In this task, the students are not asked to find an answer, …
In this task, the students are not asked to find an answer, but are asked to analyze word problems and explain their thinking. In the process, they are faced with varying ways of thinking about multiplication.
This task provides a construction of the angle bisector of an angle …
This task provides a construction of the angle bisector of an angle by reducing it to the bisection of an angle to finding the midpoint of a line segment. It is worth observing the symmetry -- for both finding midpoints and bisecting angles, the goal is to cut an object into two equal parts. The conclusion of this task is that they are, in a sense, of exactly equivalent difficulty -- bisecting a segment allows us to bisect and angle (part a) and, conversely, bisecting an angle allows us to bisect a segment (part b). In addition to seeing how these two constructions are related, the task also provides an opportunity for students to use two different triangle congruence criteria: SSS and SAS.
In this task students have to interpret expressions involving two variables in …
In this task students have to interpret expressions involving two variables in the context of a real world situation. All given expressions can be interpreted as quantities that one might study when looking at two animal populations.
In this problem students are comparing a very small quantity with a …
In this problem students are comparing a very small quantity with a very large quantity using the metric system. The metric system is especially convenient when comparing measurements using scientific notations since different units within the system are related by powers of ten.
This task requires students to work with very large and small values …
This task requires students to work with very large and small values expressed both in scientific notation and in decimal notation (standard form). In addition, students need to convert units of mass.
The famous story of Archimedes running through the streets of Syracuse (in …
The famous story of Archimedes running through the streets of Syracuse (in Sicily during the third century bc) shouting ''Eureka!!!'' (I have found it) reportedly occurred after he solved this problem. The problem combines the ideas of ratio and proportion within the context of density of matter.
In this problem, students are given a picture of two triangles that …
In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other focuses them on the work of standard G-SRT.2, using the definition of similarity in terms of similarity transformations.
This problem is part of a very rich tradition of problems looking …
This problem is part of a very rich tradition of problems looking to maximize the area enclosed by a shape with fixed perimeter. Only three shapes are considered here because the problem is difficult for more irregular shapes.
In this assessment in a one-to-one setting, a student is shown the …
In this assessment in a one-to-one setting, a student is shown the numbers from 1Đ10, one number at a time, in random order. The teacher asks, Ňwhat number is this?"
This assessment may be used in a small group or whole group …
This assessment may be used in a small group or whole group setting, give each student a piece of paper. Students who have trouble writing certain numbers can then get targeted practice.
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