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Your product's model number and version can usually be found on a sticker located on the product like this example.
If you’re wanting to play games you’ll probably want to go and find serial number (which you can only get with a \$17 “donation” to the developer).
In the first article,  I said Common Core (CC) lends itself to interpretations along reform math ideology, an ineffective method of teaching math that focuses on long, drawn-out ways to solve problems. Of interest here is that PISA, the international exam given every several years, is essentially constructed along the same reform math principles; it tests for students’ ability to apply prior knowledge in new situations. With that as introduction, this article will address the third-grade standards that pertain to fractions. These standards are formally written, but essentially define a fraction as the division of a whole into equal parts. Ultimately, the goal of the standards is to move students from a pizza-understanding of fractions to a number-line understanding.
Equivalent Fractions While aspects of the standards listed above are within reach of most third graders, others may not be. The standards above address what equivalent fractions are, how to use them to compare size of fractions, and how to represent them pictorially. The use of shapes can be extended to use of a number line to represent equivalent fractions, and can also use number lines to compare sizes of fractions. If students are required to draw their own number lines to illustrate equivalent fractions per these standards, it is advisable to 1) keep the problem straightforward, and 2) have the student use bar diagrams such as those shown in Figure 6 below.

For Next Time I will continue to address the standards for fractions, for fourth grade and higher, in subsequent articles. The mission of the Heartland Institute is to discover, develop, and promote free-market solutions to social and economic problems.
The model number for your MacBook can help you when it comes time to order parts or upgrade components for your computer. You may decide that you’re done with OS X and that you only want to run Windows on your Mac. At the time But when I provided the computer’s serial number, the buyer found out it didn’t meet their specifications. The picture above is just one of the methods for subtraction under Common Core straight from RedState editor in chief Erick Erickson’s third-grade daughter’s math book.
Please leave your own pictures of Common Core homework in the comments and share this absurdity with your friends. Then get The Morning Bell, an early morning edition of the day’s most important political news, conservative commentary and original reporting from a team committed to following the truth no matter where it leads.
In the wake of that first article, I have been asked, “How so, when the standards are touted as being neutral and not dictating pedagogy”? Interestingly, the nations that teach math in the traditional fashion seem to do quite well. This can initially be represented by shapes such as circles or rectangles, traditionally illustrated by pies, cakes, and candy bars.
But the concept of “a fraction is actually a number” means nothing to many in the third grade; it is abstract.
The ruler concept can then be extended into lines of various lengths to show that line segments can be divided into equal parts.
Students should be given examples of number lines that they can then use to either make evaluations of fractions, or to supply missing fractions on them. In the meantime, as I have said previously, I very much value and encourage readers’ interpretations of and approaches for teaching these standards. Try the Morning Bell and get the day’s most important news and commentary from a team committed to the truth in formats that respect your time…and your intelligence.
It is so because publishers, test makers, and schools take neutrality as a signal that techniques that caused many of our nation’s current math problems in the first place—and which many thought CC would fix—are to continue.
But we’re still left with the question: Where does this all leave us with respect to standardized tests, which may require reform math approaches to problems, as well as “explanations” and demonstrations of “understanding”? Basic foundational skills enable more thinking than a conglomeration of rote understandings.

This is a natural way to introduce the concept, since when children are first learning about fractions, they need to focus on things they can see. So it is important that students first gain an initial understanding of what fractions are through shapes, so they can see what the numerator and denominator of a fraction represent.
Figure 5 below provides an example from a textbook prepared by the School Mathematics Study Group (SMSG; 1962), which illustrates how exercises with number lines can be used to comply with the above standards.
For those students, a back-and-forth approach may make the transition to the number line easier. On top of so-called neutrality, throw in Common Core’s Standards for Mathematical Practice, which require students to “explain” and “understand,” and the perfect storm exists to institutionalize the problems.
I’m showing how the standards can be taught in ways that make sense, and in ways that have for many years been taught with success.
The fear is that students will do poorly on such tests because they will not know how to write explanations that demonstrate the so-called understanding. Then, a natural way to progress to the number line and to think about fractions as numbers is to use rulers, since students are already familiar with them. It should also be recognized that there may be some third-grade students who cannot fully make the transition; so shapes may be the main mechanism by which they understand equivalent fractions. In exchange, we get some expectations of  “procedural fluency” that will not be defined until we see the actual tests. I advise that teachers rearrange the order of some CC standards to impart standard algorithms earlier, rather than later. An example taken from “Arithmetic We Need, Grade 3” (Brownell, et al., 1955) is shown in Figure 2 below. While some of the topics taught in that era were inappropriately formal and abstract for the lower grades, some material in the books published under the auspices of SMSG were quite effective and realize the intents of some of the Common Core standards. The practices we are seeing written about on the Internet that require students to draw endless pictures for every problem are not dictated by Common Core, and even a lead writer of the standards (William McCallum) has said so. Forcing students to think of multiple ways to solve a problem, for example, or to write an explanation for how they solved a problem or why something works does not in and of itself cause understanding.
The “explanations” most often will have little mathematical value and are on a naive level since students don't know the subject matter well enough.

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