8th Grade Algebra 1 - Gloucester Township Public … Grade...Gloucester Township Public Schools Math...
Transcript of 8th Grade Algebra 1 - Gloucester Township Public … Grade...Gloucester Township Public Schools Math...
Gloucester Township Public Schools
Math Curriculum
8th
Grade Algebra 1
Overview
Mathematics is a universal language enmeshed in both the everyday experiences of human society and the natural world
around us. The Gloucester Township Public School District recognizes that mathematics is a fluid and intricately connected
web of conceptual understandings, as opposed to segmented isolated skills and arbitrary units of study.
A nation that trains and prepares students to become mathematically literate problem solvers is an entity that sends
citizens into the workforce ready to compete in a global economy laden with technology and problem solving opportunities. A
school district that intends to have an accomplished field of mathematicians, engineers, medical professionals, scientists, and
innovative entrepreneurs must plan and prepare standards-based curriculum that adheres to the Common Core Standards,
includes 21st Century technology skills, and explores the variety of careers steeped in mathematics.
In consideration of the rigor and depth of mastery needed by students in our Nation's public school system, we have
constructed the following curriculum guide and supporting documentation for Gloucester Township Public Schools through
adoption of the New Jersey Department of Education Model Curriculum for Mathematics. Every student in our schools shall
have the opportunity to become engaged in an enriching, real world approach to mathematics instruction that is based on solid
educational research and data-driven instruction.
Benchmark and Cross Curricular Key
__Red: ELA
__ Blue: Math
__ Green: Science
__ Orange: Social Studies
__ Purple: Related Arts
__ Yellow: Benchmark Assessment
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Math – Algebra 1
Unit 1 – Relationships between Quantities and Reasoning with Equations
Standards Topics Activities Resources Assessments N.Q.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
Conversions STEM Projects
Unit Projects
Geometer’s Sketchpad
Real-World Math
Throughout text
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
N.Q.2 Define appropriate quantities for the
purpose of descriptive modeling 8.G.2
Units of Measurement Extend 2.6
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
N.Q.3 Choose a level of accuracy
appropriate to limitations on measurement
when reporting quantities.
Precision
Extend 1.3 -STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
A.SSE.1 Interpret expressions that represent
a quantity in terms of its context.*
a. Interpret parts of an expression, such as
terms, factors, and coefficients.
*Adding and Subtracting
Polynomials
1.1
1.4
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
A.SSE.1 Interpret expressions that represent
a quantity in terms of its context.*
b. Interpret complicated expressions by
viewing one or more of their parts as single
entity. For example, interpret P(1 + r)n as
the product of P and a factor not depending
on P.
*A.SSE.1: Focus on linear, quadratic, and
an introduction to exponential expressions.
*Dividing Monomials 1.2
1.3
9.7
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
A.CED.1 Create equations and inequalities *Using Equations to Solve 1.5, 2.1, 2.2, 2.3, 2.4, -STAR Math
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in one variable and use them to solve
problems. Include equations arising from
linear functions.
**A.CED.1: Limit to linear or quadratic
equations.
Problems
*Problem Solving Using
Charts
*Cost, Income, and Value
Problems
*Rate-Time-Distance
Problems
*Area Problem
2.5, 2.9, 3.2, 5.1, 5.2,
5.3, 5.4, 5.5, 7.6, 8.5,
8.6, 8.7, 9.4, 9.5, 10.4,
11.8
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
A.CED.2 Create equations in two or more
variables to represent relationships between
quantities; graph equations on coordinate
axes with labels and scales.
*The Graphing Method
*Problem Solving with
Systems of Equations
Extend 1.7 3.1, 3.4, 3.5, 3.6, 4.1,
4.2, 4.3, 4.4, 4.5, 4.6,
4.7, 6.1, 6.2, 6.3, 6.4,
6.5, 7.5, 7.5, 8.6, 8.7,
8.8, 9.1, 9.2, 9.4, 9.5,
10.1, 10.4, 11.2, 11.8
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
A.CED.3 Represent constraints by
equations or inequalities, and by systems of
equations and/or inequalities, and interpret
solutions as viable or non-viable options in a
modeling context. For example, represent
inequalities describing nutritional and cost
constraints on combinations of different
foods.
*Problems Without
Solutions
*Solving Problems
Involving Inequalities
*Inequalities in Two
Variables
*Systems of Linear
equations
*Linear Program
4.2
5.6
6.1
6.2
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
A.CED.4 Rearrange formulas to highlight a
quantity of interest, using the same
reasoning as in solving equations. For
example, rearrange Ohm’s laws V= IR to
highlight resistance R.
***A.CED.4: Exclude cases that require
extraction of roots or inverse functions.
*Transforming Formulas 2.8
4.1
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
A.REI.1 Explain each step in solving a
simple equation as following from the
equality of numbers asserted at the previous
step, starting from the assumption that the
*Transforming Equations:
Addition and Subtraction
*Multiplication and Division
*Using Several
1.5, 2.2, 2.3, 2.4, 2.5,
2.6, 2.9, 8.6, 8.7, 8.9
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
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original equation has a solution. Construct a
viable argument to justify a solution
method.
Transformations
*Proof in Algebra
All Chapter Quizzes
A.REI.3 Solve linear equations and
inequalities in one variable, including
equations with coefficients represented by
letters.
*Transforming Equations:
Addition and Subtraction
*Multiplication and Division
*Using Several
Transformations
*Solving Inequalities
*Solving Problems
Involving Inequalities
Explore 2.2
Explore 2.3
Explore 5.2
1.5, 2.2, 2.3, 2.4, 2.5,
2.6, 2.7, 2.8, 2.9, 5.1,
5.2, 5.3, 5.4, 5.5
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
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Math – Algebra 1
Unit 2- Linear Relationships
Standards Topics Activities Resources Assessments N-RN.1. Explain how the definition of the
meaning of rational exponents follows from
extending the properties of integer
exponents to those values, allowing for a
notation for radicals in terms of rational
exponents. For example, we define 𝟓𝟏
𝟑 to be
the cube root of 5 because we want (𝟓𝟏
𝟑)𝟑
=
𝟓(
𝟏
𝟑)(𝟑)
to hold, so (𝟓𝟏
𝟑)𝟑
must equal 5.
*Fractional Exponents STEM Projects
Unit Projects
Geometer’s Sketchpad
Real-World Math
7.3 -STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
N-RN.2. Rewrite expressions involving
radicals and rational exponents using the
properties of exponents.
*Adding and Subtracting
Radicals
Extend 10.3 7.3
10.3
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
8.EE.8. Analyze and solve pairs of
simultaneous linear equations. a.
Understand that solutions to a system of two
linear equations in two variables correspond
to points of intersection of their graphs,
because points of intersection satisfy both
equations simultaneously.
*The graphing Method -STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
8.EE.8. Analyze and solve pairs of
simultaneous linear equations.
b. Solve systems of two linear equations in
two variables algebraically, and estimate
solutions by graphing the equations. Solve
simple cases by inspection. For example, 3x
+ 2y = 5 and 3x + 2y = 6 have no solution
because 3x + 2y cannot simultaneously be 5
and 6.
*The graphing Method
* The Substitution Method
*The Addition-or
Subtraction Method
*Multiplication with the
Addition-or-Subtraction
Method
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
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8.EE.8. Analyze and solve pairs of
simultaneous linear equations
c. Solve real-world and mathematical
problems leading to two linear equations in
two variables. For example, given
coordinates for two pairs of points,
determine whether the line through the first
pair of points intersects the line through the
second pair.
*Solving Problems with
Two Variables
*Multiplication with the
Addition-or Subtraction
Method
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
A.REI.5 Prove that, given a system of two
equations in two variables, replacing one
equation by the sum of that equation and a
multiple of the other produces a system with
the same solutions.
*Multiplication with the
Addition-or Subtraction
Method
6.4 -STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
A.REI.6 Solve systems of linear equations
exactly and approximately (e.g., with
graphs), focusing on pairs of linear
equations in two variables.
*The Graphing Method
*The Substitution Method
* Addition-or Subtraction
Method
*Multiplication with the
Addition-or Subtraction
Method
Extend 6.1
Extend 6.5
6.1
6.2
6.3
6.4
6.5
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
A.REI.10 Understand that the graph of an
equation in two variables is the set of all its
solutions plotted in the coordinate plane,
often forming a curve (which could be a
line).
*Equations in Two Variable
*Points, Lines, and Their
Graphs
1.6, 1.7, 3.1, 3.2, 3.4,
7.5, 9.1, 10.1
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
A.REI.11 Explain why the x-coordinates of
the points where the graphs of the equations
y = f(x) and y = g(x) intersect are the
solutions of the equation f(x) = g(x); find
the solutions approximately, e.g., using
technology to graph the functions, make
tables of values, or find successive
approximations. Include cases where f(x)
and/or g(x) are linear, polynomial, rational,
absolute value, exponential, and logarithmic
*The Graphing Method
*The Graph of
𝑦 = |𝑎𝑥 + 𝑏| + 𝑐
Extend 6.1
Extend 7.5
Extend 9.3
Extend 11.8
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
7
functions.
A.REI.12 Graph the solutions to a linear
inequality in two variables as a half-plane
(excluding the boundary in the case of a
strict inequality), and graph the solution set
to a system of linear inequalities in two
variables as the intersection of the
corresponding half-planes.
*Inequalities in two
Variables
*Systems of Linear
Inequalities
Extend 5.6
Extend 6.6
5.6
6.6
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
8.F.1. Understand that a function is a rule
that assigns to each input exactly one
output. The graph of a function is the set of
ordered pairs consisting of an input and the
corresponding output.
*Functions Defined by
Tables and Graphs
*Functions Defined by
Equations
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
8.F.2. Compare properties of two functions
each represented in a different way
(algebraically, graphically, numerically in
tables, or by verbal descriptions). For
example, given a linear function represented
by a table of values and a linear function
represented by an algebraic expression,
determine which function has the greater
rate of change.
*Comparing Functions -STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
8.F.3. Interpret the equation y = mx + b as
defining a linear function, whose graph is a
straight line; give examples of functions that
are not linear. For example, the function
𝑨 = 𝒔𝟐 giving the area of a square as a
function of its side length is not linear
because its graph contains the points (1,1),
(2,4) and (3,9), which are not on a straight
line.
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
F.IF.1 Understand that a function from one
set (called the domain) to another set (called
the range) assigns to each element of the
*Functions Defined by
Tables and Graphs
1.7 -STAR Math
Chapter Test: 2A, 2B,
8
domain exactly one element of the range. If
f is a function and x is an element of its
domain, then f(x) demotes the output of f
corresponding to the input x. The graph of
f is graph of the y = f(x).
*Functions Defined by
Equations
2C, or 2D
All Chapter Quizzes
F.IF.2 Use function notation, evaluate
functions for inputs in their domains, and
interpret statements that use function
notation in terms of a context.
1.7 -STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
F.IF.3 Recognize that sequences are
functions, sometimes defined recursively,
whose domain is subset of the integers. For
example, the Fibonacci sequence is defined
recursively by f(0) = f(1) = 1 f(n+1) = f(n)
+ f(n-1) for n ≥ 1.
3.5
7.7
7.8
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
8.F.4. Construct a function to model a linear
relationship between two quantities.
Determine the rate of change and initial
value of the function from a description of a
relationship or from two (x, y) values,
including reading these from a table or from
a graph. Interpret the rate of change and
initial value of a linear function in terms of
the situation it models, and in terms of its
graph or a table of values.
*Slope of a Line
*Interpret Rate of Change
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
8.F.5. Describe qualitatively the functional
relationship between two quantities by
analyzing a graph (e.g., where the function
is increasing or decreasing, linear or
nonlinear). Sketch a graph that exhibits the
qualitative features of a function that has
been described verbally.
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
9
F-IF.4. For a function that models a
relationship between two quantities,
interpret key features of graphs and tables in
terms of the quantities, and sketch graphs
showing key features given a verbal
description of the relationship. Key features
include: intercepts; intervals where the
function is increasing, decreasing, positive,
or negative; relative maximums and
minimums; symmetries; end behavior; and
periodicity.
Explore 3.1
Extend 4.1
1.8
3.1
7.5
9.1
9.7
10.1
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
F.IF.5 Relate the domain of a function to
its graph and, where applicable, to the
quantitative relationship it describes. For
example, if the function h(n) gives the
number of person-hours it takes to assemble
n engines in a factory, then the positive
integers would be an appropriate domain for
the function.*
1.7
7.5
7.6
9.1
10.1
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
F-IF.6. Calculate and interpret the average
rate of change of a function (presented
symbolically or as a table) over a specified
interval. Estimate the rate of change from a
graph.
Explore 3.3
Extend 7.7
Explore 9.1
3.3 -STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
F-IF.7. Graph functions expressed
symbolically and show key features of the
graph, by hand in simple cases and using
technology for more complicated cases.
a. Graph linear and quadratic functions and
show intercepts, maxima, and minima.
*Linear and Quadratic
Functions
Extend 3.2
Extend 4.1
Explore 9.3
Extend 9.3
3.1
3.2
3.4
4.1
9.1
9.3
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
F-IF.7. Graph functions expressed
symbolically and show key features of the
graph, by hand in simple cases and using
technology for more complicated cases.
b. Use the properties of exponents to
Extend 3.2
Extend 4.1
Explore 9.3
Extend 9.3
3.1
3.2
3.4
4.1
9.1
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
10
interpret expressions for exponential
functions. For example, identify percent rate
of change in functions such as y = (1.02)t, y
= (0.97)t, y = (1.01)12t, y = (1.2)t/10, and
classify them as representing exponential
growth or decay.
9.2
9.3
All Chapter Quizzes
F.IF.9 Compare properties of two functions
each represented in a different way
(algebraically, graphically, numerically in
tables, or by verbal descriptions). For
example, given a graph of one quadratic
function and an algebraic expression for
another, say which has the larger maximum.
1.7
3.6
4.3
7.8
9.1
9.3
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
F.BF.1 Write a function that describes a
relationship between two quantities.
-a-Determine an explicit expression, a
recursive process, or steps for calculation
from a context.
1.7, 3.1, 3.4, 3.6, 4.1,
4.2, 4.3, 4.4, 4.5, 4.6,
4.7, 7.6, 7.8
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
F.BF.1 Write a function that describes a
relationship between two quantitites.*
-b-Combine standard function types using
arithmetic operations. For example, build a
function that models the temperature of a
cooling body by adding a constant function
to a decaying exponential, and relate these
functions to the model.
4,2
7,6
9.3
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
F-BF.2. Write arithmetic and geometric
sequences both recursively and with an
explicit formula, use them to model
situations, and translate between the two
forms.
7.8 -STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
F.BF.3 Identify the effect on the graph of Extend 4.1 -STAR Math
11
replacing f(x) by f(x)+k, k f(x), f(kx), and
f(x+k) for specific values of k (both positive
and negative); find the value of k given the
graphs. Experiment with cases and illustrate
an explanation of the effects on the graph
using technology. Include recognizing even
and odd functions from their graphs and
algebraic expressions for them.
Explore 7.5
Explore 9.3
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
F-LE.1. Distinguish between situations that
can be modeled with linear functions and
with exponential functions.
3. Prove that linear functions grow
by equal differences over equal
intervals, and that exponential
functions grow by equal factors
over equal intervals.
3.3
3.5
7.7
9.6
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
F-LE.1. Distinguish between situations that
can be modeled with linear functions and
with exponential functions.
b. Recognize situations in which one
quantity changes at a constant rate per unit
interval relative to another.
3.5
3.6
9.6
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
F-LE.1. Distinguish between situations that
can be modeled with linear functions and
with exponential functions.
c. Recognize situations in which a quantity
grows or decays by a constant percent rate
per unit interval relative to another.
9.6 -STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
F-LE.2. Construct linear and exponential
functions, including arithmetic and
geometric sequences, given a graph, a
description of a relationship, or two input-
output pairs (include reading these from a
table).
3.5
3.6
7.5
7.6
7.7
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
12
F.LE.3 Observe using graphs and tables that
a quantity increasing exponentially
eventually exceeds a quantity increasing
linearly, quadratically, or (more generally)
as a polynomial function.
9.6 -STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
F.LE.5 Interpret the parameters in a linear
or exponential function in terms of a
context.
Extend 4-1 3.4
4.1
7.5
7.6
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
13
Math – Algebra 1
Unit 3- Descriptive Statistics
Standards Topics Activities Resources Assessments S-ID.1. Represent data with plots on the real
number line (dot plots, histograms, and box
plots).
*Statistics STEM Projects
Unit Projects
Geometer’s Sketchpad
Real-World Math
12.3
12.4
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
S-ID.2 Use statistics appropriate to the
shape of the data distribution to compare
center (median, mean) and spread
(interquartile range, standard deviation) of
two or more different data sets.
*Statistics Extend 12.8 12.3
12.4
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
S-ID.3. Interpret differences in shape,
center, and spread in the context of the data
sets, accounting for possible effects of
extreme data points (outliers).
12.3
12.4
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
8.SP.1 Construct and interpret scatter plots
for bivariate measurement data to
investigate patterns of association between
two quantities. Describe patterns such as
clustering, outliers, positive or negative
association, linear association, and nonlinear
association.
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
8.SP.2 Know that straight lines are widely
used to model relationships between two
quantitative variables. For scatter plots that
suggest a linear association, informally fit a
straight line, and informally assess the
model fit by judging the closeness of the
data points to the line.
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
14
8.SP.3 Use the equation of a linear model to
solve problems in the context of bivariate
measurement data, interpreting the slope
and intercept. For example, in a linear
model for a biology experiment, interpret a
slope of 1.5 cm/hr as meaning that an
additional hour of sunlight each day is
associated with an additional 1.5 cm in
mature plant height.
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
S-ID.5. Summarize categorical data for two
categories in two-way frequency tables.
Interpret relative frequencies in the context
of the data (including joint, marginal, and
conditional relative frequencies). Recognize
possible associations and trends in the data.
Extend 12.7 -STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
S-ID.6. Represent data on two quantitative
variables on a scatter plot, and describe how
the variables are related.
a. Fit a function to the data; use functions
fitted to data to solve problems in the
Extend 9.6 4.5
4.6
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
15
context of the data. Use given functions or
chooses a function suggested by the context.
Emphasize linear, quadratic, and
exponential models.
All Chapter Quizzes
S-ID.6. Represent data on two quantitative
variables on a scatter plot, and describe how
the variables are related.
b. Informally assess the fit of a function by
plotting and analyzing residuals.
4.6 -STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
S-ID.6. Represent data on two quantitative
variables on a scatter plot, and describe how
the variables are related.
c. Fit a linear function for a scatter plot that
suggests a linear association.
4.5
4.6
-STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
S-ID.7. Interpret the slope (rate of change)
and the intercept (constant term) of a linear
model in the context of the data.
Extend 4.1 4.1 -STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
S-ID.8. Compute (using technology) and
interpret the correlation coefficient of a
linear fit.
4.6 -STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
S-ID.9. Distinguish between correlation and
causation.
Extend 4.5 -STAR Math
Chapter Test: 2A, 2B,
2C, or 2D
All Chapter Quizzes
16
Math – Algebra 1
Unit 4 – Expressions and Equations
Standards Topics Activities Resources Assessments A.SSE.1 Interpret
expressions that represent a
quantity in terms of its
context*
a. Interpret parts of an
expression, such as terms,
factors, and coefficients.
*Adding and Subtracting
Polynomials
*Factoring Integers
STEM Projects
Unit Projects
Geometer’s Sketchpad
Real-World Math
1.1
1.4
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
A.SSE.1 Interpret
expressions that represent a
quantity in terms of its
context*
b. Interpret complicated
expressions by viewing one
or more of their parts as a
single entity. For example,
interpret P(1 + r)n as the
product of P and a factor not
depending on P.
*Multiplying Monomials
*Dividing Monomials
1.2
1.3
9.7
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
A.SSE.2 Use the structure of
an expression to identify
ways to rewrite it. For
example, see x4 – y
4 as (x
2)
2
– (y2)
2, thus recognizing it as
a difference of squares that
can be factored as (x2 – y
2)(x
2
+ y2).
*Monomial Factors of
Polynomials
*Difference of Two Squares
*Squares of Binomials
Explore 8.5
Explore 8.6
1.1, 1.2, 1.3, 1.4, 7.1, 7.2,
7.3, 7.4, 8.5, 8.6, 8.7, 8.8, 8.9
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
A.SSE.3 Choose and
produce an equivalent form
*Solving Equations by
Factoring
8.5
8.6
-STAR Math
17
of an expression to reveal
and explain properties of the
quantity represented by the
expression.
a. Factor a quadratic
expression to reveal the zeros
of the function it defines.
8.7
8.8
8.9
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
A.SSE.3 Choose and
produce an equivalent form
of an expression to reveal
and explain properties of the
quantity represented by the
expression.
b. Complete the square in a
quadratic expression to
reveal the maximum or
minimum value of the
function it defines.
*Linear and Quadratic
Functions
*Completing the Square
Extend 9.4 9.3
9.4
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
A.SSE.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 ≈
Extend 7.6 -STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
18
1.01212t to reveal the
approximate equivalent
monthly interest rate if the
annual rate is 15%
A.APR.1 Understand that
polynomials form a system
analogous to the integers,
namely, they are closed
under the operations of
addition, subtraction, and
multiplication; add, subtract,
and multiply polynomials.
*Basic Assumptions Explore 8.1
Explore 8.3
8.1
8.2
8.3
8.4
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
A.CED.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
*A Problem Solving Plan
*Solving Linear Equations
and Problem Solving with
Linear Equations
*Solve Problems Involving
Inequalities
*Solving Problems Involving
Quadratic Equations
1.5, 2.1, 2.2, 2.3, 2.4, 2.5,
2.9, 3.2, 5.1, 5.2, 5.3, 5.4,
5.5, 7.6, 8.5, 8.6, 8.7, 9.4,
9.5, 10.4, 11.8
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
A.CED.2 Create equations in
two or more variables to
represent relationships
between quantities; graph
equations on coordinate axes
with labels and scales.
*Problem Solving with
Systems of Equations
Extension 1.7
3.1, 3.4, 3.5, 3.6, 4.1, 4.2,
4.3, 4.4, 4.5, 4.6, 4.7, 6.1,
6.2, 6.3, 6.4, 6.5, 7.5, 7.6,
8.6, 8.7, 8.8, 9.1, 9.2, 9.4,
9.5, 10.1, 10.4, 11.2, 11.8
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
A.CED.4 Rearrange
formulas to highlight a
quantity of interest, using the
same reasoning as in solving
equations. For example,
rearrange OHM’s law V= IR
to highlight resistance R.
*Transforming Formulas
2.8
4.1
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
19
A.REI.4 Solve quadratic
equations in one variable.
a. Use the method of
completing the square to
transform any quadratic
equation in x into an
equation of the form (x – p)2
= q that has the same
solutions. Derive the
quadratic formula for this
form.
*Completing the Square
*Methods of Solution
9.4
10.2
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
A.REI.4 Solve quadratic
equations in one variable.
b. Solve quadratic equations
by inspection (e.g., for x2 =
49), taking square roots,
completing the square, the
quadratic formula and
factoring, as appropriate to
the initial form of the
equation. Recognize when
the quadratic formula gives
complex solutions and
write them as a ± bi for real
numbers a and b.
*Square Roots of Variable
Expressions
*Quadratic Equations with
Perfect Squares
*Completing the Square
*The Quadratic Formula
*Complex Numbers
Solving Equations by
Factoring
*Methods of Solution
8.6
8.7
8.8
9.2
9.4
9.5
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
A.REI.7 Solve a simple
system consisting of linear
equation and quadratic
equation in two variables
algebraically and graphically.
For example, find the points
of intersection between the
line y = -3x and the circle x2
+ y2 = 3.
Extend 9.3 -STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
20
Math – Algebra 1
Unit 5 – Quadratic Functions and Modeling Standards Topics Activities Resources Assessments
N.RN.3 Explain why the
sum or product of two
rational numbers is rational;
that the sum of a rational
number and an irrational
number is irrational; and that
the product of a non-zero
rational number and an
irrational number is
irrational.
STEM Projects
Unit Projects
Geometer’s Sketchpad
Real-World Math
Extension 10.2
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
8.G.6 Explain a proof of the
Pythagorean Theorem and its
converse.
*The Pythagorean Theorem -STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
8.G.7
Apply the Pythagorean
Theorem to determine
unknown side lengths in
right triangles in real-world
and mathematical problems
in two and three dimensions.
*The Pythagorean Theorem -STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
8.G.8
Apply the Pythagorean
Theorem to find the distance
between two points in a
coordinate system.
*The Pythagorean Theorem -STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
21
F.IF.4 For a function that
models a relationship
between two quantities,
interpret key features of
graphs and tables in terms of
the quantities, and sketch
graphs showing key features
given a verbal description of
the relationship. Key
features include: intercepts;
intervals where the function
is increasing, decreasing,
positive or negative; relative
maximums and minimums;
symmetries; end behavior;
and periodicity.
Explore 3.1
Extend 4.1
1.8
3.1
7.5
9.1
9.7
10.1
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
F.IF.5 Relate the domain of
a function to its graph and,
where applicable, to the
quantitative relationship it
describes. For example, if
the function h(n) gives the
number of person-hours it
takes to assemble n engines
in a factory, then the positive
integers would be an
appropriate domain for the
function.*
1.7
7.5
7.6
9.1
10.1
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
F.IF.6 Calculate and
interpret the average rate of
change of a function
(presented symbolically or as
a table) over a specified
interval. Estimate the rate of
change from a graph.
Explore 3.3
Extend 7.7
Extend 9.1
3.3 -STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
F.IF.7 Graph functions
expressed symbolically and
show key features of the
graph, by hand in simple
*Points, Lines, and Their
Graphs
*Slope of a Line
Extend 3.2
Extend 4.1
Explore 9.3
Extend 9.3
3.1
3.2
3.4
4.1
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
22
cases and using technology
for more complicated cases.
-a-Graph linear and
quadratic functions and show
intercepts, maxima and
minima
*Slope-Intercept Form of a
Linear Equation
Linear and Quadratic
Functions
9.1
9.2
9.3
All Chapter Quizzes
F.IF.7 Graph functions
expressed symbolically and
show key features of the
graph, by hand in simple
cases and using technology
for more complicated cases.
-b-Graph square root, cube
root, and piecewise-defined
functions, including step
functions and absolute value
functions. Exponential,
growth or decay.
Extend 9.7
Extend 10.1
9.7
10.1
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
F-IF.8. Write a function
defined by an expression in
different but equivalent
forms to reveal and explain
different properties of the
function.
a. Use the process of
factoring and completing the
square in a quadratic
function to show zeros,
extreme values, and
symmetry of the graph, and
interpret these in terms of a
context.
*Solving Equations by
Factoring
*Linear and Quadratic
Functions
*Completing the Square
Extend 9.4 9.2
9.4
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
F-IF.8. Write a function
defined by an expression in
different but equivalent
forms to reveal and explain
different properties of the
function.
b. Use the properties of
Extend 7.6 -STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
23
exponents to interpret
expressions for exponential
functions. For example,
identify percent rate of
change in functions such as y
= (1.02)t, y = (0.97)t, y =
(1.01)12t, y = (1.2)t/10, and
classify them as representing
exponential growth or decay.
F.IF.9 Compare properties
of two functions each
represented in a different
way (algebraically,
graphically, numerically in
tables, or by verbal
descriptions). For example,
given a graph of one
quadrant function and an
algebraic expression for
another say which has the
larger maximum.
1.7
3.6
4.3
7.8
9.1
9.3
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
F.BF.1 Write a function that
describes a relationship
between two quantities.
-a-Determine an explicit
expression, a recursive
process, or steps for
calculation from a context.
1.7, 3.1, 3.4, 3.6, 4.1, 4.2,
4.3, 4.4, 4.5, 4.5, 4.7, 7.6, 7.8
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
F.BF.1 Write a function that
describes a relationship
between two quantities.
-b-Combine standard
function types using
arithmetic operations. For
example, build a function
that models the temperature
of a cooling body by adding
a constant function to a
decaying exponential, and
4.2
7.6
9.3
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
24
relate these functions to the
model.
F.BF.3 Identify the effect on
the graph of replacing f(x)
by f(x)+k, k f(x), f(kx), and
f(x+k) for specific values of
k (both positive and
negative); find the value of k
given the graphs.
Experiment with cases and
illustrate an explanation of
the effects on the graph
using technology. Include
recognizing even and odd
functions from their graphs
and algebraic expressions for
them.
Extend 4.1
Explore 7.5
Explore 9.3
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
F.BF.4 Find inverse
functions.
-a-solve an equation of the
form f(x) = c for a simple
function f that has an inverse
and write an expression for
the inverse. For example,
f(x)=2x3 or f(x)=(x+1)/(x-1)
for x≠1
Explore 10.1
4.7
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
F.LE.3 Observe using
graphs and tables that a
quantity increasing
exponentially eventually
exceeds a quantity increasing
linearly, quadratically, or
(more generally) as a
polynomial function.
9.6
-STAR Math
Chapter Test: 2A, 2B, 2C, or
2D
All Chapter Quizzes
25
Appendix A
Adaptations for Special Education Students, English Language Learners, and Gifted and Talented Students
Making Instructional Adaptations
Instructional Adaptations include both accommodations and modifications.
An accommodation is a change that helps a student overcome or work around a disability or removes a barrier to learning for
any student.
Usually a modification means a change in what is being taught to or expected from a student.
-Adapted from the National Dissemination Center for Children with Disabilities
ACCOMMODATIONS MODIFICATIONS
Required when on an IEP or 504 plan, but can be implemented for any student to support their learning.
Only when written in an IEP.
Special Education Instructional Accommodations
Teachers will use Approaching Level Tier 2: Strategic Intervention in RtI Differentiated Instruction section of Glencoe
lessons.
Teachers will use the Targeted Strategic Intervention from the Glencoe Online Support.
Teachers shall implement any instructional adaptations written in student IEPs.
Teachers will implement strategies for all Learning Styles (Appendix B)
Teacher will implement appropriate UDL instructional adaptations (Appendix C )
26
Gifted and Talented Instructional Accommodations
Teachers will use Beyond Level in RtI Differentiated Instruction section of Glencoe lessons
Teachers will use the Enrichment Masters from the Glencoe Online Support
Teacher will implement Adaptations for Learning Styles (Appendix B)
Teacher will implement appropriate UDL instructional adaptations (Appendix C)
English Language Learner Instructional Accommodations
Teachers will use the ELL Differentiated English Language Learner Support section of Glencoe lessons.
Teachers will use the Differentiated ELL Support from the Glencoe Online Support.
Teachers will implement the appropriate
Teachers will implement the appropriate instructional adaptions for English Language Leaners (Appendix E)
27
APPENDIX B
Learning Styles Aadapted from The Learning Combination Inventories (Johnson, 1997)and VAK (Fleming, 1987)
Accommodating Different Learning Styles in the Classroom: All learners have a unique blend of sequential, precise, technical, and confluent learning styles. Additionally, all learners have a preferred mode of processing information- visual, audio, or kinesthetic. It is important to consider these differences when lesson planning, providing instruction, and when differentiating learning activities. The following recommendations are accommodations for learning styles that can be utilized for all students in your class. Since all learning styles may be represented in your class, it is effective to use multiple means of presenting information, allow students to interact with information in multiple ways, and allow multiple ways for students to show what they have learned when applicable.
Visual Utilize Charts, graphs, concept maps/webs, pictures, and cartoons Watch videos to learn information and concepts Encourage students to visualize events as they read math word problems Use flash cards to practice basic math facts Model by demonstrating tasks or showing a finished product Have written directions available for student Use power point presentations
28
Color code and highlight operation symbols (+, -, x, ÷) Color code and highlight key words in math word problems
Audio Allow students to give oral presentations or explain concepts verbally Present information and directions verbally or encourage students to read directions aloud to themselves. Allow students to work in pairs Utilize songs and rhymes Ask for choral responses in instruction, example have the entire class chant in unison multiples, evens/odds, or skip counting by 2s, 5,s or 10s Repeat, clarify, or reword directions Verbally guide students through task steps
Kinesthetic Act out concepts and dramatize events Use flash cards Use manipulatives Allow students to deepen knowledge through hands on projects
Sequential: following a plan. The learner seeks to follow step-by-step directions, organize and plan
work carefully, and complete the assignment from beginning to end without interruptions. Accommodations: Repeat/rephrase directions Provide a checklist or step by step written directions Break assignments in to chunks
29
Provide samples of desired products
Help the sequential students overcome these challenges: over planning and not finishing a task, difficulty reassessing and improving a plan, spending too much time on directions and neatness and overlooking concepts
Precise: seeking and processing detailed information carefully and accurately. The learner takes detailed
notes, asks questions to find out more information, seeks and responds with exact answers, and reads and writes in a highly specific manner. Accommodations: Provide detailed directions for assignments Provide checklists Provide frequent feedback and encouragement
Help precise students overcome these challenges: overanalyzing information, asking too many questions, focusing on details only and not concepts
Technical: working autonomously, "hands-on," unencumbered by paper-and-pencil requirements. The
learner uses technical reasoning to figure out how to do things, works alone without interference, displays knowledge by physically demonstrating skills, and learns from real-world experiences Accommodations: Allow to work independently or as a leader of a group Give opportunities to solve problems and not memorize information Plan hands-on tasks Explain relevance and real world application of the learning Will be likely to respond to intrinsic motivators, and may not be motivated by grades
Help technical students overcome these challenges: may not like reading or writing, difficulty remaining focused while seated, does not see the relevance of many assignments, difficulty paying attention to lengthy directions or lectures
Confluent: avoiding conventional approaches; seeking unique ways to complete any learning task. The
learner often starts before all directions are given; takes a risk, fails, and starts again; uses imaginative ideas and unusual approaches; and improvises. Accommodations: Allow choice in assignments Encourage creative solutions to problems Allow students to experiment or use trial and error approach
30
Will likely be motivated by autonomy within a task and creative assignments
Help confluent students overcome these challenges: may not finish tasks, trouble proofreading or paying attention to detail
31
APPENDIX C
Universal Design for Learning Adaptations
Adapted from Universal Design For Learning
Teachers will utilize the examples below as a menu of adaptation ideas.
Provide Multiple Means of Representation
Strategy #1: Options for perception
Goal/Purpose Examples To present information through different modalities such as vision, hearing, or touch.
Use visual demonstrations, illustrations, and models
Present a power point presentation.
Use appropriate manipulatives, such as base 10 block,
counters, or pattern blocks
Differentiate operation symbols by color coding
Draw pictures when possible
Use interactive websites and apps
Use modeling to help students solve problems
Provide examples of a correctly solved problem at the
32
beginning of each lesson
Have students work each step in a different color
Use songs and rhymes to help remember information
Use mnemonics like “Please Excuse My Dear Aunt Sally”
(order of operations) to remember sequenced steps
Simplify and rephrase vocabulary in word problems
Strategy #2: Options for language, mathematical expressions and symbols
Goal/Purpose Examples To make words, symbols, pictures, and mathematical notation clear for all students.
Use larger font size and/or magnifiers Highlight important parts of problems, example: key words or operation signs Use place value charts, number grids, and operation tables (addition/subtraction and multiplication/division tables) Allow students to trace important visual patterns Use graph paper to keep numbers aligned
33
Put boxes around each problem to visually separate them Simplify and rephrase vocabulary in word problem Turn lined paper vertically so the student has ready made columns Color code and highlight keywords in math word problems
Strategy #3: Options for Comprehension
Purpose Examples To provide scaffolding so students can access and understand information needed to construct useable knowledge.
Use diagrams.
Use semantic maps and diagrams Chunk pieces of information together, example: learn facts in sets of 3 Review previous lessons
34
Use a buddy system to clarify Use mnemonic aids to signal steps, example “Does McDonalds Sell Cheese Burgers” (long division: divide, multiply, subtract, check, bring down) Provide students with a strategy to use for solving word problems Use graph paper to keep numbers aligned Use modeling to help students solve problems Introduce concepts using real life examples whenever possible Teach fact families and build fluency with games and understanding When teaching number lines use tape or draw a number line on the floor for students to walk on
Provide Multiple Means of Action and Expression
Strategy #4: Options for physical action
35
Purpose Examples To provide materials that all learners can physically utilize
Use of computers when available Preferential or alternate seating Provide assistance with organization Provide graph paper to organize place value Provide appropriate manipulatives Use flash cards Provide highlighters for students when solving problems Allow students to use desk top copies of fact sheets, multiplication/division tables etc. Use individual dry-erase boards
Strategy #5: Options for expression and communication
Purpose Examples
36
To allow the learner to express their knowledge in different ways
Allow oral responses or presentations Students show their knowledge with charts and graphs Give students extra time to respond to oral questions Have students verbally or visually explain how to solve a math problem
Strategy #6: Options for executive function
Purpose Examples To scaffold student ability to set goals, plan, and monitor progress
Provide clear learning goals, scales, and rubrics Model skills Utilize checklists Give examples of desired finished product Chunk longer assignments into manageable parts Teach and practice organizational skills Use a problem solving strategy checklist so that students can monitor their progress Teach students to use self-questioning techniques Reduce the number of practice or test problems on a
37
page
Provide Multiple Means of Engagement
Strategy #7: Options for recruiting interest
Purpose Examples To make learning relevant, authentic, interesting, and engaging to the student.
Provide choice and autonomy on assignments Use colorful and interesting designs, layouts, and graphics Use games, challenges, or other motivating activities Provide positive reinforcement for effort Use manipulatives Provide learning aids such as calculators and/or operation tables (addition/subtraction and multiplication/division tables)
38
Introduce concepts using real life examples whenever possible Use individual dry-erase boards Use magnetic manipulatives examples: numbers, operation signs, ten frames, base ten blocks, etc.
Strategy #8: Options for sustaining effort and persistence
Purpose Examples To create extrinsic motivation for learners to stay focused and work hard on tasks.
Show real world applications of the lesson Utilize collaborative learning Assign a peer tutor Incorporate student interests into lesson Praise growth and effort Recognition systems Behavior plans Repeat directions as needed Provide immediate feedback
39
Strategy #9: Options for self-regulation
Purpose Examples To develop intrinsic motivation to control behaviors and to develop self-control.
Give prompts or reminders about self-control Self-monitored behavior plans using logs, records, journals, or checklists Ask students to reflect on behavior and effort Post class rules using pictures and words Post daily schedule using pictures and words Circulate around the room Develop a signal for when a break is needed Provide consistent praise to elevate self-esteem Model and role play problem solving Desensitize students to anxiety causing events
40
Appendix D
Gifted and Talented Instructional Accommodations
How do the State of NJ regulations define gifted and talented students?
Those students who possess or demonstrate high levels of ability, in one or more content areas, when compared to their chronological peers in the local district and who require modification of their educational program if they are to achieve in accordance with their capabilities.
What types of instructional accommodations must be made for students identified as gifted and talented?
The State of NJ Department of Education regulations require that district boards of education provide appropriate K-12 services for gifted and talented students. This includes appropriate curricular and instructional modifications for gifted and talented students indicating content, process, products, and learning environment. District boards of education must also take into consideration the PreK-Grade 12 National Gifted Program Standards of the National Association for Gifted Children in developing programs..
What is differentiation?
Curriculum Differentiation is a process teachers use to increase achievement by improving the match between the learner’s unique characteristics:
Prior knowledge Cognitive Level
Learning Rate Learning Style
Motivation Strength or Interest
And various curriculum components:
Nature of the Objective Teaching Activities
Learning Activities Resources
Products
41
Differentiation involves changes in the depth or breadth of student learning. Differentiation is enhanced with the use of appropriate classroom
management, retesting, flexible small groups, access to support personal, and the availability of appropriate resources, and necessary for gifted
learners and students who exhibit gifted behaviors (NRC/GT, University of Connecticut).
42
43
Gifted & Talented Accommodations Chart
Adapted from Association for Supervision and Curriculum Development
Teachers will utilize the examples below as a menu of adaptation ideas.
Strategy Description Suggestions for Accommodation
High Level Questions
Discussions and tests, ensure the highly able learner is presented with questions that draw on advanced level of information, deeper understanding, and challenging thinking.
Require students to defend answers
Use open ended questions
Use divergent thinking questions
Ask student to extrapolate answers when given incomplete information
Tiered assignments
In a heterogeneous class, teacher uses varied levels of activities to build on prior knowledge and prompt continued growth. Students use varied approaches to exploration of essential ideas.
Use advanced materials
Complex activities
Transform ideas, not merely reproduce them
Open ended activity
Flexible Skills Grouping
Students are matched to skills work by virtue of readiness, not with assumption that all need same spelling task, computation drill, writing assignment, etc. Movement among groups is common, based on readiness on a given skill and growth in that skill.
Exempt gifted learners from basic skills work in areas in which they demonstrate a high level of performance
Gifted learners develop advanced knowledge and skills in areas of talent
Independent Projects
Student and teacher identify problems or topics of interest to student. Both plan method of investigating topic/problem and identifying type of product student will develop. This product should address the problem and demonstrate the student’s ability to apply skills and knowledge to the problem or topic
Primary Interest Inventory
Allow student maximum freedom to plan, based on student readiness for freedom
Use preset timelines to zap procrastination Use process logs to document the process
involved throughout the study
Learning Centers
Centers are “Stations” or collections of materials students can use to explore, extend, or practice skills and content.
Develop above level centers as part of classroom instruction
44
For gifted students, centers should move beyond basic exploration of topics and practice of basic skills. Instead it should provide greater breadth and depth on interesting and important topics.
Interest Centers or Interest Groups
Interest Centers provide enrichment for students who can demonstrate mastery/competence with required work/content. Interest Centers can be used to provide students with meaningful learning when basic assignments are completed.
Plan interest based centers for use after students have mastered content
Contracts and Management Plans
Contracts are an agreement between the student and teacher where the teacher grants specific freedoms and choices about how a student will complete tasks. The student agrees to use the freedoms appropriately in designing and completing work according to specifications.
Allow gifted students to work independently using a contract for goal setting and accountability
Compacting A 3-step process that (1) assesses what a student knows about material “to be” studied and what the student still needs to master, (2) plans for learning what is not known and excuses student from what is known, and (3) plans for freed-up time to be spent in enriched or accelerated study.
Use pretesting and formative assessments
Allow students who complete work or have mastered skills to complete enrichment activities
45
46
Appendix E
English Language Learner Instructional Accommodations
Adapted from World-class Instructional Design and Assessment guidelines (2014), Teachers to English Speakers of Other Languages guidelines, State
of NJ Department of Education Bilingual
Math
Instruction:
Provide bilingual dictionaries.
Simplify language, clarify or explain directions.
Build background (discuss, allow for questions, and use visuals if applicable) prior to giving assessment make the text meaningful.
Pre-teach difficult vocabulary.
Highlight key word or phrases.
Allow ELL students to hear word problems twice and have a second opportunity to check their answers.
Allow ELL students extended time for word problems.
Provide specific seating arrangement (close proximity for direct instruction, teacher assistance, and buddy).
Response:
Allow for oral explanations
Allow the use of word walls and vocabulary banks.