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November 2021 Math Monthly

November’s Vocabulary: Tape Diagram

A tape diagram is a pictorial model students can draw to represent a mathematical relationship or to develop understanding of a math concept. Tape diagrams are useful for solving many different types of math problems but are commonly used with word problems. Students can use a tape diagram to organize information and communicate their mathematical thinking.

November’s Standard: Reason abstractly and quantitatively

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Tape diagrams help students bridge the gap from a concrete model to a representational or abstract model.  You can use tape diagrams In the early grades to help students represent addition and subtraction problems and understand the difference between a part and a whole. As students get older, tape diagrams help students visualize fractions and ratios and develop proportional thinking.  Once they get confident with tape diagrams, you may be surprised at the applications they find, even at the highest levels of math!