are represented by letters A and B respectively, how can multiplication and method of substitution be represented by letters?
Blackboard: a×b=b×a
Third, the application stage:
1. Fill in the figures according to additive commutative law.
()+270 = 270+80400+500 =()+()+56 =()+44a+()= b+()
2. According to the laws of multiplication and exchange, fill in the appropriate numbers in ().
34×7 1 =()×()25×976 = 976×()45×()= 55×()303×786 =()×303()×▲=()×■()×54 = 54×37()×()= c×da×()= c×a
3. Vertical calculation
64 Checking calculation: 27
×27×64
Fourth, summary:
Today, in this lesson, we learned additive commutative law and multiplication and commutation laws, and learned to express them by letters. I also learned to use these two algorithms to check addition and multiplication.
Blackboard design:
Additive commutative law sum multiplicative commutative law
8+ 18=263×6= 18
18+8=266×3= 18
8+ 18= 18+83×6=6×3
Additive commutative law: A+B = B+A multiplicative commutative law: a× b = b× a.
Teaching objectives of additive commutative law and multiplication exchange law teaching plan 3
1. After the exploration of additive commutative law and multiplicative commutative law, additive commutative law and multiplicative commutative law are expressed in letters, so as to cultivate the ability to find and ask questions and accumulate experience in mathematical activities.
2. Explain the process of additive commutative law and multiplicative commutative law by enumerating life examples, understand the rich realistic background of the algorithm, understand the use of additive commutative law and multiplicative commutative law, and cultivate the application consciousness.
Emphasis and difficulty in teaching
Teaching emphasis: Understand and master the significance and application of additive commutative law and multiplicative commutative law.
Teaching Difficulties: additive commutative law and Multiplicative Commutation Law will be represented by symbols or letters.
teaching process
First, practice importing and feel the benefits of exchange.
Firstly, the calculation problems of addition and multiplication are shown, so that students can work out the answers quickly, and then two complicated formulas are given. Can you work out the answer at once? What do you think of these two formulas?
Second, cooperative inquiry, exploring new knowledge
1, and present the addition and multiplication formulas at the same time for students to observe in groups. What are the similarities and differences between the two formulas in each group? Why can I connect the equals sign? What else did you find?
2. Create several groups of addition and multiplication formulas by imitation and verify them. Observe the teacher's examples, his own imitation, naughty and smiling formulas written in the book, and exchange his findings with his peers.
3. summary; Courseware display content;
4. Look for examples in life to explain the law of discovery.
5. I will continue to ask: Can students complete the formulas and examples about the exchange law? Can you create a simpler way to express the law of discovery?
6. Choose a method for projection comparison and ask students to explain their own methods. P23 can get a simpler letter representation (A+B = B+A; A.b=b.a) Here, we should pay attention to what ab stands for and the similarities and differences between the two algorithms.
Third, consolidate the law.
1, the rule is that I say the formula, the students say the exchange formula, add, subtract, multiply and divide in time, and the students continue to ask when there is conflict: A+B = B+A; A.b=b.a So a-b=b? a \b =？ .
Fourth, deepen practice and expand and improve.
1. Use the following example to explain why this equation holds. Understand the practical significance of exchange law through the realistic background.
2. Fill in the blanks with the rules to understand the students' mastery of the exchange rules.
3. Calculate the following questions and check them with the law. Through comparison, it is found that a vertical mode can be selected by using the exchange law in calculation, which also has the function of checking.
4. Then, at the beginning of the class, we will show the complicated operations and encourage students to use the learned exchange laws to simplify the problems.
Verb (abbreviation of verb) class summary
Tell me what you have learned from this lesson.