Students construct, analyze, and classify trapezoids, kites, parallelograms, rectangles, rhombuses, and squares. They identify properties of quadrilaterals that involve pairs of parallel sides, angle measures, side lengths, diagonals, and lines of symmetry and use these properties to create a hierarchy of quadrilaterals. They use the hierarchy to determine the most specific name of any quadrilateral and all names for the quadrilateral.

Family Math Topic A

Students find areas of rectangles with fraction side lengths, first by tiling with tiles that are squares with unit-fraction side lengths and then by tiling with rectangles with fraction side lengths. Through reasoning, students determine that the area of any rectangle, including one with fraction side lengths, can be found by multiplying the rectangle’s length by its width. Students use an area model to multiply mixed numbers, and then they solve real-world and mathematical problems involving multiplication of mixed numbers. 

Family Math Topic B

In their first formal study of volume, students count the number of unit cubes that pack right rectangular prisms. Then they build right rectangular prisms with improvised units to find volume by using something other than unit cubes. They compose and decompose right rectangular prisms into layers in different ways, finding the volume of each layer and multiplying the number of layers by the volume of each layer to find the volume of the right rectangular prism. Students explore conceptual ideas about volume and capacity by differentiating between packing with cubes and filling with a liquid.

Family Math Topic C

Students synthesize the work of topic C by determining that the volume of any right rectangular prism is calculated either by multiplying the area of the base by the height, V = B × h, or by multiplying the three dimensions of the prism, V = l × w × h. They use these two formulas to find volumes and unknown dimensions of right rectangular prisms in both mathematical and real-world problems. Students find the volume of a figure composed of right rectangular prisms by decomposing the figure into right rectangular prisms, finding the volume of each prism, and adding the volumes together. 

Family Math Topic D

base

The base of a prism is one of the faces of the prism, often thought of as the surface on which the prism rests. (Lesson 16)

composite figure

A composite figure is a geometric figure composed of two or more smaller figures. (Lesson 13)

cubic centimeter

Cubic centimeters are a unit for measuring volume. 1 cubic centimeter of volume is defined as the volume of a cube with side lengths of 1 centimeter. (Lesson 17)

cubic inch

Cubic inches are a unit for measuring volume. 1 cubic inch of volume is defined as the volume of a cube with side lengths of 1 inch. (Lesson 17)

cubic unit

Cubic units are a unit for measuring volume. 1 cubic unit of volume is defined as the volume of a cube with side lengths of 1 unit. (Lesson 17)

kite

A kite is a quadrilateral with at least two pairs of adjacent sides that are the same length. (Lesson 5)

midpoint

The midpoint of a line segment is the point on the line segment that divides it into two line segments of equal length. (Lesson 3)

plane

A plane is a flat, two-dimensional surface that extends forever.(Lesson 1)

property

A property is a characteristic that is true of every item in a category. (Lesson 1)

right rectangular prism

A right rectangular prism is a solid where all the faces are rectangles. (Lesson 16)

unit cube

A unit cube is a cube with edges that each measure 1 unit. (Lesson 17)

volume

The volume of a solid is the amount of three-dimensional space it takes up. (Lesson 17)

acute angle

acute triangle

attribute

capacity

cube

diagonal

edge

equilateral triangle

face

figure

formula

height

intersect

isosceles triangle

line of symmetry

liquid volume

obtuse angle

obtuse triangle

parallel

parallelogram

perpendicular

quadrilateral

rectangle

rhombus

right angle

right triangle

square

square unit

straight angle

supplementary angles

three-dimensional figure

trapezoid

two-dimensional figure

unit square

vertex