3rd grade children have learned the multiplication table, division table and started calculating the circumference. With that foundation, TIMO-style thinking problems expand to much better forms: calculating age, chickens and rabbits, dividing with remainders, counting multi-layered shapes, counting paths. This practice test helps children get familiar with those forms in one session.

The 15 questions below are tests prepared by the Karotto team, divided equally into 5 areas: logic, arithmetic, number theory, geometry, and combinatorics. This is not an official exam and Karotto is not affiliated with the TIMO organizing committee. Information about the exam can be found in the lesson What is TIMO?.

All answers have been checked by machine: try all cases, counting pictures on the coordinates of each line segment, calendar questions are compared with the real calendar.

How to use this practice problem

The problem has 15 questions, multiplication and division in the table, circumference, three-digit numbers. In each array, the sentence that comes before is easier than the sentence that comes after. Parents can use the question paper in three steps:

Timer: print the question paper or copy it on paper, and let your child do it in about 50 minutes (Karotto's suggestion, about 3 minutes per question). Just write down the answer, don't open the solution yet. If the child is not yet fluent in reading, parents should read the questions for help.
Do it in segments: If the child is new or gets tired easily, divide the topic into several short sessions, each session with one or two segments (3 to 6 sentences). Complete one area before moving on to the next, letting your child focus on one type of thinking.
Correction: For each question, let your child tell you how to do it first, then open "See solution". If the question is wrong, find the correct step that the child misunderstood, write it down, and let the child do it again the next day.

Tips for parents: don't judge just by the answer. A correct sentence thanks to a guess is not as rewarding as an incorrect sentence in which the child explains what he thinks. The solution below is written so that parents can read it once and explain it in their own words.

Part 1: Logic (sentences 1 to 3)

Verse 1

March 5 is Monday. What day is March 27 of the same year?

See solution

Answer: Tuesday.

  1. From the 5th to the 27th, the distance is: 27 − 5 = 22 days.
  2. Return every 7 days Exactly the same old thing. 22 days include 3 weeks (21 days) and 1 extra day.
  3. Day 5 + 21 = 26 is also Monday. One more day, the 27th is Tuesday.

Parents can open the real calendar for their children to check: days in the same column on the calendar are always 7 apart.

Verse 2

Four friends Hoa, Lan, Apricot, and Chrysanthemum stand in a row vertical. Cuc stands at the end of the line. Lan stood right in front of Cuc. Hoa is not at the front of the line. Ask who is at the front of the line?

See solution

Answer: Mai.

  1. The line has 4 seats. Cuc stands last: the 4th place is Cuc.
  2. Orchid stands right in front of Cuc: the 3rd place is Lan.
  3. There are places 1 and 2 for Hoa and Apricot. Hoa is not at the top, so Hoa is in position 2.
  4. The first place to surrender is Mai.

Draw 4 consecutive squares and then fill in the names according to each sentence. The most certain sentence (Chrysanthemum is last) should be filled in first.

Verse 3

On an island, True people always tell the truth, Gian people always lie. Friend A said: "B is Gian". Friend B said: "A and I are the same type of person". Ask A and B, who are each of you?

See solution

Answer: A is a Real person, B is a Fraudulent person.

Assume each case for A and then check:

  1. Suppose A is a Real person. Then A's sentence is correct: B is Gian. Then B's sentence "of the same type" is wrong (A True, B Gian), and B is a Gian person so saying it wrong is reasonable. There is no contradiction.
  2. Suppose A is Gian. Then A's sentence is wrong: B is a Real person. Then B speaks the truth, meaning A and B are of the same type, meaning A is also a Real person. Contradicts the assumption.

So A is a Real person, B is a Gian. This lesson is difficult because you have to keep two assumptions in mind. Have your child write each step on paper, one idea per line.

Part 2: Arithmetic (questions 4 to 6)

Question 4

Quick calculation: 6 × 7 + 6 × 3 = ?

See solution

Answer: 60.

  1. Both products have a factor of 6. "6 times 7 plus 6 times 3" means 7 times the number 6 and then 3 times the number 6.
  2. Combined is (7 + 3) times the number 6, which is 6 × 10.
  3. 6 × 10 = 60.

Check by calculating: 42 + 18 = 60. Understanding "7 times plus 3 times is 10 times" is more important than remembering the property name. Parents can illustrate with 7 boxes and 3 boxes, each box has 6 candies.

Question 5

In the cage there are 10 chickens and rabbits, count all 32 legs. How many rabbits are there?

See solution

Answer: 6 rabbits.

  1. Suppose all 10 are chickens. Then there are 10 × 2 = 20 legs.
  2. The true number is 32, missing 32 − 20 = 12 legs.
  3. Each time a chicken is changed to a rabbit, the number of legs increases by 2. Need to change 12 : 2 = 6 times.
  4. So there is 6 rabbits (and 4 chickens).

Check: 6 rabbits have 24 legs, 4 chickens have 8 legs, total 32. For children who are not yet familiar with division, let them draw 10 circles, each with 2 legs, then gradually add 2 legs to each shape until they have enough. 32.

Question 6

This year the father is 36 years old, the child is 8 years old. After how many years will the father be 3 times as old as his son?

See solution

Answer: After 6 years.

  1. The father is 36 − 8 = 28 years older than the son. Each year they both add 1 year, so the father is always 28 years older than the son.
  2. When the father's age is 3 times the son's age, considering the son's age as 1 part, the father's age is 3 parts. The father is 2 parts older than the child, and those 2 parts are 28 years old.
  3. 1 part is 28 : 2 = 14. At that time the child was 14 years old.
  4. The child from 8 years old to 14 years old took 14 − 8 = 6 years. So after 6 years.

Check: after 6 years the father is 42 years old, the son is 14 years old, 14 × 3 = 42. The key point of all age calculations is "the age difference remains constant". Parents, please emphasize this idea.

Part 3: Number theory (questions 7 to 9)

Question 7

Find the smallest number greater than 1 that leaves a remainder of 1 when divided by 2, divided by 3 or divided by 4.

See lyrics solution

Answer: 13.

  1. If the number divided by 2, 3, 4 has a remainder of 1, then when 1 is subtracted, it will be divisible by both 2, 3 and 4.
  2. Find the smallest number (non-zero) that is divisible by both 2, 3, 4: try the numbers divisible by 4 is 4, 8, 12. The number 12 is divisible by 3 and 2. So it is 12.
  3. The number to find is 12 + 1 = 13.

Check: 13 : 2 = 6 remainder 1, 13 : 3 = 4 remainder 1, 13 : 4 = 3 remainder 1. Idea "Remove the remainder to make it divisible" will still be used a lot in grades 4 and 5.

Question 8

From 1 to 100, how many numbers are divisible by 3 or divisible by 5?

See solution

Answer: 47 numbers.

  1. Numbers divisible by 3 from 1 to 100: 3, 6, 9, ..., 99. There are 99 : 3 = 33 numbers.
  2. Numbers divisible by 5: 5, 10, ..., 100. There are 100 : 5 = 20 numbers.
  3. There are numbers that are both divisible by 3 and 5, and are counted twice: 15, 30, 45, 60, 75, 90. There are 6 numbers.
  4. Number to find: 33 + 20 − 6 = 47 numbers.

Two intersecting circles (one circle "divisible by 3", one circle "divisible by 5") help children clearly see that the middle part is counted twice.

Question 9

A story book has 120 pages, numbered pages from 1 to 120. How many words must be written in total? number?

See solution

Answer: 252 digits.

  1. Page 1 to page 9: 9 pages, 1 digit per page, 9 digits.
  2. Page 10 to page 99: yes 99 − 10 + 1 = 90 pages, each page has 2 digits, giving 90 × 2 = 180 digits.
  3. Page 100 to page 120: has 120 − 100 + 1 = 21 pages, each page has 3 digits, giving 21 × 3 = 63 digits.
  4. Total: 9 + 180 + 63 = 252 digits.

A common error is counting the number of missing pages by 1 (120 − 100 = 20). Remind your child: when counting from 100 to 120, you must add 1, because the first and last pages are included.

Part 4: Geometry (questions 10 to 12)

Question 10

Combine 4 squares, each with a side of 2 cm, to form a letter L as shown below. How many centimeters is the perimeter of the L-shaped shape?

The L-shaped shape is made up of 4 equal squares: 3 squares arranged in a horizontal row below, 1 square placed above the first square on the left. Each side is 2 cm long2 cm
Question 10. L-shaped made from 4 squares with sides of 2 cm.
See solution

Answer: 20 cm.

  1. Perimeter is the length of the line surrounding the outside. Count the number of sides of the small square on the boundary: go around the L shape, count 10 sides.
  2. Each side is 2 cm long, so the perimeter is 10 × 2 = 20 cm.

Another way to check: 4 separate squares have 4 × 4 = 16 edge. There are 3 places where the two squares stick together, each place removing 2 sides from the boundary: 16 − 6 = 10 sides. A common mistake is adding sides inside the shape.

Question 11

The side square is divided into 9 equal small squares. How many squares are there in the picture?

The large square is divided into a grid of 3 rows and 3 columns of equal small squares
Question 11. The square is divided into a 3 x 3 grid.
See solution

Answer: 14 squares.

  1. Square with side 1 cell: 3 rows, each row of 3 cells, has 9 pictures.
  2. Square with side 2 cells (including 4 small cells): can be placed in 2 positions horizontally and 2 positions vertically, with 2 × 2 = 4 pictures.
  3. Square with 3 sides: is a big square, with 1 shape.
  4. Total: 9 + 4 + 1 = 14 squares.

Notice: 9 = 3 × 3, 4 = 2 × 2, 1 = 1 × 1. Grade 3 children like to discover this rule, and can guess the number of squares in a 4 × 4 grid.

Question 12

How many triangles are there in the figure?

Triangle ABC has two line segments AD and AE from vertex A to base BC, and one horizontal line segment. MQ is parallel to the base cutting AB at M, AD at N, AE at P, AC at QABCDEMNPQ
Question 12. Triangle ABC has two segments AD, AE and one horizontal segment MQ.
See text solution

Answer: 12 triangles.

  1. Every triangle in the figure has vertex A. The side opposite vertex A lies on the horizontal segment MQ or on the base BC.
  2. On segment MQ there are 4 points M, N, P, Q, creating segments: MN, NP, PQ, MP, NQ, MQ. There are 6 segments, so there are 6 triangles: AMN, ANP, APQ, AMP, ANQ, AMQ.
  3. On the base of BC there are also 4 points B, D, E, C, creating 6 segments, so there are 6 more triangles: ABD, ADE, AEC, ABE, ADC, ABC.
  4. Total: 6 + 6 = 12 triangles.

The part below segment MQ (like MBDN) is a quadrilateral, not a triangle. Tip: color each counted triangle with a different color pencil, your child will not count again.

Part 5: Combination (sentences 13 to 15)

Verse 13

Three friends An, Binh, and Chi stood in a horizontal line to take pictures. How many ways are there to arrange three friends?

See solution

Answer: 6 ways.

  1. The first place (left) has 3 ways to choose friends.
  2. The second place has 2 people left, there are 2 way.
  3. Only 1 person left at the end.
  4. Number of ways: 3 × 2 × 1 = 6 ways: An-Binh-Chi, An-Chi-Binh, Binh-An-Chi, Binh-Chi-An, Chi-An-Binh, Chi-Binh-An.

Question 14

From the four digits 0, 1, 2, 3, how many different three-digit numbers can be formed?

See solution

Answer number: 18 numbers.

  1. The hundreds digit cannot be 0, so there are 3 ways: 1, 2 or 3.
  2. The tens place must be different from the hundreds place, but can be 0: 3 ways left.
  3. The ones place must be different from both selected digits: 2 remaining way.
  4. Number of numbers: 3 × 3 × 2 = 18 numbers.

For example, the hundreds place is 1: 102, 103, 120, 123, 130, 132, exactly 6 numbers. Three such groups are 18. Have your child list a group to believe in multiplication.

Verse 15

An ant goes from A to B following the lines of the square grid as shown. Ants only go right or up. How many different paths are there?

The square grid is 3 cells wide and 2 cells high. Point A is in the lower left corner, point B is in the upper right cornerAB
Question 15. The grid is 3 cells wide and 2 cells high. Ants go from A (lower left corner) to B (upper right corner).
See solution

Answer: 10 paths.

  1. Write a number at each intersection of the grid: that number is the number of ways to go from A to that node.
  2. The buttons in the bottom row and left column have only one way (go straight), so write the number 1.
  3. Each remaining button: take the number in the left button plus the number in the button below (because ants can only reach from those two directions).
  4. Middle row, from left to right: 1, 2, 3, 4. Row top: 1, 3, 6, 10.
  5. Node B is marked with the number 10: there are 10 paths.

The "node numbering" method is a very powerful technique that can be used for even large grids. Parents print the grid on paper and let children fill in the number of each button themselves.

Arranged self-scoring board

Each correct sentence gets 1 point. Record the number of correct sentences for each array in the third column. The results by array are more useful than the total score, because it shows what kind of thinking the child needs to practice more.

ArraySentenceChildren are correctIf less than 2 sentences are correct, practice
Logic1, 2, 3…/3Practice drawing diagrams, drawing tables or arranging real objects before answering; Read each fact sentence slowly.
Arithmetic4, 5, 6…/3Practice finding pairs of numbers round tens and hundreds and drawing line diagrams for sums and differences.
Number theory7, 8, 9…/3List in order (by tens, hundreds) and underline all conditions in the problem.
Geometry10, 11, 12…/3Count from small to large shapes, name the shapes by letters, arrange sticks or real blocks to check.
Combination13, 14, 15…/3List in a table or branch diagram; Be careful of double counting (An-Binh and Binh-An are one).
Total1 to 15…/15From 12 sentences or more: your child has mastered this form. From 8 to 11 sentences: practice more weak areas. Less than 8 questions: back to more basic lessons, no need to take exam questions.

The above levels are just suggestions from Karotto for parents to choose the next step, not the scoring scale of any exam. If you want to see more about each type of lesson and how to teach it, parents should read the article Common forms of mental math in elementary schools.

Continue practicing in the Karotto app

Transparency: Karotto is the app of the team that makes this website. In the "Number Garden" Math course, the 3rd grade TIMO-style practice session is located on island M8 (for 8-year-old children), interspersed between regular courses, with all 5 areas of logic, arithmetic, number theory, geometry, and combinatorics as mentioned above.

Age calculation question in the Karotto app: mother gave birth to a bear when she was 25 years old, asked how old she was when the bear was 13 years old age
An arithmetic question (calculating age) in the TIMO-style training phase of Karotto: "Mom gave birth to bear when she was 25 years old. How old was mother when bear was 13 years old?"
  • Automatically generated practice questions: at the end of the island there is an exam-style practice test. The test is generated by the app itself, it doesn't copy the actual test, so each time it's a different test and the child can't memorize the answers.
  • There is a timer, marked by arrays: the child takes the test with a clock like taking an exam, then sees the score of each array like the self-scoring table above.
  • Review the sentence wrong: after submitting the assignment, the child reopens the correct incorrect questions to see the solution.
  • Voice reads the question: the question and instructions are read out loud in Vietnamese, so children who are not fluent in reading can still practice on their own.
  • Suggestion 3 hiccup: when stuck, the child is gently reminded first, then the illustration, and finally the answer with explanation.

Every day the child can learn a suitable amount of lessons for free, all islands are open. If you want unlimited training, the Premium package is a one-time purchase, lifetime use, no monthly or yearly subscription, no periodic deduction. The app has no ads.

In short

Let your child take a timed test, grade each section, then carefully correct each wrong sentence. One problem solved carefully is more useful than three problems done hastily. If you get less than 2 questions correct, practice that area more before taking a new test.

Frequently Asked Questions

Is this a real TIMO test?

No. This is a question prepared by the Karotto team in 5 areas of logic, arithmetic, number theory, geometry, and combinatorics, with the same format as common articles. Karotto is not affiliated with TIMO organizers. If you want to see the real test, parents should find the official documents of the organizer.

How long should your child take this test?

Suggest about 50 minutes for all 15 questions, or about 3 minutes per question. The first time can be divided into two sessions, each session has 2 or 3 segments. The important thing is that your child gets used to doing homework on time while still reading the topic carefully.

How to correct your child's homework effectively?

Let your child explain how to do it before explaining the solution. For a wrong sentence, find the correct step that your child misunderstood and then let your child try the sentence again the next day. Record points for each area to know which areas need more practice.

If a 3rd grade child gets most of it right, what should he practice next?

Let your child set up a similar problem and then ask the parents, for example, changing the numbers in the chicken and rabbit problem. Setting the problem yourself forces the child to understand why the solution is correct. After that, you can move on to grade 4 questions on the areas your child does best.

Practice mental math every day with Thỏ Bông

Automatically generated TIMO-style practice questions, with timer, marking by array, with Vietnamese voice and solutions for each wrong question.

Download on App Store → Get it on Google Play →