Sixth grade, problem solving strategies, very urgent

Hello, first question:

Set the ascent to take x hours, then the descent took (5-x) hours, because it took a total of 5 hours, then.

This calculation is x=2, which means that it took 2 hours to go up and 3 hours to go down, so the distance up the mountain is 3 meters, and the distance down is 12 meters.

Question 2: Suppose there are x chickens and y rabbits, then x+y=35 2x+4y=94 Because they all have one head and two and four claws, then the calculation is that there are 23 chickens and 12 rabbits.

Question 3: Suppose the weight of the chicken is x and the weight of the sheep is y, then 6x+8y=78, 5x=2y, the calculation is that the weight of the chicken is 3 kg, and the sheep is one kilogram.

If there's anything else you don't understand, send me another message, thanks!

The first problem is solved with an equation, and the distance up the mountain is x kilometers and the distance down the mountain is y kilometers.

The system of equations {x+y=15 x) is calculated.

The second problem, with equations, set chickens x and rabbits y.

The system of equations {x+y=35 2x+4y=94 is calculated.

The third problem, using the equation to solve, let the chicken x kilogram and the sheep y kilogram, and obtain the equation {6x+8y=78 5x=2y

They are all looking for an equal relationship, which can be replaced by words first, and then set at the end.

1.If the ascent time is x hours, then the descent time is 5-x hours.

Distance = speed x time.

Get. Distance up the mountain = (x * km.)

Downhill distance = 4*(5-x) km.

The equation can be obtained from the question.

x*solution x=2 means that the uphill time is 2 hours, and the descent time is 3 hours.

Then the distance up the mountain is kilometers.

The descent is 4*(5-2)=12km.

2.Suppose there are x chickens, then there are 35-x rabbits.

Chickens have 2 claws and rabbits have 4 claws, because there are a total of 94 claws, so.

2x+4*(35-x)=94

The solution is x=23

That is, there are 23 chickens and 35-23 = 12 rabbits.

3.If you solve the problem according to the subject, then it can't be solved, and I guess there is no size for sheep.

If it is not big or small, the solution is as follows:

Let the chickens weigh x kilograms, pass: it is known that the weight of 5 chickens is equal to the weight of 2 lambs, that is: the weight of 5 chickens = the weight of 2 sheep.

Then the weight of the sheep is half of the weight of 5 chickens, that is, the weight of the sheep: (5 2) x = 78 kg by 6 chickens and 8 sheep.

6x+8*solution x=3

That is, the chicken weighs 3 kg and the sheep weigh kg.

1. X yuan for cars and x-8 yuan for motorcycles.

Then: 3x=5(x-8).

x = 20 yuan for cars, 12 yuan for motorcycles.

2. Set a fountain pen x yuan, and a ballpoint pen is 2 5x yuan.

2*2/5x+3x=135

x = 27 fountain pen 27 yuan, ballpoint pen yuan.

I think that grades 1 to 6 belong to primary school students, so the six basic strategies in solving problems for primary school students are: drawing strategy, transformation strategy, list strategy, enumeration strategy, state mu substitution strategy, and reverse thrust strategy. For example, let's take a drawing strategy.

In the process of problem solving, the method of drawing pictures is used to draw schematic diagrams related to the meaning of the problem, and with the help of schematic diagrams to help reasoning and thinking, which is the most commonly used strategy in primary school mathematics to solve problems.

Common drawing methods include: line segment diagram, collection diagram, etc.

"Translating the text of a difficult problem into a graph" can immediately clarify the idea and find a solution strategy.

For example, there are 45 students in a class, of which 30 do not participate in the mathematics group, 20 participate in the model aircraft group, and 8 groups participate. Q: How many students are enrolled in only one group?

Analyze: Draw a set diagram.

The boxes represent everyone in the class. Area indicates classmates who only participate in math groups. Zone means a person who only participates in a model airplane group. Region means people who participate in both math and model airplane groups. Area means that neither group has anyone who is involved in the trouble.

**, graphics convey information much more efficiently than words and language.

The use of set diagrams to transform complex text concept relationships into intuitive diagrams can help children quickly sort out the logical relationships between various quantities and improve the efficiency of problem solving.

Parents should encourage their children to use different strategies when solving problems, and if they encounter difficult problems, they can be reminded to try strategies that they don't use often, and maybe inspiration will burst out.

The same knowledge content, different understanding angles, and different ways of thinking will choose different problem-solving strategies.

We usually need to grasp as many strategies as possible to solve problems, and flexibly judge and select relevant strategies for comprehensive use when encountering specific problems, so as to improve our problem-solving ability and improve our problem-solving efficiency.

Inductive ideas: Through observation and classification, summarize the ideas or methods for solving the problem.

Establish a forest model: Abstract the problem into a mathematical model or a graphical model, and establish the correspondence between the problem and the solution.

Exploration method: According to the characteristics and requirements of the problem, select the appropriate calculation method and solution strategy, try different ideas and methods, and find the optimal solution.

Verify Answers: Check and verify the results of the solution to ensure that the answers are correct and meet the requirements of the question.

Summarizing experience: Summarize the experience and methods in the process of problem solving, form your own way of thinking and strategy for problem solving, and improve your problem-solving ability and level.

If you are correct about x questions, you will be wrong about 15-x questions.

8x-4(15-x)=72

Solution x=11

Correct 11 questions.

Let the math book be x yuan, then the language book x + yuan, then.

80 (x+ solution gives x=2x+.)

2 yuan for math books, and 2 yuan for language books.

If the unit price of pears is x, then the unit price of oranges is 3x 4, then.

x+4×3x/4=16

The solution is x=43x4=3

The unit price of pears is 4 yuan catty, and the unit price of oranges is 3 yuan catty.

The place to pay attention to is to find a position and set x, and then according to the prompts in the question, use x to represent another unknown quantity, and then according to the instructions in the question, list the equation, and solve x with the dispersion loss.

Pay attention to set x, list the equations according to the x you set, and solve it.

The first question, set the correct x question, such a beat of the wrong question is 15-x, and then the equation, 8x-4 (15-x) = 72

Solve x=11, that is, do the correct and 11 questions.

The following questions are also set up like this to do the x-column equation, and you will become proficient if you do a few more questions.

Is there anything else you don't understand?

1.If we make x questions, then 8x-4(15-x)=72, and solve x=11, so we can make 11 pairs.

2.Let each math book be closed by x, then 80x=100(, so x=yuan.

3.Let the unit price of pears be x, then.

x+3 state mode 4x*4=16, Sotan is x=4

First of all, thank you very much for asking us for help, your support is our greatest encouragement! For the sixth grade math problem of Rolling Wood Primary School, you generally have to find out what it knows and does not know, and then look at what the problem requires, and then find the equivalent of the series, or find what is the number of parts of those quantities in the whole, and then column. It seems to be very simple, but it is because of the inaccurate equivalence relationship that makes the problem difficult The following two questions are given to illustrate:

1.The canteen brought a batch of coal, the first time it used 2 and 9 of the total, and the second time it used 1,000 kilograms, and the coal used as much coal as there was left. How many kilograms are there in this batch of coal.

At this time, the same amount of coal was used as the remaining coal, indicating that 1 2 of the total coal had been used, so the second time (1 2)-(2 9) = 5 18 of the total amount was used, so this batch of coal was original: 1000 (5 18) = 3600 kg 2There are 3 classes in the sixth grade of Wenwu Primary School, there are 75 students in Class A and Class B, and there are 81 students in Class B and Class C.

There are 75 students in classes A and B, and there are 81 students in classes B and C, so the number of students in the whole grade + class B = 75 + 81 = 156 people in the whole grade + the number of people in class B = the whole grade + (3 10) the whole grade = 156 the whole grade = 120 people.

The first one: (14+20)x2=68 (square centimeters).

The second: square centimeters).

Question 1: 2 (14 + 20) = 68cm

Question 2: c= d+ d2

2πr+πr

3πrr=6 c=18π

Question 3: 16

Question 4: 25-5

Question 5: 16+4

2.The circumference of the square = the side length 4c=4a

3.The area of the rectangle = length and width s = ab

4.The area of the square = the length of the side The length of the side =

5.Area of the triangle = base height 2s = ah 2

6.Area of the parallelogram = base height s = ah

7.The area of the trapezoid=(upper bottom + lower bottom) height 2s=(a+b)h 2

8.Diameter = Radius 2d = 2r Radius = Diameter 2r = d 2

9.Circumference of the circle = pi diameter = pi radius 2c= d=2 r

10.Area of the circle = pi radius radius.

11.Area of the triangle = base height 2Formula s=a H2

12.Area of the square = side length The side length formula s=a a

13.Area of the rectangle = length and width of the formula s=a b

14.Area of the parallelogram = base height formula s=a h

15.The area of the trapezoid = (upper bottom + lower bottom) height 2 formula s = (a + b) h 2

16.Sum of internal angles: The sum of the internal angles of the triangle = 180 degrees.

17.The volume of the box = length width height formula: v=abh

18.Volume of the box (or cube) = base area High formula: v=abh

19.The volume of the cube = edge length edge length edge length edge length formula: v=aaa

20.Circumference of a circle = diameter Formula: l = d = 2 r

21.Area of the circle = radius Radius Formula: s= r2

22.Table (side) area of the cylinder: Table (side) area of the cylinder 23Equal to the circumference of the base multiplied by the height. Formula: s=ch= dh=2 rh

24.Surface area of the cylinder: The surface area of the cylinder is equal to the circumference of the base multiplied by the height plus the area of the circle at both ends. Formula: s=ch+2s=ch+2 r2

25.Volume of the cylinder: The volume of the cylinder is equal to the base area multiplied by the height. Formula: v=sh

26.The volume of the cone = 1 3 The bottom area is high. Formula: v=1 3sh

The law of addition and subtraction of fractions: the fractions with the same denominator are added and subtracted, and only the numerator is added and subtracted, and the denominator remains unchanged. Fractions with different denominators are added and subtracted, first through the fractions, and then added or subtracted.

Multiplication of fractions: use the product of the numerator as the numerator and the product of the denominator as the denominator.

The division of fractions: dividing by a number is equal to multiplying by the reciprocal of that number.

2. Unit conversion.

km = 1 km, 1 km = 1000 m, 1 m = 10 dm, 1 dm = 10 cm, 1 cm = 10 mm.

square meters = 100 square decimeters, 1 square decimeter = 100 square centimeters, 1 square centimeter = 100 square millimeters.

cubic meters = 1000 cubic decimeters, 1 cubic decimeter = 1000 cubic centimeters, 1 cubic centimeter = 1000 cubic millimeters.

A little too much for you to take a closer look.

The key to answering these kinds of questions is (1) the initial amount of grass. (2) The amount of grass grown each day, replacing the cattle with sheep, the grass on this pasture can be eaten by 18 cattle for 30 days, that is, 54 sheep for 30 days, or for 11 cattle and 24 sheep, that is, 57 sheep for 24 days.

The amount of grass eaten by 1 sheep in 1 day is regarded as 1, then, the amount of grass eaten by 54 sheep in 30 days is 1*54*30=1620, and the amount of grass eaten by 57 sheep in 24 days is 1*57*24=1368, so the amount of grass grown in (30-24) days is 1620-1368=252, and the amount of grass grown in 1 day is 252 6=42, that is, the amount of grass grown in 1 day.

It can be eaten by 42 sheep for 1 dayIf the rancher is ready to raise all the sheep, then the pasture can raise a maximum of 42 sheep so that the sheep can always have grass to eat.