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Tape Diagrams

Introduction

In tape diagrams, rectangles are used to show the parts of a ratio visually. They require careful drawing because they are a visual model. They simplify and deconstruct complex mathematical word problems. They are shown as a strip of paper or a piece of tape. 

Every learner needs to be able to draw and use a tape diagram to solve mathematical problems. It helps students learn arithmetic ideas and portray relationships in a math problem. Students can use it to communicate how they approach solving problems and organize their thoughts. Students can use these illustrations to solve any word problem.

We will learn more about tape diagrams in this article, including how teachers and students use them to solve mathematical problems that involve addition, subtraction, multiplication, division, ratio, fractions, and equations.

What are Tape Diagrams?

Definition

A tape diagram is a rectangular illustration that resembles a piece of tape and has sections to help with computations. It is a frequent graphic tool for resolving mathematical word problems with ratios as their basis. A strip diagram, a bar or length model, or a fraction strip are additional names for tape diagrams that are frequently used.

Each student must be able to create and use a tape diagram to solve mathematical problems. It helps students understand mathematical concepts and illustrate relationships in mathematical problems. Students can utilize it to share their ideas on any problem and how they would go about addressing it. 

What are the advantages of using tape diagrams?

The tape diagram has the advantage of preventing students from memorization of ideas they do not comprehend. The tape diagram is used to solve a word problem in mathematics successfully. The table below shows examples of mathematical problems for which we typically use tape diagrams.

Steps in Creating a Tape Diagram

A tape diagram is simple to make if you follow a few simple steps. It uses a tape piece broken into more manageable rectangular sections to show difficult tasks graphically. Any difficult word problems are simplified with tape diagrams. To draw a tape diagram, adhere to these easy steps.

Step 1: Read and analyze the problem.

To understand the problem, reading the provided problem statement or math equation is essential. You will then comprehend the presented situation and the ways to solve it. There are many different sorts of equations and problems in arithmetic; therefore, it is essential to understand them before you try to answer them by creating a diagram.

Step 2: Gather information essential for the diagram.

After reading the problem description, the next step is to segment the problem to identify its simplest solution. By breaking the word problem down into smaller parts, you can see which parts are necessary for the diagram and which parts have already been resolved in the given data, saving you from having to do the work again.

Step 3: Draw the tape diagram.

The next step is to draw a long, rectangular segment that resembles a piece of tape and then divide it into several parts using small boxes. Depending on the problem statement, you will draw a different number of cells. There is no max limit, but you must construct at least two sections.

Step 4: Solve the problem.

Solving the problem determines whether the tape diagram is accurate by completing the provided task. Labeling the diagram and using the information provided helps to solve the entire mathematical equation.

For example, let us use a tape diagram to illustrate and solve the problem below.

Problem:  There are six sheets of red colored paper and four sheets of green colored paper. How many sheets of colored paper are there? 

Solution

Step 1: Read and analyze the problem.

The given problem requires us to identify the total number of sheets of colored paper.

Step 2: Gather information essential for the diagram.

Red colored paper: 6 sheets

Green-colored paper: 4 sheets

Step 3: Draw the tape diagram.

Step 4: Solve the problem.

Therefore, there is a total of 10 sheets of colored paper, 6 + 4 = 10.

How Do Tape Diagrams Work?

A tape diagram is a rectangular illustration that resembles a piece of tape and has sections to help with computations. The following examples use tape diagrams for addition, subtraction, multiplication, division, ratio, fractions, and equations.

Mathematical concepts in which tape diagrams are frequently used
Mathematical operations
Model ratios
Fractions
Percentages
Comparison Problems
Complex Word Problems

Tape Diagrams for Addition and Subtraction

Tape diagrams are used for addition and subtraction as a visual tool to solve problems. The following are examples of how to show equations using tape diagrams.

Examples

Example 1

Create a tape diagram that represents each equation.

( a ) 3 + 9 = 12

( b ) 10 + 4 = 14

Solution

(a ) To create a tape diagram for 3 + 9 = 12, we must create 3 equal cells and 9 more. 

An alternative illustration would be a whole rectangle with two parts, as shown below. Notice that the rectangle for 9 is longer than that of 3. 

(b ) To create a tape diagram for 10 + 4 = 14, we must create 10 equal cells and 4 more. 

An alternative illustration would be a whole rectangle with two parts, as shown below. Notice that the rectangle for 10 is longer than that of 4. 

Example 2

A florist chose seven red and five white flowers to make a bouquet. How many flowers did he use for the flower arrangement?

Solution

The problem requires us to find the total number of flowers the florist used for the flower arrangement. The following is the given information:

7 red flowers  
5 white flowers

Let us use a tape diagram to visualize the problem.

Using an equation, we may represent the solution to the problem as 7 + 5 = 12. Therefore, the florist used a total of 12 flowers in his bouquet.

Example 3

Draw a tape diagram that represents each equation.

( a ) 11 – 4 = 7

( b ) 9 – 6 = 3

( c ) 15 – 5 = 10

Solution

( a ) To create a tape diagram for 11 – 4 = 7, we must create 11 equal cells for the minuend and 4 equal cells for the subtrahend. A tape diagram is shown in the figure below for the equation 11 – 4 = 7.

( b ) To create a tape diagram for 9 – 6 = 3, we must make 9 equal cells for the minuend and 6 equal cells for the subtrahend. A tape diagram is shown in the figure below for the equation 9 – 6 = 3.

( c ) To create a tape diagram for 15 – 5 = 10, we must create 15 equal cells for the minuend and 5 equal cells for the subtrahend. A tape diagram is shown in the figure below for the equation 15 – 5 = 10.

Tape Diagram for Multiplication and Division

Tape diagrams can also be a visual tool for multiplication and division-related word problems. 

Examples

Example 1

Draw a tape diagram that represents each equation.

( a ) 2 × 6 = 12

( b ) 5 × 4 = 20

( c ) 7 × 8 = 56

Solution

( a ) For 2 × 6 = 12, both 2 and 6 are called factors. Make 6 equal cells with the number 2 written in each one as an example of a tape diagram for this.

( b ) For 5 × 4 = 20, draw 4 equal cells with the number 5 written in each one as an example of a tape diagram for this.

( c ) For ( c ) 7 × 8 = 56, draw 8 equal cells with the number 7 written in each one as an example of a tape diagram for this.

Example 2

Francis has 32 candies and plans to give them to his 4 friends. Use a tape diagram to illustrate and solve the number of candies each person receives.

Solution

This requires the process of division to find how many each of Francis’ friends will receive. So, we have 32 ÷ 4 = 8. The tape diagram below is an illustration of the problem.

Tape Diagrams for Fractions

Examples

Example 1

Use a tape diagram to solve 45 of 35.

Solution

In this example, since the fraction’s denominator is 5, it tells us that we must divide our tape diagram into 5 equal parts.

By the process of division, we can have 35 ÷ 5 = 7. Hence, we may label each cell as 7. 

Since we need to find 4 parts of the whole, we must multiply 7 by 4. 

Therefore, 45 of 35 is equal to 28.

Example 2

Stephanie is planning a party. She purchased a total of 3 dozen balloons. ¼ of these balloons are red, and the rest are blue; how many of each color did she purchase?

Solution

Let us start by determining the total number of balloons Stephanie purchased. Since she has three dozen balloons, we must multiply 3 by 12 since there are 12 balloons for every dozen. Hence, Stephanie purchased a total of 36 balloons.

The tape diagram that must be created has 4 equal parts since it is given from the denominator of the fraction ¼. Hence, 36 ÷ 4 = 9. So, let us label each cell in our tape diagram as 9.

Since ¼ of the balloons are red and ¾ are blue balloons, then we have the following solution:

Red balloons : 9 × 1 = 9

Blue balloons: 9 × 3 = 27 

Stephanie bought 36 balloons, 27 of which were blue and 9 red.

Tape Diagrams for Ratio

Another illustration of a ratio is a tape diagram. Every part in the diagram that is the same size has the same value.

Examples

Example 1

The ratio of pencils to pens in Nathalie’s collection is 3: 7. If there are 18 pencils in her collection, how many are pens?

Solution

The ratio of pencils to pens in Nathalie’s collection is shown in the diagrams below.

PencilsThis tape has 3 parts which represent the number of pencils.
Ballpens This tape has 7 parts which represent the number of pens.

Since it is given that there is a total of 18 pencils, we can have 18 ÷ 3 = 6. The quotient 6 will be used as a factor to get the total number of pens.

Thus, 7 × 6 = 42. 

With a ratio of pencils to pens of 3: 7, Nathalie has 18 pencils and 42 pens.

Example 2

Diana uses a paint mixture of 8 cups yellow and 12 cups pink. Find the ratio of yellow paint to pink paint in the mixture.  

Solution

The tape diagram below illustrates the paint mixture ratio

Cups of Yellow PaintThis tape has 8 parts representing the number of cups of yellow paint. 
Cups of Pink Paint This tape has 12 parts representing the number of cups of pink paint.

The ratio of the number of cups of yellow paint to the pink paint is 8: 12. However, 8 : 12 can still be simplified as 2 : 3 since both numbers have 4 as their common factor.

8 ÷ 4 = 2
12 ÷ 4 = 3

Therefore, the ratio of the number of cups of yellow paint to pink paint, which Diana uses in her mixture, is 2 : 3.

The tape diagram below shows that for every 2 cups of yellow paint, 3 cups of pink paint are used.

Example 3

A box of black and blue marbles has a ratio of 3 to 8. If you have 15 black marbles, how many marbles in total do you have?

Solution

The tape diagram below illustrates the paint mixture ratio

Black MarblesThis tape has 3 parts which represent the number of black marbles.
Blue Marbles This tape has 8 parts which represent the number of blue marbles.

Let us start by finding the total number of blue marbles in the box. If the ratio is 3: 8, and you have 15 black marbles, then we can compute for the factor which makes 3 to 15. Hence, we have,

15 ÷ 3 = 5

Thus, we must multiply 5 by 8 to find the total number of blue marbles. So, we have,

8 × 5 = 40

Since we have 18 black and 40 blue marbles, the total number of marbles in the box is 55 ( 15 + 40 = 55 ).

Tape Diagrams for Equations

Examples

Example 1

For each of the diagrams below, write an equation and indicate the length of each diagram. 

Choices:

3 × 7 = 21

3 + 4 = 7

( a )

( b )  

Solution

( a ) Equation: 3 + 4 = 7

The total length of the diagram = 7

( b ) Equation: 3 × 7 = 21

The total length of the diagram = 21

Example 2

Samantha is trying to solve for the value of m in 6×m= 42. Use a tape diagram to represent the equation and find the value of m.

Solution

To illustrate the problem using a tape diagram, we will use a rectangle with a total length of 42; it must be divided into 5 equal cells or parts.

We may find the value of m using the division process; we have 42÷6=7. 

Therefore, m = 7. 

Summary

A tape diagram is a rectangular illustration that resembles a piece of tape and has sections to help with computations. It is a frequent graphic tool for resolving mathematical word problems with ratios as their basis. A strip diagram, a bar or length model, or a fraction strip are additional names for tape diagrams that are frequently used.

A technique for quickly solving mathematical problems is the tape diagram. The tape diagram has the benefit of preventing students from memorization of ideas they don’t comprehend. A rule that is remembered won’t help a student unless they know how to apply it or adapt it to other circumstances. The tape diagrams, on the other hand, are simple visual aids that help students comprehend a topic better. By applying them, they will improve as problem solvers.

Steps in Creating a Tape Diagram

The following are the four easy steps to follow in using a tape diagram to answer mathematical problems.

Step 1: Read and analyze the problem.
Step 2: Gather information essential for the diagram.
Step 3: Draw the tape diagram.
Step 4: Solve the problem.

Frequently Asked Questions on Tape Diagrams (FAQs)

What is meant by tape diagrams?

A tape diagram is a rectangular illustration that resembles a piece of tape and has sections to help with computations. It is a frequent graphic tool for solving mathematical word problems with ratios as their basis. 

A tape diagram is a technique for quickly solving mathematical concepts. The tape diagram has the benefit of preventing students from memorization of ideas they do not comprehend. A rule that is remembered won’t help a student unless they know how to apply it or adapt it to other circumstances. The tape diagrams, on the other hand, are simple visual aids that help students comprehend a topic better. By applying them, they will improve as problem solvers.

What are other terms for tape diagrams?

A strip diagram, a bar or length model, or a fraction strip are additional names for tape diagrams that are frequently used.

Why do we call it a tape diagram?

A tape diagram is a visual representation that looks like a piece of tape and is used to help with ratio calculations, addition, subtraction, and, most frequently, multiplication.

What are the steps in creating tape diagrams?

A tape diagram is simple to make if you follow a few simple steps. It uses a tape piece broken into more manageable rectangular sections to show difficult tasks graphically. Any difficult word problems are simplified with tape diagrams. 

The following are the four easy steps to follow in using a tape diagram to answer mathematical problems.

Step 1: Read and analyze the problem.
Step 2: Gather information essential for the diagram.
Step 3: Draw the tape diagram.
Step 4: Solve the problem.

Why do teachers use tape diagrams?

At its foundation, a tape diagram is a straightforward solution to a challenging mathematical problem. Teachers frequently use it to improve the way they instruct their students. The diagram helps teachers by enabling them to incorporate a fun component into learning. Students who struggle with math can more easily determine which computations are required to answer word problems using tape diagrams. Additionally, tape diagrams can be utilized to create more effective learning settings where students can discover various solutions to challenging situations. They are straightforward to use for fractions, ratios, multiplication, division, addition, and subtraction.

Why do students need to learn tape diagrams?

Every learner needs to be able to draw and use a tape diagram to solve mathematical problems. It helps students learn arithmetic ideas and portray relationships in a math problem. Students can use it to communicate how they approach solving problems and organize their thoughts. Students can use these illustrations to solve any word problem.

These diagrams can be used by students of all grade levels to solve mathematical problems and equations. Students are transitioning to new grades and working with advanced arithmetic benefit greatly from knowing tape diagrams.

What are the benefits of using tape diagrams?

The tape diagram has the advantage of preventing students from memorization of ideas they do not comprehend. The tape diagram is used to solve a word problem in mathematics successfully. The table below shows examples of mathematical problems for which we typically use tape diagrams.

Mathematical concepts in which tape diagrams are frequently used
Mathematical operations
Model ratios
Fractions
Percentages
Comparison Problems
Complex Word Problems

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