# OREGON MATH STANDARDS (2021): [3.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: 3.GM.A.1

**Cluster: 3.GM.A - Reason with shapes and their attributes. **

## STANDARD: 3.GM.A.1

### Standards Statement (2021):

Understand that shapes in different categories may share attributes and that shared attributes can define a larger category.

### Connections:

Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |

2.GM.A.1 | 4.GM.A.1, 5.GM.B.3, 5.GM.D.6 | N/A | 3.G.A.1 3.GM.A Crosswalk |

### Standards Guidance:

#### Clarifications

- Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).
- Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
- There should be a focus on the investigation of quadrilaterals, specifically, but other polygons should also be explored.

#### Progressions

- Students should be able to analyze, compare, and classify two dimensional shapes by their properties. Because they have built a firm foundation of several shape categories, these categories can be the raw material for thinking about the relationships between the classes. (Please reference page 13 in the Progression document).

#### Examples

- Compare and classify shapes by their sides and angles.
- Recognize rhombi, rectangles, squares, and trapezoids as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

# 2021 Oregon Math Guidance: 3.GM.A.2

**Cluster: 3.GM.A - Reason with shapes and their attributes. **

## STANDARD: 3.GM.A.2

### Standards Statement (2021):

Partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole.

### Connections:

Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |

2.GM.A.3 | 3.GM.C.5 | 3.NF.A.1 | 3.G.A.2 3.GM.A Crosswalk |

### Standards Guidance:

#### Progressions

- Students [continue to] develop competence in the composition and decompostion of rectangular regions, that is spatially structuring rectangular arrays. They learn to partition a rectangle into identical squares by anticipating the final structure and thus forming the array by drawing rows and columns. (Please reference page 13 in the Progression document).

#### Examples

- This could include partitioning a shape into 4 parts with equal area and describe each part as 1/4 of the area of the total shape.
- Draw lines to separate a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
- Illustrative Mathematics:
- Student Achievement Partners:

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

**Cluster: 3.GM.B - Solve problems involving measurement and estimation. **

## STANDARD: 3.GM.B.3

### Standards Statement (2021):

Tell, write, and measure time to the nearest minute. Solve problems in authentic contexts that involve addition and subtraction of time intervals in minutes.

### Connections:

Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |

2.GM.D.10 | N/A | N/A | 3.MD.A.1 3.GM.B Crosswalk |

### Standards Guidance:

Clarifications

- Students should be given opportunities to determine relative time and predict time to the nearest fifteen minutes using only the hour hand of an analog clock.

#### Boundaries

- Students may use tools such as clocks, number line diagrams, and tables to solve problems involving time intervals.

#### Teaching Strategies

- Students will have opportunities to representing the problems in different ways, including using a number line diagram.
- Problems should include am/pm, start unknown, end unknown, and change unknown and addition/subtraction of time intervals.
- Students should be given opportunities to use number lines to find unknowns.

#### Examples

- The bus comes at 7:00 a.m. It takes me 15 minutes to eat breakfast and 30 minutes to get ready. What time do I need to wake up? (e.g., start unknown)
- I went to the movies at 3:15 p.m. The movie lasted 1 hour 45 minutes. What time did the movie end? (e.g., end unknown)
- After school I went to the park at 2:30 p.m. and left to go home at 3:45 p.m. How long was I at the park? (e.g., change unknown)
- Student Achievement Partners:

# 2021 Oregon Math Guidance: 3.GM.B.4

**Cluster: 3.GM.B - Solve problems involving measurement and estimation. **

## STANDARD: 3.GM.B.4

### Standards Statement (2021):

Measure, estimate and solve problems in authentic contexts that involve liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).

### Connections:

Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |

2.GM.B.4, 2.GM.C.9 | 4.GM.B.4 | 3.OA.D.8 | 3.MD.A.2 3.GM.B Crosswalk |

### Standards Guidance:

#### Clarifications

- Students should have an opportunity to compare capacity by filling one container with something and then pouring this amount into the comparison container.
- Students may use drawings (such as a beaker with a measurement scale) to represent the problem. This standard does not include conversions between units.
- The standard includes making reasonable estimates, use benchmarks to measure weight, and capacity.

#### Terminology

- The terminology below is used to clarify expectations for the teaching professional. Students are not required to use this terminology when engaging with the learning objective.
- Customary measurement units include weight (oz., lbs., tons) capacity (fl. oz, cups, pints, quarts, gallons), length (in., ft., yds., miles).

#### Boundaries

- Excludes compound units such as cm^3 and finding the geometric volume of a container.
- Excludes multiplicative comparison problems (problems involving notions of “times as much”).
- Students are not required to memorize the conversion factors.
- Students extend understanding of measuring length in different measurement systems (e.g. grams (g) to ounces (oz), kilograms to pounds (lb), liters (l) to quarts (qt)/gallons (gal), etc).

#### Progressions

- Identify and use the appropriate tools and units of measurement, both customary and metric, to solve one-step word problems using the four operations involving weight, mass, liquid volume, and capacity (within the same system and unit).

#### Teaching Strategies

- Add, subtract, multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units.
- Students should have opportunities to physically measure objects.
- Record measurement equivalents in a two-column table and/or double number line.

#### Examples

- Student Achievement Partners:

# 2021 Oregon Math Guidance: 3.GM.C.5

**Cluster: 3.GM.C - Geometric measurement: understand concepts of area and relate area to multiplication and to addition. **

## STANDARD: 3.GM.C.5

### Standards Statement (2021):

Recognize area as an attribute of plane figures and understand concepts of area measurement presented in authentic contexts by tiling and counting unit squares.

### Connections:

Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |

1.GM.A.2, 2.GM.A.3, 2.GM.B.5, 3.GM.A.2 | 3.GM.C.6, 3.GM.D.8 | N/A | 3.MD.C.5 3.GM.C Crosswalk |

### Standards Guidance:

#### Clarifications

- Concept of area is measured with unit squares tiling a plane without gaps or overlaps.
- A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
- A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

#### Teaching Strategies

- Students should use numerical and spatial reasoning to determine the area of rectangles in contextual, mathematical problems by counting or tiling.
- Instruction could include grade appropriate use of different measurement systems for area (e.g. in
^{2}/ft^{2}and cm^{2}/m^{2}, etc).

#### Progressions

- Students need to learn to conceptualize area as the amount of two dimensional space in a bounded region and to measure it by choosing a unit of area, often a square. A two-dimensional geometric figure that is covered by a certain number of squares without gaps or overlaps can be said to have an area of that number of square units. (Please reference page 17 in the Progression document).

#### Examples

- A laptop cover is being made with square vinyl stickers. There are four rows of stickers. There are 9 stickers in each row. How many square stickers were used to create the laptop cover?

# 2021 Oregon Math Guidance: 3.GM.C.6

**Cluster: 3.GM.C - Geometric measurement: understand concepts of area and relate area to multiplication and to addition. **

## STANDARD: 3.GM.C.6

### Standards Statement (2021):

Measure areas by counting standard and non-standard unit squares.

### Connections:

Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |

2.GM.A.2, 2.GM.D.11, 3.GM.C.5 | 3.GM.C.7 | N/A | 3.MD.C.6 3.GM.C Crosswalk |

### Standards Guidance:

#### Terminology

- Standard unit squares use standard measurement units, such as square feet or square meters.
- Non-standard unit squares could be improvised unit measurements such as sticky notes or floor/countertop tiles.

#### Teaching Strategies

- Area can be counted in square cm, square m, square in, square ft, and improvised units.
- Students should use numerical and spatial reasoning to determine the area of rectangles in contextual, mathematical problems.

#### Progressions

- To begin an explicit focus on area, teachers might then ask students which of three rectangles covers the most area. Students may first solve the problem with decomposition (cutting and/or folding) and re-composition, and eventually analyses with area-units, by covering each with unit squares (tiles). (Please reference page 17 in the Progression document).

#### Examples

- Students can determine the area of the top of their desk or other rectangle outlined by tape on the desk by covering it using non-standard units, such as index cards, sticky notes, tiles, etc.
- Illustrative Mathematics:
- Student Achievement Partners:

# 2021 Oregon Math Guidance: 3.GM.C.7

**Cluster: 3.GM.C - Geometric measurement: understand concepts of area and relate area to multiplication and to addition. **

## STANDARD: 3.GM.C.7

### Standards Statement (2021):

Relate area to multiplication and addition. Use relevant representations to solve problems in authentic contexts.

### Connections:

Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |

3.GM.C.6 | 4.GM.B.6, 5.NF.B.4 | 4.NBT.B.6 | 3.MD.C.7 3.GM.C Crosswalk |

### Standards Guidance:

#### Terminology

- The dimensions of a rectangle can be referred to as length and width OR base and height.
- A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area (e.g., square cm, square m, square in, square ft).

#### Teaching Strategies

- Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
- Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving problems, and represent whole-number products as rectangular areas in mathematical reasoning.
- Use tiles and/or arrays to illustrate and explain that the area of a rectangle can be found by partitioning it into two smaller rectangles and that the area of the larger rectangle is the sum of the two smaller rectangles.
- Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding.

#### Progressions

- Students can be taught to multiply length measurements to find the area of a rectangular region. But, in order that they make sense of these quantities, they first learn to interpret measurement of rectangular regions as a multiplicative relationship of the number of square units in a row and the number of rows.
- Students learn to understand and explain that the area of a rectangular region of, for example, 12 length-units by 5 length-units can be found either by multiplying 12 x 5 or by adding two products, e.g., 10 x 5 and 2 x 5, illustrating the distributive property. (Please reference pages 17-18 in the Progression document)

#### Examples

- The area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c; 4 x 7 is the same as 4 x (2 + 5) and is the sum of 4 x 2 and 4 x 5.
- In a rectangular garden, you have four rows of peanut plants. There are 9 peanut plants in each row. How many peanut plants are there in the garden?
- Student Achievement Partners:

# 2021 Oregon Math Guidance: 3.GM.D.8

**Cluster: 3.GM.D - Geometric measurement: recognize perimeter. **

## STANDARD: 3.GM.D.8

### Standards Statement (2021):

Solve problems involving authentic contexts for perimeters of polygons.

### Connections:

Preceding Pathway Content (2021) | Subsequent Pathway Content (2021) | Cross Domain Connections (2021) | Common Core (CCSS) (2010) |

3.GM.C.5 | 4.GM.B.6 | N/A | 3.MD.D.8 3.GM.D Crosswalk |

### Standards Guidance:

#### Clarifications

- Students should be given opportunities to develop a conceptual understanding of perimeter of all types of polygons including regular and irregular.
- Students should investigate perimeters of polygons with a focus on quadrilaterals.
- Students should be able to find the perimeter given the side lengths.
- Students should be able to find the unknown side length given the perimeter.

#### Terminology

- The focus of this learning objective should be on developing the conceptual understanding of perimeter, rather than on terminology.
- A polygon is a closed figure with at least three straight sides and angles; a polygon is regular only when all sides are equal and all angles are equal; and a polygon is irregular when all sides are not equal or all angles are not equal.

#### Teaching Strategies

- Finding the perimeter given the side lengths;
- Finding an unknown side length;
- Showing rectangles with the same perimeter and different area;
- Showing rectangles with the same area and different perimeters.
- Students should solve contextual, mathematical problems involving perimeter and area of rectangles.

#### Progressions

- Perimeter problems for rectangles and parallelograms often give only the lengths of two adjacent sides or only show numbers for these sides in a drawing of the shape. The common error is to add just those two numbers. Having students first label the lengths of the other two sides as a reminder is helpful. Students then find unknown side lengths in more difficult “missing measurements” problems and other types of perimeter problems. (Please reference page 16 in the Progression document).

#### Examples

- I have eighteen 1-foot panels to build a raised garden bed. How many different ways can I put these eighteen panels together to build a rectangular raised garden bed? Which rectangle will have the greatest area?