Grade 3 Mathematics Chapter 5: Shapes, Perimeter, Area and Reasoning
GRADE 3 MATH CHAPTER 5: Printable Student Text PDF | Practice Online | Fillable Workbook. This is a separate subject resource in the developing full-year course. Keep completed student work private.
Student textbook chapter. Five connected lessons with explanations and modeled work, matched to a 60-question practice workbook. This chapter is part of the developing Grade 3 course, not a complete annual textbook.
Lesson 1: Describe Polygons
Direct instruction: A polygon is a closed shape made of straight line segments. A triangle has three sides. A quadrilateral has four sides. A shape’s orientation does not change its number of sides. Draw closed lines carefully before classifying a figure.
Model and Discuss
Worked example: Draw a triangle with vertices A, B and C. Trace AB, BC and CA: three straight sides form a closed polygon. Now draw three connected segments without closing the last gap. The second drawing is not a polygon. Explain which feature matters, rather than how a figure is rotated.
Advanced extension: Advanced: classify a four-sided figure with one pair of parallel opposite sides.
Lesson 2: Sort Quadrilaterals
Direct instruction: Rectangles have four right angles; squares are rectangles with four equal sides. Rhombuses have four equal sides but need not have right angles. A parallelogram has opposite sides parallel. Classification can be inclusive: a square is a rectangle and a rhombus.
Model and Discuss
Worked example: Draw a square with four 3 cm sides and four right angles. It is a square, a rectangle, a rhombus and a parallelogram because it meets each definition. Draw a 3 by 5 cm rectangle: four right angles make it a rectangle, but unequal adjacent sides mean it is not a square.
Advanced extension: Advanced: explain why a rectangle is a parallelogram.
Lesson 3: Perimeter Problem Solving
Direct instruction: Perimeter is the linear distance around a shape. For a rectangle of 7 cm by 4 cm, the perimeter is 7+4+7+4=22 cm. Unknown side problems require reasoning about total side lengths, not multiplying the two given lengths.
Model and Discuss
Worked example: A rectangular garden is 9 m long and 4 m wide. Its boundary is 9 + 4 + 9 + 4 = 26 m. If a second garden has perimeter 26 m and length 8 m, the remaining 10 m of boundary forms two widths, so each width is 5 m.
Advanced extension: Advanced: find two different rectangles with perimeter 30 units.
Lesson 4: Area with Arrays
Direct instruction: Area counts square units needed to cover a region. A 5 by 8 rectangle has 5 rows of 8 unit squares, or 40 square units. Break an irregular rectilinear figure into nonoverlapping rectangles and sum their areas.
Model and Discuss
Worked example: Sketch a rectangle with 4 rows and 6 columns of unit squares. Count 24 squares or compute 4 × 6 = 24 square units. Split it vertically into widths 2 and 4: areas 4 × 2 = 8 and 4 × 4 = 16; together 8 + 16 = 24 square units.
Advanced extension: Advanced: draw two rectangles of equal perimeter but different area.
Lesson 5: Geometry and Measurement Assessment
Direct instruction: Classify shapes by properties rather than how they are drawn. Use appropriate units and models for area or perimeter. The following set is an independent check with a mixture of procedural and written reasoning.
Model and Discuss
Independent reasoning check: A rectangle is 8 cm by 3 cm. Its perimeter is 8 + 3 + 8 + 3 = 22 cm, while its area is 8 × 3 = 24 square cm. Write one sentence explaining why the units differ. Extension: list all positive whole-number side pairs with perimeter 18 units: (1,8), (2,7), (3,6), (4,5).
Advanced extension: Advanced: describe all integer side pairs of a rectangle with perimeter 18 units.
Standards and Context
Reference: 2019 Alabama Mathematics, Grade 3: geometry and measurement. A complete objective-by-objective Alabama crosswalk is still required. Scripture is handled within its covenant context and not treated as part of state academic standards.