Multiplication is an arithmetic operation, in which the first number is repeated as a summand as many times as the second number shows.
A number that is repeated as a term is called multiplicable (it is multiplied), the number that shows how many times the term is repeated is called multiplier... The number obtained as a result of multiplication is called work.
For example, multiply natural number 2 for a natural number 5 means finding the sum of five terms, each of which is equal to 2:
2 + 2 + 2 + 2 + 2 = 10
In this example, we find the sum by ordinary addition. But when the number of identical terms is large, finding the sum by adding all the terms becomes too tedious.
To write multiplication, use the × (oblique cross) or · (dot) sign. It is placed between the multiplier and the multiplier, with the multiplier being written to the left of the multiplication sign, and the multiplier to the right. For example, writing 2 · 5 means that the number 2 is multiplied by the number 5. To the right of the multiplication record, put the \u003d (equal) sign, after which the multiplication result is written. Thus, the complete record of multiplication looks like this:
This entry reads like this: the product of two and five is ten, or two times five is ten.
So we can see that multiplication is simply short form recording the addition of the same terms.
Multiplication test
To test multiplication, you can divide the product by a factor. If the result of division is a number equal to the multiplication, then the multiplication is correct.
Consider the expression:
where 4 is the multiplier, 3 is the multiplier, and 12 is the product. Now let's check the multiplication by dividing the product by a factor.
All other division tables are obtained in a similar way.
METHODS OF REMEMBERING THE TABLE OF DIVISION
Techniques for storing tabular division cases are associated with methods of obtaining a division table from the corresponding tabular multiplication cases.
1. Reception associated with the meaning of the action of division
With small values \u200b\u200bof the dividend and divisor, the child can either perform objective actions to directly obtain the result of the division, or perform these actions mentally, or use a finger model.
For example: 10 flower pots were placed equally on two windows. How many pots are there on each window?
To get the result, the child can use any of the above models.
For large values \u200b\u200bof the dividend and divisor, this technique is inconvenient. For example: 72 pots of flowers were placed on 8 windows. How many pots are there on each window?
Finding a result using a subject model is inconvenient in this case.
2. The trick associated with the rule of interconnection of the components of multiplication and division
In this case, the child is guided. To memorize an interconnected triplet of cases, for example:
If the child manages to remember well one of these cases (usually the basic one is the case of multiplication) or he can get it using any of the methods of memorizing the multiplication table, then using the rule “if the product is divided by one of the factors, then the second factor will be obtained”, easily get the second and third table cases.
№ 13 Methodology for studying the technique of dividing a two-digit number by a single-digit number
When studying the technique of dividing a two-digit number by a single-digit number, use the rule of dividing the sum by the number. Groups of examples are considered:
1) 46: 2 \u003d "(40 + 6): 2 \u003d 40: 2 + -" 6: 2 \u003d 20 + 3 \u003d 23 (replace the dividend with the sum of the digit terms)
2) 50: 2 \u003d (40 + 10): 2 \u003d 40: 2 + 10: 2 \u003d 20 + 5 \u003d 25 (the dividend is replaced by the sum of convenient terms - round numbers)
3) 72: 6 \u003d (60 + 12): 6 \u003d 60: 6+ 12: 6 \u003d 10 + 2 \u003d 12 (the dividend is replaced by the sum of two numbers: a round number and a two-digit number)
In all examples, these terms will be convenient if, when dividing them by a given divisor, the bit terms of the quotient are obtained.
In the preparatory period, exercises are used: select round numbers up to 100 that are divisible by 2 (10, 20, 40, 60, 80), by 3 (30, 60, 90), by 4 (40, 80), etc.; represent in different ways the numbers as the sum of two terms, each of which is divisible by given number without a remainder: 24 can be replaced by a sum, each term of which is divisible by 2: 20 + 4, 12 + 12, 10 + 14, etc .; solve in different ways examples of the form: (18 + 45): 9.
After the preparatory work, examples of three groups are considered, with great attention being paid to replacing the dividend with the sum of convenient terms and choosing the most convenient method:
42: 3= (30+12) : 3=30: 3+12: 3= 14
42:3=(27+15) :3=27: 3+15: 3=14 42:3= (24+1&) : 3 = 24: 3+18:3=14
42: 3 \u003d (36 + 6): 3 \u003d 36: 3 + 6: 3 \u003d 14, etc.
The first method can be attributed to the most convenient way, since when dividing the convenient terms (30 and 12), we get the bit terms of the quotient (10 + 4 \u003d 14).
Examples of the type: 96: 4 are difficult. In such cases, it is advisable to replace the dividend with the sum of convenient terms, the first of which expresses the largest number of tens, divisible by the divisor: 96: 4 \u003d (80 + 16): 4.
1. Bit composition of the number
2.property of dividing a sum by a number
3. Division of a number ending in 0
4. Tabular division cases
5. "Convenient" number composition.
Division with remainder.
Division with remainder is studied in grade II after completing work on out-of-table cases of multiplication and division.
Working on division with a remainder within 100 expands students' knowledge of the action of division, creates new conditions for applying knowledge of the tabular results of multiplication and division, for applying computational techniques for non-tabular multiplication and division, and also prepares students in a timely manner for the study of written division techniques.
A feature of division with a remainder in comparison with actions known to children is the fact that here, using two given numbers - the dividend and the divisor - two numbers are found: the quotient and the remainder.
In their experience, children have repeatedly encountered cases of division with a remainder, performing division of objects (sweets, apples, nuts, etc.). Therefore, when studying division with a remainder, it is important to rely on this experience of children and at the same time enrich it. It is useful to start by solving vital practical problems. For example: “Give 15 notebooks to pupils, 2 notebooks to each. How many students received notebooks and how many notebooks are left? "
Pupils distribute, lay out objects and verbally answer the questions posed.
Along with these tasks, work is carried out with didactic material and with pictures.
We divide 14 circles by 3 circles. How many times are 3 mugs in 14 mugs? (4 times.) How many circles are left? (2.) A division record with a remainder is introduced: 14: 3 \u003d 4 (remaining 2). Pupils solve several similar examples and problems using objects or pictures. Let's take the problem: "" Mom brought 11 apples and distributed them to the children, 2 apples each. How many children received these apples and how many apples are left? " Pupils solve the problem using circles.
The solution and answer to the problem are written as follows-11: 2 \u003d 5 (rest. 1).
Answer: 5 children and 1 apple remains.
Then the relationship between the divisor and the remainder is revealed, that is, the students establish: if division results in a remainder, then it is always less than the divisor. To do this, first solve examples of dividing consecutive numbers by 2, then by 3 (4, 5). For instance:
10:2=5 12:3 = 4 16:4 = 4
11: 2 \u003d 5 (rest 1) 13: 3 \u003d 4 (rest 1) 17: 4 \u003d 4 (rest 1)
12: 2 \u003d 6 14: 3 \u003d 4 (rest 2) 18: 4 \u003d 4 (rest 2)
13: 2 \u003d 6 (rest 1) 15: 3 \u003d 5 19: 4 \u003d 4 (rest 3)
Students compare the remainder with the divisor and notice that when divided by 2, the remainder is only 1 and cannot be 2 (3, 4, etc.). In the same way, it turns out that when dividing by 3, the remainder can be 1 or 2, when dividing by 4, only numbers 1, 2, 3, etc. Comparing the remainder and the divisor, the children conclude that the remainder is always less than the divisor.
To assimilate this relationship, it is advisable to offer exercises similar to the following:
What numbers can be obtained in the remainder when dividing by 5, 7, 10? How many different residuals can there be when divided by 8, 11, 14? What is the largest remainder that can be obtained by dividing by 9, 15, 18? Can the remainder be 8, 3, 10 when dividing by 7?
To prepare students to master the technique of division with remainder, it is useful to offer the following tasks:
What numbers from 6 to 60 are divisible by 6, 7, 9 without a remainder? What is the smaller number closest to 47 (52, 61) that is divisible by 8, 9, 6 without a remainder?
Revealing the general method of division with remainder, it is better to take examples in pairs: one of them for division without remainder, and the other for division with remainder, but the examples must have the same divisors and quotients.
Further, examples of division with remainder are solved without an example helper. - Let 37 be divided by 8. The student must learn the following reasoning: “37 by 8 is not divisible without a remainder. The largest number that is less than 37 and divisible by 8 without a remainder, 32. 32 divided by 8 is 4; from 37 we subtract 32, we get 5, the remainder is 5. So, 37 divided by 8, we get 4 and the remainder is 5 ".
The skill of division with a remainder is developed as a result of training, so it is necessary to include more examples of division with a remainder both in oral exercises and in written work.
Performing division with remainder, students sometimes get a remainder greater than the divisor, for example: 47: 5 \u003d 8 (remainder 7). To prevent such errors, it is useful to offer children incorrectly solved examples, let them find the error, explain the reason for its occurrence and solve the example correctly.
1. choose a number close to the dividend, which is less than it and is divisible without a remainder;
2. split this number;
3. find the remainder;
4. check the remainder, whether it is less than the divisor;
5.write an example
In II and III grades it is necessary to include as many different exercises as possible for all the cases of multiplication and division studied: examples in one and several actions, comparison of expressions, filling out tables, solving equations, etc.
№ 14. Composite task concept.
A compound task includes a number of simple tasks that are interconnected in such a way that the desired ones for some simple tasks serve as data for others. Solving a compound problem is reduced to breaking it down into a number of simple problems and solving them sequentially. In this way, to solve a complex problem, it is necessary to establish a number of connections between the data and the desired one, in accordance with which to select and then perform arithmetic operations.
In the solution of a composite problem, a significantly new thing has appeared in comparison with the solution of a simple problem: here not one connection is established, but several, in accordance with which arithmetic operations are selected. Therefore, special work is carried out to familiarize children with a compound problem, as well as to form their skills to solve compound problems.
Preparatory work to familiarize yourself with compound tasks should help students understand the main difference between a compound problem and a simple one - it cannot be solved immediately, that is, in one action, but for the solution it is necessary to isolate simple tasksby establishing the appropriate links between the data and the desired one. For this purpose, special Exercises are provided.
Task 2. How many strawberries? How many cherries? Write it down using multiplication. 3 5 \u003d 15 (h.); 3 6 \u003d 18 (in.).
- How many children can you share strawberries? (15: 3 \u003d 5 or 15: 5 \u003d 3.)
- How many children can you share cherries? (18: 3 \u003d 6 or 18: 6 \u003d 3.)
Task 3. Several rings are spread equally on three pins. There were 4 rings on each pin. How many rings did you take? (4 3 \u003d \u003d 12 (k.).)
- Spread 12 rings evenly over 4 pins. How much will each be? Write down equality. (12: 4 \u003d 3 (c.).)
Task 4. Students perform multiplication and write down the corresponding equalities with the division sign.
6 4 \u003d 24 5 6 \u003d 30 7 4 \u003d 28 8 3 \u003d 24
4 6 \u003d 24 6 5 \u003d 30 4 7 \u003d 28 3 8 \u003d 24
24: 4 = 6 30: 6 = 5 28: 4 = 7 24: 3 = 8
24: 6 = 4 30: 5 = 6 28: 7 = 4 24: 8 = 3
Task 5. Remember the tale "Turnip". Name the heroes of this tale. How many were there? (6 heroes.) My grandfather cut the turnip into 18 pieces. Will he be able to distribute them equally to all the heroes of the tale? How many pieces will each get? (18: 3 \u003d 6 (c.).)
Task 6. Students perform calculations:
15 2 - 16 \u003d 30 - 16 \u003d 14 5 5 - 19 \u003d 25 - 19 \u003d 6
6 3 + 27 \u003d 18 + 27 \u003d 45 40: 2 - 9 \u003d 20 - 9 \u003d 11
60: 2 + 36 \u003d 30 + 36 \u003d 66 20 2 + 48 \u003d 40 + 48 \u003d 88
34 2 - 26 \u003d 68 - 26 \u003d 42 9 3 + 18 \u003d 27 + 18 \u003d 45
Task 7. Make equalities from the numbers 2, 8 and 16. And let your deskmate make such equalities from the numbers 6, 3 and 18.
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 16 3 + 3 + 3 + 3 + 3 + 3 = 18
8 + 8 = 16 6 + 6 + 6 = 18
2 8 \u003d 16 3 6 \u003d 18
8 2 \u003d 16 6 3 \u003d 18
16: 2 = 8 18: 3 = 6
16: 8 = 2 18: 6 = 3
IV. Lesson summary.
- What are the actions of multiplication and division called?
Lesson 74
The meaning of arithmetic operations
The goals of the teacher: to contribute to the consolidation of ideas about the meaning of the four arithmetic operations; to promote the development of the ability to draw up rules for multiplying numbers by 1 and 0, to solve word problems, perform calculations from 0 and 1.
Subject: have ideas know how
Personal UUD: perceive the speech of the teacher (classmates), not directly addressed to the student; independently assess the reasons for their successes (failures); express a positive attitude towards the process of cognition.
regulatory:evaluate (compare with the standard) the results of activities (someone else's and one's own); cognitive:apply schemes to obtain information; compare different objects; explore the properties of numbers; solve non-standard tasks; communicative: communicate their position to all participants educational process - formulate their thoughts in oral speech; listen and understand the speech of others (classmates, teachers); solve the problem.
During the classes
I. Oral account.
1. Fill in the empty cells so that the sum of the numbers in each rectangle made up of three cells is 98.
2. Solve the short note problem.
a) How much does a pike weigh?
b) How many kilograms do carp and pike weigh?
c) How much do two carp weigh? How much do two pikes weigh?
3. Compare, without calculating, using the signs "\u003e", "<», «=».
4. Make all possible examples from the groups of numbers.
a) 26, 2, 28; b) 80, 4, 76; c) 50, 3, 47.
II. Lesson topic message.
- Today in the lesson we will make up equalities according to pictures and diagrams.
III. Textbook work.
Task 1. What arithmetic action does the first drawing represent? (Addition.) Write down equality. (5 + 7 = 12.)
- What is the name of the "+" sign?
- What arithmetic operation does the second figure represent? (Subtraction.) Write down equality. (9 – 5 = 4.)
- What is the name of the "-" sign?
- What arithmetic action does the third figure represent? (Multiplication.) Write down equality. (3-4 \u003d 12.)
- What is the name of the “·” sign?
- What arithmetic operation does the fourth figure represent? (Division.)
- Write down the equality. (9: 3 = 3.)
- What is the name of the “:” sign?
Task 2. Students relate drawing and equality.
Task 3. Perform calculations.
1 3 \u003d 1 + 1 + 1 \u003d 3
1 10 \u003d 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 \u003d 10
4 1 \u003d 1 4 \u003d 1 + 1 + 1 + 1 \u003d 4
100 1 \u003d 1 100 \u003d 100
- What conclusion can be drawn? (If you multiply any number by 1, you get the same number.)
- Perform calculations.
0 3 \u003d 0 + 0 + 0 \u003d 0
5 0 \u003d 0 5 \u003d 0 + 0 + 0 + 0 + 0 \u003d 0
100 0 \u003d 0 100 \u003d 0
- What conclusion can be drawn? (If you multiply any number by 0, you get 0.)
Task 4. Students perform calculations based on the example.
Task 5. The room has 4 corners. There is a cat in every corner. Each cat has 4 kittens. Each kitten has 4 mice.
- How many cats are in the room?
4 4 \u003d 16 (live) - kittens in the room.
16 + 4 \u003d 20 (live) - cats and kittens.
- How many mice?
16 4 \u003d 16 + 16 + 16 + 16 \u003d 32 + 32 \u003d 64 (live) - mice.
- How many animals are there?
64 + 20 \u003d 84 (live) - total.
- How many cats are smaller than mice?
64 - 20 \u003d 44 (alive) - fewer cats than mice.
Task 6. Perform calculations.
- Write down expressions from different columns for which the calculation results are the same.
Task 7. Work in pairs.
35 – 5 = 30 20 – 5 = 15 10 – 5 = 5
30 – 5 = 25 15 – 5 = 10 5 – 5 = 0
- How many people will get potatoes? (to seven people.)
IV. Work on cards.
1. Compare.
5 · 2… 5 · 3 2 · 5 ... 2 · 4
2 7 ... 8 2 3 7 ... 6 3
3 6 ... 3 5 4 8 ... 4 7
2. solve examples.
2 4 \u003d 2 3 \u003d 2 8 \u003d
4 2 \u003d 3 2 \u003d 8 2 \u003d
3. Calculate, replacing multiplication by addition:
8 5 \u003d 7 4 \u003d 16 3 \u003d
4. Insert the missing numbers:
5. Make examples for division:
V. Lesson summary.
- What new did you learn in the lesson? What are the arithmetic operations? What do we get if the number is multiplied by 1? What do we get if the number is multiplied by 0?
Lesson 75
Solving multiplication and division problems
The goals of the teacher: contribute to the development of the ability to solve word problems for multiplication and division; to promote the improvement of the ability to choose an arithmetic operation in accordance with the meaning of a word problem, to restore the correct equalities.
Planned results of education.
Subject: have ideas about the properties of numbers 0 and 1 (if you increase one factor by 2 times, and decrease the other by 2 times, the result will not change); know how increase / decrease numbers by 2 times, perform multiplication with numbers 0 and 1, find a product using addition, perform calculations in two steps, solve problems of increasing / decreasing "2 times", finding a product (using addition, dividing and by content (selection).
Personal UUD:evaluate their own educational activities: their achievements, independence, initiative, responsibility, reasons for failure.
Metasubject (criteria for the formation / evaluation of components of universal educational actions - UUD):regulatory: adjust activities: make changes to the process taking into account the difficulties and errors encountered; outline ways to eliminate them; analyze the emotional state obtained from successful (unsuccessful) activities; cognitive:search for essential information; provide examples to support the claims being made; make conclusions; are guided in their knowledge system; communicative: take a different opinion and position, admit the existence of different points of view; adequately use speech means to solve various communication problems; build monologic statements, possess a dialogical form of speech.
During the classes
I. Oral account.
1. Compare without calculating.
2. Solve the problem.
A duck needs 7 kg of feed per day, a chicken 3 kg less than a duck, and a goose 5 kg more than a chicken. How many kilograms of feed does a goose need per day?
3. Insert the missing numbers:
4. in the picture you see two trees: birch and spruce. The distance between them is 15 meters. A boy stands between the trees. It is 3 meters closer to the birch than to the spruce.
- What is the distance between a birch and a boy? (6 m.)
II. Lesson topic message.
- Today in the lesson we will solve multiplication and division problems.
III. Textbook work.
- Read problem 1. What is known? What do you need to know? Write down expressions to solve each problem.
- Find the meaning of each expression.
Formulate the answers to the problem questions.
a) 1 time - 3 r. Decision:
4 times - ? R. 3 4 \u003d 12 (p.).
b) 1 row - 9 K. Solution:
4 rows -? K. 9 4 \u003d 36 (K.).
c) 1 time - 8 points each Solution:
3 times - 9 points each 8 2 + 9 3 \u003d 16 + 27 \u003d 43 (points).
Total - ? glasses
d) 3 piles - 12 b. Decision:
1 pile -? b. 12: 3 \u003d 4 (b.).
It was 12 b. Decision:
Divided equally by 4 alive. - by? b. 12: 4 \u003d 3 (b.).
e) 3 people. - by? R. Decision:
Total - 60 rubles. 60: 3 \u003d 20 (p.).
Task 2. Determine who made how many blades. Who Forged the Most Blades?
1) 7 + 2 \u003d 9 (cl.) Forged by Dili;
2) 9 2 \u003d 18 (class) - forged Keely;
3) 9 2 \u003d 18 (class) - forged by Balin;
4) 18: 2 \u003d 9 (cl.) - forged Dvalin;
5) 9 - 2 \u003d 7 (cl.) Was forged by Bombur.
Exercise 3. How many balls should be put on the second pan to balance the scales?
Task 4. How many legs does a centipede have? (40 legs.)
Goose? (2.)
At the piglet? (4.)
The beetle? (6.)
- Make an expression to count the legs of all these animals.
IV. Frontal work.
- Make a multiplication problem and two division problems according to the picture.
Lesson 76
Solving non-standard tasks
Teacher action goals: to promote the consideration of a graphical way of solving non-standard problems (combinatorial) and with the presentation of data in a table; to promote the development of the ability to solve combinatorial problems using multiplication, to compose two-digit numbers from these numbers, to compose sums and differences, to carry out oral and written calculations with natural numbers; to promote the development of the ability to check the correctness of calculations, the ability to classify and divide into groups.
Planned results of education.
Subject: have ideas about the properties of numbers 0 and 1 (if you increase one factor by 2 times, and decrease the other by 2 times, the result will not change); know how increase / decrease numbers by 2 times, perform multiplication with numbers 0 and 1, find a product using addition, perform calculations in two steps, solve problems for increasing / decreasing "2 times", finding a product (using addition, dividing and in terms of content (selection), to solve non-standard tasks.
Personal UUD:assess their own learning activities; apply the rules of business cooperation; compare different points of view.
Metasubject (criteria for the formation / evaluation of components of universal educational actions - UUD):regulatory:control their actions for accurate and operational orientation in the textbook; define and formulate the goal of the lesson with the help of the teacher; cognitive:orientate themselves in their knowledge system, supplement and expand them; communicative: enter into collective educational cooperation, convey their position to all participants in the educational process - formulate their thoughts in oral and written speech; listen and understand the speech of others (classmates, teachers); solve the problem.
During the classes
I. Oral account.
1. Write in the missing terms so that the value of the sum of the numbers along each side of the triangle is equal to the number written inside the triangle.
2. Indicate with an arrow which box each pencil comes from.
3. Coffee, juice and tea were poured into a glass, cup and jug. There is no coffee in the glass. There is no juice or tea in the cup. There is no tea in the jug. What is the container that is poured in?
II. Textbook work.
- Today in the lesson we will solve tasks in different ways.
Task 1. How many boys were there? Girls? How many different pairs are there? Make different pairs using the diagrammatic picture.
- Write down the total number of pairs using addition and then using multiplication.
3 + 3 + 3 \u003d 9 (p.). 3 3 \u003d 9 (p.).
Task 2. Solve the combinatorial problem using the table.
- How many pairs did you get? (20 pairs)
- Count in different ways.
4 5 \u003d 20 5 4 \u003d 20
Task 3. Compose, working in pairs, all possible products according to the scheme ○ · □, where ○ is an odd number, □ is an even (including 0).
- Calculate all these works.
- How many pieces can you compose?
Task 4. The checkbox consists of two stripes of different colors. How many of these flags can you make out of four different paper colors? (24 flags.)
- How many tricolor flags can you make? (6 checkboxes.)
- How many more three-color flags are there than two-color ones? (6 – 2 = 4.)
Task 5. Make a table for solving the combinatorial problem.
Answer:20 options.
Task 6 (work in pairs).
- Make two-digit numbers from the numbers 2, 4, 7, 5.
Recording: 24, 25, 27, 22.
- Make the sum and difference of these pairs of numbers. Find their meanings.
Task 7. The menu in the dining room has three first courses and six second courses. How many ways are there to choose a two-course meal? (6 3 \u003d 18.)
Students complete the table.
- In addition to the first and second, you can also choose one of three desserts. Multiply the number of options for a three-course meal. (18 3.)
- Count this number by adding.
18 3 \u003d 18 + 18 + 18 \u003d 36 + 18 \u003d 54.
Lesson 77
Meet new actions
(reiteration)
The goals of the teacher: create conditions for the successful repetition of addition, subtraction, multiplication, division, and the use of appropriate terms; contribute to the formation of ideas about the use of multiplication in ancient Egypt.
Planned results of education.
Subject: have ideas about the properties of numbers 0 and 1 (if you increase one factor by 2 times, and decrease the other by 2 times, the result will not change); know how increase / decrease numbers by 2 times, perform multiplication with numbers 0 and 1, find a product using addition, perform calculations in two steps, solve problems for increasing / decreasing "2 times", finding a product (using addition, dividing and by content (selection); know about the methods of calculation in Ancient Egypt.
Personal UUD:motivate their actions; express readiness to act in accordance with the rules of conduct in any situation; show kindness, trust, attentiveness, help in specific situations.
Metasubject (criteria for the formation / evaluation of components of universal educational actions - UUD):regulatory:know how to evaluate their work in the classroom; analyze the emotional state obtained from successful (unsuccessful) activities in the lesson; cognitive: compare different objects - select from a set one or more objects that have common properties; provide examples to support the claims being made; communicative: take a different opinion and position, admit the existence of different points of view; adequately use speech means to solve various communication problems.
During the classes
I. Oral account.
1. Sasha and Petya fired 3 shots at the shooting range, after which their targets looked like this:
- state the name of the winner.
- Find the third term.
2. The girl read the book in three days. On the first day she read 9 pages, and on each subsequent day she read 3 more pages than on the previous day. How many pages are in the book?