|
MCSD Mathematics
Curriculum
7th Grade
Planned Instruction
|
| Title of Planned Instruction:
Mathematics for Grade 7 Subject Area: Mathematics
Grade Level: Grade 7
Prerequisites: Grade 6 Mathematics
Course Description: This course continues the student’s
preparation for understanding the world according to
mathematics. Decimals, percents, and their applications should
be strengths for successful students of this course. Algebraic
skills and concepts are intertwined with the geometry,
probability, and statistical problems that a student faces in
this course. Opportunities presented in this course provide the
students with daily challenges that should enrich their lives.
Required Time: 180 days
Major Text(s) and Resources: |
| |
Mathematics: Applications and Connections
(Course 2),
Copyright 1995 by Glencoe/McGraw-Hill |
| Names of District Subject Area
Curriculum Writing Committee: |
| |
Diane K. Bray-- Lewistown Middle School
Lewis W. Brill -- Strodes Mills Middle School
Suzanne M. Boyer -- Strodes Mills Middle School
Diane L. Griffith -- Indian Valley Middle School
Gregory L. Hetrick -- Lewistown Middle School
Judy A. Waddell -- Indian Valley Middle School |
|
Date of Board Approval: July 24, 2003 |
| Major Topics |
|
- 1 Integers and rational numbers
- 2 Statistics
- 3 Percents
- 4 Probability
|
- 5 Algebra
- 6 Graphing
- 7 Geometry
- 8 Applications
|
| Course Objectives
and Performance Indicators Strand: 2.1
Standard: Numbers, Number Systems and Relationships
Grade: 7/ Mathematics |
| |
Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.1.7A |
Represent and use
numbers in equivalent forms (integers, fractions to repeating
decimals, scientific notation, percents, and perfect squares). |
1 Represent integers
as points on a number line. 2 Write an integer for a
situation (e.g., profit, loss).
3 Convert a fraction to its repeating decimal.
4 Convert between standard and scientific notation.
5 Represent percent as a fraction or decimal.
6 Represent a perfect square in exponent and standard form. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.1.7B
|
Simplify numerical
expressions containing grouping symbols. |
1 Evaluate numerical
expressions using order of operations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.1.7C
|
Order and compare
integers. Order and compare positive rational numbers. |
1 Write a math
sentence with integers using <, >, or = symbols. 2 Put
integers in order from least to greatest.
3 Put decimals in order from least to greatest.
4 Write a mathematical sentence using <, >, or = with
decimals.
5 Compare two fractions by common denominator method. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.1.7D |
Apply ratio and
proportion to mathematical problem situations involving distance,
rate, and time. |
1 Express two
measurements with different units of measure as a rate. 2
Set up and solve a proportion given a problem situation involving
distance, rate, and/or time.
|
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.1.7F |
Use the number line
model to demonstrate integers and their applications. |
1 Graph integers on a
number line. 2 Use the number line to picture loss or
gain. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.1.7G |
Use addition,
subtraction, multiplication, and division properties of equality
to determine unknown quantities in equations involving positive
rational numbers. |
1 Solve simple
equations using inverse operations. 2 Solve equations
involving square roots (e.g., using thee Pythagorean Theorem to
find missing sides of a right triangle). |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
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Strand: 2.2
Standard: Computation and Estimation
Grade: 7/ Mathematics |
| |
Grade Level
Objectives |
Performance
Indicators |
Assessment
Options |
| 2.2.7A |
Evaluate numerical and simple
algebraic expressions involving parentheses and exponents. |
1 Use proper symbols for mathematical operations.
2 Use the order of operations to simplify
expressions (use of a memory aid for the order of operations is
encouraged).
3 Recognize the advantages and disadvantages
of using calculators to evaluate numerical expressions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.2.7B |
Add, subtract, multiply and divide
rational numbers. |
1 Add, subtract, multiply, and
divide all forms of rational numbers. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.2.7C |
Estimate the value of irrational
square roots. |
1 Estimate the value to the
desired place for non-perfect square roots. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.2.7D |
Estimate amount of discounts using
percents. |
1 Estimate the amount of discount
for percent discounts by converting them to common fractions
before calculating. 2 Use rounding techniques on the cost
and/or percent so that mental calculations can be used to find the
amount of discount. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.2.7E |
Determine the appropriateness of
overestimating or underestimating in computation. |
1 Identify specific situations
where overestimating or underestimating is appropriate. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.2.8F |
Identify the difference between
exact value and approximation and determine which is appropriate
for a given situation. |
1 Use correct symbols to identify
exact or approximate value. 2 Determine if exact or
approximate value is suitable for a problem situation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
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Strand: 2.3
Standard: Measurement and Estimation
Grade: 7/Mathematics |
| |
Grade Level
Objectives |
Performance
Indicators |
Assessment
Options |
| 2.3.7A |
Develop formulas and procedures
for determining area and perimeter. |
1 Use appropriate formulas to find
the area and perimeter/circumference of polygons and circles. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.3.7B |
Solve rate problems. |
1 When given the rate and time,
find the distance. 2 When given the principal, rate, and,
time; find the simple interest. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.3.7C |
Use a protractor to measure angles
less than 180 degrees. |
1 Measure an angle to the nearest
degree using a protractor.
2 Estimate the measures of an angle (non-standard position)
in degrees less than or equal to 180 degrees.
|
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.3.7D1 |
Estimate areas. |
1 Estimate the areas of polygons
and circles by using estimated dimensions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.3.7D2 |
Solve problems involving areas and
perimeters. |
1 Solve problems involving areas
and perimeters. 2 List the steps used to find the
perimeter or area of a polygon.
3 List the steps used to find the circumference or area of a
circle. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.3.7D3 |
Explain the difference between
linear and square units. |
1 Explain the difference between
linear and square units. 2 Correctly use linear or square
units in a problem situation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.3.7F |
Set up and solve problems
involving scale drawings. |
1 Set up and solve problems
involving scale drawings. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.3.7G |
Create and use scale models. |
1 Develop a scale model for a
given situation. 2 Use the scale from a model to
calculate actual dimensions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
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Strand: 2.4
Standard: Mathematical Reasoning and Connections
Grade: 7/Mathematics |
| |
Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.4.7A |
Make conjectures based
on logical reasoning and test conjectures by using
counter-examples. |
1 Make conjectures
about prime and composite numbers based on logical reasoning and
test the conjectures. 2 Make conjectures and test by
using counter-examples. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.4.7C |
Use if…then arguments
to construct simple, valid arguments. |
1 Use if…then
statements to construct an argument for geometric situations
(e.g., if a rectangle has four congruent sides, then it is a
square). |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.4.7D |
Construct, use, and
explain algorithmic procedures for computing and estimating with
integers. |
1 Explain and use the
procedures for adding, subtracting, multiplying, and dividing
integers. 2 Explain and use the procedures for estimating
sums, differences, products, and quotients of rational numbers. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.4.7F |
Use measurements and
statistics to quantify situations. |
1 Use measurements and
statistics to describe real life situations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
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Strand: 2.5
Standard: Mathematical Problem Solving and Communication
Grade: 7/Mathematics |
| |
Grade Level
Objectives |
Performance
Indicators |
Assessment
Options |
| 2.5.7A |
Invent, select, use, and justify
the appropriate methods, materials and strategies to solve
problems. |
1 Solve problems by selecting an
appropriate strategy from the following list: trial and error,
working backwards, finding patterns, making drawings, or making a
list or chart. 2 Solve problems by using different
methods of computation (pencil and paper, calculator, mental math,
and estimation). |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.5.7B |
Verify and interpret results using
precise mathematical language, notation and representations,
including numerical tables and equations, simple algebraic
equations and formulas, charts, graphs, and diagrams. |
1 Provide a representation (table,
equation, formula, chart, graph, or diagram) that verifies the
solution to a problem situation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.5.7C |
Justify strategies and defend
approaches used and conclusions reached. |
1 Determine if an answer is
reasonable. 2 Explain the steps used in solving a problem
and why they were chosen. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.5.7D |
Determine pertinent information in
problem situations and whether any further information is needed
for solution. |
1 Select and use the information
necessary to solve a problem. 2 Indicate which
information is needed to solve a problem. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
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Strand: 2.6
Standard: Statistics and Data Analysis
Grade: 7/Mathematics |
| |
Grade Level
Objectives |
Performance
Indicators |
Assessment
Options |
| 2.6.7A |
Compare and contrast different
plots of data using values of mean, median, mode, and range. |
1 Calculate mean, median, mode,
and range from a line plot, stem-and-leaf plot, and a frequency
table. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.6.7B |
Recognize when statistics and
graphs are misleading. |
1 Recognize misleading statistics.
2 Recognize how graphs are misleading.
3 Explain how a statistic is misleading.
4 Explain how a graph is misleading. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.6.7 D |
Design and carry out a random
sampling procedure. |
1 Design a random sampling
procedure by writing a question, taking a survey, and displaying
data. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.6.7E |
Analyze and display data in
stem-and-leaf plots. |
1 Make a stem-and-leaf plot from a
set of data. 2 Compare and contrast the mean, median,
mode, and range from the set of data shown in a stem-and-leaf
plot. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.6.7 F |
Use a scientific calculator to
compute with decimals and fractions in certain problem solving
situations. |
1 Use a calculator to compute the
mean and median for a set of data from a problem solving
situation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
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Strand: 2.7
Standard: Probability and Predictions
Grade: 7/Mathematics |
| |
Grade Level
Objectives |
Performance
Indicators |
Assessment
Options |
| 2.7.7. B |
Present the results of an
experiment using visual representations. |
1 Use graphs and tables to
represent the results of an experiment. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.7.7C |
Analyze predictions. |
1 Justify predictions by giving
reasons to support your conclusions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.7.7 D |
Compare and contrast results from
observations and mathematical models. |
1 Determine the probability of a
simple event as a fraction in simplest form. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.7.7E |
Make valid inferences, predictions
and arguments based on probability. |
1 Select the situation that has
the highest probability of a given event. 2 Make a valid
inference based on probability.
3 Given information about a first event, determine the
probability of a specified second event. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
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Strand: 2.8
Standard: Algebra and Functions
Grade: 7/Mathematics |
| |
Grade Level
Objectives |
Performance
Indicators |
Assessment
Options |
| 2.8.7A |
Apply simple algebraic patterns to
basic number theory. |
1 Recognize and extend a pattern
for a sequence. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.8.7C |
Create and interpret expressions
and equations that model problem situations. |
1 Find an expression or equation
that represents a given situation. 2 Use an expression or
equation that represents a given situation to answer questions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.8.7E |
Use properties of equality to
solve one- and two-step equations, explain the solutions, and
check the solutions for accuracy. |
1 Solve one- and two-step
equations by "undoing" the operation(s) done to the variable.
2 Explain how an equation was solved.
3 Show the check of accuracy for the solution of an
equation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.8.7H |
Graph a linear function from a
table. |
1 Using the ordered pairs from a
table, graph a linear function. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.8.7J |
Show that an equality relationship
between two quantities remains the same as long as the same change
is made to both quantities. |
1 Add (subtract, multiply, or
divide) the same number to both sides of an arithmetic equation to
show that it remains balanced. 2 Explain the property of
equality in everyday language using diagrams or manipulatives. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
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Strand: 2.9
Standard: Geometry
Grade: 7/Mathematics |
| |
Grade Level
Objectives |
Performance
Indicators |
Assessment
Options |
| 2.9.7A |
Construct figures incorporating
perpendicular and parallel lines, the perpendicular bisector of a
line segment, and an angle bisector using a compass and
straightedge. |
1 Construct a line perpendicular
to a given line. 2 Construct a line parallel to a given
line.
3 Construct the perpendicular bisector of a given line.
4 Construct the angle bisector for a given angle. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.9.7B |
Draw, label, measure, and list the
properties of complimentary, supplementary, and vertical angles. |
1 Measure an angle with a
protractor. 2 Define and recognize complimentary,
supplementary, and vertical angles.
3 Correctly label angles. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.9.7C |
Classify familiar polygons as
regular or irregular up to a decagon. |
1 Determine if a polygon is
regular or irregular based on its’ given characteristics. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.9.7D |
Identify, name, draw, and list all
properties of polygons, quadrilaterals, triangles, and circles. |
1 Identify and name squares,
parallelograms, quadrilaterals, trapezoids, polygons, rectangles,
rhombi, circles, and triangles. 2 List all of the
properties for the above named shapes. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.9.7G |
Approximate the value of pi
through experimentation. |
1 Measure the circumference and
diameter for various circular objects, and use the ratio of those
measurements to discover an approximation of pi. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.9.7J |
Analyze geometric patterns and
develop descriptions of the patterns. |
1 Recognize and describe geometric
patterns when given a sequence. 2 Develop a formula to
generalize a geometric pattern (e.g., (n-2)(180) can be used to
find the angle sum for polygons). |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
| 2.9.7K |
Analyze objects to determine
whether they illustrate tessellations, symmetry, congruence,
similarity, and scale. |
1 Recognize any symmetry in an
object. 2 Define congruent and similar with respect to
figures.
3 Tell if a pair of figures are congruent, similar, or
neither.
4 Identify the base figure in a tessellation.
5 Use the scale from a figure to answer questions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
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Strand: 2.11
Standard: Concepts of Calculus
Grade: 7/Mathematics |
| |
Grade Level
Objectives |
Performance
Indicators |
Assessment
Options |
| 2.11.7B |
Describe the concept of unit rate
and ratio in the context of rate of change. |
1 Create a unit rate or a ratio
from the information given in a problem. 2 Solve
proportions that involve unit rate and other ratio problems. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
District Recommended Instructional Approaches For
the Course
To Drive Teacher’s Instructional Activities
- Whole group instruction
- Small group instruction
- Projects
- Class discussion
- Peer evaluation
- Teacher and peer conferencing
- Oral presentations
- Individual instruction
- Research
- Dramatization
- Role playing
- Independent reading
- Read aloud
- Directed reading-thinking activities
- Modeling process
- Games
- Self-reflection
- Self-evaluation
- Independent study
- Guest speaker
- Guest reading
- Writing activities
- Thematic units
- Study guides
- Notebooks
- Computer technology
| Grades 6-8 |
| [ Planned Instruction ] |
[ Scope/Sequence ] |
[ Framework for
Assessment Tasks ] |
|
6
7
8 |
6
7
8
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6
7
8
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