Mental math activities grade 5: Mental Math 5th Grade
Posted on22 Mental Math Classroom Games and Teaching Resources
Mental math is a students ability to make calculations in their mind without the guidance of pencil and paper, calculators, or other aids. It is often used as a way to calculate and estimate quickly, using math facts that students have committed to memory, such as multiplication, division, doubles facts, etc.
Therefore, to develop as a mental math whiz, students must have a strong number sense.
In the early years, subitizing activities are extremely useful to lay the foundations of students developing a strong number sense. This early maths skill encourages children to rapidly recognize quantities. These subitizing flashcards, used daily, are a great way to improve your students’ skills.
This first set of flash cards is simply black dots – ask your students to quickly tell you how many dots they see on each flashcard.
This second set of flash cards has some black dots and some white.
Ask your students to tell you how many black dots, how many white dots and then how many dots altogether?
Finally, some of these colored subitizing flash cards have three different colors, this is a good extension for those students who have well developed subitizing skills.
As children learn to add numbers, they become very reliant on counting. This is OK with small numbers, however, it can cause difficulties down the road when students begin to add larger numbers mentally. For example, if a student used counting strategies, such as counting on by ones or using tally marks, to add 35 + 45, they would most likely loose count. It is also not an efficient way to work out this sum. Therefore, embedding basic number fact and place value knowledge in students is another important step in the process of being able to solve math problems mentally.
A knowledge of number facts then transforms into the different mental strategies that can be used. We have a variety of posters and resources that can help in this part of the teaching process:
Encourage ‘number talks‘ daily! Students discussing their strategies is imperative in teaching mental math.
Every morning in my classroom, we had ‘number talks’. I would put a couple of math problems on the board and students would work out each problem in their head. Once they had an answer they would place their hands on their head.
They discussed their answer and selected a strategy with a partner and then with the class. The discussions that took place were some of the best teaching moments I had that year! Seeing the ‘lightbulb’ light up in students heads as they heard their friends explain to them how they had worked it out!
Along with the explicit teaching and discussing of different strategies, it is also important to provide a number of other handson opportunities for students to cement different strategies. Here are some of my favorite:
101 and out!
Kids love playing this! Especially if they play it against their teacher!
Explain to the class that initially they will be playing against you, then against each other. The aim of the game is to get to 100 without going over!
Each team rolls a dice (or two). They then decide if they are going to use the total as a place value of tens or ones/units. For example, if they roll a 6 they can choose to add 6 to their total or 60. Each team needs to then record their running total on a sheet of paper and color the different sub totals on their hundreds board.
Play BINGO!
Bingo is always a very popular game to play in the classroom. We have a variety of multiplication, division, addition, and subtraction bingo games available. These can assist in cementing certain math facts in your students.
A game using addition, subtraction, multiplication, and division.
The aim of the game is to cover each of the numbered boxes on the game card by correctly answering the calculation that has been drawn out.
Use whichever combination of operation cards to adjust the difficulty of the game.
Move Up the Ladder
Race against the clock!
Kids always love a bit of a challenge. Using our Number Ladder template, students must roll two dice and then add the numbers together as they ‘climb’ the ladder.
Who can climb their ladder the quickest?
Laminate the ladder and use a white board marker so that it can be played again and again!
Create Mental Math Flip Books
Using our addition flashcards, create an addition flip book. A quick and easy resource that can be used all year round. I used to set the timer for 5 minutes and get the students to write the answer (the answer only) of as many sums as they can. Who got the most correct?
We also have subtraction flashcards, division flashcards, and multiplication flashcards available to download.
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Mental arithmetic: what it is, examples, how to learn it
Photo: Chris Liverani / Unsplash
Foxford methodologist Anastasia Kuznetsova tells how mental arithmetic helps to solve creative problems and prepares the child for the future
 What is it
 History
 Benefit
 Scientific opinion
 Training
 How to choose a school
About the expert: Anastasia Kuznetsova, methodologist at the Foxford online school, author and teacher of refresher courses in mental arithmetic.
What is mental arithmetic
Mental arithmetic is a way to develop children’s intelligence through quick mental arithmetic. First, the child learns to count on the abacus and trains fine motor skills of the hands. Then the scores are removed, the child imagines them in his head — he counts mentally. Develops imagination and creativity.
Try to solve an example in a few seconds without a draft and a calculator:
Children solve such problems in their minds using mental arithmetic. This is a system for the development of intelligence, built on teaching oral counting.
Modern parents often talk about the undeveloped imagination and fantasy of the child. The fact is that we train the left hemisphere of the child’s brain — it is responsible for logic and mathematical abilities — but we develop the right hemisphere very little. The right hemisphere of the brain recognizes complex visual and auditory patterns. Responsible for concentration and imagination. The child’s cognitive abilities depend on the harmonious development of the two hemispheres of the child’s brain [1].
Having mastered mental arithmetic, the child copes with any intellectual and creative work much easier. He knows how to quickly solve problems and apply a nonstandard approach to them.
The history of mental arithmetic
Mental arithmetic was invented about 5 thousand years ago. The technique was used in ancient Greece, India and Rome to teach children to count. It is based on the ability to calculate on ancient abacus.
Over time, the abacus was modified to a calculator, in 1993 the concept of «mental arithmetic» was formulated. Today, mental arithmetic is used in 50 countries around the world. In Japan and China, it has become part of the school curriculum.
The abacus is the main instrument of mental arithmetic. In the classroom, students work with the board and abacus, and after that they count only in their heads. In Japan, such abacus is called soroban.
(Photo: Unsplash)
Benefits of mental arithmetic
Being able to quickly calculate mentally is not the end goal. At the moment of refusal to work with real abacus accounts, the right hemisphere of the brain begins to work more actively. At the same time, children develop logical thinking and counting, for which the left hemisphere is responsible.
Strengthened work of both hemispheres of the brain becomes a habit and helps the child to solve life problems more creatively. Concentrate, look at the problem more broadly and build logical chains to solve it. Another plus is the development of several types of memory at once: longterm, shortterm and photographic.
What scientists think about mental arithmetic
American researchers tested the influence of mental arithmetic on the intellectual abilities of first and second grade students during the year [2]. The results were mixed — firstgraders did not cope with mental arithmetic, secondgraders did better, but scientists did not reveal a noticeable improvement in cognitive abilities.
In 2016, psychologist David Barner conducted a similar study in India by a group of scientists, but the children were followed for three years [3]. Mental arithmetic has helped some students learn better, but the result may also depend on the abilities of a particular student. Most of the other studies also tested arithmetic skills. There is not yet enough data on how mental arithmetic affects cognitive abilities, so it is too early to draw conclusions.
When and where to study mental arithmetic
The most suitable age for training is from 4 to 1214 years old. At this time, the brain develops more intensively than in other periods of growing up. After 1214 years of age, the ability of the brain to acquire and use complex skills in such a quantity and pace decreases.
Mental arithmetic classes with the elderly are now gaining popularity. Such brain training is an excellent method of preventing diseases associated with memory and concentration.
Selfstudy can be a challenge. Studying requires perseverance, attentiveness and a variety of formats of classes. To properly teach a child mental arithmetic, it is better to contact a qualified teacher.
How to choose a mental arithmetic school or course
To choose the right mental arithmetic school for your child, check:
 How many children are in the group. The younger the children, the smaller the group should be. The recommended group size for preschoolers is up to eight people, for primary school up to ten people.
 What is the teacher’s qualification. The teacher needs specialized skills. He can get them at mental arithmetic centers. Find out about the education of a teacher and see his certificates. An international certificate in mental arithmetic is an additional plus.
 Do they provide educational materials. One of the most important conditions for learning is the ability to observe every action of the teacher. So you can check the teaching materials and the quality of education. An online platform can be a good solution.
 Are there any homework assignments. Mental arithmetic involves regular consolidation of the acquired knowledge, so it is important to pay attention to the quality and format of homework.
 Is there a trial lesson. It is a safe opportunity for a child to try mental arithmetic, for you it is a test of the quality of a school or course.
How to count on an abacus
The mental counting system or mental arithmetic allows you to teach children to perform all arithmetic operations in their mind very quickly. For teaching, a special counting board is used — an abacus. First, children learn to perform arithmetic operations with the help of this device, and then they begin to perform all the operations in the mind.
Contents:
 How to count on an abacus
 Score rules
 Addition and subtraction on abacus
 Multiplication and division
The abacus was invented in Mesopotamia around the third millennium BC. Similar counting devices were used in almost all countries — Ancient Greece, Rome, Egypt, China, India, Japan.
Nowadays, all calculations are carried out with the help of computers. And the abacus became the main tool for the development of intellectual abilities — mental arithmetic. You can start classes from an early age, when the child learns to count to ten.
How to count on an abacus
The abacus is a rectangular frame with vertical spokes. The frame is divided by a transverse crossbar into two unequal parts. Knuckles are strung on the needles — four pieces at the bottom, and one at the top. The total number of spokes may vary depending on the model of the counting board.
To count on the abacus, you need to remember a few basic rules:
 numbers on the counting board are typed from left to right;
 the lower knuckles represent numbers from 1 to 4, the upper knuckle corresponds to the number 5;
 lowered upper bone indicates that the number is greater than five;
 each spoke corresponds to one digit — ones, tens, hundreds, thousands, and so on.
To display a number on the abacus, you need to bring the corresponding number of bones to the inner crossbar. For example, for the number 6, you need to move the upper bone (5) down on the leftmost knitting needle and raise one lower one (1). For example, the number 66 is displayed similarly. Only for this you need to use two knitting needles — one for units, the second for tens.
Has your child already tried counting on an abacus? It is very exciting and perfectly develops intelligence, concentration, attention, creativity. You can find out if your child will like unusual math classes at a free interactive lesson in our center. Most likely, the kid will decide that he has a new interesting entertainment, and you will be surprised at the effectiveness of mental mathematics. Let’s check?
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Counting rules
Children learn to count on the abacus very quickly, just explain the principle to them and show them a few examples. One hand is used to count units — the right hand, if you need to count tens and ones, then both hands are used.
The hand should be clenched into a fist, thumb and forefinger straightened. The lower bones are raised with the thumb, and lowered with the index finger. The upper knuckle is worked with only the index finger. If you need to add bones from above and below, then this is done simultaneously with two fingers. The removal of bones is carried out in the same way.
See also Japanese soroban abacus
Addition and subtraction on abacus
Adding and subtracting with a counting board is very easy. First, the first number is typed on the abacus, the second number is added to it on the corresponding knitting needles. Adding begins with the smaller of the two numbers. If more than 9 bones are obtained on the needle, then one bone is added to the next one.
When subtracting from the first number, remove the required number of bones on each needle.