Linden Community Schools
Content Standard 1: Collection, Organization and Presentation of Data- Students collect and explore data, organize data into a useful form, and develop skill in representing and reading data displayed in different formats.
Grade Level: 7th Grade
|
Benchmark |
Performance Description |
Recommended Activities |
Recommended Assessments |
|
Benchmark 2 |
D.RE.07.01 Represent
and interpret data using circle graphs, stem and leaf plots, histograms, and
box-and-whisker plots, and select appropriate representation to address
specific questions. D.AN.07.02 Create
and interpret scatter plots and find line of best fit and use an estimated
line of best fit to answer questions about the data. |
Students should engage in activities in which they
construct and or determine properly constructed graphs: picture graphs,
circle graphs, stem-and-leaf-plots, box-and-whisker plots, coordinate graphs,
histograms, bar graphs, scatter plots and line plots. They should be able to
analyze the data in the graphs, identify questions that can be answered from
a particular graph, and identify which type of graph is being used or should
be used in particular situations. |
Conduct a survey to determine if students in your school
are interested in buying bagels and juice on Fridays. Record your data in a
spreadsheet and develop an appropriate table, chart, or graph to display
results. Middle school students should be comfortable producing graphs
electronically. |
|
Benchmark 3 |
D.RE.07.01 Represent
and interpret data using circle graphs, stem and leaf plots, histograms, and
box-and-whisker plots, and select appropriate representation to address
specific questions. D.AN.07.02 Create
and interpret scatter plots and find line of best fit and use an estimated line of best fit to answer questions about the data. |
Students should engage in activities in which they
evaluate the strengths and weaknesses of the following types of graphs and
when they are appropriate to use: picture graphs, circle graphs,
stem-and-leaf plots, box-and-whisker plots, coordinate graphs, histograms,
bar graphs, scatter plots and line plots. Pay particular attention to which
graphs display two variable data (bivariate), one
variable data (univariate), scales
on axes, continuous and non-continuous data. |
In small groups, use three graphical representations of
the same data and decide why one representation is preferred to the others.
Justify your decisions. |
Content Standard 2: Description and Interpretation- Students examine data and describe characteristics of a distribution, relate data to the situation from which they arose, and use data to answer questions convincingly and persuasively.
|
Benchmark |
Performance Description |
Recommended Activities |
Recommended Assessments |
|
Benchmark 2 |
D.AN.07.04 Find
and interpret the median, quartiles, and interquartile
range of a given set of data. |
Students should engage in
activities in which they are given a box-and-whisker plot and asked how the
length of the box conveys information about data distribution. They should
specifically be aware of information the boxplot
contains about median, range, and outliers. Students will be given data or
graphs and may be asked to find the mean, median, mode, range, a fraction,
probability, or a number to be added or dropped to get a certain type of
statistic. Foils on multiple choice questions will usually include another
measure of central tendency (e.g., when finding the median, the mean will be
a distractor). |
The test scores in Mr. Davis’
class are listed below: 72, 88, 97, 65, 100, 25, 79,
75, 90, 75, 82, 85, 67, 96, 71, 75 Which box-and-whisker plot
accurately reflects these data?
A. 1 Answer A [The middle of the box is the median, the right of the box is the 1st quartile, that is
the middle of the lower half of the data. The left end is the 3rd quartile.] |
|
Benchmark 3 |
D.RE.07.01 Represent
and interpret data using circle graphs, stem and leaf plots, histograms, and
box-and-whisker plots, and select appropriate representation to address
specific questions. D.AN.07.02 Create
and interpret scatter plots and find line of best fit and use an estimated
line of best fit to answer questions about the data. |
Prepare presentations that use data to convince the class of a certain conclusion. Write persuasive letters in which conclusions are presented and are supported by data. Stage a class debate in which each side bases its arguments on data it has collected and presented |
Formulate conclusions based on a data set. Then write a persuasive letter in which conclusions are presented and supported by data including a description of the shape, center, and spread. Include a graphical representation of the data. |
Linden
Community Schools
Content Standard 1: Shape and Shape Relationships- Students develop spatial sense, use shape as an analytic and descriptive tool, identify characteristics and define shapes, identify properties and describe relationships among shapes.
Grade
Level: 7th Grade
|
Benchmark |
Performance
Description |
Recommended
Activities |
Recommended
Assessments |
|
Benchmark 4 |
G.SR.07.01 Use a ruler and other tools to draw squares, rectangles, triangles and parallelograms with specified dimensions |
Students should engage in
activities in which they sketch or plot familiar 2- and 3-dimensional shapes
from descriptions or coordinates. Sketching does not involve construction
with a protractor or compass. Students may be asked to make accurate shapes
from given angle and side length measures with a protractor and ruler. |
A parallelogram can be drawn
many different ways. Complete the following 2 parts. Show all of your work. A. Using your ruler, draw a
parallelogram with at least one right angle. B. Identify 3 other
characteristics of your parallelogram. |
|
Benchmark 5 |
G.SR.07.02 Use compass and straightedge to perform basic geometric constructions: the perpendicular bisector of a segment, an equilateral triangle, and the bisector of an angle; understand informal justifications |
Students will engage in activities such as: Using a compass and a straight edge, make inscribed triangles, hexagons, and octagons and develop creative designs. |
Make a triangle and construct the perpendicular bisector of each of its sides. Where the perpendicular bisectors intersect, place your compass and inscribe the triangle. Inscribe several triangles using the above method and give an informal explanation of why this can work for any triangle. |
|
Benchmark 7 |
A.PA.07.04 For directly proportional or linear situations, solve applied problems using graphs and equations; e.g., the heights and volume of a container with uniform cross-section; height of water in a tank being filled at a constant rate; degrees Celsius and degrees Fahrenheit; distance and time under constant speed. A.PA.07.05 Understand and use directly proportional relationships of the form y = mx, and distinguish from linear relationships of the form y =mx + b, b is non-zero; understand that in a directly proportional relationship between two quantities one quantity is a constant multiple of the other quantity. |
Students should engage in activities in which they use shape properties and relationships to solve problems in the physical world. They should use shape properties, (e.g., angle measurements, area, perimeter, and volume of shapes with specified dimensions, parallel and congruent sides, regular polygons) to describe the physical world. This includes naming everyday objects with geometric shapes. Solving problems usually requires more than one step. |
Could a 3x5 picture be enlarged to an 8x10 picture and still be similar? [NOTE: No, there would be a distortion because you can double both width and length of the 3x5 and make a 6 by 10 picture. To make an 8x10, you would have to stretch one dimension more than the other, causing distortion.] |
Content Standard 3: Measurement- Students compare attributes of two objects or of one object with a standard (unit) and analyze to determine what measurement(s) should be made and to what level of precision.
Grade Level: 7th Grade
|
Benchmark |
Performance Description |
Recommended
Activities |
Recommended
Assessments |
|
Benchmark 1 |
G.SR.07.01 Use a ruler and other tools to draw squares, rectangles, triangles and parallelograms with specified dimensions. G.SR.07.02 Use compass and straightedge to perform basic geometric constructions: the perpendicular bisector of a segment, an equilateral triangle, and the bisector of an angle; understand informal justifications. |
Students should engage in activities in which they use protractors, compasses, and rulers. When measuring lengths, students should be aware of using portions of centimeters. For instance 3 centimeters + 6 millimeters = 3.6 centimeters. They may be given pictures of angles and lengths to measure. Using appropriate tools, they may be asked to apply their measurements to a problem, such as finding surface area. |
Using isometric dot paper, construct shapes that conform to given specifications (e.g., make a trapezoid with 2 right angles), and determine when it is impossible to create a certain shape (e.g., make a parallelogram with only 2 right angles). |
|
Benchmark 4 |
G.TR.07.06 Understand and use the
fact that when two triangles are similar with scale factor of r, their areas
are related by a factor of r2 |
Students should engage in activities in which they answer questions about the comparisons of volume, area, and perimeter when changed by scale factors. Relationships between these measurements may be given as ratio (3:5, 8:10, etc.). Borders like picture frames and other objects show the differences between area and side lengths (3x5, 8x10,etc.). |
Draw a pair of plane figures, double or triple 1 measurement, and discover what happens to the perimeter and area of the second figure. Compare measurements of sets of objects and draw conclusions about the dependence or independence of measurements such as if 2 squares have the same area, then they have the same perimeter (and vice versa); however 2 triangles can have the same area but different perimeters. |
|
Benchmark 5 |
G.TR.07.03 Understand that in similar polygons, corresponding angles are congruent and the ratios of corresponding sides are equal; understand the concepts of similar figures and scale factor. G.TR.07.04 Solve problems about similar figures and scale drawings. G.TR.07.05 Show that two triangles are similar using the criteria: corresponding angles are congruent (AAA similarity); the ratios of two pairs of corresponding sides are equal and the included angles are congruent (SAS similarity); ratios of all pairs of corresponding sides are equal (SSS similarity); use these criteria to solve problems and to justify arguments. G.TR.07.06
Understand and use the fact that when two triangles are similar with
scale factor of r, their areas are related by a factor of r2 N.FL.07.05 Solve simple proportion problems using such methods as unit rate, scaling, finding equivalent fractions, and solving the proportion equation a/b = c/d; know how to see patterns about proportional situations in tables. |
Students should engage in activities in which they may be given an area and a side length and asked to find the perimeter, or similar types of problems. Scale models from pictures or models to real life, including ratios, may be used. Objects may have side lengths, perimeters, area, or volume given and students will be asked questions regarding side lengths, perimeter, area, and volume. |
Mr. Tanaka needs to determine
the height of a tree so there will be enough clearance between the house and
tree when it is cut down. The tree casts a shadow 16 feet 3 inches long when
his 5 foot 9 inch height casts a shadow 2 feet long. About how tall is the
tree?
A. 32.5 feet Answer B Students have a tendency to
change 5 feet 9 inches to 5.9 feet rather than 5.75 feet. This common mistake
leads to the 16.3 • 5.9 ÷ 2 |
48.1 foot Linden Community Schools
Content Standard 1: Concepts and Properties of Numbers- Students
experience counting and measuring activities to develop intuitive sense about
numbers, develop understanding about properties of numbers, understand the need
for and existence of different sets of numbers, and investigate properties of
special numbers.
Grade Level: 7th Grade
|
Benchmark |
Performance Description |
Recommended Activities |
Recommended Assessments |
|
Benchmark 2 |
N.MR.07.06 Understand
the concept of square root and cube root, and estimate using calculators. |
Students should engage in
activities such as computing square and cube roots with calculators or
finding square or cube roots of perfect squares and cubes. Students should be able to
estimate square roots of numbers that are not perfect squares without using
the calculator. |
Estimate the square root of 48. Use your calculator to check
your estimation and round to the nearest hundredth. |
|
Benchmark 3 |
A.PA.07.11 Understand
and use basic properties of real numbers: additive and multiplicative
identities, additive and multiplicative inverses, commutativity,
associativity, and the distributive property of
multiplication over addition. A.FO.07.12 Add,
subtract, and multiply simple algebraic expressions of the first degree,
e.g., (92x + 8y) – 5x + y, or – 2x (5x – 4), and justify using properties of
real numbers. |
Students should engage in activities in which they explore
multiplicative and additive inverses, as well as the meaning of sum,
difference, product, and quotient. Students should be able to order all types
of numbers and know results of operations with 1 and 0. They should be aware
of |
What is the product of a number and its multiplicative inverse? A.
0 Answer B |
, and the
additive and multiplicative inverses.
) that are
used to approximate area and circumference of a circle, and that the decimal
representation is not a repeating decimal.Content Standard 2: Representation and Uses of Numbers- Students recognize that numbers are used in different ways such as counting, measuring, ordering and estimating, understand and produce multiple representations of a number, and translate among equivalent representations.
|
Benchmark |
Performance Description |
Recommended Activities |
Recommended Assessments |
|
Benchmark 4 |
N.MR.07.06 Understand
the concept of square root and cube root, and estimate using calculators. N.FL.07.09 Estimate
results of computations with rational numbers. |
Using media sources, estimate and compare the cost of various purchases including discounts, sales tax, and rebates before finding the totals with a calculator. Compare several students’ estimates of the same quantity and discuss which is the closest estimate. Discuss
the strategies used in arriving at estimates, such as the gym holds 700
students so the courtyard will hold 7000 because it is 10 times bigger than
the gym, and explore the effectiveness of the methods. |
About 700 cubic feet of freshly mowed hay weighs approximately one ton. About how many tons does a rectangular stack of hay weigh if it measures 8 ft x 10.5 ft x 16.5 ft? A.
one ton Answer B |
|
Benchmark 5 |
N.FL.07.02 Solve
problems involving derived quantities. N.FL.07.05 Solve
simple proportion problems using such methods as unit rate, scaling, finding
equivalent fractions, and solving the proportion equation a/b = c/d; know how
to see patterns about proportional situations in tables. |
Students should engage in activities in which they solve
real-world problems that use numbers- decimals, fractions, integers, and
percents. They will be given a situation and will have to use their own
strategy to answer a question from the given situation. |
Give the numerical value for points A to F on the number line.
Discussion questions: If the number represented by B is multiplied by 5, where will be the result? (The answer should be less than one, on or near E.) If the number represented by D is multiplied by itself, mark the approximate location of the product. (The answer is between B and C.) |
Content Standard 3: Number Relationships- Students investigate relationships such as equality, inequality, inverses, factors and multiples, and represent and compare very large and very small numbers.
|
Benchmark |
Performance Description |
Recommended Activities |
Recommended Assessments |
||||||||||||
|
Benchmark 2 |
N.ME.07.01 Understand derived quantities such as density,
velocity, and weighted averages. N.MR.07.04 Convert ratio
quantities between different systems of units such as feet per second to
miles per hour. A.PA.07.01 Recognize
when information given in a table, graph, or formula suggests a proportional
or linear relationship. A.RP.07.02 Represent
directly proportional and linear relationships using verbal descriptions,
tables, graphs, and formulas, and translate among these representations. A.PA.07.03 Given a
directly proportional or linear situation, graph and interpret the slope and intercept(s) in terms of the original situation;
evaluate y = kx for specific x values, given k,
e.g., weight vs. volume of water, base cost plus cost per unit. A.PA.07.05 Understand
and use directly proportional relationships of the form y = mx, and distinguish from linear relationships of the form
y = mx + b, b non-zero; understand that in a
directly proportional relationship between two quantities one quantity is a
constant multiple of the other quantity. A.PA.07.06 Calculate the
slope from the graph of a linear function as the ratio of “rise/run” for a
pair of points on the graph, and express the answer as a fraction and a
decimal; understand that linear functions have slope that is a constant rate
of change. A.PA.07.07 Represent
linear functions in the form y = x + b, y = mx, and
y = mx + b, and graph, interpreting slope and
y-intercept. |
Students should engage in activities in which they become
familiar with ratios and rates and identify the ratio/rate used in a certain
situation or use a ratio/rate to solve a given problem. Students may be given
a ratio relationship between 2 items and asked to find how many of each item
if they are given the other quantity. Related benchmarks will use scale
factors for perimeter (triple side lengths, perimeter tripled), area (triple
side lengths, area 3 x 3 = 9 times as much), and volume (triple side lengths,
volume 3 x 3 x 3 = 27 times as much). |
A A. 65 miles Answer C
The
box indicates that the picture shown is in a 1:16 ratio. What is the actual
diameter of the flying disc? A.
10 inches Answer
B |
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|
Benchmark 4 |
N.MR.07.06 Understand
the concept of square root and cube root, and estimate using calculators. |
Students should engage in
activities such as computing square and cube roots with calculators or
finding square or cube roots of perfect squares and cubes. Students should be able to
estimate square roots of numbers that are not perfect squares without using
the calculator. |
Estimate the answer to each of the following. Then use calculators to find the answer. Describe any surprises or similarities you notice. [NOTE: The square root of 25 and 251/2 give the same answer. Students may be surprised that 56 is greater than 65.]
|
||||||||||||
|
Benchmark 5 |
N.FL.07.02 Solve
problems involving derived quantities. N.FL.07.03 Calculate
rates of change including speed. N.FL.07.05 Solve simple
proportion problems using such methods as unit rate, scaling, finding
equivalent fractions, and solving the proportion equation a/b = c/d; know how
to see patterns about proportional situations in tables. A.PA.07.04 For directly
proportional or linear situations, solve applied problems using graphs and
equations, e.g., the heights and volume of a container with uniform
cross-section, height of water in a tank being filled at a constant rate,
degrees Celsius and degrees Fahrenheit, distance and time under constant
speed. |
Students should engage in activities in which they
recognize number relationships including equality, inequality, inverses,
factor, multiples. Students will be asked to compare
numbers to each other using differences, ratios, rates, etc. Expect applied
problem solving questions requiring more than one step; read carefully. |
Ann swam 54 laps in 45
minutes. If she continues at this rate, how many laps would you expect her to
complete in 1 hour? A. 36 Answer C [NOTE: Ann swam 18 laps in 15 minutes, four 15-minute intervals in one hour, or 4•18 = 72].
Answer B |
inches on
the map represent? 
Linden Community Schools
Content Standard 1: Operations and their Properties- Students
understand and use various types of operations (e.g., addition, subtraction,
multiplication, division) to solve problems.
Grade Level: 7th Grade
|
Benchmark |
Performance Description |
Recommended Activities |
Recommended Assessments |
|
Benchmark 2 |
N.FL.07.08 Add,
subtract, multiply and divide negative rational numbers. N.FL.07.09 Estimate
results of computations with rational numbers. |
Students should engage in activities in which they
evaluate rather than compute algebraic expressions. The section, “explain
what they are doing and how they know which operations to perform in a given
situation” should be tested using constructed-response items. The types of
problems asked in this benchmark will not be 1-step problems. For example,
instead of just calculating how many pounds are needed of a particular item,
a cost per pound and limiting factors for how much money can be spent might
be part of a problem. Fractions, decimals, integers, negative rational
numbers, and expressions will be used. Asking for approximate answers or
asking what estimation strategies would be mathematically correct
to use in a given situation may be used to test estimation. Students should
read the problems very carefully to be sure they have answered the question
being asked. |
Given both withdrawals and
deposits, students should be able to balance an account. Students should be able to place
a variety of rational numbers on a number line. (e.g. -1/2, -2/3, -.4, 0, 1,
etc) |
|
Benchmark 3 |
A.PA.07.11 Understand
and use basic properties of real numbers: additive and multiplicative
identities, additive and multiplicative inverses, commutativity,
associativity, and the distributive property of
multiplication over addition. |
Students should engage in
activities in which they make a drawing or diagram that illustrates different
properties such as associative, commutative, and distributive. For example,
students may be given 4 different expressions and asked to select the one
that illustrates the commutative property. They may be given a situation
using a property and asked to match the expression that will model the
situation. |
Use a number line or an area model to demonstrate the associative and commutative properties for addition or multiplication with rational numbers and integers. Explore
why subtraction and division are not commutative nor
associative. |
|
Benchmark 4 |
A.RP.07.02 Represent
directly proportional and linear relationships using verbal descriptions,
tables, graphs, and formulas, and translate among these representations. A.PA.07.05 Understand
and use directly proportional relationships of the form y = mx, and distinguish from linear relationships of the form
y = mx + b, b non-zero; understand that in a
directly proportional relationship between two quantities one quantity is a
constant multiple of the other quantity. A.PA.07.07 Represent
linear functions in the form y = x + b, y = mx, and
y = mx + b, and graph, interpreting slope and
y-intercept. A.PA.07.09 Recognize
inversely proportional relationships in contextual situations; know that
quantities are inversely proportional if their product is constant, e.g., the
length and width of a rectangle with fixed area, and that an inversely
proportional relationship is of the form y = k/x where k is some non-zero
number. |
Students should engage in
activities such as graphing equations and data from tables. They should be able to identify the slope,
y-intercept, and whether it is a linear relationship from the equation. Students should be able to
derive an equation from a graph or a table. Students should be able to
interpret changes in equations and how they change the corresponding graphs. Students should be able to
recognize and graph equations that are inversely proportional. |
Using a graphing calculator,
have students interpret the changes in graphs of different equations. (e.g. changing the
y-intercept makes the graph move up and down.) |
10 ÷ 8, 10 -
(5 - 3) Content Standard 2: Algebraic
and Analytic Thinking- Students
analyze problems to determine an appropriate process for solution, and use
algebraic notations to model or represent problems.
Grade Level: 7th Grade
|
Benchmark |
Performance Description |
Recommended Activities |
Recommended Assessments |
|
Benchmark 1 |
A.FO.07.12 Add,
subtract, and multiply simple algebraic expressions of the first degree,
e.g., (92x + 8y) – 5x + y, or – 2x (5x – 4), and justify using properties of
real numbers. |
Given an algebraic expression, write a situation that it models. Given a real-world mathematical situation, write it as an expression, equation or inequality and solve, if possible. Solve the inequality 3x - 4 > 22 by adding 4 to each side, then dividing each side by three. You get x > 6. You may wish to have students show answer on a number line. |
Create
a real life-situation that could be represented by 15x + 10. |
|
Benchmark 3 |
A.FO.07.08 Know
that the solution to a linear equation corresponds to the point at which its
graph crosses the x-axis. A.FO.07.13 From
applied situations, generate and solve linear equations of the form ax + b =
c and ax + b = cx + d, and interpret solutions. |
Use geometric representations, including graphs in the Cartesian plane, to model solutions of linear equations in two variables. Use graphing calculators to find solutions to linear equations. |
Given
the equation y = x - 1, find the value of x when y
= 4. Solve 4 = x - 1. y = x -1
|
|
Benchmark 4 |
A.PA.07.04 For
directly proportional or linear situations, solve applied problems using
graphs and equations, e.g., the heights and volume of a container with
uniform cross-section, height of water in a tank being filled at a constant
rate, degrees Celsius and degrees Fahrenheit, distance and time under
constant speed. A.PA.07.07 Represent
linear functions in the form y = x + b, y = mx, and
y = mx + b, and graph, interpreting slope and
y-intercept. |
Students should engage in
activities in which they determine whether decimal or fractional answers are
appropriate and whether to round up or down, and whether an over- or
under-estimate is appropriate. A real-world situation for a linear function
will be given. Students could be asked which expression or equation would
help them solve the problem given. Relationships such as distance = (rate)
(time), ratios, and scale factors for perimeter are some of the types of
linear relationships that will be explored. |
When given a graph, table, or equation of a linear function, students identify the x-value when the y-value is given (e.g., from a temperature conversion chart from Celsius to Fahrenheit degrees, find the temperature after the effect of the wind chill factor is applied). In
A. k
• p = 2.2 Answer C [B, C, and D are correct
relationships, but when you are given the amount of kilograms and want to
find the number of pounds, C will give you the answer directly without any
additional changing of the equation.] |
|
Benchmark 5 |
A.PA.07.04 For
directly proportional or linear situations, solve applied problems using
graphs and equations, e.g., the heights and volume of a container with
uniform cross-section, height of water in a tank being filled at a constant
rate, degrees Celsius and degrees Fahrenheit, distance and time under
constant speed. |
