Students should know:

• A table of adding single-digit numbers and corresponding subtractions; a table of multiplication of single-digit numbers and corresponding table division cases (at automated skill level);
• name of action components, rules for finding action components;
• the properties of arithmetic actions: addition (move and combination); multiplication (move, combination and distribution); division of sum by number; division of number by work.
• rules for performing actions in a numeric expression containing 3-4 actions with and without brackets;
• units of quantities (length, mass, area, time) and relations between them, indication of units;
• the concept of the perimeter and area of the rectangle, the perimeter of the polygon;
• multiplication for 4th grade

Learners must be able:

• Read, write, compare numbers within a million;
• perform oral calculations within 100, and with large numbers in cases easily reducible to actions within 100;
• perform written computations (addition, subtraction, one-digit, two-digit, and three-digit numbers; division into one-digit and two-digit numbers); solve the simplest numerical puzzles;
• calculate the value of a numeric expression containing 4-5 actions (with and without brackets) based on the rules of the order of actions;
• solve equations by applying rules of finding components;
• recognize and depict basic geometrical figures (triangle, rectangle, square), build a rectangle and a square on checkered paper; solve simple cutting problems;
• to draw with a ruler a piece of the set length, to measure length of a piece;
• calculate perimeter and area of a rectangle, perimeter of a polygon;
• to solve the problems in several actions connected with the meaning of the relations “less by …”, “more by …”, “less by …”, “more by …”, as well as the problems of finding the unknown component and the proportional dependence of the quantities, the problems of motion.
• Workbooks for 4th grade

Introductory work on mathematics in the Lyceum is carried out in written form. The work consists of 5 questions covering the following topics:

“Text Tasks.”

Example 1: Solve a task with an explanation:

A cyclist was riding from the City of Kurchatov to Kursk for 4 hours at 12 km/h, and on the way back he spent 6 hours. How many kilometers per hour did the bicyclist change his speed?

Example 2: Solve the problem with an explanation:

There were 700 seedlings in the garden nursery. Three stores bought 70 seedlings each and two 90. How many more seedlings did the nursery have left?

Example 3: Two travellers from two cities went to meet each other. The distance between the two cities is 63 miles. One traveled at 3 miles 125 fathoms per hour, and the other 7 miles 125 fathoms per hour. How long will they meet? (1 versts 500 fathoms)

2. “Perform arithmetic operations.”

Example 1: Calculate: (1833: 47 + 467) ∙ 57 – 47 ∙ 307

Example 2: Perform the calculations: 502 ∙ 68 – (3 685 +3182): 63

3. “Equations.”

Example 1: Solve equation: 96 ∙ (3 ∙ x + 3) = 6 048

Example 2: Solve equation: (3 ∙ x – 21): 6 + 127 =39996:303

4. “Tasks per unit of magnitude (length, mass, area, time) and the ratios between them.

Example 1: Convert the quantities into the same units of measurement and compare them.

(a) 14 months … 1 year 3 months,

b) 208 dm … 2 m 8 dm ..,

c) 16 cm2 … 160 mm2.

Example 2: Find missed numbers in an expression:

(6 c 25 kg) ∙ 6 = … t … c kg

5. “Non-standard tasks include numerical puzzle tasks, cutting tasks, transfusion tasks, weighing tasks, worst case tasks, and other logical tasks.

workbooks for 4th grade

Example 1: Valera, Pavlik and Kirill were fishing and caught different numbers of fish (each caught at least one). Valera and Pavlik caught 6 fish together, Valera and Cyril caught 4 fish. How many fish did Cyril catch

Example 2: Grisha, Zina, Lyuda, Petya were born on 12 January, 6 April, 12 June, 27 June. Petya and Lyuda were born in the same month, and Zina and Petya were born on the same day of different months. When was Grisha born? Indicate the date and month.

Example 3: Chickens and goats walk in the yard, all together have 44 legs and 14 heads. How many chickens and goats walk in the yard?

Example 4: One cup of scales has 6 identical apples and 3 identical pears, the other cup has 3 identical apples and 5 identical pears. The scales are in equilibrium. Which is lighter: an apple or a pear?

Example 5: There are 6 suitcases and 6 keys to these suitcases. What is the highest number of samples you will need to do to find your own key to each suitcase?

Example 6: Tanya needs 20 p. to buy 8 balloons. If she buys 5 balloons, she will have 110 p. left. How much money does Tanya have?

The choice of topics is due not only to the requirements for mathematical training of future fifth graders, but also to the appropriate mathematics programs in the Lyceum. Each question is evaluated in points according to its complexity: from 0 to 3 points inclusive. The maximum number of points is 15.