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MIFFLIN COUNTY SCHOOL DISTRICT
Grade 8 Mathematics Curriculum
8th Grade
Planned Instruction
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Major Topics
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- Rational and Irrational Numbers
- Probability
- Percents
- Statistics
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- Algebra
- Slope and Graphing
- Geometry/Trigonometry
- Applications
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Course Objectives and Performance Indicators Strand: 2.1
Standard: Numbers, Number Systems and Relationships
Grade: 8/ Mathematics
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.1.8A |
Represent and use numbers in
equivalent forms (square roots and repeating decimals to
fractions). |
Change between repeating decimals and
fractions. Change between fractions, decimals, and percents.
Estimate square roots to the nearest tenth.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.1.8B |
Simplify numerical expressions
involving scientific notation. |
Change numbers between standard form
and scientific notation. Multiply and divide numbers in
scientific notation.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.1.8C1 |
Distinguish between rational and
irrational numbers. |
Classify a number as rational or
irrational. |
- Observation
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- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.1.8C2 |
Order and compare all rational
numbers. |
List rational numbers from greatest
to least and from least to greatest. Compare rational numbers by
changing to all fractions with common denominators.
Compare rational numbers as decimals.
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- Observation
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- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.2
Standard: Computation and Estimation
Grade: 8/ Mathematics |
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.2.8B |
Add, subtract, multiply and divide rational
numbers. |
Add, subtract, multiply, and divide integers,
decimal fractions, fractions, and mixed numbers. Calculate with
percents.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.8D |
Estimate amount of tips and discounts using
ratios and proportions. |
Estimate the amount of tip given to a service
person using ratios, proportions, and percents. Estimate the amount of
discounts in a sale situation using ratios, proportions, and percents.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.8E |
Determine the appropriateness of
overestimating or underestimating in computation. |
Determine when to overestimate computations
in real life problem situations. Determine when to underestimate
computations in real life problem situations.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.8F |
Identify the difference between exact value
and approximation and determine which is appropriate for a given
situation. |
In a given situation, decide if an exact
value answer is needed. In a given situation, decide if an approximate
value answer is needed.
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- 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: 8/Mathematics
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.3.8A |
Develop formulas and procedures for
determining volume and surface area of rectangular solids. |
Develop and use formulas to find volumes of rectangular solids.
Develop and use formulas to find surface areas of rectangular solids.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.3.8D1 |
Estimate volumes. |
Estimate the volume of a three-dimensional
solid. |
- Observation
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- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.3.8D2 |
Solve problems involving volume. |
Solve problem situations involving volume by
using the appropriate formulas for the given situation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.3.8D3 |
Explain the difference between linear,
square, and cubic units. |
Describe a linear unit and provide an example.
Describe a square unit and provide an example.
Describe a cubic unit and provide an example.
Contrast linear, square, and cubic units.
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- Observation
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- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
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| 2.3.8D4 |
Solve problems involving scale drawings. |
Solve problem situations involving scale
drawings by using ratios and proportions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.3.8E |
Describe how a change in linear dimension of
an object affects its perimeter, area, and volume. |
Describe how an increase in a linear dimension of an object affects its
perimeter, area, or volume.
Describe how a decrease in a linear dimension of an object affects its
perimeter, area, or volume.
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Strand: 2.4
Standard: Mathematical Reasoning and Connections
Grade: 8/Mathematics |
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.4.8A |
Make conjectures based on logical reasoning
and test conjectures by using counter-examples. |
Draw a conclusion based on given information and logical reasoning.
Make conjectures based on a problem.
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- Observation
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- Performance assessments
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| 2.4.8B |
Combine numeric relationships to arrive at a
conclusion. |
Solve multi-step problems involving rational
numbers. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.8C |
Use if…then arguments to construct Simple,
valid arguments. |
Draw a conclusion based on simple data.
Draw a logical conclusion based on simple if/then statements such as
polygon classifications.
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- Observation
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- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.8E |
Distinguish between inductive and deductive
reasoning. |
Form a general rule from many examples.
Given a rule, generate a conclusion for a specific situation.
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- Observation
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- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.8F |
Use measurements and statistics to quantify
situations. |
Use mean, median, and mode to describe a set
of data. |
- 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: 8/Mathematics |
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.5.8A |
Invent, select, use, and justify the
appropriate methods, materials and strategies to solve problems. |
Select and use the appropriate methods and strategies (e.g.,
estimating, guess/check, eliminating possibilities, work backwards, use an
equation, classify information, use a Venn diagram, make a list, find a
pattern, use a formula, draw a diagram, solve a simpler problem, use a
graph, and make a model) and materials (e.g., calculators, rulers,
protractors) to solve problems.
Explain the strategy or method used to solve a problem and why.
Create a strategy to solve problems. |
- Observation
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- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
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| 2.5.8B |
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. |
Use precise mathematical language to discuss mathematical solutions.
Use precise mathematical notation to represent solutions to problems.
Use numerical tables, equations, formulas, charts, graphs, and diagrams
to represent and display solutions or situations.
Interpret numerical tables, charts, graphs, or diagrams.
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- Observation
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- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
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| 2.5.8C |
Justify strategies and defend approaches used
and conclusions reached. |
Explain why and how you solved a problem in
written form (or through an oral presentation). |
- Observation
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- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.5.8D |
Determine pertinent information in problem
situations and whether any further information is needed for solution. |
Given a written problem with too much information, choose the important
information and solve the problem.
Given a written problem with too little information, decide what
further information is needed to solve the problem.
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- Observation
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- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.6
Standard: Statistics and Data Analysis
Grade: 8/Mathematics |
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.6.8A |
Compare and contrast different plots of data
using values of mean, median, mode, quartiles, and range. |
Given a bar graph, line graph, circle graph, table, chart, or stem and
leaf plot, find the median, mean, mode, quartile, and range of the data.
Compare and contrast the mean, median, and mode of a set of data and
explain which one best describes the data.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.8B |
Explain effects of sampling procedures and
missing or incorrect information on reliability. |
Explain how sampling procedures affect reliability.
Explain the difference between a biased and unbiased sample.
Explain how missing or incorrect information affects reliability.
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- Observation
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- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.8C |
Fit a line to the scatter plot of two
quantities and describe any correlation of the variables. |
Construct a scatter plot of two quantities and find a line of best fit.
Determine if there is a positive, negative, or no relationship between
the two quantities given in a scatter plot.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.8D |
Design and carry out a random sampling
procedure. |
Design and carry out a random sampling
procedure by explaining the procedure used and displaying the results in a
chart, table, or graph. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.8E |
Analyze and display data in box-and-whisker
plots. |
Construct a box-and-whisker plot given a set of data.
Analyze a set of data by using its box-and-whisker plot to find the
median, upper and lower quartiles, range, and extreme values.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.8F1 |
Use computer spreadsheets to organize and
analyze data. |
Read and analyze data found on a computer
spreadsheet. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.8F2 |
Learn the functions on a scientific
calculator. |
Use the following function keys found on a
scientific calculator: +, -, x, ÷, powers, and square roots. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.8G |
Determine the validity of the sampling method
described in studies published in local or national newspapers. |
Determine whether the sampling method described in studies published in
local or national newspapers is biased or unbiased.
Determine how bias affects the validity of a published study.
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- 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: 8/Mathematics
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.7.8B |
Present the results of an experiment using
visual representations. |
Show the results of an experiment by making a
bar graph, line graph, frequency table, circle graph, line plot or box-and
–whisker plot. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.7.8C |
Analyze predictions. |
Make predictions from statistics and
determine their validity. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.7.8D |
Compare and contrast results from
observations and mathematical models. |
Compare results from graphs and determine
their similarities and differences. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.7.8E
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Make valid inferences, predictions and
arguments based on probability. |
Make predictions from graphs.
Make predictions from probability information.
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- 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: 8/Mathematics
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.8.8A |
Apply simple algebraic patterns to spatial
relations. |
Discover and generalize simple numerical
patterns. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.8B |
Discover, describe, and generalize patterns
(linear). |
Find simple numerical patterns in problem solving.
Identify an algebraic pattern.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.8C |
Create inequalities that model problem
situations. |
Write an inequality for a problem situation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.8D |
Use concrete objects to model algebraic
concepts. |
Show balance concepts with real-life objects
such as scales or seesaws. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.8E |
Use properties of equality to solve
equations, solve inequalities, explain the solutions, and check the
solutions for accuracy. |
Use equality properties of add, subtract, multiply, and divide to solve
equations and inequalities.
Explain and check solutions for inequalities by using a number line.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.8F |
Solve (and graph) equations and inequalities
using scientific calculators (graphing calculators and computer
spreadsheets, if possible). |
Use a calculator to help solve equations and inequalities.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.8G |
Represent relationships with tables or graphs in the coordinate plane
and verbal or symbolic rules.
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Graph ordered pairs of numbers on the
coordinate plane. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.8H |
Graph a linear function from a rule. |
Graph a line from a given equation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.8I |
Generate a table or graph from a function and
use graphing calculators and computer spreadsheets to graph and analyze
functions. |
Complete a table from a function. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.8J |
Show that an equality relationship between
two quantities remains the same as long as the same change is made to both
quantities. |
Given an expression, identify an equivalent
expression (e.g., use the distributive property). |
- Observation
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- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.9
Standard: Geometry
Grade: 8/Mathematics
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
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2.9.8D
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Identify, name, draw, and list all properties
of three-dimensional solids. |
Identify and name cubes, pyramids, spheres, prisms, and cylinders.
Draw cubes, pyramids, spheres, prisms, and cylinders.
List the properties of cubes, pyramids, spheres, prisms, and cylinders.
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- Observation
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- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.9.8E |
Construct parallel lines, draw a transversal,
and measure and compare angles formed. |
Construct parallel lines and draw a transversal.
Given parallel lines cut by a transversal, measure the angles.
Given parallel lines cut by a transversal, name the angles and identify
the relationships between these angles (e.g., alternate interior.
alternate exterior, corresponding, vertical, and adjacent angles).
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- Observation
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- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.9.8F |
Distinguish between similar and congruent
polygons. |
Identify two similar polygons and explain why they are similar.
Identify two congruent polygons and explain why they are congruent.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.9.8H |
Rotate simple geometric figures to create
transformational figures in three dimensions. |
Recognize a solid from its net and sketch it. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.9.8I |
Generate transformations (using computer
software, if possible). |
Graph translations on a coordinate plane (or
with the use of computer software). |
- Observation
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- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.10
Standard: Trigonometry
Grade: 8/Mathematics |
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.10.8A |
Compute measures of sides and angles using
proportions, the Pythagorean Theorem, and right triangle relationships. |
Use the Pythagorean Theorem to find the
measures of a leg or hypotenuse in a right triangle. Use a proportion to
find the 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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| 2.10.8B |
Solve problems requiring indirect measurement
for lengths of sides of triangles. |
Solve problems involving similar triangles. |
- 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: 8/Mathematics
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.11.8A |
Analyze graphs of related quantities for
minimum and maximum values and justify the findings. |
Given a double bar graph or line plots of
related quantities, find the maximum and minimum values. Explain why a
value is a maximum or minimum. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.11.8B |
Describe the concept of slope in the context
of rate of change. |
Describe the context of slope in terms of
positive and negative relationships. Identify the effect on distance
when time is modified in a distance, rate, and time relationship. |
- Observation
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- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
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District Recommended Instructional Approaches For the
Course
To Drive Teacher’s Instructional Activities
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- 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
- Notebooks
- Study guides
- Computer technology
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| Grades 6-8 |
| [ Planned Instruction ] |
[ Scope/Sequence ] |
[ Framework for
Assessment Tasks ] |
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