Unit 6

Measurement Conversions and Two-Dimensional Figures

Grade 5


Unit Length and Description:


30 days


During unit 6, students will continue the study of polygons, rhombuses, rectangles, squares, triangles and quadrilaterals previously learned in fourth grade. Students will continue to learn about properties of sides and angles as they classify two-dimensional figures into categories based on their properties. Students will reason about the attributes (properties) of shapes as they create a graphic organizer to classify shapes and make sense of the hierarchy of shapes. Finally, students will create shapes using a coordinate plane and ordered pairs.


In Unit 6 students also convert both customary and metric measurements within the same system of measurement. Practice will involve the use of conversions in solving multi-step, real-world problems. Students convert measurements into larger or smaller units within a measurement system using place value for whole numbers and decimals and the connection between fractions and decimals.




Supporting Clusters


Convert like measurement units within a given measurement system.



Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.


Additional Cluster: G: Geometry


Classify two-dimensional figures into categories based on their properties.



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).



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.



Classify two-dimensional figures in a hierarchy based on properties.

Foundational Standards


Use place value understanding to round whole numbers to the nearest 10 or 100.


Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and 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.


Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb., oz.; l, ml; hr., min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. For example, know that 1 ft. is 12 times as long as 1 in. Express the length of a 4 ft. snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...


Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.


Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Standards for Mathematical Practices

1.   Make sense of problems and persevere in solving them.

2.   Reason abstractly and quantitatively.

3.   Construct viable arguments and critique the reasoning of others.

4.   Model with mathematics.

5.   Use appropriate tools strategically.

6.   Attend to precision.

7.   Look for and make use of structure.

8.   Look for and express regularity in repeated reasoning.

Instructional Outcomes


o   I can convert units of measurement within the same measurement system.

o   I can solve multi-step, real world problems that involve converting measurement units.


o   I can construct a coordinate system and recognize the origin.

o   I can identify the x-and y-axis.

o   I can explain the relationship of an ordered pair and the location on the coordinate plane.

o   I can identify the x-coordinate as the distance to move right from the origin and the y-coordinate as the distance to move up from the x-axis.


o   I can recognize a two-dimenstional shape is classified into a category and its subcategories.

o   I can recognize that the same attributes can belong to several two-dimensional figures.



o   I can classify two dimensional figures into categories and/or subcategories based on their attributes.

o   I can group shapes that share a single property, and then among these shapes group those that share a second property.



Enduring Understandings:


         Relationships between measurement units of the same length, capacity, or mass can be expressed as an equation. Relationships exist that enable one to convert between units of length by multiplying or dividing.

         Ordered pairs are used to locate specific locations on a coordinate plane.

         Plane shapes have many properties that make them different from one another. Polygons can be described and classified by their sides and angles.

         Any subcategory of a shape must also belong to the more general category of a shape.

         Two dimensional figures can be classified into categories based on their properties.


Essential Questions:


         How do I use the language of math to make sense of/solve a problem?

         What is the best way to categorize a particular shape?

         What are the properties of 2 dimensional figures?

         What is the relationship between the units being converted?

         How do I write and solve an equation to show conversion of units?

         What is the relationship of an ordered pair and its location on the coordinate plane?

         How do I construct a coordinate system, recognize the origin, recognize the x and y axes and identify an ordered pair?