Write one letter A, B, or C in each box to represent the story each kid read. Yet the confusion doesn’t arise from the math; it’s the fault of the English.

The problem includes students (who have no names), book titles, letter labels for the books that are different from the titles, all buried in a problem that is meant to be about comparing fractions with unlike denominators.

use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from, put-together, take-apart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations.

Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

My take is that the standards are in line with effective programs, such as Singapore Math, but textbook publishers and other curriculum providers are creating confusion with overly complex explanations, ill-written problems, and lessons that confuse pedagogy with content.

Many of the “fuzzy math” complaints seem to focus on materials that ask students to engage in multiple approaches when tackling arithmetic problems.

While a student should ultimately be able to answer problems of this sort without visual aids, this kind of “modeling” can help lay the foundation that students need to solve increasingly complicated problems through the grades.

Such “models” can be even more useful for students when it comes to making sense of fractions and answering fraction problems. gave several examples of blunders when he complained to his 3 million followers that the Common Core curriculum at his daughter’s school—with its bewildering math problems and related tests—was making her cry.

Here, students are not limited to lining up numbers, carrying the one, or borrowing but are able to use manipulatives or drawings to arrive at answers or illustrate their understanding of what it means to add or take away one.

This video gives a clear sense of how a student might use a “10 frame” or number cubes to count and to add, and it shows how useful such a model can be in helping students learn numbers.

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