4 th Grade Mathematics Instructional Week 30 Geometry Concepts Paced Standards: 4.G.1: Identify, describe, and draw parallelograms, rhombuses, and

Transcription

1 4 th Grade Mathematics Instructional Week 30 Geometry Concepts Paced Standards: 4.G.1: Identify, describe, and draw parallelograms, rhombuses, and trapezoids using appropriate tools (e.g., ruler, straightedge and technology). 4.G.2: Recognize and draw lines of symmetry in two-dimensional figures. Identify figures that have lines of symmetry. Connections to other 4 th Grade Standards: 4.G.3: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint. 4.G.4: Identify, describe, and draw rays, angles (right, acute, obtuse), and perpendicular and parallel lines using appropriate tools (e.g., ruler, straightedge and technology). Identify these in two-dimensional figures. 4.G.5: Classify triangles and quadrilaterals based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles (right, acute, obtuse). Prerequisite/Foundational Standards: 3.G.2: Understand that shapes (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize and draw rhombuses, rectangles, and squares as examples of quadrilaterals. Recognize and draw examples of quadrilaterals that do not belong to any of these subcategories. 2.G.1: Identify, describe, and classify two- and three-dimensional shapes (triangle, square, rectangle, cube, right rectangular prism) according to the number and shape of faces and the number of sides and/or vertices. Draw two-dimensional shapes. 4 th Grade ISTEP+ Toolkit

2 4.G.1 Standard: 4.G.1: Identify, describe, and draw parallelograms, rhombuses, and trapezoids using appropriate tools (e.g., ruler, straightedge and technology). Teacher Background Information: What makes shapes alike and different can be determined by an array of geometric properties. For example, shapes have sides that are parallel, perpendicular, or neither; they have line symmetry, rotational symmetry, or neither; they are similar, congruent, or neither. Elementary and Middle School Mathematics: Teaching Developmentally, John Van de Walle 2004 In the classification of quadrilaterals and parallelograms, the subsets are not all disjoint. For example, a square is a rectangle and a rhombus. All rectangles are parallelograms, but not all parallelograms are rectangles. Some definitions of trapezoid specify only one pair of parallel sides, in which case parallelograms would not be trapezoids. The University of Chicago School Mathematics Project (UCSMP) uses the at least one pair definition, meaning that parallelograms and rectangles are trapezoids. For the purposes of ISTEP, trapezoids will be defined as having exactly one pair of parallel sides. Definitions: o parallelogram: a quadrilateral with both pairs of opposite sides parallel o rhombus: a parallelogram with four congruent sides o trapezoid: a quadrilateral with only one pair of parallel sides Process Standards to Emphasize with Instruction of 4.G.1: 4.PS.2: Reason abstractly and quantitatively. 4.PS.3: Construct viable arguments and critique the reasoning of others. 4.PS.4: Model with mathematics. 4.PS.5: Use appropriate tools strategically. 4.PS.7: Look for and make use of structure.

3 4.G.2 Standard: 4.G.2: Recognize and draw lines of symmetry in two-dimensional figures. Identify figures that have lines of symmetry. Teacher Background Information: Students need experiences with figures which are symmetrical and non-symmetrical. Figures include both regular and non-regular polygons. Folding cut-out figures will help students determine whether a figure has one or more lines of symmetry. If a shape can be folded on a line so that the two halves match, then it is said to have line symmetry (or mirror symmetry). Notice that the fold line is actually a line of reflection the portion of the shape on one side of the line is reflected onto the other side, demonstrating a connection between line symmetry and transformations (flip). Some students confuse a shape having line symmetry with the ability to be divided into two congruent pieces. Introduce situations in which this is the case. Example: This rectangle can be divided into two congruent triangles by its diagonal. The diagonal is not, however, a line of symmetry. (The rectangle does have two other lines of symmetry.) Example: This parallelogram can also be divided into two smaller congruent parallelograms. The line shown is not a line of symmetry. In fact this parallelogram has 0 lines of symmetry. Example: For each figure, draw all of the lines of symmetry. What pattern do you notice? How many lines of symmetry do you think there would be for regular polygons with 9 and 11 sides. Sketch each figure and check your predictions. Regular polygons with an odd number of sides have lines of symmetry that go from a midpoint of a side through a vertex. Process Standards to Emphasize with Instruction of 4.G.2: 4.PS.3: Construct viable arguments and critique the reasoning of others. 4.PS.4: Model with mathematics. 4.PS.5: Use appropriate tools strategically. 4.PS.6: Attend to precision. 4.PS.8: Look for and express regularity in repeated reasoning.

4 Instructional Week 30 4 th Grade Mathematics Assessment Name: 1) Pablo is thinking of a shape that has two pairs of parallel sides and an equal number of acute and obtuse angles. Which shape could Pablo be thinking of? A) rhombus B) parallelogram C) rectangle D) all of the above 2) Think about the characteristics of a: rectangle parallelogram rhombus trapezoid Write the word true in the box for every statement that is true in the row that lists the shape. Leave the box blank if the characteristic is not true. The example shows that three of the characteristics are true for a square. Complete the table by identifying the characteristics of a rectangle, parallelogram, rhombus, and trapezoid. characteristics Exactly one set of parallel sides Two pairs of parallel sides Must have right angles Must have 4 equal sides square true true true rectangle parallelogram rhombus trapezoid

5 3) Look at the shapes below. A B C D E F Which list below contains all the parallelograms in the shapes above? A) C, E B) C, E, F C) A, C, D, E D) A, C, E 4) Which figure has at least one line of symmetry? A. C. B. D. 5) Which shape has exactly one line of symmetry? A. C. B. D.

6 6) Fill in the grid to show how many lines of symmetry are in the rectangle below.

7 Instructional Week 30 4 th Grade Assessment Answer Key Question Correct Answer Standard(s) 1 D 4.G.1 2 characteristics Exactly one set of parallel sides Two pairs of parallel sides Must have right angles Must have 4 equal sides square true true true rectangle true true parallelogram true rhombus true true trapezoid true 4.G.1 3 C 4.G.1 4 D 4.G.2 5 C 4.G.2 6 2* 4.G.2 *The paper/pencil version of ISTEP Part 2 will include gridded-response items in Grade 4. This item is included as practice for those schools opting for the paper/pencil version.