ALEX Classroom Resources

   View Standards     Standard(s): [MA2019] (5) 20 :

20. Graph points in the first quadrant of the coordinate plane, and interpret coordinate values of points to represent real-world and mathematical problems.

Students are introduced to graphing on the coordinate plane, in the first quadrant, using (x, y) coordinates. This CYBERCHASE activity is motivated by a video clip in which the CyberSquad is lost, and landmarks are ambiguous. They use the map's grid to construct a coordinate system using letters and numbers.

   View Standards     Standard(s): [MA2019] (5) 2 :

2. Generate two numerical patterns using two given rules and complete an input/output table for the data.

a. Use data from an input/output table to identify apparent relationships between corresponding terms.

b. Form ordered pairs from values in an input/output table.

c. Graph ordered pairs from an input/output table on a coordinate plane.

[MA2019] (5) 20 :

20. Graph points in the first quadrant of the coordinate plane, and interpret coordinate values of points to represent real-world and mathematical problems.

Students will use mathematics to determine what is required to beat world champion Usain Bolt in a 200-meter race. This video focuses on systems of equations that are visualized by completing a table of values and looking for a point of intersection in a set of line graphs. 

   View Standards     Standard(s): [ARTS] DAN (3) 6 :

6) Illustrate directions or spatial pathways in a dance phrase by drawing a picture map or using a symbol.

[ARTS] DAN (4) 6 :

6) Illustrate the relationship between two or more dancers in a dance phrase by drawing a picture or using symbols.

Example: Draw a formation or pathway of dancers using symbols.

[ARTS] DAN (5) 6 :

6) Illustrate changes in a dance sequence through media technology, written symbols, or words.

Example: Record changes in choreography in dance journal.

[MA2019] (3) 16 :

16. For a given or collected set of data, create a scaled (one-to-many) picture graph and scaled bar graph to represent a data set with several categories.

a. Determine a simple probability from a context that includes a picture.

b. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled graphs.

[MA2019] (4) 20 :

20. Interpret data in graphs (picture, bar, and line plots) to solve problems using numbers and operations.

a. Create a line plot to display a data set of measurements in fractions of a unit (¹/₂,¹/₄,¹/₈).

b. Solve problems involving addition and subtraction of fractions using information presented in line plots.

[MA2019] (5) 20 :

20. Graph points in the first quadrant of the coordinate plane, and interpret coordinate values of points to represent real-world and mathematical problems.

Students will compare and contrast quilting and square dancing.  This lesson has three options based on time allotment.  Students will graph a figure, choreograph and perform a square dance.     

   View Standards     Standard(s): [MA2015] (5) 23 :

23 ) Use a pair of perpendicular number lines, called axes, to define a coordinate system with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). [5-G1]

[MA2019] (5) 20 :

20. Graph points in the first quadrant of the coordinate plane, and interpret coordinate values of points to represent real-world and mathematical problems.

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).

   View Standards     Standard(s): [MA2019] (5) 2 :

2. Generate two numerical patterns using two given rules and complete an input/output table for the data.

a. Use data from an input/output table to identify apparent relationships between corresponding terms.

b. Form ordered pairs from values in an input/output table.

c. Graph ordered pairs from an input/output table on a coordinate plane.

[MA2019] (5) 20 :

20. Graph points in the first quadrant of the coordinate plane, and interpret coordinate values of points to represent real-world and mathematical problems.

Applications of the coordinate plane in the real world are the focus of Module 6, Topic D. Students use the coordinate plane to show locations, movement, and distance on maps. Line graphs are also used to explore patterns in the coordinate plane and make predictions based on those patterns (5.G.2, 5.OA.3). To close their work with the coordinate plane, students solve real-world problems.

   View Standards     Standard(s): [MA2019] (5) 9 :

9. Model and solve real-word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers.

Example: Recognize an incorrect result ²/₅+ ¹/₂= ³/₇ by observing that ³/₇ < ¹/₂.

[MA2019] (5) 11 :

11. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

a. Model and interpret a fraction as division of the numerator by the denominator (^a/_b= a ÷ b)

b. Use visual fraction models, drawings, or equations to represent word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers

[MA2019] (5) 14 :

14. Model and solve real-world problems involving multiplication of fractions and mixed numbers using visual fraction models, drawings, or equations to represent the problem.

[MA2019] (5) 15 :

15. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

a. Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions and illustrate using visual fraction models, drawings, and equations to represent the problem.

b. Create a story context for a unit fraction divided by a whole number, and use a visual fraction model to show the quotient.

c. Create a story context for a whole number divided by a unit fraction, and use a visual fraction model to show the quotient.

[MA2019] (5) 17 :

17. Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real-world problems.

[MA2019] (5) 19 :

19. Relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume.

a. Use the associative property of multiplication to find the volume of a right rectangular prism and relate it to packing the prism with unit cubes. Show that the volume can be determined by multiplying the three edge lengths or by multiplying the height by the area of the base.

b. Apply the formulas V = l x w x h and V = B x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems.

c. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the two parts, applying this technique to solve real-world problems.

[MA2019] (5) 20 :

20. Graph points in the first quadrant of the coordinate plane, and interpret coordinate values of points to represent real-world and mathematical problems.

Module 6, Topic E provides an opportunity for students to encounter complex, multi-step problems requiring the application of the concepts and skills mastered throughout the Grade 5 curriculum. Students use all four operations with both whole and fractional numbers in varied contexts. The problems in Topic E are designed to be non-routine problems that require students to persevere to solve them.  

While wrestling with complexity is an important part of Topic E, the true strength of this topic is derived from the time allocated for students to construct arguments and critique the reasoning of their classmates. After students have been given adequate time to ponder and solve the problems, two lessons are devoted to the sharing of approaches and solutions. Students partner to justify their conclusions, communicate them to others, and respond to the arguments of their peers.