Students' first experience with transformations is likely to be with specific shapes …
Students' first experience with transformations is likely to be with specific shapes like triangles, quadrilaterals, circles, and figures with symmetry. Exhibiting a sequence of transformations that shows that two generic line segments of the same length are congruent is a good way for students to begin thinking about transformations in greater generality.
This task has two goals: first to develop student understanding of rigid …
This task has two goals: first to develop student understanding of rigid motions in the context of demonstrating congruence. Secondly, student knowledge of reflections is refined by considering the notion of orientation in part (b).
An interactive applet and associated web page that demonstrate the concept of …
An interactive applet and associated web page that demonstrate the concept of congruent triangles. Applets show that triangles a re congruent if the are the same, rotated, or reflected. In each case the user can drag one triangle and see how another triangle changes to remain congruent to it. The web page describes all this and has links to other related pages. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.
The purpose of this task is to have students think about the …
The purpose of this task is to have students think about the meaning of multiplying a number by a fraction, and to use this understanding of fraction multiplication to make sense of the commutative property of multiplication in the case of fractions.
Unit 2: Introducing Ratios Lesson 9: Constant Speed In the previous lesson, …
Unit 2: Introducing Ratios Lesson 9: Constant Speed
In the previous lesson, students used the context of shopping to explore how equivalent ratios and ratios involving one can be used to find unknown amounts. In this lesson, they revisit these ideas in a new context—constant speed—and through concrete experiences. Students measure the time it takes them to travel a predetermined distance—first by moving slowly, then quickly—and use it to calculate and compare the speed they traveled in meters per second.
Here, double number lines are used to represent the association between distance and time, and to convey the idea of constant speed as a set of equivalent ratios (e.g., 10 meters traveled in 20 seconds at a constant speed means that 0.5 meters is traveled in 1 second, and 5 meters is traveled in 10 seconds). Students come to understand that, like price, speed can be described using the terms per and at this rate.
The idea of a constant speed relating the quantities of distance and time is foundational for the later, more abstract idea of a constant rate, and is important in the development of students’ ability to reason abstractly about quantities (MP2).
Unit 7: Rational Numbers Lesson 12: Constructing the Coordinate Plane In this …
Unit 7: Rational Numbers Lesson 12: Constructing the Coordinate Plane
In this lesson, students explore the idea of scaling axes appropriately to accommodate data where coordinates are rational numbers. Students attend to precision as they plan where to place axes on a grid and how to scale them to represent data clearly (MP6). In an optional activity, students practice working with coordinates in all 4 quadrants as they navigate a maze on a coordinate grid. This lesson gives students the opportunity to develop fluency with plotting coordinates in all 4 quadrants and scaling axes to fit data that is essential for the context-driven work over the next few lessons.
The construction of the perpendicular bisector of a line segment is one …
The construction of the perpendicular bisector of a line segment is one of the most common in plane geometry and it is undertaken here. In addition to giving students a chance to work with straightedge and compass, the problem uses triangle congruence both to show that the constructed line is perpendicular to AB and to show that it bisects AB.
The applets in this section allow you to see how the common …
The applets in this section allow you to see how the common Xbar control chart is constructed with known variance. The Xbar chart is constructed by collecting a sample of size n at different times t.
This task is for instruction purposes. Part (b) is subtle and the …
This task is for instruction purposes. Part (b) is subtle and the solution presented here uses a "dynamic" view of triangles with two side lengths fixed. This helps pave the way toward what students will see later in trigonometry but some guidance will likely be needed in order to get students started on this path.
This short video and interactive assessment activity is designed to give fifth …
This short video and interactive assessment activity is designed to give fifth graders an overview of conversion between units of weight (english units).
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