7 Useful Manipulatives For Teaching Ratio And Proportion Concepts

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A ratio is used for comparison between two or more quantities. Whereas a proportion defines that two ratios are equal through a mathematical equation. Ratio and proportion are sometimes tricky to understand, and many students confuse the two concepts. Students also face trouble solving questions in terms of different contexts. 

In order to make things simple for students, multiple types of manipulatives can be used to give a practical view of the concept. Manipulatives are excellent tools to facilitate learning and help students absorb the concepts so they know the “why” behind a calculation. 

Any object could serve as a manipulative. However, its choice will depend on the lesson that needs to be taught.In this post, we will discuss some engaging manipulatives, which you can use to teach ratio and proportions to students in fun and creative way.

Manipulatives to explain ratio and proportion concepts in class

1. Cuisenaire rods

 Cuisenaire rods

These are a collection of rectangular rods in various colors and lengths. You can use these in the class to introduce ratio and proportion concepts and later to investigate and reinforce the topic. Cuisenaire rods allow students to make continuous models and assign values to each of them corresponding to the question.

To teach ratio and proportion using Cuisenaire rods you can begin by introducing the concept and then demonstrate how ratios can be depicted using the rods. Later, you can ask the students to arrange the rods to create ratios for better understanding.

2. Tangrams


A tangram is a geometrical puzzle that consists of seven pieces of polygons that one can arrange in different ways to make other shapes. Tangrams usually consist of triangles, squares, and parallelograms capable of being recombined to explain a mathematical concept. These are excellent tools to teach ratios in class.

You can begin by arranging the tangrams to form a big square and explain how the smaller pieces represent a particular ratio corresponding to the large square. For example, arrange the tangrams in such a way that the larger triangles together represent ½ of the entire area. Similarly, one large triangle would represent ¼ of the entire area.

3. Unifix cubes

Unifix cubes

Unifix cubes are colorful blocks or cubes which you can use to teach a wide range of mathematical concepts. These cubes have interlocking features and can be connected with each other. The cubes are made of plastic and are easy to use by children.

To start teaching ratios using Unifix cubes, you can show two blue cubes and three red cubes in a line together and explain to them how the ratio of blue cubes to red cubes is 2:3. Let the students link them together to see the pattern. Then you can present two blue cubes and ask them the number of red cubes they would need to make the same pattern. Once the kids get the concept, you can ask them to represent different ratios using Unifix cubes.

4. Pattern blocks

Pattern blocks

Pattern blocks are a collection of colorful shapes that can be used to explain the concept of a ratio and imbibe proportional reasoning in students’ minds. They can use pattern blocks to solve ratios and determine if two ratios are equal.

You can present a triangle and a hexagon to the students and ask them to find the number of triangles required to make one hexagon. As six equilateral triangles make one hexagon, one triangle would be ⅙ of a hexagon. You can also make pattern block riddles for students to solve using the manipulatives.

5. Color Counters

 Color Counters

Color counters are a useful tool for students in terms of getting a hang of a math concept. They are perfect for concepts like sorting, counting, probability, and even ratios. In addition, two-color counters are convenient to use for individual or small group activities.

Show your students how they can use counters to illustrate different ratios. These can be laid out horizontally or vertically to express a particular ratio. Let’s say the ratio of milk and water in a bottle is 5:10 which can be presented by laying 5 red counters and 10 yellow counters in a horizontal line.The red counters will depict the ratio of milk in the bottle while the yellow ones will depict the ratio of water. 

6. Color Tiles

Color Tiles

Similar to color counters, color tiles are practical means of teaching ratio and proportion. One can arrange these one-inch colorful tiles in different ways to represent ratios and explain the concepts of proportional reasoning. Tiles are easy to use and can help in the process of learning.

Explain to the students how tiles of different colors can be arranged vertically to form a tower of tiles. For example, make a tower of 3 red tiles alongside a tower of 5 blue tiles to form the ratio 3:5. Now let students double the number of tiles to form the ratio 6:10 and so on.

7. Beads


Colorful beads can also be used to represent different ratios and proportions. You can ask the kids to put the beads in a string to solve their problem. Besides helping learn the topic, beads also enhance students’ fine motor skills, sorting skills, and hand-eye coordination. 

Another idea to teach the concept is by putting two red beads in the bag and asking the students to put five blue beads for every two red beads. It will help the students understand the correlation between the two colors representing the ratio.

Tips to use manipulatives for providing a great learning experience

  • Use one manipulative consistently for teaching a particular concept. Repeated use of a similar manipulative tool helps the student relate to it and better grasp the idea. In addition, it helps in building confidence and gaining clarity on the topic.
  • Choose manipulatives that go well with the topic and are easier for students to comprehend. For example, Cuisenaire rods are a good first choice for introducing ratio and proportion as these are of similar shape and can be arranged in different ways to solve a problem.
  • Avoid objects with distracting features that could divert a student’s thought process. Instead, try to use a simple object to keep the attention on the topic of discussion.
  • Explain clearly how the manipulative relates to the ratio and proportion concept. It’s easier for us to see the relationship as we already know about it. Still, it may be hard for students who are new to the topic.
  • Utilize different manipulatives to strengthen the concepts once the students grasp the topic well after repeatedly using one manipulative for some time. Using manipulatives of different shapes and sizes will allow them to use their abstract thinking and correlate it with the tools used.

Final thoughts

Manipulatives can help teachers guide the students about ratios and proportions as these provide hands-on experience relating to the concept. But before beginning the topic in detail, it is imperative that you first introduce the vocabulary that you are going to use for discussion. Let the students develop a clear understanding of the ratio sign and what it means before using any manipulatives. 

A proper mix of physical and virtual manipulatives can help students gain a strong hold over the concept. It is always better to end the session with an evaluation to know how far the lesson has been effective. Students may take a couple of sessions to understand the topic as it is a little complex, but with the right tools, you can facilitate the students to apprehend this abstract topic.

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