Author:
Mark Freed
Subject:
Mathematics
Material Type:
Teaching/Learning Strategy
Level:
Upper Primary
Tags:
License:
Creative Commons Attribution
Language:
English

Education Standards

OREGON MATH STANDARDS (2021): [5.GM]

OREGON MATH STANDARDS (2021): [5.GM]

Overview

The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards. 

Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

2021 Oregon Math Guidance: 5.GM.A.1

ODE and Oregon Math Project Logo

Cluster: 5.GM.A - Graph points on the coordinate plane to solve real-world and mathematical problems.

STANDARD: 5.GM.A.1

 Standards Statement (2021):

Graph and name coordinate points in the first quadrant using the standard (x, y) notation. Understand the coordinate points values represent the distance traveled along the horizontal x-axis and vertical y-axis.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

3.NF.A.2

5.GM.A.2

5.NBT.B.7, 6.NS.C.6

5.G.A.1

5.GM.A Crosswalk

 Standards Guidance:

Clarifications

  • This is students' first formalized introduction to the conventions of coordinate graphing: 
    • The first number indicates the distance from the origin on the x-axis.
    • The second number indicates the distance from the origin on the y-axis.
    • The names of the two axes and coordinates (or ordered pairs) correspond (x-axis and x-coordinate, y-axis and y-coordinate).
  • In addition to whole numbers, ordered pairs should include the decimal and fractional values of halves and fourths.

Boundaries

  • Graphing beyond the first quadrant is not a requirement at this grade.
  • All four quadrants of the coordinate plane can be displayed, but students will only plot and label within the first quadrant.

Teaching Strategies

  • Students should be provided with a variety of real-life, mathematical problems involving graphing points in the first quadrant.
  • Students should interpret coordinate values of points in the context of the problem or situation.

Progressions

  • Although students can often “locate a point,” these understandings are beyond simple skills. For example, initially, students often fail to distinguish between two different ways of viewing the point (2, 3), say, as instructions: “right 2, up 3”; and as the point defined by being a distance 2 from the y -axis and a distance 3 from the x -axis. In these two descriptions the 2 is first associated with the x -axis, then with the y -axis. (Please reference page 17 in the Progression document).

Examples

2021 Oregon Math Guidance: 5.GM.A.2

 ODE and Oregon Math Project Logo

Cluster: 5.GM.A - Graph points on the coordinate plane to solve real-world and mathematical problems.

STANDARD: 5.GM.A.2

 Standards Statement (2021):

Represent authentic contexts and mathematical problems by graphing points in the first quadrant of the coordinate plane. Interpret the meaning of the coordinate values based on the context of a given situation.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

3.NF.A.2, 5.GM.A.1

6.GM.A.3, 6.NS.C.8

5.NF.A.2, 6.RP.A.3

5.G.A.2

5.GM.A Crosswalk

 Standards Guidance:

Clarifications

  • Students should be given ample experience with organizing, representing, and analyzing data from real-life contexts.
  • Data should not be limited to numerical data collected from linear measurements.
  • Students should continue to create dot plots (line plots) with measurements in fractions of a unit.

Terminology

  • Distribution refers to how the data is spread across the graph.
  • Dot plots and line plots can be used interchangeably.
  • Dot plots should be used for numerical data representation on a number line.
  • Numerical data is data that expressed in numbers rather than natural language.  An example of numerical data that could be collected is the number of people who attended the movie theater over the course of a month.
  • Categorical data is a type of data that is used to group information with similar characteristics. Examples of categorical data that could be collected might be marital status, favorite sport, or favorite type of movie.

Progressions

  • Students connect ordered pairs of (whole number) coordinates to points on the grid, so that these coordinate pairs constitute numerical objects and ultimately can be operated upon as single mathematical entities. Students solve mathematical and real-world problems using coordinates.
  • For example, they plan to draw a symmetric figure using computer software in which students’ input coordinates that are then connected by line segments. (Please reference pages 17-18 in the Progression document).

Examples

2021 Oregon Math Guidance: 5.GM.B.3

 ODE and Oregon Math Project Logo

Cluster: 5.GM.B - Classify two-dimensional figures into categories based on their properties.

STANDARD: 5.GM.B.3

 Standards Statement (2021):

Classify two-dimensional figures within a hierarchy based on their geometrical properties, and explain the relationship across and within different categories of these figures.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

3.GM.A.1, 4.GM.A.2

6.GM.A.3

 N/A

5.G.B.4

5.GM.B Crosswalk

 Standards Guidance:

Clarifications

  • Students should explore, compare, and contrast polygons based on properties.
  • Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

Boundaries

  • This objective does not require students to create a hierarchy.
  • Standards expecations inclue the inclusive definitions for the classification of shapes are used.
  • Polygons should include triangles, quadrilaterals including kites and trapezoids (rectangles, squares, rhombuses, and other parallelograms), pentagons, hexagons, and octagons.
  • Properties may include angles, side lengths, symmetry, congruence, and the presence or absence of parallel or perpendicular lines

Progressions

  • Based on analysis of properties, students classify two-dimensional figures in hierarchies. For example, they conclude that all rectangles are parallelograms, because they are all quadrilaterals with two pairs of opposite, parallel, equal-length sides (MP3). In this way, they relate certain categories of shapes as subclasses of other categories.
  • This leads to understanding propagation of properties; for example, students understand that squares possess all properties of rhombuses and of rectangles. Therefore, if they then show that rhombuses’ diagonals are perpendicular bisectors of one another, they infer that squares’ diagonals are perpendicular bisectors of one another as well. (Please reference page 18 in the Progression document).

Examples

  • Explain that since all rectangles have four right angles, and squares are rectangles, then all squares have four right angles.
  • Explain that parallelograms and trapezoids are both quadrilaterals, and both have at least one set of parallel sides, but that they differ in that trapezoids have exactly one set and parallelograms have exactly two sets.
  • Illustrative Mathematics: 

2021 Oregon Math Guidance: 5.GM.C.4

 ODE and Oregon Math Project Logo

Cluster: 5.GM.C - Convert like measurement units within a given measurement system.

STANDARD: 5.GM.C.4

 Standards Statement (2021):

Convert between different-sized standard measurement units within a given measurement system.  Use these conversions in solving multi-step problems in authentic contexts.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

4.GM.B.4, 4.GM.B.5

HS.NQ.B.3

5.NBT.B.7

5.MD.A.1

5.GM.C Crosswalk

 Standards Guidance:

Boundaries

  • Fifth grade is the first time students are expected to convert between different units within the same measurement system.
  • Conversion chart should be provided.
  • Students should be presented with contextual problems involving distance, weight, volume, and time that are practical and relevant to their everyday lives.
  • Students should have opportunities to solve problems involving conversions within both metric and customary systems
    • Customary measurement units include weight (oz., lbs., tons) capacity (fl. oz, cups, pints, quarts, gallons), distance (in., ft., yds., miles).
    • Common metric units include weight (grams), capacity (liters), distance (meters)
      • Common metric conversions include Kilo- (1000), centi- (1/100), & milli- (1/1000)

Teaching Strategies

  • Instruction could include grade appropriate use of different measurement systems and the conversion between similar units (e.g. kilometer (km) and miles (mi), kilograms (kg) and pounds (lb), liters (l) to gallons (g), etc).

Progressions

  • In Grade 5, students extend their abilities from Grade 4 (4.MD.A.1) to express measurements in larger or smaller units within a measurement system. This is an excellent opportunity to reinforce notions of place value for whole numbers and decimals, and make connections between fractions and decimals (e.g., 2 1/2 meters can be expressed as 2.5 meters or 250 centimeters).  (Please reference page 26 in the Progression document).

Examples

2021 Oregon Math Guidance: 5.GM.D.5

 ODE and Oregon Math Project Logo

Cluster: 5.GM.D - Geometric measurement: understand concepts of volume.

STANDARD: 5.GM.D.5

 Standards Statement (2021):

Recognize that volume is a measurable attribute of solid figures.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

3.GM.C.5

5.GM.D.6, 5.GM.D.7

 N/A

5.MD.C.3

5.GM.C Crosswalk

 Standards Guidance:

Teaching Strategies

  • A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. 
  • A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

Progressions

  • “Packing” volume is more difficult than iterating a unit to measure length and measuring area by tiling. Students learn about a unit of volume, such as a cube with a side length of 1 unit, called a unit cube (5.GM.D.5). They pack cubes (without gaps) into right rectangular prisms and count the cubes to determine the volume or build right rectangular prisms from cubes and see the layers as they build (5.GM.D.6). (Please reference page 27 in the Progression document).

Examples

2021 Oregon Math Guidance: 5.GM.D.6

  ODE and Oregon Math Project Logo

Cluster: 5.GM.D - Geometric measurement: understand concepts of volume.

STANDARD: 5.GM.D.6

 Standards Statement (2021):

Measure the volume of a rectangular prism by counting unit cubes using standard and nonstandard units.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

4.GM.A.2, 5.GM.D.5

5.GM.D.7

 N/A

5.MD.C.4

5.GM.D Crosswalk

 Standards Guidance:

Teaching Strategies

  • Students should have opportunities to use metric, customary and improvised units

Progressions

  • “Packing” volume is more difficult than iterating a unit to measure length and measuring area by tiling. Students learn about a unit of volume, such as a cube with a side length of 1 unit, called a unit cube (5.GM.D.5). They pack cubes (without gaps) into right rectangular prisms and count the cubes to determine the volume or build right rectangular prisms from cubes and see the layers as they build (5.GM.D.6). (Please reference page 27 in the Progression document).

Examples

 

2021 Oregon Math Guidance: 5.GM.D.7

  ODE and Oregon Math Project Logo

Cluster: 5.GM.D - Geometric measurement: understand concepts of volume.

STANDARD: 5.GM.D.7

 Standards Statement (2021):

Relate volume of rectangular prisms to the operations of multiplication and addition.  Solve problems in authentic contexts involving volume using a variety of strategies.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

5.GM.D.5, 5.GM.D.6

6.GM.A.2

 N/A

5.MD.C.5

5.GM.D Crosswalk

 Standards Guidance:

Terminology

  • Total volume is defined as the total number of units that fill the space.
    • A solid figure packed with n unit cubes is said to have a volume of n cubic units.
  • The dimensions of a rectangular prism can be referred to as length, width, and height.
  • A cube with side length 1 unit, called “a unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume (e.g., cubic cm, cubic m, cubic in, cubic ft).

Boundaries

  • Work with volume at fifth grade is limited to whole number edge lengths.
  • If students are provided with an image of a right rectangular prism, the unit cubes should be visible.

Teaching Strategies

  • Students should be provided opportunities to use a variety of strategies including counting cubes, addition and multiplication, and applying the formula.
  • Students should explore the volume of solid figures from real-life contexts by packing them with unit cubes with no gaps or overlaps.

Progressions

  • Students understand that multiplying the length times the width of a right rectangular prism can be viewed as determining how many cubes would be in each layer if the prism were packed with or built up from unit cubes. They also learn that the height of the prism tells how many layers would fit in the prism. (Please reference page 27 in the Progression document).

Examples