High School Math
Element Cards
FLS: MAFS.912.S-ID.1.1
In grades 6 – 8, students describe center and spread in a data distribution. Here they choose a
summary statistic appropriate to the characteristics of the data distribution, such as the shape of the
distribution or the existence of extreme data points.
AP:
MAFS.912.S-ID.1.AP.1a
Essential Understandings
Strand: Data, Probability, and
Statistics
Complete a graph given the data, using dot plots, histograms,
or box plots.
Family: Represent and Interpret Data
Concrete Understandings:
 Match the source of the values at the
bottom of the x-axis with the
appropriate category of the related
data table.
 Describe the elements within a graph
(e.g., in a box plot the line is the
median, the line extending from each
box is the lower and upper extreme,
and the box shows the lower quartile
and the upper quartile).
Representation:
 Complete the steps of the task
analysis to complete a box plot.
 Understand the following concepts
and vocabulary: quartile, median,
intervals, upper and lower extremes,
box plot, histograms, dot plots.
Suggested Instructional Strategies:
 Follow steps of task analysis to complete box plot, dot plots, or histograms (these can be found
on internet or many calculators).
 Model-Lead-Test*
Supports and Scaffolds:
 Technology (e.g., computers)
 Graphing calculators
 Self-monitoring task analysis for student independence
FLS: MAFS.912.S-ID.1.4
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate
population percentages. Recognize that there are data sets for which such a procedure is not
appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
AP:
MAFS.912.S-ID.1.AP.4a
Essential Understandings
Strand: Data, Probability, and
Statistics
Use descriptive stats like range, median, mode, mean, and
outliers/gaps to describe the data set.
Family: Represent and Interpret Data
Concrete Understandings:
 Given a scatter plot, identify outliers in
the data set.
 Identify the highest and lowest value in
a data set given a number line and
matching symbols (concept of range).
 Identify the representation (use plastic
snap cubes to represent the tally
showing the number of occurrences) of
the concept of mode.
 Identify the concept of median using
concrete representations of data
(create a bar graph with an odd
number of bars using snap cubes;
arrange from shortest to tallest; student
place fingers on two outside towers,
knock towers over and move inward
until they reach the one middle tower
left standing).
 Find the mean using concrete
materials.
Representation:
 Identify the mode and the spread of
the data using a line drawing of the
distribution.
 Calculate the mean using preslugged template of data points.
 Order data set using numeric
symbols.
 Understand the following concepts
and vocabulary: median, mode,
mean, outliers.
Suggested Instructional Strategies:
 Task analysis for finding range, median, mode, mean
 Explicit vocabulary instruction for outliers
 Multiple exemplars for outliers*
 Model data descriptions
 Use concrete materials to find the mean (leveled plastic snap cubes: using the same bar graph
with snap cubes, re-arrange cubes into equal stacks).
Supports and Scaffolds:
 Template for finding mean
 Assistive technology/voice output devices
 Interactive whiteboard
 Provide a graph of the data set
 Templates with sentence starters
 Manipulatives
FLS: MAFS.912.G-CO.1.5
Given a geometric figure and a rotation, reflection or translation, draw the transformed figure using, e.g.,
graph paper, tracing paper or geometry software. Specify a sequence of transformations that will carry a
given figure onto another.
AP:
MAFS.912.G-CO.1.AP.5a
Essential
Understandings
Strand: Geometry
Transform a geometric figure given a rotation, reflection, or
translation using graph paper, tracing paper, or geometric
software.
Family: Transforming and Graphing
Concrete Understandings:
 Use coordinates to draw plane figures in
a coordinate plane.
Representation:
 Distinguish between orientations of
plane figures.
 Distinguish between translations,
rotations, and reflections.
Suggested Instructional Strategies:
 Model-Lead-Test: Use math tools (e.g., tangrams, Legos, stickers) to demonstrate the
transformation of the shape. Demonstrate one transformation at a time.*
 Use most-to-least prompting to teach students to demonstrate transformations
 Given a picture or drawing of a shape, students use whatever tool is appropriate to transform the
shape.
 Label the sides of a cube (dice) with letters or stickers (whichever is more recognizable to the
student), rotate the cube and note the change.
Suggested Supports and Scaffolds:
 Manipulatives such as Geoboards, tangram shapes, pattern blocks, magnetic pattern blocks
 Legos to construct then manipulate the object
 Graphic Organizer
 Provide an arrow to show the direction of the movement of the object to create a flip, a turn, or a
slide (transformation).


Assistive Technology
Virtual manipulatives
Additional Resources
www.mathisfun.com/geometry – Point & click to transform the shape
http://www.eduplace.com/kids/mw/swfs/robopacker_grade4.html – Transform shapes to create
a robot
FLS: MAFS.912.N-Q.1.1
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and
interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data
displays.
AP:
MAFS.912.N-.1.AP.1d
Essential
Understandings
Strand: Measurement
When solving a multi-step problem, use units to evaluate the
appropriateness of the solution.
Family: Problem Solving Using Measurement Processes
Concrete Understandings:
 Determine what units are used in
problem (e.g., money, time, units of
measurement, etc.).
 Match the action of combining with
vocabulary (i.e., in all; altogether) or the
action of decomposing with vocabulary
(i.e., have left; take away, difference) in
a word problem.
Representation:
 Apply conversions of units while
solving problems (e.g., Recognize
that monetary units can be combined
to equal other monetary units).
 Translate wording into numeric
equation.
Suggested Instructional Strategies:
 Task analysis
 Model-Lead-Test *
 Least-to-Most prompts*

Create relevant, story-based problems. For example, the story may be used to solve a
problem about money and shopping at the grocery store. Use graphic organizers to
provide students a means for organizing their work. Break down and isolate each step in
solving the math task.
Suggested Supports and Scaffolds:
 $1, $5, and $10 bills
 Number line labeled with $1/unit, $5/unit, and $10/unit
 Calculator, software that counts, or other means of hand tallying
 Graph paper where each square equals a unit
FLS: MAFS.912.A-REI.1.2
Solve simple rational and radical equations in one variable, and give examples showing how extraneous
solutions may arise.
AP:
MAFS.912.A-REI.1.AP.2a
Strand: Measurement
Solve simple rational and radical equations in one variable.
Family: Perimeter, Area, and Volume Problems
Concrete Understandings:
Essential Understandings


Identify the variables in an equation.
Substitute numbers for variables.
Representation:
 Understand the following related
vocabulary: variable, rational
numbers.
 Understand system of equations.
(e.g., John bought four pizzas and six
sodas. How much did he spend?
What is the price of the pizza? What
is the price of the soda? 2p+10s
=$44 and 4p+6s=$60.) Solving by
substitution – p+5s=22, 2p+3s=30,
p=22-5s, 2(22-5s)=3s=30, (4410s)=3s=30, 44-7s=30, -7s= -14, s=2
sodas are $2.
Suggested Instructional Strategies:
 Tiling/fill-in space and count
 Sequence: 1. Area 2. Volume 3. Missing attribute
 “If the area of a rectangle is 24cm² and it has a base of 6cm, what would the height be?”
 Task analysis with Least Intrusive Prompts
 Replace a letter (variable representing an unknown quantity) with a number or representation of a
number (symbols, manipulatives).

Provide a labeled prism and the equation V = L x W x H. Ask the student to
draw/indicate the label on the prism to the letter in the equation. Break down and isolate
each step in solving the math task.

Provide nets to be taken apart (unfolding) to illustrate three-dimensional objects. This process
can also be used for the study of the surface area of prisms.
Suggested Supports and Scaffolds:
 Pre-made formula
 Use of calculator
 Manipulatives (2-D shapes, prism, cube (e.g., box))
 Counters (e.g., tally counter) and counting mechanism (e.g., number line)
FLS: MAFS.912.N-RN.1.2 Rewrite expressions involving radicals and rational exponents using the
properties of exponents.
AP:
MAFS.912.N-RN.1.AP.2a
Essential
Understandings
Strand: Number Operations (Real
Numbers)
Convert from radical representation to using rational exponents
and vice versa.
Family: Understanding base Ten Number System
Concrete Understandings:
 Identify expressions with exponents.
 Create a model with objects to show that
the exponent of a number says how many
times to use the number in a
multiplication (substitute a chip for each
“a” – a7 = a × a × a × a × a × a × a =
aaaaaaa).
Representation:
 Simplify expression into expanded form:
(x⁴)(x³) = (xxxx)(xxx)
 Simplify expression into the simplest
form: (x⁴)(x³) = (xxxx)(xxx) = (xxxxxxx) = x7.
 Understand the concepts, symbols, and
vocabulary for: expression, exponent,
raising to a power.
Suggested Instructional Strategies:
 Task analysis
o Identify 10 as the place value.
o Identify the exponent.
o Multiply by the coefficient.
 Model-Lead-Test through the steps of the task analysis*
 Video resource: http://www.youtube.com/watch?v=H578qUeoBC0
Supports and Scaffolds:
 Internet converters such as: http://www.webmath.com/sn_convert.html
 Graphic organizer
 Calculator
 Website support: http://www.aaamath.com/nam-g6_71fx1.htm
FLS: MAFS.A.SSE.2.3 Choose and produce an equivalent form of an expression to reveal and explain
properties of the quantity represented by the expression.
c) Use the properties of exponents to transform expressions for exponential functions. For example the
expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent
monthly interest rate if the annual rate is 15%.
AP:
MAFS.912.A-SSE.2.AP.3a
Essential
Understandings
Strand: Number Operations (Real
Numbers)
Write expressions in equivalent forms by factoring to find the
zeros of a quadratic function and explain the meaning of the
zeros.
Family: Perform Operations with Whole Numbers
Concrete Understandings:
 Identify expressions with exponents.
 Create a model with objects to show that
the exponent of a number says how many
times to use the number in a
multiplication. (Substitute a chip for each
“a.”)
7
a = a × a × a × a × a × a × a = aaaaaaa
Representation:
 Simplify expression into expanded form
(x⁴)(x³)= (xxxx)(xxx)
 Simplify expression into the simplest form
(x⁴)(x³)=(xxxx)(xxx) =(xxxxxxx)=x7
 Understand the following concepts,
symbols, and vocabulary: expression,
exponent, raising to a power.
Suggested Instructional Strategies:
 Explicitly teach rules for simplification.
 Multiple exemplars (example/non-example) expression with exponents*
Supports and Scaffolds:
 Templates
 Calculator
FLS: MAFS.912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve
problems. Include equations arising from linear and quadratic functions, and simple rational and
exponential functions.
AP:
MAFS.912.A-CED.1.AP.1a
Essential
Understandings
Strand: Patterns, Relationships and
Functions
Create linear, quadratic, rational, and exponential equations
and inequalities in one variable and use them in a contextual
situation to solve problems.
Family: Problem Solving and Using Variables
Concrete Understandings:
 Match an equation with one variable to a
real-world context.
Representation:

Create a pictorial array of a simple
equation to translate wording.

Know the following vocabulary and
symbols: +, -, X, ÷, =, linear, variable.
Suggested Instructional Strategies:

Task analysis
o Present the story problem based on a real-world, relevant context and provide a template for
recording facts/operation to solve the real-world problem.
o Highlight key information in the problem; strike through irrelevant information.
o Identify what question is being asked (define x).
o Identify the facts.
o Fill in the facts in the order presented in the story problem on the template.
o Determine the operation(s) (+, - X, ÷).
o Identify what operation should be completed first.
o Fill in the operation.
o State the equation.
o Solve for x.
o Answer the problem statement.
Suggested Supports and Scaffolds:
 Counters
 Multiplication chart
 Calculator
FLS: MAFS.912.F-LE.1.1 Distinguish between situations that can be modeled with linear functions and
with exponential functions.
AP:
MAFS.912.F-LE.1.AP.1a
Essential Understandings
Strand: Patterns, Relationships
and Functions
Select the appropriate graphical representation of a linear
model based on real-world events.
Family: Proportional Relationships and Graphing
Concrete Understandings:
 Match a point on a line as being part of a
data set for a given line.
 Determine if a point is or is not on a line.
Representation:

Identify coordinates (points) on a graph
and in a data table.

Select a graph that represents a simple
linear equation.

Match or plot the points from a data
table on a graph.

Understand the following concepts and
vocabulary: x axis, y axis, x intercept, y
intercept, line, slope.
Suggested Instructional Strategies:
 Model lines, graphs, and coordinates of varying slopes; match coordinates to graphs.
 Explicitly teach the relationship between positive slope and a line that slopes up left to right and negative
slope and a line that goes down left to right.
 Task analysis:
o Present a story problem and a simple equation (e.g., y = 5x).
o Create a formula template and substitute x for at least three values to determine y.
o Create a table (T-chart) listing coordinates (x,y).
o Plot points on a coordinate grid; connect the points.
o Identify the coordinates on the line graph.
o Reverse the steps and begin with a line graph; identify the coordinates of at least three points, create
a table listing the x and y coordinates; write a simple linear equation to represent the line graph.
Suggested Supports and Scaffolds:






Grid paper with raised perpendicular lines (horizontal and vertical lines) and points
Models
T-chart, graphic organizer
Rulers, straightedge
Graphing calculator
Interactive white board