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6-8 Accelerated 6 Unit 1

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IM K-5 Math
IM 6-8 Math
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Unit 1

Glossary

Accelerated 6

Area is the number of square units that cover a two-dimensional region without gaps or overlaps.

The area of region A is 8 square units.
The area of the shaded region of B is \(\frac12\) square unit.

Figure A on the left composed of 8 identical shaded squares arranged in 3 rows. Figure B on the right consists of one square with a diagonal segment from corner to corner. Half of the square is shaded.

used in:

Any side of a parallelogram or triangle can be chosen its base. The length of this side is also called the base.

Three identical, scalene, obtuse triangles oriented the same way. Each triangle has a different one of its sides labeled base.

used in:

A base is a specific face of a prism or pyramid.

A prism has 2 identical bases that are parallel. A pyramid has 1 base.

A prism or pyramid is named for the shape of its base.

A pentagonal prism. There are two identical pentagons on the top and bottom. Each vertex of a pentagon is connected by a vertical segment to the corresponding vertex of the other pentagons. The pengatons are each shaded, with the word base pointing to each.

A hexagonal pyramid. There is a hexagon on the bottom shaded green. From a point above the hexagon extend 6 segments, each connected to a vertex of the hexagon.

used in:

The word compose means “put together.” To compose a shape, put figures together to make a new shape.

Image on left shows three separate parts of a shape; image on right shows those three parts put together to create an oval.

From an earlier course.

The word decompose means “take apart.” To decompose a shape, take it apart to make more than one new shape.

Image on left shows three parts put together to create an oval; the image on the right shows the oval separated into the three parts.

From an earlier course.

Each flat side of a polyhedron is called a face.

For example, a cube has 6 faces that are all squares.

used in:

The height is the shortest distance from the base of the shape to the opposite side (for a parallelogram) or to the opposite vertex (for a triangle).

The height can be shown in more than one place. It is always perpendicular to the chosen base.

<p>2 parallelograms with height and base measurements</p>

used in:

A net is a two-dimensional figure that can be folded to make a three-dimensional figure.

Here is a net for a cube.

Six squares arranged with 4 in a row, 1 above the second square in the row, and one below the second square in the row.

used in:

For each side of a triangle, there is 1 vertex that is not on that side. This is the opposite vertex.

Point \(A\) is the opposite vertex to side \(BC\).

triangle with points labeled A, B, C.

used in:

A parallelogram is a type of quadrilateral that has 2 pairs of parallel sides.

Here are 2 examples of parallelograms.

Parallelogram with the angles and side lengths provided. Top and bottom sides = 5 units. Left and right sides = 4.24 units. Top left and bottom right angles = 135 degrees. Top right and bottom left angles = 45 degrees.

Parallelogram with the angles and side lengths provided. Top and bottom sides = 9.34 units. Left and right sides = 4 units. Top left and bottom right angles = 27.2 degrees. Top right and bottom left angles = 152.8 degrees.

From an earlier course.

A polygon is a closed, two-dimensional shape with straight sides that do not cross each other.

Figure \(ABCDE\) is an example of a polygon.

Polygon with 5 sides

used in:

A polyhedron is a closed, three-dimensional shape with flat sides. When there is more than one polyhedron, they are called polyhedra.

Here are some drawings of polyhedra.

<p>3 polyhedra, from left to right shapes resemble a house, drum, and star.</p>

used in:

A prism is a type of polyhedron with 2 bases that are identical and parallel. The bases are connected by parallelograms.

Here are some drawings of prisms.

A triangular prism. — triangular prism

A pentagonal prism. — pentagonal prism

A rectangular prism. — rectangular prism

used in:

A pyramid is a type of polyhedron that has 1 base. All the other faces are triangles that meet at a single vertex.

Here are some drawings of pyramids.

A rectangular pyramid. — rectangular pyramid

A hexagonal pyramid. — hexagonal pyramid

A heptagonal pyramid. — heptagonal pyramid

used in:

A quadrilateral is a type of polygon that has 4 sides.

A rectangle is an example of a quadrilateral.
A pentagon is not a quadrilateral, because it has 5 sides.

From an earlier course.

A region is the space inside of a shape.

Examples of two-dimensional regions are the inside of a circle and the inside of a polygon.
Examples of three-dimensional regions are the inside of a cube and the inside of a sphere.

used in:

The surface area of a polyhedron is the number of square units that covers all of its faces with no gaps or overlaps.

For example, the 6 faces of a cube each have an area of 9 cm². So, the surface area of the cube is \(6 \boldcdot 9\), or 54 cm².

used in:

Unit 1 Resources

Student Materials