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Math, as they say, is everywhere we look around. And knowingly or unknowingly, several math concepts taught to us in our academics, find use in our daily life, such as geometry, trigonometry, and calculus. To ensure that ‘your adult self’ can seamlessly use these mathematical concepts, the ‘student you’ needs to work hard and brush up on the math around you.
As teachers, you can make math fun by using fun math manipulatives, which are essential tools when you want your students to fiddle around happily with mathematical concepts. Math is known to be the queen of sciences but is mostly theoretical when compared to other sciences. Hence, manipulatives will actually help students ‘see’ the mathematical concepts that they had only read in their textbooks.
Having emphasized math manipulatives, let us dive into the next section that briefly discusses some more advantages that these tools bring across the table.
Benefits of using math manipulatives for middle school
Things such as games, objects, activities, and charts that help in engaging the students and enable them in learning math concepts in a way that is fun, are called math manipulatives. They generally suit learners and students of various multitudes and help them in grasping the concepts better because they are able to ‘see’ the math happening live in front of them rather than just visualizing it with their imagination.
Here are some more benefits of math manipulatives:
1. Literally makes math fun
As discussed above, practical learning i.e. learning with the help of games, objects, and activities are more beneficial and effective than learning restricted to theories. With games and activities, ‘fun’ is intangible.
2. Helps build cognitive and reasoning ability
When using manipulatives, students visualize what they would have otherwise imagined and get to fiddle around in real with their visualization. They associate their thoughts and integrate them with their knowledge, which lets them build a higher level of cognitive ability gradually.
3. Helps keep math fear at bay!
Several students have reported that they find math boring and dull because all it has are numbers and formulae. This paves the way to ineffective learning and using blind strategies to mug up formulae and concepts without actually understanding them. Teaching using manipulatives is an excellent strategy to help students engage with the subject and help them increase their self-confidence in dealing with the subject.
4. Has a positive impact on student achievement
Math is a scoring subject and every mark counts when considering ranking in a class or university. Studies have shown that utilizing manipulatives to teach students has had a positive impact on their achievement in terms of scoring and conceptual learning. The same study also shows that students with special needs also tend to understand math better when manipulatives are used.
5. Math manipulatives also help build upon CRA
CRA – Concrete, Representational, and Abstract, form the basis for mathematical foundations. With the help of math manipulatives, students develop the ability to build up conceptual understanding through hands-on practice rather than just relying on memorization and memory recall.
List of math manipulatives
1. The number path – Understanding integers
Integers are an important concept for middle schoolers. They form the basis for several other concepts such as calculus which is taught in higher grades. To excel in math concepts of higher grades, the fundamentals of integers must be clear. Hence, to help middle schoolers with integers, the number line can be used as a manipulator.
Mathematical operations such as addition and subtraction are loosely coupled and come with abstract rules when it comes to signs. These signs play a vital role in determining the quantity or value of a number. By using the number line manipulatives to understand integers, students can minimize the errors surrounding this concept.
Most number path manipulatives have an in-built slider. While counting, students need to simply slide it and place it in such a way that they can clearly see the two numbers using which they have to either perform addition, subtraction, multiplication, or division. Also, Number Paths are color-coded, meaning every group of 5 numbers is color coded, which helps students with grouping as well!
2. Clocks – Exploring the relationship between seconds, minutes, and hours
Being able to tell the time (both in a 12-hour format and a 24-hour format) is essential for everyone. Concepts relating to being able to tell the time correctly, and describing time elapsed are important areas of discussion in a middle schooler’s academic curriculum. It is important to be able to interpret time in general life.
Along with time concepts, some critical questions like, ‘How many times in a day do the minute hand and the hour hand pass each other?’ can be easily taught with such a manipulative, Also, such questions require students to think quickly as these require promptness and are asked in competitive exams and interviews.
To make this simpler, clocks themselves can be used as manipulatives. Teachers can use wall clocks or table clocks and rotate the seconds, minutes, and the hour hand to teach the students the concept of time and the importance it holds from the examination and interview perspective.
3. Pattern Blocks – Exploring Geometry
Geometry particularly deals with mathematical concepts that challenge one’s ability to visualize, which is one of the strongest pursuits of humans. It finds use in several domains such as architecture, art, typography, surveying, cartography, and engineering among others.
In middle school, geometry mostly revolves around understanding and experimenting with lines, angles, and shapes. Having a clear understanding of these concepts will help students do better in topics such as trigonometry taught in high schools.
Pattern blocks can help students get well-equipped with basic geometrical concepts. They are tiny blocks of either plastic or wood and come in a plethora of shapes. Each of the shapes is designed in such a way that every side can fit with another block. The kit is equipped with a set of pattern cards that have drawings of a figure which the students can use to replicate with the blocks. One can also consider DIY tangrams that be used as pattern blocks. They can also choose to be creative and use their own imagination to make the big picture! Find some alternative manipulatives for teaching geometry here.
4. Playing Cards – Understanding Probability
Dealing with 0s, 1s, and positive rational numbers to describe the occurrence of an event is what probability is all about! It explores concepts with a multitude of situations involving dice, calendars, toffees, and most importantly, the playing cards.
Playing cards find use not just for entertainment but also in determining the occurrence of events – independent or dependent events. Teachers can start off by teaching students to acquaint themselves with the deck of cards by explaining to them about suits and basic card properties.
To ensure better understanding, teachers can teach them basic games that will put into use the properties of cards. Once students are well versed, they can use this deck of cards to solve problems based on ‘card-based probability’ questions such as, ‘A deck of cards is well shuffled. Find the probability of drawing an Ace.’
5. Coins – Understanding decimals and counting
Money keeps you moving! Be it grocery shopping, buying clothes, paying your doctor, or pretty much anything else, money helps you with the transaction. It fulfills all your needs, wants, and desires.
To ensure a better understanding of decimals, fractions, place value, and currency exchange, teachers can use playable coins and coins and currency of monopoly to teach students about the concept of money. They can also conduct role plays and scenarios which involve a transaction.
6. Geoboards – Learn area and perimeter
Area and perimeter are important mensuration concepts that find a vast deal of importance in higher grades. They are not just limited to higher grades but they also find use in various domains including architecture and engineering.
Every shape has an area and perimeter and different formulae to calculate the same. Since these two concepts find use in daily life, students need to be well-versed in them. Some challenges that students may face are difficulty in understanding the formulae or how it is derived, and the units of measurement.
Geoboards can help students establish the basic concepts of area and perimeter. These are boards embedded with pegs or nails which are at a certain distance, say ‘x’ units from each other. You can also make this geoboard quickly at home by following some easy DIY instructions. This ‘x’ is variable and depends on the size of the geoboard you purchase. Students can use either rubber bands, threads, or strings to construct shapes along these ‘x’ units. You can also assign them specific tasks such as, ‘Design a right-angled triangle with a perimeter of 10 cm.’
7. Abacus – Mastering Arithmetics
Arithmetics deals with basic mathematical operations between numbers such as addition, subtraction, multiplication, and division. It lays the foundation for mathematics as a whole.
In middle school, students are taught basic arithmetic such as operations on numbers and properties of numbers such as associative property, distributive property, and more. These concepts can become very monotonous if they are only limited to learning from books. To make these concepts interesting, teachers can utilize Abacus!
The abacus consists of a rigid frame with multiple rods, each having up to 5 beads. They are grouped as 4+1 beads where one bead is separated by a horizontal rod and often deals with ‘tens’ in the place value system. These instruments are a great way to help with mental math as well, as frequent use of them can paint a picture of the same in the minds of students and they can calculate mentally!
8. Cuisenaire rods – Interpreting data
Cuisenaire rods are a great way to represent data as they resemble graphs. Graphs are known to display large amounts of data and one of the most common forms of graphs is the bar graph. The ability to analyze graphs will help middle school students fare well in high school as data interpretation is an important topic from an examination point of view.
Cuisenaire rods are versatile and can be used to teach fractions as well as bar graphs. In the case of bar graphs, Cuisenaire rods need to be joined one after the other to solve the given problem.
You can assign each student a set of data and ask them to represent it on the bar graph using Cuisenaire rods. Once they get acquainted with using graphs, you can move to a more complex set of data. Additionally, you can find some more manipulatives for data interpretation using graphs right here.
9. Dice – Brush up BODMAS!
BODMAS stands for Bracket Of Division Multiplication Addition and Subtraction and defines the very fundamentals of solving a mathematical equation. Since middle schoolers just get started with important concepts like linear equations, quadrilaterals, and polynomials, it is important that they know the concept of BODMAS by heart.
Skipping the BODMAS rule can lead to terrible blunders while solving equations. Hence, students must know the universal rule of BODMAS. To inculcate BODMAS in students, teachers can divide them into groups of 4 or 5.
You can hand in at least 3 dice to each group and ask them to roll the dice. Now, it is the teacher’s duty to immediately form equations with the numbers that appear on the dice. The group must be quick to answer the question. It will be like a fun rapid-fire round! The group getting the most answers right wins the game.
10. Dominoes – Understanding fractions
Fractions are the stepping stone to the world of algebra! To solve algebraic numerics and problems, students must be able to have a good grip on fractions, decimals, and integers, for which the manipulatives have been covered above!
Algebra is mostly an interlinking of all the aforementioned concepts. Besides, individual concepts like fractions find use in baking, denoting the time, determining the weather and forecast, and much more! To help students brush up on their basics of fractions, teachers can deploy games using dominoes
One such game is adding up fractions using dominoes. Have all the dominoes flipped upside down? The first student picks up two dominoes and at the command of the teacher, performs basic mathematical operations such as addition, subtraction, multiplication, and/or division. The student sitting next in line must determine if the answer is correct. If it is, then the first student gets a point and the second student must pick up two more dominoes and repeat the procedure. But if not, the second student must give the right answer, and the game goes on.
Math manipulatives have time and again proven to help students understand math concepts better, be it for kindergarten, middle schoolers, or high schoolers. There is an abundance of math manipulatives and almost every concept can be taught using not one but several alternatives. Also, you can try out virtual math manipulatives that are also as good as the aforementioned manipulatives. We hope this article has given you great ideas for implementing math manipulatives for teaching middle schoolers!
- Kontaş, H. (2016). The Effect of Manipulatives on Mathematics Achievement and Attitudes of Secondary School Students. Journal of Education and Learning, 5(3), 10. https://doi.org/10.5539/jel.v5n3p10
- Gafoor, K. A., & Kurukkan, A. (2015). Why High School Students Feel Mathematics Difficult? An Exploration of Affective Beliefs. Why High School Students Feel Mathematics Difficult? An Exploration of Affective Beliefs. http://files.eric.ed.gov/fulltext/ED560266.pdf