Strategy

Tape Diagram

Strip Diagrams, Bar Models, Length Models

UDL 2.3

A tape diagram is a visual model that looks like a segment of tape and is used for representing number relationships and word problems. Using this method, students draw and label rectangular bars to illustrate the quantities in a problem. Bars representing known quantities are labeled with their value, while a question mark is often used to indicate an unknown quantity. Students then use the diagram to solve the given problem. Tape diagrams are typically used in grades 2-8 to solve problems that involve the four operations with whole numbers, fractions, and ratios. Tape diagrams can help students develop problem-solving skills and algebraic thinking. When students are instructed on how to create a clear tape diagram displaying the key information from a problem, they can more easily determine which operation(s) to use to find the solution. As such, this method for visualizing information can be particularly helpful for students with processing, attention, and memory difficulties. Consistent use of tape diagrams can also prepare students for algebra and higher-level mathematics, as they gain practice identifying known and unknown quantities in a problem and their relation to one another.

Implementation Tips

Practice
Creating tape diagrams for ratio problems can be challenging for some students. Provide frequent opportunities for students to practice creating tape diagrams independently and in small groups.
Introduction
When introducing tape diagrams at any grade level, it is a good idea to start with simple problems (e.g.“Marty has $27, and Kevin has $11. How much more money does Marty have?”), and focus on teaching students how to properly set up a diagram based on the information provided. Give students multiple opportunities to practice with these types of problems before moving on to more complex problems.
Equivelant Representations
Encourage students to draw neat tape diagrams that closely represent the information in the problem. For example, rectangles that represent the same quantity should be approximately the same size and labeled with key information. This will help students better visualize the information in the problem.
Types of Problems to Use
When planning a lesson emphasizing tape diagrams as a problem-solving strategy, check to make sure that the given problems can be effectively modeled using the method. Tape diagrams work best for real-world problems that include comparisons, part-whole calculations, ratios, proportions, or rates of change.
Extension Activity
To challenge students, provide an example of a completed tape diagram with the worked out solution. Ask students to create a word problem that corresponds with the given diagram.
Video Demo
For a demonstration of how to solve problems using tape diagrams, check out [[https://vimeo.com/71593727|this video]] from EngageNY.
Interactive Tool
[[http://www.mathplayground.com/thinkingblocks.html |Thinking Blocks]] by Math Playground is a great, interactive tool that students can use to practice modeling word problems using tape diagrams.

Examples

Upper Elementary
To reinforce the relationship between multiplication and division, a teacher can model solving the examples presented below using tape diagrams. Example 1: There are 7 boxes of markers. Each box holds 8 markers. How many markers are there in all? Example 2: A grower picks 45 apples and packs them equally into 5 boxes. How many apples does the grower pack in each box? After modeling both problems, the teacher can then lead the class in a discussion of what they noticed about how you solved the two problems and the tape diagrams you created for each one.
Middle School
Tape diagrams are a great way to help students visualize ratio problems. For instance, with a class that has some practice using tape diagrams, display the following problem on the board: Hillview High School hosted a basketball tournament. The ratio of boys to girls who participated in the tournament was 5:2. There were 15 boys. How many girls participated? Working with partners, ask students to create tape diagrams that represent the information presented in the problem. (Students should focus on creating the tape diagram at this stage, not finding the solution.) Combine pairs to create groups of four. Ask groups to compare their tape diagrams, and determine which one best illustrates the problem. (Groups can draw a new tape diagram, if needed). Provide an opportunity for groups to share their diagrams with the class. With the whole class, demonstrate creating a tape diagram for the problem, while addressing any misconceptions observed from student examples. Ask students to return to their groups and use their tape diagrams to solve the problem.
High School
At the high school level, tape diagrams can be used with small groups or individual students when providing intervention support, especially to reinforce foundational math skills. For example, for students who lack a conceptual understanding of the relationship between fractions, decimals, and percents, model creating tape diagrams to illustrate equivalent ratios (e.g. one-fourth, 0.25, and 25% of a number).

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