In this unit students will cultivate spatial awareness by: • further developing understandings of basic geometric figures • identifying plane figures and solid figures based on geometric properties • describing plane figures and solid figures according to geometric properties • expanding the ability to see geometry in the real world • partitioning shapes into equal shares by cutting, slicing, or dividing • represent halves, thirds, and fourths using rectangles and circles to create fraction models • compare fractions created through partitioning same-sized rectangular or circular wholes in different ways • understand what an array is and how it can be used as a model for repeated addition • organize and record data using tallies, simple tables and charts, picture graphs, and bar graphs
Students describe and analyze shapes by examining their sides and angles. Students investigate, describe, and reason about decomposing and combining shapes to make other shapes. Through building, drawing, and analyzing two- and three-dimensional shapes, students develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades.
STANDARDS FOR MATHEMATICAL CONTENT
Reason with shapes and their attributes. MGSE2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. MGSE2.G.2 Partition a rectangle into rows and columns of same-size squares to find the total number of them. MGSE2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. Represent and interpret data. MGSE2.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.
BIG IDEAS
By the conclusion of this unit, students should be able to demonstrate the following competencies: • Describe plane figures according to their characteristics (sides, corners, angles) • Describe solid figures according to their characteristics (faces, edges, vertices). • Describe and understand the relationships (similarities and differences) between solid figures and plane figures. • Recognize the relationship between geometry and the environment. • Compare geometric figures to similar objects in everyday life. • Identify and represent the fractional parts of a whole or of a set (halves, thirds, fourths). • Recognize and represent that differently partitioned fractional parts of same-sized rectangles or circles are equal. • Identify the number of rows and columns in an array and count the same-size squares to find the total. • Pose questions that will result in data that can be shown on a bar graph or picture graphs. • Use charts, simple tables, and surveys to collect data that can be shown on a bar graph or picture graph. • Graph data on a bar graph or picture graph and in a simple table. Interpret data shown on a bar graph or picture graph. • identify plane figures and solid or hollow figures according to geometric properties • describe plane figures and solid or hollow figures according to geometric properties • develop an understanding of the relationship between solid or hollow figures and plane figures • understand that the faces of solid or hollow figures are plane figures • further develop spatial awareness of geometric solids and figures • investigate what happens when geometric figures are combined • investigate what happens when geometric figures are cut apart • recognize plane and solid figures in the real world • Repeatedly adding the same quantity or forming a rectangular array are strategies for repeated addition. • Fractional parts are equal shares of a whole number, whole object, or a whole set. • The more equal sized pieces that form a whole, the smaller the pieces (fraction) will be. • When the numerator and denominator are the same number, the fraction equals the number one or one whole (entire object or set). • The fraction name (half, third, fourth) indicates the number of equal parts in the whole. • Equal shares of identical wholes may not have the same shape. For example, fourths can be represented in multiple ways (i.e. with diagonal, horizontal, vertical cuts) and although they look different they represent the same amount/size piece.