This task serves as a bridge between understanding place-value and using strategies based on place-value structure for addition.
The purpose of the task is to have students reflect on the meaning of repeating decimal representation through approximation. A formal explanation requires the idea of a limit to be made precise, but 7th graders can start to wrestle with the ideas and get a sense of what we mean by an "infinite decimal."
This task presents students with some creative geometric ways to represent the fraction one half. The goal is both to appeal to students' visual intuition while also providing a hands on activity to decide whether or not two areas are equal.
This task provides a context for indentifying different ways of representing half of a rectangle.
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.
The task is intended to address standards regarding sample space, independence, probability distributions and permutations/combinations.
In this task students draw the graphs of two functions from verbal descriptions. Both functions describe the same situation but changing the viewpoint of the observer changes where the function has output value zero. This small twist forces the students to think carefully about the interpretation of the dependent variable.
This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle: the fact that these triangles are always right triangles is often referred to as Thales' theorem. It does not have a lot of formal prerequisites, just the knowledge that the sum of the three angles in a triangle is 180 degrees.
The result here complements the fact, presented in the task ``Right triangles inscribed in circles I,'' that any triangle inscribed in a circle with one side being a diameter of the circle is a right triangle. A second common proof of this result rotates the triangle by 180 degrees about M and then shows that the quadrilateral, obtained by taking the union of these two triangles, is a rectangle.
The purpose of this task is to give students an opportunity to explore various aspects of exponential models (e.g., distinguishing between constant absolute growth and constant relative growth, solving equations using logarithms, applying compound interest formulas) in the context of a real world problem with ties to developing financial literacy skills.
This task requires graphing time and distance.
his task is intended as a classroom activity. Student pool the results of many repetitions of the random phenomenon (rolling dice) and compare their results to the theoretical expectation they develop by considering all possible outcomes of rolling two dice. This gives them a concrete example of what we mean by long term relative frequency.
Students practice rounding whole numbers with this task.
This problem is an exponential function example.
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.
This task uses geometry to find the perimeter of the track. Students may be surprised when their calculation does not give 400 meters but rather a smaller number.
The goal of this task is to model a familiar object, an Olympic track, using geometric shapes. Calculations of perimeters of these shapes explain the staggered start of runners in a 400 meter race.
The purpose of this task is for students to compare two fractions that arise in a context. Because the fractions are equal, students need to be able to explain how they know that.
This word problem asks students to think about fractions.
In this task students use ratio and rate reasoning to solve the real-world problem of a runners rate and distance.