In Module 6, Topic A, students revisit a Grade 3 activity in which lined paper is used to subdivide a length into n equal parts. In Grade 5, this activity is extended as students explore that any line, regardless of orientation, can be made into a number line by first locating zero, choosing a unit length, and partitioning the length-unit into fractional lengths. Students are introduced to the concept of a coordinate as describing the distance of a point on the line from zero.
As they construct number lines in various orientations on a plane, students explore ways to describe the position of points not located on the lines. This discussion leads to the discovery that a second number line, perpendicular to the first, creates an efficient, precise way to describe the location of these points. Thus, points can be located using coordinate pairs, by traveling a distance of a units from the origin along with the x-axis and b units along a line parallel to the y-axis.
Students describe given points using coordinate pairs and then use given coordinate pairs to plot points (5.G.1). The topic concludes with an investigation of the patterns in coordinate pairs along vertical or horizontal lines, which leads to the discovery that these lines consist of the set of points whose distance from the x- or y-axis is constant.
In Module 6, Topic B, students plot points and use them to draw lines on the plane (5.G.1). Students begin by investigating patterns relating the x- and y-coordinates of the points on the line and reasoning about the patterns in the ordered pairs, which lays important groundwork for Grade 6 work with proportional reasoning. Topic B continues as students use given rules (e.g., multiply by 2, and then add 3) to generate coordinate pairs, plot points, and investigate relationships. Patterns in the resultant coordinate pairs are analyzed to discover that such rules produce collinear sets of points or lines. Students next generate two number patterns from two given rules, plot the points, and analyze the relationships within the sequences of the ordered pairs and graphs (5.OA.3). Patterns continue to be the focus as students analyze the effect on the steepness of the line when the second coordinate is produced through an addition rule as opposed to a multiplication rule (5.OA.3). They also create rules to generate number patterns, plot the points, connect those points with lines, and look for intersections.
In Module 6, Topic C, students draw figures in the coordinate plane by plotting points to create parallel, perpendicular, and intersecting lines. They reason about what points are needed to produce such lines and angles, and they investigate the resultant points and their relationships. In preparation for Topic D, students recall Grade 4 concepts such as angles on a line, angles at a point, and vertical angles—all produced by plotting points and drawing figures on the coordinate plane (5.G.1). To conclude the topic, students draw symmetric figures using both angle size and distance from a given line of symmetry (5.G.2).
In this interactive activity, students will be led through steps to interpret data shown in double-line graphs. There are teaching activities as well as practice activities available. A handout that reviews the strategies taught during the activity can be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.
In this interactive activity, students will be led through steps to plot points on a coordinate plane using ordered pairs. There are teaching activities as well as practice activities available. A handout that reviews the steps taught during the activity can be printed. After utilizing this resource, the students can complete the short quiz to assess their understanding.