This task asks students to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible.
Material Type: Activity/Lab
This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols.
Material Type: Activity/Lab
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.
Material Type: Activity/Lab
This task requires students to apply the Pythagorean Theorem.
Material Type: Activity/Lab
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.
Material Type: Activity/Lab
This task introduces the fundamental statistical ideas of using data summaries (statistics) from random samples to draw inferences (reasoned conclusions) about population characteristics (parameters). In the task built around an election poll scenario, the population is the entire seventh grade class, the unknown characteristic (parameter) of interest is the proportion of the class members voting for a specific candidate, and the sample summary (statistic) is the observed proportion of voters favoring the candidate in a random sample of class members.
Material Type: Activity/Lab
The purpose of this task is to help students see that when you have a context that can be modeled with a ratio and associated unit rate, there is almost always another ratio with its associated unit rate (the only exception is when one of the quantities is zero), and to encourage students to flexibly choose either unit rate depending on the question at hand.
Material Type: Activity/Lab
This task can be used to either build or assess initial understandings related to rational approximations of irrational numbers.
Material Type: Activity/Lab
The instructions for the two expressions sound very similar, however, the order in which the different operations are performed and the exact wording make a big difference in the final expression. Students have to pay close attention to the wording: Ňsubtract the result from 1Ó and Ňsubtract 1 from the resultÓ are very different.
Material Type: Activity/Lab
This task involves solving equations with rational coefficients, and requires students to use the distributive law ("combine like terms"). The equation also provides opportunities for students to observe structure in the equation to find a quicker solution, as in the second solution presented.
Material Type: Activity/Lab
This task requires students to find the measure of an angle.
Material Type: Activity/Lab
In this problem students must transform expressions using the distributive, commutative and associative properties to decide which expressions are equivalent.
Material Type: Activity/Lab
The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. The purpose of this first task is to see the relationship between the side-lengths of a cube and its volume.
Material Type: Activity/Lab
There are two aspects to fluency with division of multi-digit numbers: knowing when it should be applied, and knowing how to compute it. While this task is very straightforward, it represents the kind of problem that sixth graders should be able to recognize and solve relatively quickly.
Material Type: Activity/Lab
This is the sixth problem in a series of seven that use the context of a classroom election. While it still deals with simple ratios and easily managed numbers, the mathematics surrounding the ratios are increasingly complex.
Material Type: Activity/Lab
The purpose of this task is to help students extend their understanding of division of whole numbers to division of fractions, and given the simple numbers used, it is most appropriate for students just learning about fraction division because it lends itself easily to a pictorial solution.
Material Type: Activity/Lab
This task is intended strictly for instructional purposes with the goal of building understandings of linear relationships within a meaningful and, hopefully, somewhat familiar context.
Material Type: Activity/Lab
The purpose of this task is to strengthen students' understanding of area. It could be assigned in class to individuals or small groups or given as a homework exercise to generate interesting discussions the following day. The relatively high levels of complexity and technical demand enhance its instructional value.
Material Type: Activity/Lab
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.
Material Type: Activity/Lab
This is a simple task about interpreting the graph of a function in terms of the relationship between quantities that it represents.
Material Type: Activity/Lab
