This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
Material Type: Activity/Lab
In this task students use different representations to analyze the relationship between two quantities and to solve a real world problem. The situation presented provides a good opportunity to make connections between the information provided by tables, graphs and equations.
Material Type: Activity/Lab
The purpose of this task is to have students work on a sequence of area problems that shows the advantage of increasingly abstract strategies in preparation for developing general area formulas for parallelograms and triangles.
Material Type: Activity/Lab
This is the first version of a task asking students to find the areas of triangles that have the same base and height, and is the most concrete.
Material Type: Activity/Lab
This is the second version of a task asking students to find the areas of triangles that have the same base and height. This presentation is more abstract as students are not using physical models.
Material Type: Activity/Lab
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
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. This problem is based on ArchimedesŐ Principle that the volume of an immersed object is equivalent to the volume of the displaced water.
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. Here, we are given the volume and are asked to find the height.
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. In this iteration, we do away with the lines that delineate individual unit cubes (which makes it more abstract) and generalize from cubes to rectangular prisms.
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
The purpose of this task is to provide students with a multi-step problem involving volume and to give them a chance to discuss the difference between exact calculations and their meaning in a context.
Material Type: Activity/Lab
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: The vertices of eight polygons are given below. For each polygon: * Plot the points in the coordinate plane connect the points in the order that they a...
Material Type: Activity/Lab
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
Material Type: Activity/Lab
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.
Material Type: Activity/Lab
This is the second of two fraction division tasks that use similar contexts to highlight the difference between the ŇNumber of Groups UnknownÓ a.k.a. ŇHow many groups?Ó (Variation 1) and ŇGroup Size UnknownÓ a.k.a. ŇHow many in each group?Ó (Variation 2) division problems.
Material Type: Activity/Lab
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.
Material Type: Activity/Lab
One common mistake students make when dividing fractions using visuals is the confusion between remainder and the fractional part of a mixed number answer.
Material Type: Activity/Lab
These two fraction division tasks use the same context and ask ŇHow much in one group?Ó but require students to divide the fractions in the opposite order. Students struggle to understand which order one should divide in a fraction division context, and these two tasks give them an opportunity to think carefully about the meaning of fraction division.
Material Type: Activity/Lab
This is the first of two fraction division tasks that use similar contexts to highlight the difference between the ŇNumber of Groups UnknownÓ a.k.a. ŇHow many groups?Ó (Variation 1) and ŇGroup Size UnknownÓ a.k.a. ŇHow many in each group?Ó (Variation 2) division problems.
Material Type: Activity/Lab
It is much easier to visualize division of fraction problems with contexts where the quantities involved are continuous. It makes sense to talk about a fraction of an hour. The context suggests a linear diagram, so this is a good opportunity for students to draw a number line or a double number line to solve the problem.
Material Type: Activity/Lab
