This task builds on a fifth grade fraction multiplication task and uses the identical context, but asks the corresponding ŇNumber of Groups UnknownÓ division problem.
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These problems are meant to be a progression which require more sophisticated understandings of the meaning of fractions as students progress through them.
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In this task students are asked to label negative numbers on a numberline and then answer questions about which are greater or less than.
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This division task asks studnets to consider the conceptual understanding of something usually taught as a rote procedure. To be successful with this task, students must make sense of the procedure and how place value is represented and abbreviated within it.
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The first two parts of this task ask students to interpret the meaning of signed numbers and reason based on that meaning in a context where the meaning of zero is already given by convention.
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The purpose of this task is for students to solve problems involving decimals in a context involving a concept that supports financial literacy, namely inflation.
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This task provides a context for some of the questions asked in "6.NS Multiples and Common Multiples." A scaffolded version of this task could be adapted into a teaching task that could help motivate the need for the concept of a common multiple.
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The purpose of this task is to help solidify students' understanding of signed numbers as points on a number line and to understand the geometric interpretation of adding and subtracting signed numbers.
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The purpose of this task is meant to reinforce students' understanding of rational numbers as points on the number line and to provide them with a visual way of understanding that the sum of a number and its additive inverse (usually called its "opposite") is zero.
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The purpose of the task is to get students to reflect on the definition of decimals as fractions (or sums of fractions), at a time when they are seeing them primarily as an extension of the base-ten number system and may have lost contact with the basic fraction meaning. Students also have their understanding of equivalent fractions and factors reinforced.
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The purpose of the task is to have students reflect on the meaning of repeating decimal representation through approximation. A formal explanation requires the idea of a limit to be made precise, but 7th graders can start to wrestle with the ideas and get a sense of what we mean by an "infinite decimal."
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This task requires students to be able to reason abstractly about fraction multiplication as it would not be realistic for them to solve it using a visual fraction model. Even though the numbers are too messy to draw out an exact picture, this task still provides opportunities for students to reason about their computations to see if they make sense.
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This task is appropriate for assessing student's understanding of differences of signed numbers. Because the task asks how many degrees the temperature drops, it is correct to say that "the temperature drops 61.5 degrees." However, some might think that the answer should be that the temperature is "changing -61.5" degrees. Having students write the answer in sentence form will allow teachers to interpret their response in a way that a purely numerical response would not.
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This task can be used to either build or assess initial understandings related to rational approximations of irrational numbers.
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This task is intended for instructional (rather than assessment) purposes, providing an opportunity to discuss technology as it relates to irrational numbers and calculations in general. The task gives a concrete example where rounding and then multiplying does not yield the same answer as multiplying and then rounding.
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This task requires students to determine whether a number is rational or irrational. The task assumes that students are able to express a given repeating decimal as a fraction.
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When students plot irrational numbers on the number line, it helps reinforce the idea that they fit into a number system that includes the more familiar integer and rational numbers.
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Standard 8.NS.1 requires students to "convert a decimal expansion which repeats eventually into a rational number." Despite this choice of wording, the numbers in this task are rational numbers regardless of choice of representation. For example, 0.333 and 1/3 are two different ways of representing the same number.
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This task is intended for instructional purposes so that students can become familiar and confident with using a calculator and understanding what it can and cannot do. This task gives an opportunity to work on the notion of place value (in parts (b) and (c)) and also to understand part of an argument for why the square root of two is not a rational number.
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