Download PUSD Math News – Mathematics 1 Module 8: Connecting Algebra

PUSD Math News – Mathematics 1
Module 8: Connecting Algebra to Geometry
Module 8 Overview – Connecting
Algebra to Geometry
(Standards: F.IF.9, F.BF.1, F.BF.3, G.GPE.4,
G.GPE.5, G.GPE.7)
Student and Teacher materials can be found at
Mathematics Vision Project
http://www.mathematicsvisionproject.org/
(Curriculum>Secondary Mathematics
One>Module 8: Connecting Algebra to
Geometry)
Module 8 makes explicit the bridge between
algebra and geometry as it uses the tools and
definitions of each to connect the two. This is done
through the exploration of coordinate geometry
and the development of compound functions that
connect two or more existing functions to produce
something new. Students now have all the tools to
discuss the functions they have studied
algebraically, graphically, numerically, in tables
and verbally. The distance formula is introduced
as it is used along with all they have learned in the
previous units to perform coordinate proofs.
Students continue to gain proficiency in the
Standards for Mathematical Practices. The
predominant SMP is MP7 (look for and make use
of structure). The structure of mathematics is laid
open for students through the connections they
are making between all of the different
representations of functions and the properties of
each. They recognize the connections between
algebra and geometry and shift their perspective
in order to gain new understanding. They see
complex algebraic expressions as being composed
of simpler expressions, each of which contributes
to the whole expression and determines its
values. When this is expressed as a function they
recognize that each part of the expression has an
effect of the graph of the whole.
Scan the QR code below to take you
directly to the PUSD Secondary Math
Resources webpage for
Mathematics 1, Module 8: Connecting
Algebra to Geometry
You will find the student text, newsletter,
standards for the module, homework help
links and more!
https://goo.gl/r8SFWI
Vocabulary and Major Mathematical
Concepts
Sections designated with the letter H will appear in the
Honors Mathematics 1 course only
Prerequisite Concepts and Skills:
 Apply the Pythagorean Theorem
 Graph linear and exponential
functions
 Write linear equations in standard,
slope-intercept, and point-slope form
 Identify/solve for slope and x- and yintercepts of linear functions
 Solve multi-step equations
 Identify basic geometric shapes and
characteristics
 Use function notation
PUSD Math News – Mathematics 1
Module 8: Connecting Algebra to Geometry
Additive identity – the value that when added
to any number will result in the number itself,
that value is zero.
Component form of a vector – a notation for
writing a vector that includes the horizontal and
vertical components of movement. Component
form is written as <a, b>, where a represents the
horizontal distance and b represents the vertical
distance.
Example:
Image- http://www.printable-math-worksheets.com/additiveidentity.html
Additive inverse – the value that when added to
a number will result in zero, opposites add to
zero.
Image- https://quizlet.com/9167697/mth-277-chapter-11-section-1flash-cards/
Image- http://www.knowmia.com/watch/lesson/20369
Associative property – states that when adding
or multiplying, grouping can be done in any
order.
Determinant – a function which as an input
accepts n x n matrix and whose output is a real
or a complex number that is called the
determinant of the input matrix. An example for
a 2 x 2 matrix is given below.
Example:
Image- http://www.printable-math-worksheets.com/associativeproperty.html
Commutative property – states numbers can be
added or multiplied in any order.
Imagehttp://www.statistica.com.au/finding_determinant_of_2_x_2_m.html
Directed line segment – an arrow that is drawn
to represent a vector.
Direction – when examining vectors direction is
in reference to the change in location from preimage to image (left, right up, down, left and
down, right and up, etc).
Image- http://www.mathsisfun.com/definitions/commutative-law.html
PUSD Math News – Mathematics 1
Module 8: Connecting Algebra to Geometry
Distance formula – given two points (x1, y1) and
(x2, y2), the distance between the two points is
given by the formula
d = (x2 - x1 )2 + (y2 - y1 )2 .
Magnitude – when examining vectors magnitude
refers to the distance an object moves from preimage location to image location.
Matrix multiplication –
Imagehttp://www.teacherschoice.com.au/maths_library/analytical%20geomet
ry/alg_15.htm
Distributive property – the rule that
multiplying a(b + c) gives the same result as
ab + ac.
Image- http://functionspace.com/topic/1007/Algorithm-formultiplication-of-two-square-matrix
Multiplicative identity – the value that a
number could multiply by and have the result be
the number itself, that value is 1.
Image- http://www.printable-math-worksheets.com/multiplicativeidentity.html
Multiplicative inverse – the value that when
multiplied by a number will result in 1.
Reciprocals when multiplied together will result
in 1.
Image- http://nc5thgrademath.weebly.com/distributive-property-ofmultiplication.html
Hypotenuse – the longest side of a right triangle,
it is the side opposite the right angle.
Kite – a quadrilateral that has two pair of
congruent adjacent sides.
Examples:
Image- http://slideplayer.com/slide/2557575/
Parallel – a description of two or more coplanar
lines or line segments that have the same slope.
Example:
Image- http://www.ck12.org/book/CK-12-GeometryConcepts/r2/section/6.7/Kites---Intermediate/
Image- https://new.edu/resources/parallel-and-perpendicular-lines
PUSD Math News – Mathematics 1
Module 8: Connecting Algebra to Geometry
Perpendicular – a description of two lines or
line segments that intersect at a 90-degree angle.
Their slopes are opposite (negative) reciprocals
of another.
Example:
Scalar multiplication – multiplying a vector by
a scale factor. This changes the magnitude of the
vector, but not the direction. For example
multiplying a vector by 3 represents a vector
that has the same direction as the original, but
whose magnitude is three times the original.
Slope triangle – a visual tool that helps to find
the slope of a line by drawing in the vertical and
horizontal distance between two points.
Image- https://new.edu/resources/parallel-and-perpendicular-lines
Reciprocal – a pair of numbers whose product is
one. A number and its multiplicative inverse are
reciprocals of one another.
Image- http://www.math.com/school/subject1/lessons/S1U4L1DP.html
Resultant vector – the vector that results when
two or more vectors are added together.
Example:
Image- http://study.com/academy/lesson/what-is-slope-intercept-formdefinition-equation-examples.html
Square matrix – a matrix with the same number
of rows and columns. An n-by-n matrix is a
square matrix of order n. Any two square
matrices of the same order can be added and
multiplied. Square matrices are often used to
represent simple linear transformations.
Translation form equation – an equation
written in a form so that the vertical and/or
horizontal translation(s) from pre-image to
image can be seen in the equation. For example if
f(x) is the pre-image and g(x) is the image that
has been translated up 3 units, then g(x)=f(x)+3
is the translation form equation for that
transformation.
Vector – a quantity that has both magnitude and
direction. Usually represented by an arrow or
directed line segment.
Image- http://calculator.tutorvista.com/resultant-vectorcalculator.html#
PUSD Math News – Mathematics 1
Module 8: Connecting Algebra to Geometry
Main Topics
Sections designated with the letter H will appear in the
Honors Mathematics 1 course only
Section in student text – Task done in class
Related Homework Help Videos
8.4 – Write the equation f(t)=m(t)+k by
comparing parallel lines and finding k
Function transformations
https://goo.gl/B41xKq
8.1 – Use coordinates to find distances and
determine the perimeter of geometric shapes
8.5 – Determine the transformation from one
function to another
Slope triangles
https://goo.gl/DTmfTb
Describing statistical distributions
https://goo.gl/tkpfnO
Distance between points
https://goo.gl/pAzo73
Spread of distribution
https://goo.gl/raLZ48
8.2 – Prove slope criteria for parallel and
perpendicular lines
8.6 – Translating linear and exponential
functions using multiple representations
Writing equations of lines in point-slope form
https://goo.gl/Uiv0u1
Graphing exponential functions
https://goo.gl/tLIzdW
Writing equations of lines in standard form
https://goo.gl/CEus7k
Proving relationships using a coordinate grid
https://goo.gl/9rnJbx
Slopes of parallel and perpendicular lines
https://goo.gl/CnPRJa
8.3 – Use coordinates to algebraically prove
geometric theorems
Perimeters of geometric shapes
https://goo.gl/kfsJaF
Properties of quadrilaterals
https://goo.gl/9kkclQ
8.7H – Defining and operating with vectors as
quantities with magnitude and direction
Arithmetic of vectors
https://goo.gl/PGOJMg
Solving equations
https://goo.gl/WKQ63B
8.8H – Examining properties of matrix
addition and multiplication, including
inverse properties
Properties of matrix arithmetic
https://goo.gl/2IMIaQ
Solving systems of equations
https://goo.gl/9J3EwK
PUSD Math News – Mathematics 1
Module 8: Connecting Algebra to Geometry
8.9H – Finding the determinant of a matrix
and relating it to the area of a parallelogram
Determinant of a matrix
https://goo.gl/RXDRnS
Solving systems with matrices
http://goo.gl/fgjDQr
8.10H – Solving a system of linear equations
using the multiplicative inverse matrix
Solving systems with inverse matrices
https://goo.gl/iqnzNi
Properties of arithmetic
https://goo.gl/BDL2kC
Finding inverse matrices of 3x3 matrices
https://goo.gl/L1ZVFm
Solving 3x3 systems using inverse matrices
https://goo.gl/yJhgJM
8.11H – Using matrix multiplication to reflect
and rotate vectors and images
Transformation using matrices
https://goo.gl/iYHlU7
Function transformations with tables
https://goo.gl/yUugcY
8.12H – Solving problems involving
quantities that can be represented by vectors
Scatterplots and trend lines
https://goo.gl/AM97s2