This task presents an incomplete problem and asks students to choose numbers …
This task presents an incomplete problem and asks students to choose numbers to subtract (subtrahends) so that the resulting problem requires different types of regrouping. This way students have to recognize the pattern and not just follow a memorized algorithm--in other words, they have to think about what happens in the subtraction process when we regroup. This task is appropriate to use after students have learned the standard US algorithm.
The purpose of this task is to engage students in geometric modeling, …
The purpose of this task is to engage students in geometric modeling, and in particular to deduce algebraic relationships between variables stemming from geometric constraints. The modelling process is a challenging one, and will likely elicit a variety of attempts from the students.
Parts (a) and (b) of the task ask students to find the …
Parts (a) and (b) of the task ask students to find the unit rates that one can compute in this context. Part (b) does not specify whether the units should be laps or km, so answers can be expressed using either one.
This task, while involving relatively simple arithmetic, codes to all three standards …
This task, while involving relatively simple arithmetic, codes to all three standards in this cluster, and also offers students a good opportunity to practice modeling (MP4), since they must attempt to make reasonable assumptions about the average length of vehicles in the traffic jam and the space between vehicles. Teachers can encourage students to compare their solutions with other students.
It is much easier to visualize division of fraction problems with contexts …
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.
This task examines, in a graphical setting, the impact of adding a …
This task examines, in a graphical setting, the impact of adding a scalar, multiplying by a scalar, and making a linear substitution of variables on the graph of a function f. The setting here is abstract as there is no formula for the function f. The focus is therefore on understanding the geometric impact of these three operations.
This task gives students a chance to explore several issues relating to …
This task gives students a chance to explore several issues relating to rigid motions of the plane and triangle congruence. As an instructional task, it can help students build up their understanding of the relationship between rigid motions and congruence.
The purpose of this task is to emphasize the adjective "geometric" in …
The purpose of this task is to emphasize the adjective "geometric" in the "geometric" series, namely, that the algebraic notion of a common ratio between terms corresponds to the geometric notion of a repeated similarity transformation.
This task provides a good opportunity for group work and class discussions …
This task provides a good opportunity for group work and class discussions where students generate and compare equivalent expressions. In class discussion, students should be asked to connect the terms of an expression with quantities shown in the diagram.
In this task students must investigate this conjecture to discover that it …
In this task students must investigate this conjecture to discover that it does not work in all cases: Pick any two integers. Look at the sum of their squares, the difference of their squares, and twice the product of the two integers you chose. Those three numbers are the sides of a right triangle.
In this task, we are given the graph of two lines including …
In this task, we are given the graph of two lines including the coordinates of the intersection point and the coordinates of the two vertical intercepts, and are asked for the corresponding equations of the lines. It is a very straightforward task that connects graphs and equations and solutions and intersection points.
This task provides an opportunity for students to construct linear and exponential …
This task provides an opportunity for students to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
This task provides an opportunity for students to construct linear and exponential …
This task provides an opportunity for students to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
This is a task from the Illustrative Mathematics website that is one …
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.
This task combines two skills from domain G-C: making use of the …
This task combines two skills from domain G-C: making use of the relationship between a tangent segment to a circle and the radius touching that tangent segment (G-C.2), and computing lengths of circular arcs given the radii and central angles (G-C.5). It also requires students to create additional structure within the given problem, producing and solving a right triangle to compute the required central angles (G-SRT.8).
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