āž• 7th Grade Math Ā· Unit 4

Geometry

29 short narrated lessons in 6 chapters, each with pictures, a quiz with a hint and a second try, and an explanation for every answer.

Standards: 7.G.A.1 7.G.A.2 7.G.A.3 7.G.B.5 7.G.B.4 7.G.B.6

7th Grade Math Ā· 6 units
  1. 1Operations with Rational Numbers
  2. 2Expressions and Equations
  3. 3Ratios and Proportional Relationships
  4. 4Geometry
  5. 5Statistics
  6. 6Probability
Picture from the lesson ā€œUnderstanding Scaleā€
Understanding Scale
Picture from the lesson ā€œFinding Actual Lengthsā€
Finding Actual Lengths
Picture from the lesson ā€œFinding Actual Areasā€
Finding Actual Areas

What your child will learn

Scale drawings

  1. Understanding ScaleExplain what a scale like one inch to ten feet means on a map or drawing.
  2. Finding Actual LengthsUse a scale to find actual lengths from a scale drawing.
  3. Finding Actual AreasFind the actual area of a space from a scale drawing and explain why area scales by the square of the scale factor.
  4. Redrawing at a Different ScaleReproduce a scale drawing at a new scale.
  5. Scale Drawings Review ReviewReview reading scales, finding actual lengths and areas and redrawing at a new scale.

Drawing geometric shapes

  1. Drawing Shapes with Given ConditionsDraw shapes with a ruler and protractor to match given side lengths and angles.
  2. The Triangle InequalityDecide whether three side lengths can make a triangle by checking that any two sides add to more than the third.
  3. Triangles from Three AnglesExplain why three angles that add to one hundred eighty degrees make many triangles of different sizes.
  4. Unique TrianglesDecide whether given conditions make exactly one triangle, more than one triangle or no triangle.
  5. Drawing Geometric Shapes Review ReviewReview drawing shapes from conditions and deciding how many triangles fit given measurements.

Cross sections

  1. Slices of SolidsDescribe the flat shape you get when you slice a three-dimensional figure with a plane.
  2. Cross Sections of PrismsIdentify the cross sections of right rectangular prisms sliced in different directions.
  3. Cross Sections of PyramidsIdentify the cross sections of right rectangular pyramids sliced parallel or perpendicular to the base.
  4. Cross Sections Review ReviewReview describing cross sections of prisms and pyramids.

Angle relationships

  1. Complementary and Supplementary AnglesIdentify complementary angles that add to ninety degrees and supplementary angles that add to one hundred eighty degrees.
  2. Vertical and Adjacent AnglesIdentify vertical angles that are equal and adjacent angles that share a side.
  3. Finding Unknown AnglesWrite and solve an equation like x plus forty equals ninety to find an unknown angle.
  4. Angle Relationships Review ReviewReview complementary, supplementary, vertical and adjacent angles and solving for unknown angles.

Circles

  1. Parts of a CircleName the center, radius, diameter and circumference of a circle.
  2. Circumference and PiFind the circumference of a circle using pi times the diameter.
  3. Area of a CircleFind the area of a circle using pi times the radius times the radius.
  4. Circle ProblemsSolve real-world problems involving circumference and area of circles and half circles.
  5. Circles Review ReviewReview parts of a circle, circumference, area and circle word problems.

Area, surface area and volume

  1. Area of Composite FiguresFind the area of a figure made of triangles, rectangles and other polygons by breaking it into parts.
  2. Surface Area of PrismsFind the surface area of a prism by adding the areas of all its faces.
  3. Volume of PrismsFind the volume of a prism by multiplying the area of the base by the height.
  4. Surface Area and Volume ProblemsDecide whether a real-world problem needs area, surface area or volume and solve it.
  5. Area, Surface Area and Volume Review ReviewReview area of composite figures and surface area and volume of prisms.
  6. Unit 4 Test: GeometryShow what you learned in the whole unit (Scale drawings, Drawing geometric shapes, Cross sections, Angle relationships, Circles, Area, surface area and volume) by answering mixed questions.

Try a question from this unit

From the lesson ā€œUnderstanding Scaleā€

A scale bar of three striped blocks, the first marked 1 cm, with distances 0, 25 m, 50 m and 75 m underneath.

This scale bar comes from a park map. Each striped block is 1 centimeter long. What is the map's scale?

  • 1 centimeter to 75 meters
  • 1 centimeter to 25 meters
  • 3 centimeters to 25 meters
  • 1 centimeter to 3 meters
Show the answer

1 centimeter to 25 meters. Each 1 centimeter block ends 25 meters farther along the bar, so 1 centimeter stands for 25 meters. The 75 meters is the whole bar, which is 3 centimeters long.

Hint kids see after a wrong try: ā€œLook at how far the distances under the bar go up across just one block.ā€

Key words

  • scale
  • scale drawing
  • actual length
  • area
  • scale factor
  • reproduce
  • protractor
  • ruler
  • triangle inequality
  • angle sum
  • unique
  • cross section
  • plane
  • right rectangular prism
  • right rectangular pyramid
  • parallel
  • perpendicular
  • complementary
  • supplementary
  • vertical angles
  • adjacent angles
  • unknown angle
  • radius
  • diameter
ā† Ratios and Proportional Relationships All 7th Grade Math units Statistics ā†’

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