Name _ _ _ _ _
The first unit equation
Knowledge point: Equation: The equation representing equality is called equation.
Exercise: 1 In the following formula, it is an equation. Draw "√" at the back).
x+ 18 = 36()x+2； 10()72-x()x = 3()
Knowledge point: Equation: An equation with an unknown number is an equation.
Exercise: 1 In the following formula, it is an equation. Draw "√" at the back).
x+ 18 = 36()x+2； 10()72-x()x = 3()
Knowledge points: the relationship between equation and equality: the equation must be an equation, and the equation is not necessarily an equation.
Exercise: 1, which are equations and which are equations, please fill in the corresponding lines. (Fill in serial number)
①3+x = 12②3.6+x③4+ 17.5 = 2 1.5④48+x￠63
Equation _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _; Equation: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
2. Formulas containing unknowns are called equations. () judgment
3. Equations are all equations. () Judgment 4. Equations are equations. () judgment
Knowledge points: the properties of equations
Exercise: 1, Solving Equation
x-97 = 145 1. 15+x = 6.8 13.5-x = 8.2 3x = 3.9
x÷3 = 2. 1. 15x = 240-x = 28÷x = 42
2. Wu Bing bought 1 exercise book and three pencils, while Zhang Lan bought the same seven pencils, and both spent the same amount of money. The price of an exercise book is equal to the price of () pencils. fill up a vacancy
Knowledge points: solving simple practical problems with equations.
Exercise: Solve practical problems with equations.
1. The area of the parallelogram is 2.4 square centimeters, and its base is 0.8 meters long. How many centimeters is its height?
Guangming Bookstore sold 350 books in the morning, 35 more than in the afternoon. How many books did you sell in the afternoon?
Guangming Bookstore sold 350 books in the morning, 35 fewer than in the afternoon. How many books did you sell in the afternoon?
There are two layers of books on the shelf. There are 180 books in the upper level, which is three times that of the lower level. How many books are there on the lower floor? (written on the right)
Knowledge point: the sum of five consecutive natural numbers (or consecutive odd numbers and even numbers) is equal to five times the middle number.
Exercise: 1, the sum of three consecutive natural numbers is 24, which are (), () and () respectively.
2. The sum of five consecutive odd numbers is 35, and the smallest number among the five consecutive odd numbers is ().
Unit 3 Common Factor and Common Multiple
Knowledge points: common factor and greatest common divisor
Exercise: 1 Write the greatest common factor of each group of numbers below.
3 and 5 () 4 and 8 () 1 and 13 () 13 and 26 ()
4 and 9 () 17 and 5 1 () 2 1 and 36() 22 and 55 ()
2, ⊙= 5 (both are non-zero natural numbers), and the greatest common factor of sum is ().
3.sum is two adjacent nonzero natural numbers, and the greatest common factor of sum is ().
4. Divide a rectangular piece of paper with a length of 18cm and a width of 12cm into squares with the same size and no redundancies. The maximum side length of each small square is () cm, which can be divided into at least ().
Two steel pipes, A pipe is 36 decimeters long and B pipe is 40 decimeters long. Cut them into small pieces of the same length, and there is nothing left. Each piece is at least () decimeter long and can be cut into () sections.
Knowledge points: common multiple and minimum common multiple
Exercise: 1 Write the least common multiple of each group number below.
3 and 5 () 4 and 8 () 1 and 13 () 13 and 26 ()
4 and 9 () 17 and 5 1 () 2 1 and 36() 22 and 55 (),
2, ⊙= 5 (both are nonzero natural numbers), and the least common multiple of sum is ().
3.sum is two adjacent nonzero natural numbers, and the least common multiple of sum is ().
A rectangular floor tile is 8cm long and 6cm wide. Paving a square requires at least () tiles. The area of a square is at least () square centimeters.
During the summer vacation, Kobayashi and Xiaojun both went to swimming training. Kobayashi comes every six days, and Xiaojun comes every eight days. Take part in swimming training on July 3rd1day, and meet again on July ().
6. During the summer vacation, both Xiao Lin and Xiao Jun went swimming training. Kobayashi comes every six days, and Xiaojun comes every eight days. 1 In August, they both participated in swimming training at the same time, and met again in August ().
7, 3 and 7 are multiples of () ① factor ② common factor ③265438 +0 {Select}
8,8 is a multiple of () ① factor ② greatest common factor ③24 and 64 {select}
Unit 4 Cognitive Score
Knowledge point: unit "1"
Exercise: 1, "eating a box of apples" means taking () as the unit of "1", dividing it into () portions on average, and eating () portions accounts for the total.
2. The time of a class is hours, that is, () is the unit 1, which is divided into () copies on average, and the time of a class accounts for () copies.
Knowledge point: the meaning of score
Exercise: 1, there are 12 pencils, which are distributed to 2 students on average. Each pencil accounts for the total number of pencils. Give everyone the total number of pencils.
2. There is a 20-meter-long rope, which is divided into 10 segments on average, each segment is () meters long, and each segment is the total length.
3. There is () in the library and () in 1.
The decimal unit of 4 is that it has () such decimal units plus () such decimal units, which is the smallest prime number.
5, said (). According to the relationship between fraction and division, it also means ().
6. Cut the 3-meter-long rope into four sections on average, each section belongs to this rope, each section is meters long, and two sections belong to this rope.
7. If a project is completed within 9 days, it will be completed every day on average, and it will be completed in () days.
8. My mother bought seven apples and has eaten five. She has eaten these apples.
There are 27 boys and 35 girls in Class Five (2). The number of boys is female, the number of girls is male, the number of boys is the class number, and the number of girls is the class number.
Knowledge points: true points and false points
Exercise: 1, denominator is 5, true score has (), and false score with numerator of 5 has ().
2, the unit of the score is (), plus () such a unit score is the smallest false score.
3. Among the scores of,,,,, and, the real score is _ _ _ _ _ _ _ _ _,
The false score is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
4. The true scores are all less than 1. () judgment 5. False scores are all greater than 1. () judgment
6. There are 12 pears, the number of oranges is pears, and there are () oranges. fill up a vacancy
Knowledge points: the relationship between fraction and division
Exercise: 1, expressed in fractions.
5÷6= 67÷20= 22÷ 19= 6 decimeters = 8 mm = cm
23 cents = 7 cents = 6 cents 7 cents = 3 centimeters = 27 grams = kilograms.
2. Write the following score in the form of division.
=( )÷( ) =( )÷( ) 1 =( )÷( )
3, the score, when (), is a true score; When (), it is a false score.
4. Divide the 4-meter-long steel pipe into 9 segments on average, each segment is meters long, each segment accounts for the whole length, and 3 segments account for the whole length.
5. Divide the three ropes 1 meter into five pieces, each piece has three meters, which is meters.
6. The meter means 1 meter, which also means 5 meters.
Knowledge points: False scores become integers or take scores.
Exercise: 1= 3= 8= 4=
=( ) =( ) =( ) =( )
Knowledge points: reciprocity of fractions and decimals
Exercise: 1 Decimal decomposition into components.
0.6= 1.3= 2.4= 0. 17= 1.25=
2. Decimal part.
= = 4 = 5 = 3 = 1 = 1 =
3. Using fractions to express the quotient of the following questions is to convert false fractions into component numbers or integers.
25÷9= 18÷26= 54÷7=
4. Fill in ○, ○ or =.
○0.2 ○0.7 0.56○ ○0. 125
5. To make it a false score and a true score, the value of should be ().
6. There are () real scores greater than smaller scores.
7. Horses can run 1. 1 km per minute, cheetahs can run 6 km in 5 minutes, and swordfish can run 5 km in 4 minutes. What kind of animal runs fastest? Please compare and explain.
8. Chen Xiao and Xiao Wu play the same role. Xiao Chen needs 1. 1 hour, and Xiao Wu needs hours. Who does it fast?
Basic properties of unit 6 score
Knowledge point: the basic nature of score
Exercise: 1, = () ÷ 24 = 9 ÷ () = () (fill in decimal places)
2、 = = = =
3, the numerator plus 6, to make its size unchanged, the denominator should be added ().
The score is obtained by reducing the numerator by 2 times and enlarging the denominator by 3 times. The original score was ().
5. The numerator and denominator of a fraction are multiplied or divided by the same number at the same time, and the size of the fraction remains unchanged. () judgment
Knowledge point: approximate point
Exercise: 1, divided by the following fraction, the result is to turn the false fraction into an integer or a fraction.
= = = = =
2. Write all the simplest true fractions, and the denominator is18 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
Fill in the simplest score in ().
80 cm = () meters 3600 square meters = () hectares 45 minutes = ()
34 kg = () tons 64 hours = () days 150 ml = () liters.
4. Calculate the following questions to simplify the number to the simplest score.
+ = + = - = + =
5. About integration.
= = = = = =
= = = = = =
Knowledge points: common points
Exercise: 1 Divide into the following groups.
And, and, and, and, and.
2. In,,,,, and, the score is less than ().
3.200 kilograms of seawater contains 5 kilograms of salt, and water accounts for salt water. If you add 5 kilograms of salt, salt accounts for salt water.
4, processing the same kind of parts, a worker with 24 minutes, b workers with hours, () done quickly.
5、 15÷( )= =0.6= =
Unit 8 Addition and subtraction of fractions
Exercise: 1, calculating
+ = + = - = 1- = + = 2- =
2. A road maintenance team built a road and built kilometers on the first day, less than the next day. The next day, it built kilometers, and two days, it built kilometers.
3. The master and the apprentice cooperated to make a batch of parts. The master finished the parts, and the master made more parts than the apprentice.
4. A plot of land is planned to be ploughed for three days, the first day, the second day and the third day.
There is a garden in the campus of Hongshan Primary School, in which the area of Chinese rose flowers accounts for, the area of peony flowers accounts for, and the rest is lawn. What is the area of the lawn?
6. There is a garden on the campus of Hongshan Primary School, covering an area of hectares, including Chinese rose flowers, peony flowers and lawns. What is the area of the lawn?
8. Simple calculation
-( + ) - - + + +( + )
- + + + + - + -
The second unit determines the position
Knowledge points: when determining the position, the vertical line is called the column, and the horizontal line is called the line. Determine which column is generally counted from left to right and which row is generally counted from front to back.
Exercise: 1 A school gives students a number, with boys 0 1 and girls ending in 02. If Wang Hao, in Class 4, Grade 2, entered the school in 2005, and her student number is 36, and his student number is 0520436 1, then his cousin Li Shan entered the school in 2003. She is in Class 9, Grade 5, and her student number is ().
2. Xiaohong's position in the classroom is (3, 4). She sits in column () and row (). Xiaoli's position in the classroom is column 6, line 2, which is represented by a number pair (_ _ _ _ _ _ _ _ _ _ _ _).
Second, the operation question: look at the picture and answer the question.
(1) The positions of the three vertices A, B and C of a triangle in the graph are represented by number pairs.
(2) Translate the triangle to the left by 7 squares, draw the translated triangle first, and then use several pairs to display the positions of the three vertices A', B' and C' of the translated triangle.
(3) Rotate the triangle 90 degrees counterclockwise around point A each time, and draw the figures after the first, second and third rotations respectively. C 1, C2 and C3 respectively represent the rotated position of point C, and they are represented by several pairs. Connect C, C 1, C2, C3 and C in turn to see what the number is. A: _ _ _ _ _ _.
Unit 5 Looking for the Law
Knowledge points: number of translations+number of squares per time = total number of squares.
Exercise: 1 There are 24 seats in a row of cinemas. Mother took her daughter to the movies, and mother sat on her left. How many different ways are there in the same row?
1 2 3 4 5 6 7 8
2, (as shown in the figure) box out two adjacent numbers at a time, and one * * * gets () different sums; Box out three adjacent numbers at a time, and one * * * gets () different sums; Box out four adjacent numbers at a time, and one * * * gets () different sums.
3. Arrange the natural numbers as follows.
1 2 3 4 5 6 7 8
9 10 1 1 12 13 14 15 16
17 18 19 20 2 1 22 23 24
25 26 27 28 29 30 3 1 32
In this number array, Xiao Ming squares nine numbers.
(1) How many times do you move at will? What is the relationship between the sum of box 9 and the middle number?
(2) If the sum of the nine numbers in the box is 225, can we make an equation and find the middle number?
(3) How many different amounts can a * * * cover? A: _ _ _ _ _ _ _ _ _ _ _ _ _ _.
Unit 9 Strategies for Solving Problems
Exercise:
1 Xiaoming has some stamps. He gave Xiaohong more than half, leaving 50. How many sheets does he have?
Xiaoming and Xiaohong have 50 stamps. If Xiaoming gives Xiaohong eight stamps, then their stamps are equal. How many stamps does Xiaoming have?
3. Xiao Juan and Xiao Lei should make paper cranes, with 5 points for paper cutting, 25 points for origami cranes, and 10 points for putting paper cranes into a string. If it is to be completed in 10 am, when will they start at the latest?
Mr. Wang needs a 32 cm long wire to do the experiment. He cut off half of a metal wire and then cut it by 4 cm, which met the experimental requirements. How long was the original wire?
5. When a number is divided by 12, Xiao Ming regards 12 as 18, and the result quotient is 20. What is the correct quotient?
Unit 10 Circle
Knowledge points: radius, diameter, axisymmetric figure.
Radius diameter
1.2 cm
0.48 m
9 cm
1.5 decimeter
Exercise: 1 Fill in the table below.
2. Compare the sizes of two circles.
(1) A with a radius of 4cm；; B, the radius is 3 cm. () big
(2) One, with a diameter of 8 cm; B, radius of 5cm. () big
3. Judges.
The radius of (1) is the line segment from the center to any point on the circle. ( )
(2) The diameter is a line segment with two ends on the circle. ( )
(3) Draw a circle with a diameter of 6 cm, and the distance between the two feet of the compass is 6 cm. ( )
Draw a circle with a diameter of 4 cm, mark the center, radius and diameter, and use crossword puzzles to represent it.
5. The circle is a () figure with () as its axis of symmetry. () determines the position of the circle, and () determines the size of the circle.
Knowledge point: the circumference of a circle
Exercise: 1 Write the following values. (π takes 3. 14)
2π= 3π= 4π= 5π= 6π= 7π= 8π= 9π=
2. A circular iron ring with a diameter of 20 cm requires () iron wires to make such an iron ring.
3, a clock, the hour hand is 4 decimeters long, and its day and night journey is () decimeters.
4. The radius of the bicycle wheel is 40 cm, and the wheel rotates 100 times per minute. This bike runs () meters per minute.
5. Wrap a 20m-long rope around the trunk for 6 weeks, leaving1.16m. The diameter of this trunk is about 100 meter.
6. Fold a semicircle with a piece of circular paper with a diameter of 12cm, and find the circumference of this semicircle.
7. The diameter of the circular flower bed is 2 1 m.. How many azaleas should be planted every 3 meters along its edge?
8. The circumference of a circle is () times the diameter and () times the radius.
9. The radius, diameter, perimeter and area of the circle are enlarged by 3 times, () times and () times respectively.
10. Cut out the largest circle on a rectangular paper with a length of 18 cm and a width of 15 cm. The circumference of this circle is () cm and the area is () cm2.
1 1. A circle has a circumference of 25.12cm, a radius of () cm and a diameter of () cm.
12. Cut the largest circle in a square with a side length of 6 cm. The circumference of this circle is () cm and the area is () cm2.
Knowledge point: the area of a circle
Exercise: 1, fill in the blanks
( 1) = 1cm，= () cm2 (2) = 4cm，= () cm2。
(3) = 3cm，= () cm2 (4) = 4cm，= () cm2。
2. Cut a circle into an approximate rectangle. Measure the width of the rectangle is 3 cm, the diameter of the circle is () cm, and the length of the rectangle is () cm.
3. If a circle has a radius of 10 decimeter, a diameter of () decimeter, a circumference of () decimeter and an area of () square decimeter.
4. If the circumference of a circle is 12.56 cm, the radius is () cm and the area is () cm2.
5. The radius of the big circle is equal to the diameter of the small circle, and the area of this big circle is () times that of the small circle.
6. The radius of the front wheel of the roller is 0.5m.. If the front wheel rotates 7 times per minute, it can be pressed from one end of the road to the other in 10 minutes. This road is about () meters long.
7. A circular pool with a radius of 4 meters is surrounded by a path with a width of 2 meters, with an area of () square meters.
8. The circumference of a square and a circle is equal, and their area is greater than ().
9. The outer diameter of the bicycle wheel is 50 cm, and it can turn 100 times per minute. It takes 10 minutes for Xiaoming to go to school by bike from home. Xiaoming is () meters away from school.
10, find the area of the shaded part. Unit: centimeter (16 minutes)