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Grade 8 Math

Idaho Department of Education
Content Standards		 Objective Sub Objectives Task Analysis Essential Vocabulary Sample Assessment
Standard 4: Concepts and Principles of Geometry
Goal 4.1: Apply concepts of size,
shape, and spatial relationships.		 8.M.4.1.1 Describe and classify relationships among
types of one-, two-, and three- dimensional geometric
figures, using their defining properties.

CL: C, D
Calc: CN
Content Limit: Classify only. Figures may include
triangles and quadrilaterals. Triangles may be classified
by angles (acute, equiangular, obtuse, or right) or by
sides (equilateral, isosceles, or scalene) or both (e.g., an
obtuse isosceles triangle). Quadrilaterals may be
classified according to number and position of parallel
sides as well as angle measure (square, trapezoid,
paralle logram , rectangle, or rhombus). Three-dimensional
figures can include cubes, rectangular
prisms, spheres, pyramids, cones, and cylinders.
‘Describe’ to be assessed in the classroom, not on the
ISAT.

 • Describe and classify relationships among types of
two- and three- dimensional geometric figures, using
their defining properties		 • identify two- and three-dimensional figures according
to their defining characteristics
• compare characteristics of two- and three-dimensional
figures		 • acute • equiangular • obtuse • right • equilateral •
isosceles • scalene • parallel • trapezoid • parallelogram
• rhombus • cube • prism • sphere • pyramid • cone •
cylinder • quadrilateral		  
 
  8.M.4.1.2 Draw and measure various angles and shapes
using appropriate tools.

CL: C
Calc: YES
Content Limit: Measure only using superimposed
protractor. ‘Draw’ to be assessed in the classroom, not
on the ISAT

 • Draw and measure various angles and shapes using
appropriate tools		 • recall properties of angles and shapes
• make use of tools to create or measure angles and
shapes		 • compass • protractor  
  8.M.4.1.3 Apply the fundamental concepts, properties,
and relationships among points, lines, rays, planes, and
angles.

CL: C
Calc: CN
Content Limit: Items may include parallel, intersecting
and perpendicular lines including two parallel lines cut
by a transversal and the congruent and supplementary
angles formed. Angles may include acute, right, obtuse,
and straight. Angle relationships may include
complementary, supplementary, and congruent.
Symbols used may include: capital letter for points, two-headed
arrow above two capital letters for lines, line
segment above two capital letters for line segments, one
headed arrow above two capital letters for rays, angle
symbol with one capital letter or angle symbol with
three capital letters for angles, and symbols for parallel,
perpendicular, and right angle.

 • Apply the fundamental concepts, properties, and
relationships among points, lines, rays, planes, and
angles		 #NAME? • point • line • segment • ray • plane • complementary •
supplementary • congruent • transversal • intersect •
perpendicular • corresponding angles • vertical angles		  
  8.M.4.1.4 Identify and model the effects of reflections,
translations, rotations, and scaling on various shapes.

CL: D, E
Calc: CN
Content Limit: When using three-dimensional shapes:
Transformations may include reflections, rotation and
translations. Items are limited to one transformation per
item. Rotations occur in increments of 90º. When using
two-dimensional shapes: Transformations may include
reflections, rotation, translations, and change of scale .
Items are limited to two transformations per item.
Rotations occur in increments of 45º. Algebraic rules
limited to translations and reflections when the figure is
shown on a coordinate grid . No algebraic rules are
required for items involving more than one
transformation. Rotations must indicate clockwise or
counterclockwise.

 • Identify and model the effects of reflections,
translations, rotations, and scaling on various shapes		 • use coordinate geometry to represent and examine the
properties of geometric shapes
• describe sizes, positions, and orientations of shapes
under transformations such as: reflections, rotations,
translations and dilations		 • clockwise/counterclockwise • reduction /enlargement •
reflection • rotation • translation • dilation • scale factor		  
  8.M.4.1.5 Identify congruence, similarities, and line
symmetry of shapes.

CL: E
Calc: CN
Content Limit:
Shapes limited to two-dimensional figures.

 • Identify congruence, similarities, and line symmetry of
shapes		 • explain and illustrate the congruence, similarity and
line symmetry of objects		 • symmetry • congruent • similar  
  8.M.4.1.6 Explain the concept of surface area and
volume (capacity).

CL:
Calc:
Content Limit: Assessed in the classroom, not on the
ISAT.

 • Explain the concept of surface area and volume
(capacity)		 • compare and contrast the concepts of area, surface
area and volume of figures		 • surface area • volume • capacity • square units • cubic
units		  
  8.M.4.1.7 Use appropriate vocabulary and symbols.

CL:
Calc:
Content Limit: Assessed in the classroom, not on the
ISAT.		 • Use appropriate vocabulary and symbols • see content limit of 8.M.4.1.3 for correct figure
symbols
• communicate using correct mathematical terminology		    
Goal 4.2: Apply the geometry of right
triangles.		 No objectives at this grade level.        
Goal 4.3: Apply graphing in two
dimensions.		 8.M.4.3.1 Identify and plot points on a coordinate plane.

CL: C
Calc: CN
Content Limit: Points limited to integer ordered pairs .
Points may appear in any of the four quadrants or on
either axis.		 • Identify and plot points on a coordinate plane • list ordered pair for given point
• plot given points in coordinate plane
• name 4 quadrants		 • x-axis • y-axis • origin • coordinate plane • ordered
pair • quadrants		  
 
Standard 5: Data Analysis, Probability, and Statistics
Goal 5.1: Understand data analysis. 8.M.5.1.1 Analyze and interpret tables, charts, and
graphs, including frequency tables, scatter plots, broken
line graphs, line plots, bar graphs, histograms, circle
graphs, and stem-and-leaf plots.

CL: D, E
Calc: CR
Content Limit: Graphics may have at most ten data
categories. Circle graphs may have at most eight
sectors. Scales are in increments appropriate to the
application. Histogram intervals must be consistent.		 • Analyze and interpret tables, charts, and graphs,
including frequency tables, scatter plots, broken line
graphs, line plots, bar graphs, histograms, circle graphs,
and stem-and-leaf plots		 • discuss and identify the correspondence between data
sets and their graphical representations		 • outlier • frequency table • histogram • scatter plot •
broken line graph • line plot • circle graph • stem-and-leaf
plot		  
 
  8.M.5.1.2 Explain and justify conclusions drawn from
tables, charts, and graphs.

CL:
Calc:
Content Limit: Assessed in the classroom, not on the
ISAT

 • Explain and justify conclusions drawn from tables,
charts, and graphs		 • identify the relationship between data sets in tables,
charts or graphs
• determine and discuss any positive or negative
correlation
• support conclusions using mathematical reasoning		 • positive/ negative correlation  
  8.M.5.1.3 Use appropriate vocabulary and notations.

CL:
Calc:
Content Limit: Assessed in the classroom, not on the
ISAT		 • Use appropriate vocabulary and notations • communicate using correct mathematical terminology    
Goal 5.2: Collect, organize, and display
data		 8.M.5.2.1 Collect, organize, and display data with
appropriate notation in tables, charts, and graphs,
including scatter plots, broken line graphs, line plots,
bar graphs, histograms, and stem-and-leaf plots.

CL: C
Calc: CN
Content Limit: Given data, choose a display. Displays
limited to scatter plots, broken line graphs, line plots,
bar graphs, histograms, and stem-and-leaf plots.
‘Collect’ to be assessed in classroom, not on the ISAT.		 • Collect, organize, and display data with appropriate
notation in tables, charts, and graphs, including scatter
plots, broken line graphs, line plots, bar graphs,
histograms, and stem-and-leaf plots		 • select appropriate graphical representation for given
data
• organize data as needed to create visual displays
• discuss benefits of various types of graphs
• draw, label, and create selected graphical
representation for data		    
 
Goal 5.3: Apply simple statistical
measurements.		 8.M.5.3.1 Choose and calculate the appropriate measure
of central tendency – mean, median, and mode.

CL: C
Calc: YES
Content Limit: Items should be set in a real-world
context. Items may assess finding the range, mean,
median, or mode of a set of data presented in a chart,
table, graph, or plot (e.g., scatter plot, line plot, or stem-and-
leaf plot). Items that assess understanding of these
concepts may ask students to draw conclusions from an
analysis of range and/or central tendency measures.
Data set should include no more than 12 data points.
Data set may have an even or an odd number of data
points and does not need to be in numeric order. No
more than three categories of information should be
used in data sets.		 • Choose and calculate the appropriate measure of
central tendency – mean, median, mode and range		 • calculate mean, median, mode E78and range of data
sets
• choose measure of central tendancy which best
represents data		 • mean • median • mode • range • central tendancy  
 
  8.M.5.3.2 Explain the significance of distribution of
data, including range, frequency, gaps, and clusters.

CL:
Calc:
Content Limit: Assessed in the classroom, not on the
ISAT.		 • Explain the significance of distribution of data,
including range, frequency, gaps, and clusters		 • cite any trends which appear in data
• analyze the significance of these trends		 • frequency • clusters • distribution • gaps  
Goal 5.4: Understand basic concepts of
probability.		 8.M.5.4.1 Model situations of probability using
simulations.

CL:
Calc:
Content Limit: Assessed in the classroom, not on the
ISAT.		 • Model situations of probability using simulations • perform experiments and simulations and draw
conclusions about probability		 • probability • experimental/theoretical probability •
event		  
 
  8.M.5.4.2 Recognize equally likely outcomes .

CL: C, D
Calc: CN
Content Limit: Items describe familiar situations such
as spinning a spinner, rolling one or two dice (does not
include sum of two dice ), or drawing different colored
objects from a container. Equally likely outcomes must
pertain to the same event.		 • Recognize equally likely outcomes • compare and predict outcomes of common situations
involving equally likely outcomes		 • equally likely outcome • random  
  8.M.5.4.3 Explain that probability ranges from 0% to
100% and identify a situation as having high or low
probability.

CL:
Calc:
Content Limit: Assessed in the classroom, not on the
ISAT.		 • Explain that probability ranges from 0% to 100% and
identify a situation as having high or low probability 		• compare fraction, percent & decimal representations
of probability
• recognize and compare the range of possible outcomes		    
  8.M.5.4.4 Use the language of probability.

CL:
Calc:
Content Limit: Assessed in the classroom, not on the
ISAT		 • Use the language of probability • define probability terms • take care in using chances versus odds in probability
• favorable outcome		  
Goal 5.5: Make predictions or decisions
based on data.		 8.M.5.5.1 Make predictions based on experimental and
theoretical probabilities.

CL: D, E
Calc: YES
Content Limit: Items may include combinations of
events (e.g., rolling a number cube then spinning a
spinner or drawing two cards without replacement).
Items may not include conditional probability. Items
may require comparison between experimental and
theoretical probabilities.		 • Make predictions based on experimental and
theoretical probabilities		 • distinguish between experimental and theoretical
probability
• calculate theoretical probability
• perform experiments, collect data, and find
experimental probability
• predict future outcomes based on probabilites
• calculate the probability of compound events (with or
without replacment)		 • experimental/theoretical probability •
simple/compound event • replacement		  
 
  8 M 5.5.2 Conduct straight experiments and interpret
results using tables, charts, or graphs

CL:
Calc:
Content Limit: Assessed in the classroom, not on the
ISAT.

 • Conduct statistical experiments and interpret results
using tables, charts, or graphs		 • perform probability experiments
• collect and organize data using tables, charts or graphs
• draw conclusions from the data		    
  8.M.5.5.3 Use appropriate vocabulary and notations.

CL:
Calc:
Content Limit: Assessed in the classroom, not on the
ISAT		 • Use appropriate vocabulary and notations • communicate using correct mathematical terminology    
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