Online Math Center

5 Math Skills You Need For Competitions

Have you looked at the tests given in math competitions this year? Middle school students might be familiar with the Math Kangaroo exams, an international math competition where students can verify and testify to their math skills. Our tutors looked over the paper exams for this year and prepared 5 math skills that any middle school student needs in order to score higher at any math competition.  

5 Math Skills you need for competitions

Spatial vision


Recognizing shapes in the world around us is one of the fundamental skills that children develop early in life. Mathematics, however, encourages us to upgrade spatial vision in order to identify not only shapes but also understand the relationships between them. Middle school students should learn how to: 


  • Identify different shapes
  • Identify the relationship between shapes


A sample question that the Math Kangaroo 2022 edition published for middle school which requires spatial vision was: 


Cistercian numerals were used in the early thirteenth century. Any integer from 1 to 99 can be represented by a single glyph formed by combining two of the glyphs shown below.

math competitions 2023

Quite challenging, isn’t it? Try to answer the question and then check your answer here

Logical thinking


This skill is overly advertised, however, logical thinking has to be a pre-school exercised skill. There are various games that pre-schoolers can play in order to develop logical thinking. Most math competition exercises that require logical thinking test logical correlations. See the example below, taken from Math Kangaroo, 2021, edition. 


10 elves and trolls each were given a token with a different number from 1 to 10 written on it. They were each asked what number was on their token and all answered with a number from 1 to 10. The sum of the answers was 36. Each troll told a lie and each elf told the truth. What is the smallest number of trolls there could be in the group?


(A) 1      (B) 3       (C) 4        (D) 5         (E) 7


Check your answer here

Mental algebra 


Fundamental algebra can easily be calculated mentally. There are a couple of math tricks that help you solve the four basic operations: addition, subtraction, multiplication, and division mentally. Besides nailing the four basic operations, middle school students also have to know the Rule of three by heart in order to find out the unknown variable in a problem. Check out the example below, taken from Math Kangaroo, 2019. 


A glass full of water weighs 400 grams. An empty glass weighs 100 grams. How many

grams does a glass half-full with water weigh?


(A) 150          (B) 200            (C) 225        (D) 250              (E) 300


Proportional understanding 


Fractions are often used in practical applications such as recipes, shopping, or painting. They are also an important part of any math competition. Check the 2022 Math Kangaroo paper exam and try to solve the following fraction problem:  

A painter wanted to mix 2 liters of blue paint with 3 liters of yellow paint to make 5 liters of green paint. However, by mistake he used 3 liters of blue and 2 liters of yellow so that he made the wrong shade of green. What is the smallest amount of this green paint that he must throw away so that, using the rest of his green paint and some extra blue and/or yellow paint, he could make 5 liters of paint of the correct shade of green? 


(A)53 liters             (B) 32 liters            (C) 23 liters               (D) 35 liters         (E)59 liters

Measuring quantities 


Middle school students will be introduced to fundamental geometry and units of measurement quite early in the curriculum. Measuring quantities is a most necessary skill in real life. We have to measure quantities when we bake, when we fill up a gas tank, or even when we have fish pets. Beyond that, units of measurement are at the basis of any construction. In 2021, Math Kangaroo for middle school graders came up with this challenge



The area of the large square is 16 cm2 and the area of each small suare is 1cm2. What is the total area of the black flower?


(A) 3 cm2      (B) 72 cm2             (C) 4 cm2           (D) 112cm2                (E) 6 cm2

math problem

Our math tutors at the OMC have worked over the years with thousands of students getting ready for math competitions. Students that are ready for a positive and fun challenge can enroll in any of our programs since we provide tutoring for both middle school and individual competitions. Contact us and let’s get those high scores! 

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