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MIFFLIN COUNTY SCHOOL DISTRICT
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MCSD Mathematics
Curriculum
6th Grade
Planned Instruction
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| Title of Planned Instruction:
Mathematics for Grade 6 Subject Area: Mathematics
Grade Level: Grade 6
Prerequisites: Grade 5 Mathematics
Course Description: This course strengthens and stretches
previously established work with decimals, fractions,
probability, statistics, geometry, percents, and problem
solving. Simple algebraic skills and concepts are stressed which
prepare students for more abstract thought. Grade 6 mathematics
provides students with daily opportunities to develop,
experience, and apply math concepts and skills in order to
become confident problem solvers in their world.
Required Time: 180 days
Major Text(s) and Resources: |
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Mathematics: Applications and Connections
(Course 1),
Copyright 1995 by Glencoe/McGraw-Hill |
| Names of District Subject Area
Curriculum Writing Committee: |
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Beth E. Aumiller -- Lewistown Middle School
Tina K. Goss -- Indian Valley Middle School
Paul J. Maidens -- Strodes Mills Middle School
Vicki V. Shepherd -- Indian Valley Middle School
Christina A. Short -- Lewistown Middle School |
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Date of Board Approval: July 24, 2003 |
| Major Topics
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- Decimals
- Fractions and Mixed Numbers
- Percents
- Estimating
- Applications
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- Integers and Solving One Step Equations
- Time
- Probability
- Statistics
- Geometry (angles, area, perimeter)
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Course Objectives and Performance Indicators
Strand: 2.1
Standard: Numbers, Number Systems and Relationships
Grade: 6/ Mathematics
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.1.6A |
Represent and explain relationships among decimals,
fractions, and percents and determine appropriate form to use to
solve problems. |
Write decimals through ten-thousandths.
Estimate sums, differences, products, and
quotients using the rounding technique.
Estimate sums and differences using the front-
end technique.
Find divisibility patterns.
Change between mixed numbers and improper
fractions.
Convert between decimals, fractions and
percents.
Pick the appropriate form of a number to use
when solving problems. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.1.6B |
Simplify numerical expressions including ones that contain
exponents and use the order of operations when required. |
Simplify fractions.
Simplify expressions using order of operations.
Simplify expressions involving powers.
Apply distributive property to simplify
expressions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
- Timed tests
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| 2.1.6C |
Compare and order fractions, decimals, and integers. |
Round decimals and fractions.
Use a number line to compare (and order)
fractions, decimals, or integers.
Compare (and order) decimals and integers using
place value.
Compare (and order) fractions using common
denominators, cross products or converting into decimals.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.1.6D |
Apply ratio and proportion to mathematical situations. |
Use appropriate ratios and proportions to solve
problems.
Solve proportions.
Use scale to find dimensions for a drawing or
the actual dimensions.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.1.6E |
Classify numbers including prime, composite, factors, and
multiples. |
Identify prime numbers and explain why the
number is prime.
Identify composite numbers and explain why the
number is composite.
Write a composite number as a product of prime
numbers.
Find factors for numbers and compare common
ones.
Find greatest common factor.
Use prime factorization to find greatest common
factor.
Find multiples for numbers and compare common
ones.
Find least common multiple.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.1.6F |
Model and solve real life situations
using one step equations. |
Establish a simple mathematical
equation that represents a real life situation and use it to
find possible solutions to the problem. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.1.6G |
Use the inverse relationships between addition, subtraction,
multiplication, and division to determine unknown quantities in
equations and simple problems. |
Solve equations and problems that contain whole
numbers, fractions, mixed numbers, or decimals by undoing
the operation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
- Timed tests
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Strand: 2.2
Standard: Computation and Estimation
Grade: 6/ Mathematics
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.2.6A |
Calculate the value of numerical expressions including the
use of order of operations (* or /, + or -). |
Simplify expressions (or evaluate ones that
contain variables) using the order of operations.
Explain how an expression was simplified. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.6B |
Describe and calculate expressions that involve operations
with decimals, fractions, and mixed numbers.\
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Explain algorithms for operations with
decimals, fractions, or mixed numbers. Add, subtract, multiply, and divide decimals,
fractions, and mixed numbers.
Use divisibility patterns to aid in division.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
- Timed test
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| 2.2.6D |
Define percent and estimate solutions to percent problems. |
Define percent.
Solve percent problems by estimating the answer
using appropriate techniques.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.6E |
Determine the appropriateness of overestimating or
underestimating in computation. |
Use estimation and rounding skills to determine
reasonable answers.
Explain why an answer should be either an overestimate or
underestimate based on the problem. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.6F |
Identify the difference between exact value and approximation
and determine which is appropriate for a given situation. |
Solve problems that require exact answers and
explain why exact answers are required.
Solve problems that require estimated or
rounded answers and explain why those types of answers are
required.
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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: 6/Mathematics
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.3.6B |
Add and subtract measures of time. |
Using an analog clock, add and subtract
measures of time.
Calculate elapsed time. |
Observation
Evaluate written work
Performance assessments
Tests, quizzes
Problem solving journal/activity
Evaluate oral response
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| 2.3.6C1 |
Classify angles as acute, obtuse, right, or straight. |
Discuss, identify, and classify all types of
angles. |
Observation
Evaluate written work
Performance assessments
Tests, quizzes
Problem solving journal/activity
Evaluate oral response
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| 2.3.6C2 |
Estimate the measure of an angle (in standard position) in
degrees less than or equal to 180 degrees. |
Estimate angle measure. |
Observation
Evaluate written work
Performance assessments
Tests, quizzes
Problem solving journal/activity
Evaluate oral response
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| 2.3.6C3 |
Measure angles using tools of geometry (compass, protractor) |
Use the tools of geometry to measure angles and
line segments.
· Use the tools of geometry to create congruent
shapes, and bisect angles or line segments.
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Observation
· Evaluate written work
· Performance assessments
· Tests, quizzes
· Problem solving journal/activity
· Evaluate oral response
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| 2.3.6D1 |
Estimate linear distances. |
Estimate linear distances using customary and
metric units for length. |
Observation
· Evaluate written work
· Performance assessments
· Tests, quizzes
· Problem solving journal/activity
· Evaluate oral response
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| 2.3.6D2 |
Solve problems involving linear measurements. |
Solve perimeter and area problems using
customary and metric units of measure. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.3.6D3 |
Label answers with appropriate linear and square units. |
Solve area, perimeter, and volume problems
making sure to use the correct units with the answers. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.3.6D4 |
Estimate, use, and describe measures of circles
(circumference, radius, and diameter). |
Calculate the circumference of a circle using
the radius or diameter and pi.
Determine the radius of a circle if given the
diameter.
Determine the diameter of a circle if given the
radius. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.3.6F |
Solve problems involving scale drawings. |
Find the area of a surface using customary and
metric units of measure.
Find actual and scale measurements using the
scale for a map or a diagram.
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Observation
Evaluate written work
Performance assessments
Tests, quizzes
Problem solving journal/activity
Evaluate oral response
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| 2.3.6G |
Use scale models. |
Find the area of a complex shape by solving
simpler problems and using customary and metric units of
measure. |
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: 6/Mathematics
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.4.6A |
Make conjectures based on logical reasoning and test
conjectures by using counter-examples. |
Estimate, predict, solve problems, and use
logical reasoning with whole numbers, fractions, mixed
numbers, and decimals. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.6B |
Combine numeric relationships to arrive at a conclusion. |
Develop story problems which represent learned
concepts. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.6C |
Use if…then arguments to construct simple, valid arguments. |
Estimate solutions to problems.
Predict possible outcomes using given
information.
Check problems using the four step plan for
problem solving. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.6D |
Construct, use, and explain algorithmic procedures for
computing and estimating with whole numbers, fractions, mixed
numbers, and decimals. |
Solve problems using order of operations.
Solve problems using inverse operations.
Solve problems by adding, subtracting,
multiplying, and dividing decimals, fractions, and mixed
numbers.
Explain algorithms used in computing and
estimating. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
- Timed test
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| 2.4.6F |
Use measurements and statistics to quantify situations. |
Calculate elapsed time.
Calculate mean, median, and mode.
Use standard and metric measurement units in
the appropriate 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: 6/Mathematics
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.5.6A |
Invent, select, use, and justify the appropriate methods,
materials and strategies to solve problems. |
Utilize the following methods to solve problems
(and explain your choice): guess and check, making
predictions, picking a formula, determining a method of
computation, make a list, eliminate possibilities, and draw
a diagram.
Solve problems by classifying information, and
eliminating possibilities. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.5.6B |
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. |
Analyze the results of problems that contained
the following:
- variables and expressions (solving equations)
- line graphs, bar graphs, circle graphs, and making
a table
- formulas for area and perimeter
- range/scale by answering questions about the problems.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.5.6C |
Justify strategies and defend approaches used and conclusions
reached. |
Explain why a particular strategy was chosen to
solve a problem.
Apply knowledge of misleading statistics,
making predictions, problem solving, and decision making to
defend solutions to problems. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.5.6D |
Determine pertinent information in problem situations and
whether any further information is needed for solution. |
Solve problems that contain too much
information.
Solve problems that need more 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: 2.6
Standard: Statistics and Data Analysis
Grade: 6/Mathematics
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.6.6A |
Given a set of data, calculate mean, median, mode, and range. |
Calculate mean, median, mode, range, scale, and
interval. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.6B |
Recognize when statistics and graphs are misleading. |
Interpret information presented in statistics,
circle graphs, bar graphs, and line graphs. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.6.6D |
Carry out a sampling procedure. |
Survey a population to collect data.
Construct a frequency table.
Calculate range, scale, mean, median, and mode.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.6.6F |
Use a calculator to compute with decimals and fractions in
certain problem solving situations. |
Correctly use a
calculator to compute with fraction and decimal data. |
- 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: 6/Mathematics |
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.7.6A |
Find all possible combinations and arrangements involving a
limited number of variables. |
Solve problems using
patterns and making a list. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.7.6B |
Present the results of an experiment using visual
representations. |
Present results by
constructing tables, line graphs, bar graphs, and circle graphs. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.7.6C |
Analyze predictions. |
Use understanding of
guess and check, misleading statistics and graphs to analyze and
conclude when given a problem situation. |
- 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: 6/Mathematics
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.8.6C |
Interpret expressions, equations, or, inequalities that model
problem situations. |
Solve problems with variable expressions and equations.
Evaluate order of operation problems (involving
variables).
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.6E |
Use inverse operations to solve one-step equations, explain
the solution, and check the solution for accuracy. |
Solve equations containing whole numbers,
decimals, and fractions by undoing the operation.
Explain equation solving process.
Check potential solutions for accuracy.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
- Timed tests
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Strand: 2.11
Standard: Concepts of Calculus
Grade: 6/Mathematics |
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Grade Level Objectives |
Performance Indicators |
Assessment Options |
| 2.11.6C |
Continue a pattern of numbers or objects that could be
extended infinitely. |
Identify and continue
a number pattern or sequence. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluation of oral response
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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
- · Notebooks
- · Study guides
- · Computer technology
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| Grades 6-8 |
| [ Planned Instruction ] |
[ Scope/Sequence ] |
[ Framework for
Assessment Tasks ] |
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