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Campus: Huddleston Intermediate Author(s): Charles, Pappas, Segleski, Stovall Date Created / Revised: 10/4/2014 Six Weeks Period: 4th Grade Level & Course: 6th Grade Mathematics Timeline: 13 Days Unit Title: Unit 09: Geometry and Measurement Stated Objectives: TEK # and SE Lesson # 1 of 1 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (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 (4) Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is expected to: (H) convert units within a measurement system, including the use of proportions and unit rates (8) Expressions, equations, and relationships. The student applies mathematical process standards to use geometry to represent relationships and solve problems. The student is expected to: (A) extend previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle; (B) model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes; (C) write equations that represent problems related to the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers; and (D) determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers See Instructional Focus Document (IFD) for TEK Specificity Key Understandings Misconceptions Key Vocabulary Units of measures may be converted using proportions and unit rates. The longest side of triangle is always opposite the largest angle in the triangle, whereas the shortest side of a triangle is always opposite the smallest angle in the triangle. The sum of any two sides of a triangle must be greater than the length of the third side. Parallelograms, trapezoids, and triangles can be decomposed and rearranged in order to model area formulas. The area of rectangles and parallelograms may be found by finding the product of the base and the height of the figure and represented with an equation and formula. The area of trapezoids may be found by finding the half of the product of the height of the figure and sum of its bases and represented with an equation and formula. The area of triangles may be found by finding the half of the product of the base and height of the figure and represented with an equation and formula. The volume of rectangular prisms may be found by multiplying dimensions and represented with an equation and formula. Some students may multiply only the base and height to find the area of a triangle and forget to multiply by or divide by 2. Some students may multiply by a side length that they believe represents the height of a trapezoid, triangle, or parallelogram, rather than using the actual height of the figure. Some students may not realize that a parallelogram can always be formed from two congruent trapezoids or two congruent triangles. Acute – an angle that measures less than 90° Angle – two rays with a common endpoint (the vertex) Angle congruency marks – angle marks indicating angles of the same measure Area – the measurement attribute that describes the number of square units a figure or region covers Base of a rectangular prism – any two congruent, opposite and parallel faces shaped like rectangles; possibly more than one set Congruent – of equal measure, having exactly the same size and same shape Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other Face – a flat surface of a three-dimensional figure Height of a rectangular prism – the length of a side that is perpendicular to both bases Obtuse – an angle that measures greater than 90° but less than 180° Polygon – a closed figure with at least 3 sides, where all sides are straight (no curves) Positive rational numbers – the set of numbers that can be expressed as a fraction , here a and b are whole numbers and b ≠ 0, which includes the subsets of whole numbers and counting (natural) numbers (e.g., 0, 2, , etc.) Right – an angle (formed by perpendicular lines) that measures exactly 90° Side congruency marks – side marks indicating side lengths of the same measure Three-dimensional figure – a figure that has measurements including length, width (depth), and height Triangle – a polygon with three sides and three vertices Two-dimensional figure – a figure with two basic units of measure, usually length and width Unit rate – a ratio between two different units where one of the terms is 1 Volume – the measurement attribute of the amount of space occupied by matter Suggested Day 5E Model Instructional Procedures Day 1 Engage Explore Explain Goal: Metric vs Customary Materials, Resources, Notes (Engage, Explore, Explain, Extend/Elaborate, Evaluate) Real World Examples for measurement units STAAR Math Charts Polygon Vocab Foldable Triangle Classification Foldable Grid paper Record Notes in Journal – Capacity, Weight & Mass, Length for each system of measurement; how we can use hand and body to ‘guesstimate’ customary & metric equivalencies Have real world examples to show class Engage – Brain POP (Metric and Customary) Practice – Pizzazz D-7 Day 2/3 Engage Explore Explain Goal: Unit Conversions Engage: Math Snacks – Overruled Record Notes in Journal; show how we use our STAAR Math Chart to help us solve problems involving unit conversions Practice: Pizzazz D-11, D-19, D23 Day 4 Explore Explain Goal: Intro to Polygons Record notes in journal – Vocab Foldable Practice: D-40 Day 5 Elaborate Goal: Triangle Classification Record notes in journal – Triangle Classification Foldable Practice: CScope Day 6 Explore Explain Goal: Sum of Angles in Triangles Record notes in journal – show how we can take the three angles and make a straight line which is equivalent to 180° Practice: Pizzazz D-34 & D-35 Day 7 Explore Explain Elaborate Goal: Classify Quadrilaterals Geome‘tree’ Foldable Quadrilateral cut-outs Grid paper Grid paper Record Notes in Journal – Geome ‘tree’ Foldable Practice: Pizzazz D-38 & D-39 Day 8 Explore Explain Goal: Sum of Angles in Quadrilaterals Record Notes in Journal – show how we can take the four angles and make a “circle” which is equivalent to 360°; emphasize how this is true for all quadrilaterals Practice: CScope Day 9/10 Engage Explore Explain Goal: Area and Perimeter of Rectangles, Parallelograms, & Trapezoids Record Notes in Journal – cut out parallelograms on grid paper and show how we can “move” the triangle inside the parallelogram to form a rectangle; cut out trapezoids on grid paper and show how we can “move and flip” the triangle inside the trapezoid to form a parallelogram; show where to find formula on the STAAR Mathematics Chart Practice: Pizzazz D-53 &D-54 Day 11 Explore Explain Goal: Area and Perimeter of Triangles Record notes in journal – show how we can double our triangles to make a quadrilateral; explain the relationship to our equations for area of triangles and quadrilaterals; show where to find formula on the STAAR Mathematics Chart Practice: Pizzazz D-56 Day 12 Elaborate Goal: Volume of Rectangular Prisms Record notes in journal and show where to find formula on the STAAR Mathematics Chart Practice: Pizzazz D-64 Day 13 Explore Explain Goal: Review Geometry and Measurement Practice: Measuring Up & Texas Go Math Accommodations for Special Populations Accommodations for instruction will be provided as stated on each student’s (IEP) Individual Education Plan for special education, 504, at risk, and ESL/Bilingual.