4.3 Understand angle and area as measurable attributes of real-world and mathematical objects. Use various tools to measure angles and areas. Use translations, reflections and rotations to establish congruency and understand symmetries.
Vocabulary
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Standard Benchmarks
Benchmark: 4.3.1.1 Triangles
Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts. Benchmark: 4.3.1.2 Quadrilaterals Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts. Benchmark: 4.3.2.1 Measure Angles Measure angles in geometric figures and real-world objects with a protractor or angle ruler. Benchmark: 4.3.2.2 Compare & Classify Angles Compare angles according to size. Classify angles as acute, right and obtuse. For example: Compare different hockey sticks according to the angle between the blade and the shaft. Benchmark: 4.3.2.3 Area & Multiplication Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. For example: How many copies of a square sheet of paper are needed to cover the classroom door? Measure the length and width of the door to the nearest inch and compute the area of the door. Benchmark: 4.3.2.4 Area of a Rectangle Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements. Benchmark: 4.3.3.1 Translations Apply translations (slides) to figures. Benchmark: 4.3.3.2 Reflections Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry. Benchmark: 4.3.3.3 Rotations Apply rotations (turns) of 90˚ clockwise or counterclockwise. Benchmark: 4.3.3.4 Congruence Recognize that translations, reflections and rotations preserve congruency and use them to show that two figures are congruent. Big Ideas and Essential Understandings
Fourth graders focus on triangles and quadrilaterals as they analyze and categorize shapes. They examine the characteristics of sides and measures of angles that make each polygon unique. They identify the specific type of triangle and quadrilateral based on their characteristics.
Fourth graders recognize, describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. They describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Fourth graders measure angles in real-world objects and geometric figures using protractors or angle rulers. They compare angles according to size and categorize angles as acute, right, or obtuse. Fourth graders develop a conceptual understanding of area as they find the area of two dimensional figures by finding the total number of same-size square units that cover the shape without gaps or overlaps. Fourth graders build on their informal understanding of slides, flips and turns as they construct definitions of the terms translation, reflection and rotation. They will use these mathematical terms and their applications to show that two shapes are congruent. Fourth graders find lines of symmetry and relate reflections to lines of symmetry. Triangles and Quadrilaterals: What students should know and be able to do [at a mastery level] related to these benchmarks:
Angles: What students should know and be able to do [at a mastery level] related to these benchmarks:
What students should know and be able to do [at a mastery level] related to these benchmarks:
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From a small seed a mighty trunk may grow.
-Aeschylus
-Aeschylus