Math Unit Template
El Rancho Unified School District
Topic/Main Idea:
MULTIPLE REPRESENATIONS OF LINEAR EQUATIONS
Objectives/Concept/Skill (DOK):
Students will be investigating connections between the four
representations of data: graphs, tables, patterns, and equations.
Students will be able to analyze a given situation and create the
graph, table, pattern, and equation.
CCSS: HSA-CED.A.2 & HSA-REI.D.10
Timeline: 9 DAYS
Connections to earlier and next grade levels:
PRIOR: Evaluating expressions
Graphing linear equations
Input/output tables
CPM Algebra Connections
Chapter 3
FUTURE: Systems of Equations & Inequalities
In-depth meaning of y=mx+b (CPM Ch.7)
Performance Task/Activity (DOK):
Grade 11 Performance Task: Thermometer Crickets:
http://www.smarterbalanced.org/wordpress/wpcontent/uploads/2012/09/performance-tasks/crickets.pdf
Sound Bit that would be helpful:
http://www.youtube.com/watch?client=mvgoogle&gl=US&hl=en&v=T1MwKxUAYu0&nomobile=1
Helpful Cricket Chirp Calculator:
http://www.csgnetwork.com/crickettempcalc.html
Relevance/Rationale:
Multiple representations help students see a problem
from different perspectives.
SBAC Assessment Item References:
Grade 11 Performance Task: Thermometer Crickets:
http://www.smarterbalanced.org/wordpress/wpcontent/uploads/2012/09/performance-tasks/crickets.pdf
Academic Vocabulary:
Growth factor, y=mx+b, slope-intercept form, yintercept, starting point, slope, x-intercept, zero
slope, undefined slope
Textbook References (i.e., Homework Resources):
CPM Algebra Connections (Ch.4), CPM Extra Practice/Parent Guide,
Kuta Software website
Materials/Manipulatives:
Graph paper, pencil, ruler, pencil, CPM resource pages,
CPM textbook
Mathematical Practices
____ 1.
__x_ 2.
____ 3.
__x_ 4.
Makes sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with Mathematics.
____ 5.
__x_ 6.
____ 7.
____ 8.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Explanation:
Students must understand the meaning of slope and y-intercept and how it relates to the multiple representations. Confusing such information
can give different outcomes.
Lesson
Topic:
LOL (Learning
Finding
Connections
Between
Representations
We will discover connections between all of the
representations of a pattern: a table, a graph, a geometric
presentation, and an equation. We will also look at
different ways to represent the connections. We will
demonstrate our findings through posters.
CPM 4-1
HW: 4-2 thru 4-7
Seeing Growth
in Different
Representations
We will write linear algebraic rules relating the figure
number of a geometric pattern and its number of tiles. We
will identify connections between the growth of a pattern
and its linear equation. We will visualize this by color coding
our discoveries on our handout.
CPM Resource Page 4.1.2 *students must keep for next
day’s lesson*
http://www.cpm.org/pdfs/stuRes/AC/chapter_04/4.1.2
.pdf
CPM 4-8 thru 4-11
HW 4-13 thru 4-17
Connecting
Linear Rules and
Graphs
Y=mx+b
Objective with Language):
We will connect linear geometric patterns with patterns in a
graph, specifically focusing on how a geometric pattern
grows and how the size of figure zero can be determined
from information in a graph. We will visualize this by color
coding our discoveries on our handout.
We will develop new connections between multiple
representations of patters and identify rules for these
patterns using slope/intercept form of an equation. We will
then apply this understanding of m as growth factor (slope)
and b as figure zero or the starting point of the pattern
(Y-intercept) to write a rule from a graph or table.
Resources (Instructional
Strategies, Textbook
References, etc.):
CPM Resource page 4.1.2
http://www.cpm.org/pdfs/stuRes/AC/chapter_04/4.1.2
.pdf
CPM 4-18 through 4-19
HW 4-21 through 4-25
CPM 4-26 through 4-28
HW 4-32 through 4-36
What are the
connections
We will apply our understanding of growth, figure zero and
connections between multiple representations to situations
to generate a complete pattern. We will apply our
understanding of growth and figure zero to new contexts in
order to generate complete representations.
CPM 4-37
HW 4-39 through 4-45 and
4-47 through 4-48
CPM 4-49 through 4-52
HW CPM 4-54 through 4-58
Graphing a line
without an x->y
table
We will apply our knowledge of m as growth factor and b as
figure zero or the starting value of the pattern to create
graphs quickly without using an X->Y table. We will also
apply our knowledge of slope and figure zero when given a
graph to create a rule without using an X->Y table.
Optional resources;
http://www.kutasoftware.com/FreeWorksheets/PreAlg
Worksheets/
Graphing%20Lines%20in%20SlopeIntercept%20Form.pdf
http://www.kutasoftware.com/FreeWorksheets/PreAlg
Worksheets/Writing%20Linear%20Equations.pdf
Completing the
Web –
(Optional)
We will practice moving from one representation of a
pattern to another. We will create a graph, a table and a
rule to represent a pattern.
CPM 4-59 through 4-61
HW 4-62 through 4-65
Line of Best Fit
We will learn how to graph line of best fit. We will collect
data and present our findings on graph paper, and the job
would be to create the line of best fit.
http://mathbits.com/MathBits/TISection/Statistics1/Li
neFit.htm (graphing calculator optional)