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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The purpose of this task is for students to apply their knowledge of integers in a real-world context.
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This task "Uses facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure (7.G.5)" except that it requires students to know, in addition, something about parallel lines, which students will not see until 8th grade.
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This word problem task involves ratios.
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In this task students are asked to write an equation to solve a real-world problem. There are two natural approaches to this task. In the first approach, students have to notice that even though there is one variable, namely the number of firefighters, it is used in two different places. In the other approach, students can find the total cost per firefighter and then write the equation.
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This problem uses the same numbers and asks similar mathematical questions as "6.NS The Florist Shop," but that task requires students to apply the concepts of multiples and common multiples in a context.
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This problem uses the same numbers and asks essentially the same mathematical questions as "6.NS Bake Sale," but that task requires students to apply the concepts of factors and common factors in a context.
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This task could be used in instructional activities designed to build understandings of fraction division. With teacher guidance, it could be used to develop knowledge of the common denominator approach and the underlying rationale.
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The purpose of this task is to show three problems that are set in the same kind of context, but the first is a straightforward multiplication problem while the other two are the corresponding "How many groups?" and "How many in each group?" division problems.
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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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This task could be put to good use in an instructional sequence designed to develop knowledge related to students' understanding of linear functions in contexts. Though students could work independently on the task, collaboration with peers is more likely to result in the exploration of a range of interpretations.
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The purpose of this task is for students to translate between measurements given in a scale drawing and the corresponding measurements of the object represented by the scale drawing.
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This real world word problem about calculating a tip in a restaurant requires multiple steps.
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In this task students use ratio and rate reasoning to solve the real-world problem of a runners rate and distance.
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This task requires students to solves multistep ratio and percent problem.
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This task requires students to work with unit rates.
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The purpose of this task is to foster a classroom discussion that will highlight the difference between multiplicative and additive reasoning.
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The three tasks in this set are not examples of tasks asking students to compute using the standard algorithms for multiplication and division because most people know what those kinds of problems look like. Instead, these tasks show what kinds of reasoning and estimation strategies students need to develop in order to support their algorithmic computations.
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This problem includes a percent increase in one part with a percent decrease in the remaining and asks students to find the overall percent change. The problem may be solved using proportions or by reasoning through the computations or writing a set of equations.
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Building on their fifth grade experiences with operations on decimal numbers, sixth grade students should find the task to be relatively easy. The emphasis here is on whether students are actually fluent with the computations, so teachers could use this as a formative assessment task if they monitor how students solve the problem.
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