Mt. Whitney to Death Valley
(View Complete Item Description)The purpose of this task is to engage students in an open-ended modeling task that uses similarity of right triangles, and also requires the use of technology.
Material Type: Activity/Lab
All resources in Oregon Mathematics
G-GPE Explaining the equation for a circle
(View Complete Item Description)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: This problem examines equations defining different circles in the $x$-$y$ plane. Use the Pythagorean theorem to find an equation in $x$ and $y$ whose s...
Material Type: Activity/Lab
Slopes and Circles
(View Complete Item Description)The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever _AXB is a right angle.
Material Type: Activity/Lab
A Midpoint Miracle
(View Complete Item Description)This classroom task gives students the opportunity to prove a surprising fact about quadrilaterals: that if we join the midpoints of an arbitrary quadrilateral to form a new quadrilateral, then the new quadrilateral is a parallelogram, even if the original quadrilateral was not.
Material Type: Activity/Lab
G-GPE, G-CO, G-SRT Unit Squares and Triangles
(View Complete Item Description)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: Three unit squares and two line segments connecting two pairs of vertices are shown. What is the area of $\triangle ABC$?...
Material Type: Activity/Lab
Is this a rectangle?
(View Complete Item Description)The goal of this task is to provide an opportunity for students to apply a wide range of ideas from geometry and algebra in order to show that a given quadrilateral is a rectangle. Creativity will be essential here as the only given information is the Cartesian coordinates of the quadrilateral's vertices. Using this information to show that the four angles are right angles will require some auxiliary constructions. Students will need ample time and, for some of the methods provided below, guidance. The reward of going through this task thoroughly should justify the effort because it provides students an opportunity to see multiple geometric and algebraic constructions unified to achieve a common purpose.
Material Type: Activity/Lab
N-RN Evaluating a Special Exponential Expression
(View Complete Item Description)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: Three students disagree about what value to assign to the expression $0^0$. In each case, critically analyze the student's argument. Juan suggests that...
Material Type: Activity/Lab
N-RN Evaluating Exponential Expressions
(View Complete Item Description)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
Extending the Definitions of Exponents, Variation 2
(View Complete Item Description)The goal of this task is to develop an understanding of why rational exponents are defined as they are (N-RN.1), however it also raises important issues about distinguishing between linear and exponential behavior (F-LE.1c) and it requires students to create an equation to model a context (A-CED.2
Material Type: Activity/Lab
Felicia's Drive
(View Complete Item Description)This task provides students the opportunity to make use of units to find the gas need (N-Q.1). The key point is for them to explain their choices. This task provides an opportunity for students to practice MP2, Reason abstractly and quantitatively, and MP3, Construct viable arguments and critique the reasoning of others.
Material Type: Activity/Lab
How Much is a Penny Worth?
(View Complete Item Description)Pennies have a monetary face value of one cent, but they are made of material that has a market value that is usually different. It is the value of the materials that requires attention in this problem. While it is interesting to compare the face value with the value of the materials, this does not have any bearing on the calculations. Interference between these two notions of value is a possible area of difficulty for some students.
Material Type: Activity/Lab
Ice Cream Van
(View Complete Item Description)The purpose of this task is to engage students, probably working in groups, in a substantial and open-ended modeling problem. Students will have to brainstorm or research several relevant quantities, and incorporate these values into their solutions.
Material Type: Activity/Lab
Runners' World
(View Complete Item Description)This task provides students with an opportunity to engage in Standard for Mathematical Practice 6, attending to precision. It intentionally omits some relevant information -- namely, that a typical soda can holds 12 oz of fluid, that a pound is equivalent to 16 dry ounces, and that an ounce of water weighs approximately 1.04 dry ounces (at the temperature of the human body) -- in the interest of having students discover that these are relevant quantities. The incompleteness of the problem statement makes the task more amenable to having students do work in groups.
Material Type: Activity/Lab
Selling Fuel Oil at a Loss
(View Complete Item Description)This task is a modeling problem which ties in to financial decisions faced routinely by businesses, namely the balance between maintaining inventory and raising short-term capital for investment or re-investment in developing the busines
Material Type: Activity/Lab
F-IF, N-Q Solar Radiation Model
(View Complete Item Description)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
N-Q Giving raises
(View Complete Item Description)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: A small company wants to give raises to their 5 employees. They have $10,000 available to distribute. Imagine you are in charge of deciding how the rai...
Material Type: Activity/Lab
New Cuyama
(View Complete Item Description)The purpose of this task is to provide a fun context to examine the pitfalls of disregarding units when reporting and manipulating quantities. Teachers might use this as a discussion-starter about appropriate and careful use of units. In this particular example, the units of the three quantities are so diverse that it is not surprising Lisa laughed when looking at the ''arithmetic'' on this sign.
Material Type: Activity/Lab
Traffic Jam
(View Complete Item Description)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.
Material Type: Activity/Lab
Harvesting the Fields
(View Complete Item Description)This is a challenging task, suitable for extended work, and reaching into a deep understanding of units. The task requires students to exhibit MP1, Make sense of problems and persevere in solving them. An algebraic solution is possible but complicated; a numerical solution is both simpler and more sophisticated, requiring skilled use of units and quantitative reasoning. Thus the task aligns with either A-CED.1 or N-Q.1, depending on the approach.
Material Type: Activity/Lab
Weed killer
(View Complete Item Description)The principal purpose of the task is to explore a real-world application problem with algebra, working with units and maintaining reasonable levels of accuracy throughout.
Material Type: Activity/Lab