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Standard 3.MD.3 has students creating scaled picture graphs and scaled bar graphs and then mentions doing one- and two-step “how many more/less” problems in scaled bar graphs. Why was the problem solving with picture graphs left out ? Where does simply interpreting the graphs come in? Would it be fair to assess students on problems other than “how many more/less” (like basic interpretation problems)?
Standard 4.MD.4 has students creating line plots with fraction labels only. Can whole numbers be used for labels as well? Can students be asked to simply interpret the line plot (since this is the first grade level that they are doing line plots)? Should they be expected to do problems other than adding/subtracting values pulled from the line plot? It is a great way to reinforce operations with fractions but it seems that they have to have a good understanding of how to just interpret line plots in general before we ask them to solve problems using data from the line plot. If they miss an assessment item, will we know if it is because they don’t know how to interpret the line plot or they don’t know how to do the computation?Re “interpreting line plots”: I’m not sure, but I think you might be asking about what to teach and assess in the classroom rather than at the end of the grade. The standard is about what students are expected to know at the end of grade, so interpreting line plots might occur in curriculum before the end of the grade. Similarly, students might start their study of line plots using measurements in whole-number units—the standards don’t dictate how students learn about line plots, just what they are able to do with line plots at the end of the grade.
End-of-year assessments can be designed to distinguish between facility with computation and with interpretation—and the hope is that that will actually happen. (Sample items are here: http://www.parcconline.org/; and here: http://sampleitems.smarterbalanced.org/itempreview/sbac/index.htm, though I don’t see any on 4.MD.4.) Also, there are separate standards that involve computation, e.g., the NF standards.
I just want to add that whole numbers are fractions, so a line plot with whole number labels is not excluded by 4.MD.4. Of course, students should also see line plots with labels that are not whole numbers.
Whole numbers can be written as fractions but I don’t think we can go as far as to say “whole numbers are fractions.” While a standard that refers to fractions can certainly include whole numbers, wouldn’t that statement also open up all standards that refer to performing calculations and solving problems with “whole numbers” to include using fractions?
In grade 4, wherever we see “fractions” does that also include mixed numbers?
Can you also respond to the Gr. 3 question above regarding using other types of problems besides “how many more/less” and whether those problems can also be from scaled picture graphs?
The set of fractions contains the set of whole numbers. So, a standard about fractions includes the possibility that those fractions might be whole numbers. But no, it’s not true the other way around; a standard about whole numbers is limited to whole numbers. In general fractions includes mixed numbers, yes, but see the discussion here.
As for your question about interpreting graphs, I thought Cathy answered it. Interpretation might well be part of a curriculum designed to help students meet the standard. The same goes for using picture graphs to solve problems. That’s a preparatory step for using bar graphs, which involve a little more sophistication with regard to understanding the meaning of the unit. As for other sorts of word problems arising from bar graphs, the over-riding criterion for whether to include something or not is whether it leads to students being able to meet the standards, so if you can make a case for including something based on that, then it’s fine to include it. In this case, the relevant standards would be 3.MD.3 and 3.OA.8.
Standards are not curriculum. Standards set goals; curriculum is designed to achieve them. From page 5 of the standards:
These Standards do not dictate curriculum or teaching methods. For example, just because topic A appears before topic B in the standards for a given grade, it does not necessarily mean that topic A must be taught before topic B. A teacher might prefer to teach topic B before topic A, or might choose to highlight connections by teaching topic A and topic B at the same time. Or, a teacher might prefer to teach a topic of his or her own choosing that leads, as a byproduct, to students reaching the standards for topics A and B.
In 5.MD.2 the first sentence lists “fractions of a unit (1/2, 1/4, 1/8).”
Are these the only fractions that should be assessed, as there’s no qualifier as is used elsewhere (such as “e.g.” or “including”)?
Also, is the decimal form of those fractions included, or is there something particular about the common fraction format on line plots that we need to get across to students?Yes, I think it is a reasonable interpretation to limit assessment focused on this standard to those fractions. And decimals forms are fine as well; the point of view taken in the Common Core is that decimals are fractions (with denominator 10, 100, etc.), and that 0.25 and 1/4 are just two ways of naming the same fraction. In Grade 5 students are working with decimals to the thousandths (5.NBT.3).
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