Download and Measurement

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
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Misconceptions
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Key Vocabulary
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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.
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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)
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Positive rational numbers – the set of numbers that can be expressed as a fraction
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here a and b are whole numbers and b ≠ 0, which includes the subsets of whole
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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)
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Real World Examples
for measurement
units
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STAAR Math Charts
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Polygon Vocab
Foldable
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Triangle
Classification
Foldable
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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
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Geome‘tree’ Foldable
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Quadrilateral cut-outs
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Grid paper
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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.