Math 

Unit 5   Geometry and Fractions

Students will independently use their learning to …

• TG1 Solve problems in everyday life by connecting geometric and spatial thinking with their physical world. 

Students will understand that…

• U1 Geometry and spatial sense provide a way to describe our physical environment.

• U2 Geometric figures can be composed and decomposed. There are shapes within shapes.

• U3 Two and three dimensional objects can be described, classified, and analyzed by their attributes.

• U4 There are many ways to represent a quantity, but the best way is based on the problem in front of you.

Students will keep considering …

• EQ1 What geometric models describe everyday objects?

• EQ2 How can I create a new shape by putting shapes together or breaking shapes apart?

• EQ3 How do we describe, sort, and classify 2-D and 3-D figures in more than one way?

• EQ4 What is the best way to represent this number?

Students will know …

• K1 an attribute is a characteristic or component of a geometric figure.

• K2 a polygon can be divided into equal parts.

• K3 a polygon is a plane figure with 3 or more sides.

• K4 polygons form the faces of 3-D solids.

• K5 fractions can describe equal parts of geometric figures.

• K6 2-D shapes can be described by the number of sides and vertices.

• K7 3-D solids can be described by the number of faces, edges, and 

• vertices.

• K8 some shapes can be combined to make new shapes.

• K9 some shapes can be decomposed into other shapes.

• K10 properties of geometric figures are common characteristics of a

• group or class of figures.

• K11 a fraction names one equal part of a whole.

• K12 the relationship between the number of fractional parts in a whole 

• and the size of the parts.

• K13 a whole can be divided into an infinite number of equal parts.

Students will be skilled at …

• S1 creating shapes based on given attributes.

• S2 combining 2-D shapes to make a target shape when given properties.

• S3 composing 3-D solids based on given attributes.

• S4 decompose a 2-D shape to create a new shape.

• S5 decomposing a 2-D shape into equal parts and identifying the parts.

• S6 identifying 2-D and 3-D figures by name.

• S7 classifying and sorting 2-D shapes and 3-D solids based on attributes.

• S8 using formal geometric language.

• S9 using models to represent fractions.

• S10 partitioning objects into halves, fourths, and eighths.

• S11 counting by fractional parts beyond one.

• S12 identifying examples and non-examples of halves, fourths, and eighths.

• S13 identifying the number of fractional parts it takes to make a whole.

• S14 naming the whole when given a fractional part.

• S15 applying the mathematical process standards. 

Standards

2.1 The student uses mathematical processes to acquire and demonstrate mathematical understanding.

(A) apply mathematics to problems arising in everyday life, society, and the workplace; 

(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution; 

(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems; 

(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate; (E) create and use representations to organize, record, and communicate mathematical ideas; 

(F) analyze mathematical relationships to connect and communicate mathematical ideas; and 

(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

2.3 The student applies mathematical process standards to recognize and represent fractional units and communicates how they are used to name parts of a whole. 

(A) partition objects into equal parts and name the parts, including halves, fourths, and eighths, using words

(B) explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part

(C) use concrete models to count fractional parts beyond one whole using words and recognize how many parts it takes to equal one whole

(D) identify examples and non-examples of halves, fourths, and eighths

2.8 The student applies mathematical process standards to analyze attributes of two-dimensional shapes and three-dimensional solids to develop generalizations about their properties.

(A) create two-dimensional shapes based on given attributes, including number of sides and vertices

(B) classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), and triangular prisms, based on attributes using formal geometric language

(C) classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices

(D) compose two-dimensional shapes and three-dimensional solids with given properties or attributes

(E) decompose two-dimensional shapes such as cutting out a square from a rectangle, dividing a shape in half, or partitioning a rectangle into identical triangles and identify the resulting geometric parts

Texas Focal Point 4: Applying knowledge of two-dimensional shapes and three-dimensional solids, including exploration of early fraction concepts