The first class:
Teaching content:
P28/ Example 1 (additive commutative law) P29/ Example 2 (Additive Binding Law)
Teaching objectives:
1. Guide students to explore and understand additive commutative law and the law of association.
2. Cultivate students' awareness and ability to choose algorithms according to specific conditions, and develop the flexibility of thinking.
3. Let students feel the connection between mathematics and real life, and use what they have learned to solve simple practical problems.
Teaching process:
First, the theme map introduction
Observe the picture and ask questions according to the conditions.
(1) How many kilometers did Uncle Li ride today?
(2) How many kilometers did Uncle Li ride in three days?
Wait a minute.
Guide students to observe the theme map
The teacher writes on the blackboard according to the questions raised by the students.
Second, new funding.
List the comprehensive formulas in the exercise book in your own way and answer the questions on the blackboard.
Teachers patrol to find out the answers needed in class and ask students to act them out.
Students observe the first set of formulas and find out their characteristics.
Guide students to observe the first set of formulas and summarize:
40+56=56+40
Give as many examples as possible.
Write it on the blackboard according to the students' examples.
What do you find through these formulas?
Students find the law: two addends exchange positions, and the sum remains the same. This is called additive commutative law.
The teacher writes on the blackboard according to the students' summary.
Can you express additive commutative law in your favorite way?
Blackboard: a+b=b+a
Students express themselves in various forms.
Symbol: △+☆ = ☆+△
Guide students to observe the second set of formulas and summarize:
(88+104+96) = 88+(104+96) Students observe the second set of formulas and find out the characteristics.
Students continue to observe several groups of formulas.
Show:
(69+ 172)+28
69+( 172+28)
155+( 145+207)
( 155+ 145)+207
What do you find through the above formula?
Students summarize the observed laws.
Teacher's blackboard writing: add the first two numbers, or add the last two numbers first, and the total remains the same. This is the so-called association rule.
Students express the laws of addition and association in their favorite ways.
Symbol: (△+☆)+○ = △+(☆+○)
Teacher's blackboard writing:
(a+b)+c=a+(b+c)
According to these two algorithms, students give some examples in life.
Third, consolidate the practice.
P28/ Do it
P3 1/4、 1
Four. abstract
Students summarize the arithmetic of addition learned in this lesson.
What did you learn in this class today?
Can you apply these to your future study?
Verb (abbreviation of verb) Homework: P3 1/3
Blackboard design:
Arithmetic of addition
(1) How many kilometers did Uncle Li ride today? (2) How many kilometers did Uncle Li ride in three days?
40+56 = 96km 56+40 = 96km 88+ 104+96 104+96
= 192+96 =200+88
=288 km =288 km
40+56=56+40 (88+ 104)+96=88+( 104+96)
┆ (for example, students) (69+172)+28 = 69+(172+28)
The two addends switch places, and the sum remains the same. 155+( 145+207)=( 155+ 145)+207
This is called additive commutative law. Add the first two numbers, or add the last two numbers.
The same. This is the so-called law of additive association.
a+b=b+a (a+b)+c=a+(b+c)
Summary after class:
The second class:
Teaching content:
P30/ Example 3 (Application of the Law of Addition)
Teaching objectives:
1. You can do some simple operations with the algorithm.
2. Cultivate students' awareness and ability to choose algorithms according to specific conditions, and develop the flexibility of thinking.
3. Let students feel the connection between mathematics and real life, and use what they have learned to solve simple practical problems.
Teaching process:
First, review and consolidate.
Think back to the addition algorithm you learned last class.
(1) additive commutative law
(2) Additive associative law
Write it on the blackboard according to the student's report.
Second, new funding.
Show: Example 5
The following is uncle Li's itinerary for the next four days.
Day 4 City A→B
Day 5 City B→C
Day 6 City C→D
Day 7 City D→E
A → b115km
B → c132km
C → d118km
D→E 85 km
According to the above conditions, what questions can be asked?
The teacher writes questions on the blackboard selectively according to the students' questions.
Please list the comprehensive formulas in your exercise books to answer the questions on the blackboard.
Give your answers and explain the reasons.
Focus on guiding students to the last question (according to the plan, how many kilometers will Uncle Li ride in the next four days? ) to report.
Students may have objections to brackets.
Teachers can guide correctly. In addition, in order to reflect the operation order more clearly, brackets should be added.
Additive commutative law and additive associative laws are both used.
What other algorithms have we applied to this problem?
Usually, in simple calculation, additive commutative law and additive combination law are used at the same time.
Third, consolidate the practice.
P30/ Do it
Four. abstract
Students report what they have learned and what they have gained.
What did you learn from this course?
Verb (abbreviation of verb) Homework: P32/5-7
Blackboard design:
Application of addition algorithm
According to the plan, how many kilometers will Uncle Li ride in the next four days?
1 15+ 132+ 1 18+85
=115+85+132+118/additive commutative law.
= (115+85)+(132+118) ← additive associative law
=200+250
=450 km
Summary after class:
The third category:
Teaching content:
Application practice course of addition algorithm
Teaching objectives:
1. Can skillfully use the algorithm to perform some simple operations.
2. Cultivate students' awareness and ability to choose algorithms according to specific conditions, and develop the flexibility of thinking.
3. Let students feel the connection between mathematics and real life, and use what they have learned to solve simple practical problems.
Teaching process:
First, basic exercises
Oral answer:
(1) Fill in the appropriate numbers in the following () according to the algorithm.
46+( )=75+( )
( )+38=( )+59
24+ 19=( )+( )
a+57=( )+()
Ask the students to say what algorithm to use to fill the numbers.
(2) Each group directly tells the result of the second formula according to the first formula.
632+85=7 17 85+632=( )
304+2 15=5 19 2 15+304=( )
(3) The following categories are in line with additive commutative law.
140+250=260+ 130
20+70+30=70+30+20
260+450=460+250
a+400=400+a
Through the above questions, can you sum up what we have reviewed? (Write on the blackboard according to the students' answers)
Student summary.
Exercise books are completed independently:
(1) A train goes from Beijing to Jinan via Tianjin. The railway from Beijing to Tianjin is 137 km long, and the railway from Tianjin to Jinan is 357 km long. How many kilometers is the railway station from Beijing to Jinan?
(2) Yumen County needs to build a highway, with 400 kilometers built and 260 kilometers not built. How many kilometers is this highway?
Q:
(1) Draw a line segment.
(2) Column calculation.
Compare the difference between the two problems in the application of algorithm.
In the aspect of paying more attention to students' clarity, only the law of additive combination is applied in the 1 question, while in the second question, additive commutative law is used to exchange the positions of 75 and 480, and then the law of additive combination is applied to add 325 and 75, which makes the calculation simple.
Teachers and students make the same changes. Briefly explain how to draw a line segment diagram and make a brief explanation. )
(3) According to the algorithm, fill in the appropriate numbers in the following □.
369+258+ 147=369+(□+ 147)
(23+47)+56=23+(□+□)
654+(97+a)=(654+□)+□
(4) Which of the following equations conforms to the law of additive association?
a+(20+9)=(a+20)+9
15+(7+b)=(20+2)+b
( 10+20)+30+40= 10+(20+30)+40
(5) Calculate with a simple method:
9 1+89+ 1 1 78+46+ 154
168+250+32 85+4 1+ 15+59
Calculation: 480+325+75
325+480+75
Second, summary
Students talk about harvest.
Summary after class:
The fourth class:
Teaching content:
P34/ Example 1 (Multiplicative commutative law) Example 2 (Multiplicative associative law)
Teaching objectives:
1. Guide students to explore and understand multiplication, commutative law, associative law, and use algorithms to perform some simple operations.
2. Cultivate students' awareness and ability to choose algorithms according to specific conditions, and develop the flexibility of thinking.
3. Let students feel the connection between mathematics and real life, and use what they have learned to solve simple practical problems.
Teaching process:
First, the theme map introduction
Observe the picture and ask questions according to the conditions.
(1) How many people are responsible for digging holes and planting trees?
(2) How many buckets of water does a * * * need to pour?
Students solve problems independently in their exercise books.
Guide students to observe the theme map.
Write properly on the blackboard according to the questions put forward by the students.
Second, new funding.
Guide students to report the problems they have solved.
(1)4×25= 100 (person)
25×4= 100 (person)
What are the characteristics of the two formulas?
Can you give other similar examples?
The teacher writes on the blackboard according to the students' examples.
Can you give this law of multiplication a name?
Blackboard: Swap the positions of two factors, and the product remains the same. This is the so-called multiplication commutative law.
Can you try using letters?
The letters on the student report card indicate: a× b = b× a.
Did we use multiplication and commutative laws in the initial research? When checking multiplication, you can use the position of the exchange factor to recalculate, that is, use the multiplication exchange law.
Can you try to learn another multiplication formula by yourself according to the method of addition and association law mentioned above?
Teachers patrol and give timely guidance.
(2)(25×5)×2 25×(5×2)
= 125×2 = 10×25
=250 (barrel) =250 (barrel)
Group cooperative learning.
(1) What does this set of formulas find?
(2) Give a few such examples.
(3) Use language to express the rules and name them. Four letters.
Team report.
According to the students' reports, the teacher arranges the blackboard books.
Third, consolidate the practice.
P35/ Do it 1, 2
Four. abstract
Students summarize the learning content of this lesson.
The teacher guides the students to recall the main points of the class.
Perfect blackboard writing.
Verb (abbreviation of verb) Homework: P37/2-4
Blackboard design:
Multiplicative commutative law and multiplicative associative law
(1) How many people are responsible for digging holes and planting trees? (2) How many buckets of water does a * * * need to pour?
25×4= 100 (person) 4×25= 100 (person) (25×5)×2 25×(5×2)
25×4=4×25 = 125×2 = 10×25
┆ (for example, students) =250 (barrels) =250 (barrels)
(25×5)×2=25×(5×2)
┆ (Examples of students)
Swap the positions of two factors, and the product remains the same. Multiply the first two numbers or multiply the last two numbers.
This is the so-called multiplication commutative law. The product remains unchanged. This is the so-called law of multiplication and association.
a×b=b×a (a×b)×c=a×(b×c)
Summary after class:
The fifth category:
Teaching content:
Practical course of multiplicative commutative law and multiplicative associative law
Teaching objectives:
1. You can do some simple operations with the algorithm.
2. Cultivate students' awareness and ability to choose algorithms according to specific conditions, and develop the flexibility of thinking.
3. Let students feel the connection between mathematics and real life, and use what they have learned to solve simple practical problems.
Teaching process:
First, basic exercises
(1) oral calculation:
50×2= 100 50×20= 1000
25×4= 100 25×8=200 25× 12=300 25×40= 1000
125×8= 1000 125× 16=200
125×24=3000 125×80= 10000
You worked out the result quickly through the oral calculation just now. You know there are three pairs of good friends in multiplication. Who are they?
Blackboard: 5×2 25×4 125×8
(2) In □
30×6×7=30×(□×□)
125×8×40=(□×□)×□
(3) Calculation:
43×25×4 25×43×4
Comparing two problems, what is the difference when applying the law of multiplication?
On the basis of discussion, students are inspired to conclude that the multiplication of the last two numbers in 1 can make the calculation simple. The second question, first put 4 in front and multiply 25 by 4, or put 25 after 43 and multiply 25 by 4, and then use the multiplicative associative law to make the calculation simple.
Summary: There are two ways to use the multiplicative associative law for simple calculation: one is to use the multiplicative associative law alone to make the calculation simple, and the other is to combine the two algorithms to make the calculation simple. The key is to master the content of the algorithm and use it flexibly according to the characteristics of the topic.
Guide students to distinguish between them in comparison.
(4) Teachers and students compete to see who can tell the result directly.
25×42×4 68× 125×8
4×39×25
(5) Contrast exercises:
4×25+ 16×25
4×25× 16×25
(25+ 15) ×4
(25× 15)×4
46×25
(40+6)×25
49×49+49×5 1
49×99+49
(68+32)×5
68+32×5
After students divide their work into groups, they can do it independently, and then communicate with each other in groups.
Report.
Second, summary
Students talk about harvest.
Summary after class:
The sixth class:
Teaching content:
P36/ Example 3 (Law of Multiplication and Distribution)
Teaching purpose:
1. Guide students to explore and understand multiplication and division.
2. Cultivate students' awareness and ability to choose algorithms according to specific conditions, and develop the flexibility of thinking.
3. Let students feel the connection between mathematics and real life, and use what they have learned to solve simple practical problems.
Teaching focus:
Significance and application of multiplication and distribution law.
Teaching difficulties:
Response function of multiplication and distribution law.
Teaching process:
First, pave the way for pregnancy ambush
Think about the problem.
When learning the arithmetic of multiplication, we observed a theme map, and some students also asked a question: How many students participated in this tree planting activity?
Second, new funding.
Discuss in groups and try to solve it in different ways.
Teachers guide students to answer in various ways.
Students report their own solutions. Guide students to explain the reasons of different algorithms.
( 1)(4+2)×25
=6×25
= 150 (person)
4+2 is the number of people in each group. Multiply by 25 to get the number of people in 25 groups.
(2)4×25+2×25
= 100+50
= 150 (person)
4×25 indicates how many people in 25 groups are responsible for digging holes and planting trees, and 2×25 indicates how many people in 25 groups are responsible for carrying water and watering trees. Add them up again and you will get a * * * number.
Teamwork:
(1) What are the similarities between the two formulas?
(2) What is the difference between the two formulas?
(3) What is the connection between the two formulas?
Report.
Teachers should guide flexibly and summarize the main points according to students' reports.
Can you name other groups of formulas like this?
Students give examples.
Write it on the blackboard according to the students' examples.
Does our example conform to this law? Ask the students to verify.
Ask the students to express the discovered rules in words.
Blackboard: the sum of two numbers multiplied by one number. You can multiply this number separately and then add it up. This is the so-called law of multiplication and division.
(a+b)×c=a×c+b×c
a×(b+c)=a×b+a×c
Do you have any good methods to help us all remember multiplication and division and distribution?
The abbreviation is:
Sum times a number = product addition.
Third, consolidate the practice.
P36/ Do it
P38/5
In the exercise summary, help students remember multiplication and division and distribution.
Four. abstract
Students report their gains.
Teachers guide the summary and improve the blackboard writing accordingly.
Blackboard design:
Powder companion
How many students took part in this tree planting activity?
( 1)(4+2)×25 (2)4×25+2×25
=6×25 = 100+50
= 150 (person) = 150 (person)
(4+2)×25=4×25+2×25
┆ (Examples of students)
(a+b)×c=a×c+b×c
a×(b+c)=a×b+a×c
When the sum of two numbers is multiplied by a number, you can multiply it by this first.
Multiply these numbers separately and then add them up. This is the so-called law of multiplication and division.
Summary after class:
The seventh class:
Teaching content:
Application of Multiplicative Distribution Law
Teaching purpose:
1. Guide students to do some simple operations by using multiplication and division methods and distribution methods.
2. Cultivate students' awareness and ability to choose algorithms according to specific conditions, and develop the flexibility of thinking.
3. Let students feel the connection between mathematics and real life, and use what they have learned to solve simple practical problems.
Teaching process:
First, review preparation
Show:
1. Oral calculation:
73+27 138× 100
100-64 64× 1
8×9× 125
(4+40)×25
2. Fill in the appropriate number in □.
302=300+□
(300+2)×43=300×□+2×□
2003=2000+□
(2000+3)× 14=2000×□+□×□
Second, new funding.
We have learned multiplication and division, and today we continue to study how to apply multiplication and division to make the calculation simple.
Show me 102× ()
Students fill in a two-digit number at will.
The teacher quickly gave out its score instead of calculating it by hand.
Show:
Calculation 102×43
Group discussion completed.
Students may appear:
( 1)( 100+2)×43
(2) 102×(40+3)
On the basis of comparison, teachers guide students to observe the characteristics of the topic and how to apply multiplication and division method, so that students can clearly multiply two numbers, make one of them closer to the sum of integer ten, integer hundred and integer thousand and a number, and then apply multiplication and division method, which can make the calculation simple.
Small exercise:
(1) in □
300 1×84=□×84+□×84
92×203=92×(200+□)
=92×200+92×□
(2) Calculate 102×24
Display: 9×37+9×63
Students finish their homework independently.
( 1)9×37+9×63
=333+567
=900
(2)9×37+9×63
=9×(37+63)
=9× 100
=900
Find different ways to implement the performance of the board of directors.
Guide students to compare the two methods, and focus on understanding and explaining the second method.
Summary: The structural feature of this kind of questions is that the operation symbols of formulas generally adopt the form of ×,+and ×, that is, the sum of two products.
In two multiplication formulas, there is the same factor, that is, the sum of two numbers multiplied by that number.
The other two different factors are generally two numbers, which can add up to whole ten, whole hundred and whole thousand.
Small training: (80+8)×25
32×(200+3)
35×37+65×37
38×29+38
Discussion: Does this question conform to the structural form of multiplication and division? Can it be converted into the form of multiplication and distribution law? How to apply multiplication and division to simple calculation?
When modifying, explain how to simplify the calculation by using the algorithm.
Guide the students to sum up: when we use multiplication and division, we must carefully examine the questions and observe the characteristics of the formula. Some of them can't be simplified directly, but we can simplify them by changing the questions slightly.
Third, consolidate the practice.
1. Teachers and students ask questions.
We use what we have just learned to solve problems. You work out a multiplication formula and I work out a multiplication formula, but these two formulas should be combined and simplified by multiplication and division and distribution.
2. According to the law of multiplication and distribution, connect the equal formulas with "=".
23× 12+23×88
(35+45)× 12
( 1 1×25)×4
25×(4+40)
Discussion: What are the topics of 2 and 3? What should be done to make the formulas on both sides of the equal sign equal and conform to the form of multiplication and division?
3.P38/5
Four. abstract
Talk about harvest.
Verb (abbreviation of verb) Homework: P38/6-8
Blackboard design:
Application of Multiplicative Distribution Law
Calculation102× 43 9× 37+9× 63 9× 37+9× 63 38× 29+38.
102×43 =333+567 =9×(37+63) =38×(29+ 1)
=( 100+2)×43 =900 =9× 100 =38×40
= 100×43+2×43 =900 = 1520
=4300+86
=4386