You may have come across the term “tape diagram.” A tape diagram is a simple sketch that uses rectangles to represent the sections of a ratio. Students can use a tape diagram as a visual model to help them solve mathematical problems. The visual model helps students organize their thinking and communicate their understanding. Teachers can use tape diagrams to help their students develop their conceptual understanding of ratio relationships. For example, the tape diagram below might help students solve a ratio problem such as this:

• There are a total of 1400 students in 3 schools. School B has twice as many students as School A, and School C has twice as many students as School B. How many students are in each school?

If a student can model the problem using a tape diagram, it shows they understand the ratio relationship between the number of students at each school. In this case, each square represents 100 students, so School A has 200 students, School B has 400 students, and School C has 800 students for a total of 1400 students. A tape diagram is also helpful for showing equivalent ratios. For example, this tape diagram helps show that 5:8 = 10:16. Tape diagrams are a good way for students to demonstrate their conceptual understanding, and they’re a useful tool for illustrating number relationships. It’s beneficial for students to be able to use a number of different approaches when they’re solving problems; tape diagrams are just one approach students can use when they work with ratios.