LESSON PLAN RUBRIC
Criteria |
Unacceptable (6 or less) |
Acceptable (7-8 points) |
Exemplary (9-10 points) |
Score |
Standards |
Standards are poorly written and/or does not capture the essence of why the lesson should be taught |
Standards are written well and attempts to capture the essence of the lesson and why it should be taught |
Standards concisely capture the essence of the lesson and why it should be taught |
|
Essential Concepts -Vocabulary -Product -Whole vs. DI |
Essential concepts are not provided or well-developed |
Essential concepts are provided and adequately developed |
Essential concepts are provided and well-developed |
|
Pre-Assessment |
Pre-assessment poorly reflects knowledge and skills needed for successful completion of lesson |
Pre-assessment reflects some knowledge and skills needed for successful completion of lesson |
Pre-assessment reflects into students developmental levels and readiness for the lesson |
|
Activator |
Activator is not evidence or poorly attempts at grabbing the students’ attention and/or does not flow into lesson |
Activator attempts to grab the students’ attention and somewhat flows into lesson |
Activator grabs students’ attention, sets the stage, and flows into lesson |
|
SRSD Model -Strategy Development |
Strategy development is sketchy and employs questionable pedagogical techniques for the content and age level |
Strategy development is logical, detailed, and employ appropriate pedagogical techniques for the content and age level |
Strategy development is explicit and systematically developed toward mastery of objectives, using pedagogical best practices for the content and age level |
|
SRSD Model -Think Aloud |
Think aloud is sketchy and employs questionable pedagogical techniques for the content and age level |
Think aloud is logical, detailed, and employ appropriate pedagogical techniques for the content and age level |
Think aloud is explicit and systematically developed toward mastery of objectives, using pedagogical best practices for the content and age level |
|
SRSD Model -Guided Practice |
Guided practice is sketchy and employs questionable pedagogical techniques for the content and age level |
Guided practice is logical, detailed, and employ appropriate pedagogical techniques for the content and age level |
Guided practice is explicit and systematically developed toward mastery of objectives, using pedagogical best practices for the content and age level |
|
SRSD Model -Independent Practice |
Independent practice is sketchy and employs questionable pedagogical techniques for the content and age level |
Independent practice is logical, detailed, and employ appropriate pedagogical techniques for the content and age level |
Independent practice is explicit and systematically developed toward mastery of objectives, using pedagogical best practices for the content and age level |
|
Summarizer/ Assessment |
Assessment is inconsistent with the standards, essential concepts, and lesson procedures |
Assessment closely matches the standards, essential concepts, and lesson procedures |
Assessment exactly matches the standards, essential concepts, and lesson procedures |
|
Total |
/90 |
Lesson Plan
*FROM THE ACTIVATOR TO INDEPENDENT PRACTICE, THE LESSON NEEDS TO BE SCRIPTED*
Content, Process, Product, Affect Planning:
Standards: Students to demonstrate proficiency in reading comprehensions independently Students to demonstrate proficiency in purposes for reading Students to read with sufficient accuracy and fluency to support comprehension more so on fourth grade-level text with purpose and understanding. Students to know and apply grade level phonics and word analysis skills in decoding words when reading comprehensions |
|
Unit: Reading comprehensions |
|
Unit EQ: Proficiency in reading comprehensions independently, and understanding the purposes of the comprehensions |
|
Essential Concepts: Making connections Making inferences Understanding Reading skills |
Differentiated Concepts: Read grade-level comprehension with prose Read with accuracy, and appropriate rate |
Unit Vocabulary: Proficiency Letter-sounds correspondences Syllabication patterns Word morphology |
Differentiated Vocabulary: Prose-reading Accuracy Fluency Reading ability/rate |
Whole Class Product: Grade level texts, and comprehensions to be introduced, and read by all students in the lass |
Differentiated Product: Each student to be allowed a text of their choice that they can read with proficiency, and accuracy |
Process: This lesson plan will start with applying grade level phonics and word analysis skills in decoding words when reading texts and comprehensions |
|
Diagnostic (Pre) Assessment: For the readiness of the class, students will demonstrate their ability to read sentences constructed in the class with sufficient accuracy and proficiency. They will then proceed to read short paragraphs before reading full texts, stories, or comprehensions. |
|
Whole Class Checklist: Students are able to read various or multiple sentences, paragraphs, and texts without difficulties |
Differentiated Checklist: Students are able to read a given sentence, paragraph, and text in prose, with proficiency, and accuracy |
Activator (Context for Learning) All students encounter different reading materials in their academic or home life. Your interest should be drawn to trying to understand what is written in the different materials. This can only be achieved through reading the material, making reading a key process to understanding texts or comprehensions |
|
|
|
Develop Strategy and Self-Regulation: Introduction of Strategy Develop Background Knowledge-I will provide you with a list of sentences, text paragraphs, and full texts or comprehensions for reading Discuss Strategy-We will read the sentences, text paragraphs, and comprehensions together before you read alone Review-Each of you will retreat and read a sentence, text paragraph, or comprehension Practice Memorization-You will internalize these reading sentences and paragraphs to strengthen your reading ability Obtain Commitment-I will collaborate with all students to support self-regulation, but this will be a fading support in identifying abstract nouns. Goal-Read with proficiency, and accuracy multiple texts provided Summarizer-We will identify, and list together comprehensions that are suitable to your grade level before I allow you to read alone to perfect your reading skills |
|
Model-Think Aloud: Think of all sentences, and stories that you have seen and can read Think of the stories as examples of comprehensions that you can practice your reading skills |
|
We Do-Guided Practice (Generalizing): Let us now read together some of the sentences, and comprehensions you have identified together Let us ensure that each one of us can accurately decode the sentences, and comprehensions, while consistently monitoring comprehensions Each one of us should read with sufficient accuracy and fluency to support the comprehension We should also ensure we read the fourth grade-level texts with purpose and understanding We should all also read with proficiency, accuracy, appropriate rate, and expression on successive readings. While reading the comprehensions to understand, we should use context to confirm or self-correct word recognition and understand that rereading is necessary to boost our reading skill I will first read out loud a sentence or paragraph before allowing you to read to know what I expect from you as we read the different texts Example of a sentence to read; · The teacher provides scaffolding support or prompting to help the learner read a whole sentence successfully. |
|
You-Independent Practice: Now it is your turn to read the sentence shown above Ensure you do not stammer, but read with proficiency, and accuracy |
|
Summarizer: Each students will list and read at least one sentence or comprehension to proof sufficient accuracy of at least 80%, and proficiency in reading |
|
Assessment: Through common reading assessments in class, students should demonstrate their ability to read with proficiency and accuracy at a high reading rate grade level sentences, and comprehensions |
|
Affect: By the end of the lesson on reading comprehensions, students will have gained a lot of proficiency in reading comprehensions independently, and proficiency in purposes for reading and understanding the texts |
CARLISLE AREA SCHOOL DISTRICT
Carlisle, PA 17013
Math
Grade 3
Date of Board Approval: August 16, 2007
1
CARLISLE AREA SCHOOL DISTRICT PLANNED INSTRUCTION COVER PAGE
Title of Course: Math______ Subject Area:_Math________ Grade Level: 3________________
Course Length: (Semester/Year): Year Duration: _20-25 minutes Frequency: 5 times per cycle____
Prerequisites: __Not Applicable Credit: Not Applicable Level: Not Applicable
Course Description/Objectives: The district shall provide for attainment of the academic standards per Chapter 4,
Section 4.12. Each student shall demonstrate proficiency in the following area: numbers, number systems and number
relationships; computation and estimation; measurement and estimation; mathematical reasoning and connections,
mathematical problem solving and communication; statistics and data analysis; probability and predictions; algebra and
functions; geometry; trigonometry; and concepts of calculus.
Major Text(s)/Resources:
Harcourt Math 2002
Name of Writing Committee:
Mary Ann Brenneman Mary Kay Durham Denise Eschenmann
Cindy Birdwell Deb Trozzo
2
Strand 2.1 Numbers, Number Systems and Number Relationships Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
A. Count using whole numbers (to 10,000) and by 2’s, 3’s, 5’s, 10’s, 25’s and
100’s.
Count using whole numbers (to 10,000) by: 1’s (e.g., 8987,----,----,8990), 2’s,
3’s, 5’s, 10’s, 25’s, 100’s (all M)
(PSSA).
Teacher made tests and quizzes
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Pennsylvania System of School
Assessment (PSSA) – Grade 3
B. Use whole numbers and fractions to
represent quantities
Use whole numbers to represent quantities. (R)
Use fractions (1/2 (R), 1/3, 1/4, 1/5 (M)) to represent quantities.
Use mixed numbers to represent quantities. (I)
C. Represent equivalent forms of the same
number through the use of concrete
objects, drawings, word names and
symbols.
Represent equivalent forms of the same number (1-10,000) through the use of:
concrete objects (R), drawings (R),
word names (M), symbols. (M)
(PSSA).
C. Represent equivalent forms of the same
number through the use of concrete
objects, drawings, word names and
symbols.
Write several number sentences that represent a given number (1-
10,000).(M)
D. Use drawings, diagrams or models to
show the concept of fraction as part of a
whole.
Use models (geometric shapes) to show fractions as part of a whole: (M)
Identify a fraction of a geometric shape,
Identify a fraction of a set (PSSA).
3
Strand 2.1 Numbers, Number Systems and Number Relationships Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
D. Use drawings, diagrams or models to
show the concept of fraction as part of a
whole.
Use drawings or diagrams to show fractions as part of a whole. (M)
(PSSA)
Identify the numerator and denominator of a fraction. (M)
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Pennsylvania System of School
Assessment (PSSA) – Grade 3
E. Count, compare and make change using
a collection of coins and one-dollar
bills.
Match the name and value of a penny, nickel, dime, and quarter. (R)
Match the name and value of a half- dollar, one-dollar, and five-dollar bill.
(M)
E. Count, compare and make change using
a collection of coins and one-dollar
bills.
Count a collection of coins and one- dollar bills. (M) (PSSA)
Compare collections of coins and one- dollar bills. (M) (PSSA)
Make change up to $5.00. (M) (PSSA)
F. Apply number patterns (even and odd)
and compare values of numbers on the
hundred boards.
Apply number patterns (even and odd). (M) (PSSA)
Compare values of numbers on a hundred chart. (M)
G. Use concrete objects to count, order and
group.
Use concrete objects to count. (R)
Classify groups by the number of items in each group. (R)
4
Strand 2.1 Numbers, Number Systems and Number Relationships Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
H. Demonstrate an understanding of one-
to-one correspondence.
Demonstrate one-to-one correspondence. (R)
Teacher made tests and quizzes
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Curriculum-based assessments
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Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
I. Apply place –value concepts and
numeration to counting, ordering and
grouping.
Apply place-value concepts and numeration to counting, ordering and
grouping to 10,000. (M) (PSSA)
Write numbers in expanded notation to 5 places. (M)
I. Apply place –value concepts and
numeration to counting, ordering and
grouping.
Read and use whole numbers through 10,000. (M) (PSSA)
Apply knowledge of place value to read and write numbers in expanded form
(1000+100+10+1=1111). (M)
J. Estimate, approximate, round or use
exact numbers as appropriate.
Round numbers to the nearest 10 or 100 or 1000 (up to 9000). (PSSA)
K. Describe the inverse relationship between addition and subtraction.
Describe and use the commutative property of addition. (M)
Describe and use the commutative property of multiplication. (M)
5
Strand 2.1 Numbers, Number Systems and Number Relationships Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
K. Describe the inverse relationship between addition and subtraction.
Write fact families. (R)
Demonstrate the inverse relationship between addition and subtraction using
fact families.
Teacher made tests and quizzes
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Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
L. Demonstrate knowledge of basic facts
in four basic operations.
Demonstrate knowledge of basic facts in addition. (R)
Demonstrate knowledge of basic facts in subtraction, multiplication (0-10) and
division (in a reasonable amount of
time). (M) (PSSA)
L. Demonstrate knowledge of basic facts
in four basic operations.
Apply addition strategies of counting on, making ten and adding doubles.
(M)
Apply subtraction strategies of counting up. (M)
L. Demonstrate knowledge of basic facts
in four basic operations.
Add fractions having like denominators with sums less than one. (R)
6
Strand 2.2 Computation and Estimation Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
A. Apply addition and subtraction in
situations involving concrete objects.
Apply addition situations using concrete objects. (R)
Apply subtraction situations using concrete objects. (R)
Teacher made tests and quizzes
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Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
B. Solve single and double-digit addition
and subtraction problems with
regrouping in vertical form.
Add 2-digit numbers with regrouping in vertical form and horizontal form. (R)
(PSSA)
Add 3-digit numbers with regrouping in vertical form and horizontal form. (M)
(PSSA)
B. Solve single and double-digit addition
and subtraction problems with
regrouping in vertical form.
Subtract 2- and 3-digit numbers with regrouping in vertical form and
horizontal form. (M) (PSSA)
Solve addition and subtraction problems that involve zero. (M)
(PSSA)
B. Solve single and double-digit addition
and subtraction problems with
regrouping in vertical form.
Check subtraction with addition. (M)
Explain and use the associative property of addition (e.g., column
addition). (I)
C. Demonstrate the concept of multiplication as repeated addition.
Demonstrate the concept of multiplication using the following
strategies: repeated addition, doubling,
and skip counting. (M) (PSSA)
7
Strand 2.2 Computation and Estimation Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
C. Demonstrate the concept of multiplication as repeated addition.
Demonstrate concept of arrays: Identify, make and describe arrays in
terms of factors and products. (M)
(PSSA), use arrays to write
multiplication sentences. (M),
(continued)
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Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
C. Demonstrate the concept of multiplication as repeated addition.
Recognize that the product of 1 and any number is that number. (M), explain the
zero property. (M)
C. Demonstrate the concept of multiplication as repeated addition.
Multiply using 1-digit multipliers. (M)
Multiply mentally with multiples of 10. (M)
C. Demonstrate the concept of multiplication as repeated addition.
Explain and use the associative property of multiplication. (M)
Solve problems involving multiplication through the 9’s tables
through 9 x 5.
D. Demonstrate the concept of division as
repeated subtraction and as sharing.
Demonstrate the concept of division as repeated subtraction and as sharing.
(M)
Recognize and describe the relationship between multiplication and division
using fact families. (M)
8
Strand 2.2 Computation and Estimation Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
D. Demonstrate the concept of division as
repeated subtraction and as sharing.
Solve division problems with remainders. (M)
Teacher made tests and quizzes
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Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
E. Use estimation skills to arrive at
conclusions.
Use rounding skills to arrive at conclusions. (M) (PSSA)
F. Determine the reasonableness of
calculated answers.
Determine the reasonableness of calculated answers in numbers up to
hundreds. (M)
G. Explain addition and subtraction
algorithms with regrouping.
The student will explain addition and subtraction algorithms with reqrouping,
both orally or in written form up to
hundreds. (M)
9
Strand 2.3 Measurement and Estimation Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
A. Compare measurable characteristics of
different objects on the same
dimensions.
Compare measurable characteristics of different objects on the same
dimensions (e.g., time, temperature,
area, length, weight, capacity,
perimeter, and volume). (M) (PSSA)
Teacher made tests and quizzes
Chapter tests and quizzes
Curriculum-based assessments
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Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
A. Compare measurable characteristics of
different objects on the same
dimensions.
Order objects on basis of weight, capacity, and length. (M) (PSSA)
B. Determine the measurement of objects
with non-standard and standard units
Measure to the nearest ½ inch or centimeter. (M) (PSSA)
Read and write temperature to nearest degree (Fahrenheit and Celsius). (M)
C. Determine and compare elapsed times.
Find elapsed time to increments of 5 minutes (limited to 2 adjacent hours)
(PSSA)
Identify times of the day and night as A.M. and P.M. (PSSA)
C. Determine and compare elapsed times.
Determine elapsed time between two dates on a calendar. (M)
10
Strand 2.3 Measurement and Estimation Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
D. Tell time (analog and digital) to the
minute.
Read and write time to the minute on digital and analog clocks. (M) (PSSA)
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Chapter tests and quizzes
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Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
E. Determine the appropriate unit of measure.
Determine the appropriate unit of measure, using US customary or metric
units (meters, yards, kilometers, miles,
ounces, pounds, tons, grams,
kilograms). (M) (PSSA)
F. Use concrete objects to determine area
and perimeter.
Measure area by counting or multiplying squares. (M) (PSSA)
Measure perimeter and area of rectangles and write dimensions using
correct labels. (M) (PSSA)
G. Estimate and verify measurements.
Estimate and verify measurements (lengths). (R) (PSSA)
Estimate and verify measurements (weights and capacity). (I) (PSSA)
G. Estimate and verify measurements.
Estimate line segments to the nearest ½ inch; to the nearest centimeter and
verify by measuring the line. (M)
(PSSA)
11
Strand 2.3 Measurement and Estimation Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
H. Demonstrate that a single object has
different attributes that can be
measured in different ways (e.g.,
length, mass, weight, time, area,
temperature, capacity and perimeter.)
Select appropriate units of measure for length, weight and capacity. (M)
Teacher made tests and quizzes
Chapter tests and quizzes
Curriculum-based assessments
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Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
12
Strand 2.4 Mathematical Reasoning and Connections Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
A. Make, check and verify predictions
about the quantity, size and shape of
objects and groups of objects.
Verbalize estimation strategies. (I)
Compare estimations and results. (I)
Revise estimates. (I)
Use a calculator to check estimation. (M)
Teacher made tests and quizzes
Chapter tests and quizzes
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Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
B. Use measurements to determine the
geography of the school building.
Use measurements in everyday situations (e.g., determine the size of
the gym, the length, width, height of
hallways or classroom, size of
doorways). (M)
13
Strand 2.5 Mathematical Problem Solving and Communication Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
A. Use appropriate problem-solving
strategies such as guess and check and
working backwards.
Use appropriate problem-solving strategies: Guess and check (M), Work
backwards (M), Draw pictures or
diagrams (M), Make lists, charts, or
tables (M), Use patterns. (R)
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Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
B. Determine when sufficient information is present to solve a problem and
explain how to solve a problem.
Determine when sufficient information is present to solve a problem. (M)
Explain how to solve a problem and show the process. (M)
C. Select and use an appropriate method,
materials and strategy to solve
problems, including mental
mathematics, paper and pencil, and
concrete objects.
Select and use appropriate method to solve problems: Mental math (M),
Paper and pencil (M), Concrete objects
(M), Choose the correct operation(s) to
solve word problem (no more than 2
operations using +, - and/or x).
14
Strand 2.6 Statistics and Data Analysis Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
A. Gather, organize and display data using
pictures, tallies, charts, bar graphs and
pictographs.
Make & interpret a chart. (M) (PSSA)
Make a pictograph. (M) (PSSA)
Teacher made tests and quizzes
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Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
B. Formulate and answer questions based
on data shown on graphs.
Formulate questions and draw conclusions from charts, pictographs,
and bar graphs and explain them orally
and in writing. (M) (PSSA)
C. Predict the likely number of times a
condition will occur based on analyzed
data.
The student will make predictions about the probability of events
occurring based on analyzed data. (M)
(PSSA)
D. Form and justify an opinion on whether
a given statement is reasonable based
on a comparison to data.
Form and justify an opinion on whether a given statement is reasonable based
on a comparison of data. (M)
15
Strand 2.7 Probability and Predictions Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
A. Predict and measure the likelihood of
events and recognize that the results of
an experiment may not match predicted
outcomes.
Determine if an event is equally likely or not equally likely to occur. (M)
(PSSA)
Recognize that the results of an experiment may not match predicted
outcomes. (M)
Teacher made tests and quizzes
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Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
B. Design a fair and an unfair spinner.
Design a fair and unfair spinner. (M)
C. List or graph the possible results of an
experiment.
The student will list or graph the possible results of an experiment and
explain the data. (M)
D. Analyze data using the concepts of
largest, smallest, most often, least often
and middle.
The student will use the concept of middle to analyze data. (M)
16
Strand 2.8 Algebra and Functions Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
A. Recognize, describe, extend, create and
replicate a variety of patterns including
attribute, activity, number and
geometric patterns.
Introduce function tables in addition and multiplication tables grade
appropriate. (I)
Investigate and create arrays. (M)
Teacher made tests and quizzes
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Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
A. Recognize, describe, extend, create and
replicate a variety of patterns including
attribute, activity, number and
geometric patterns.
Describe attributes of attribute blocks, geometric figures, etc.
Investigate, create, and extend patterns. (M)
A. Recognize, describe, extend, create and
replicate a variety of patterns including
attribute, activity, number and
geometric patterns.
Extend or find a missing element in a pattern of numbers or shapes (pattern
must show 3 repetitions-if multiples are
used, limit to 2, 3, or 5.) (PSSA)
A. Recognize, describe, extend, create and
replicate a variety of patterns including
attribute, activity, number and
geometric patterns.
Identify/describe the rule for a pattern shown (pattern must show 3 repetitions
– if multiples are used, limit to 1, 3, or
5.) (PSSA)
B. Use concrete objects and trial and error
to solve number sentences and check
whether solutions are sensible and
accurate.
Use concrete objects and trial and error to solve number sentences involving
addition, subtraction, multiplication,
and division. (M)
Check to see if solutions are sensible and accurate. (M)
17
Strand 2.8 Algebra and Functions Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
C. Substitute a missing addend in a
number sentence.
Substitute a missing addend or in a number sentence beyond 20. (M).
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Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
C. Substitute a missing addend in a
number sentence.
Find a missing number that makes a number sentence true (1 digit or 2 digit
numbers up to 18 using +, - or x
through 9 x 5.) (PSSA)
C. Substitute a missing addend in a
number sentence.
Identify the missing symbol (+, -, =, <, >) that makes a number sentence true.
(PSSA)
D. Create a story to match a given
combination of symbols and numbers.
The student will create and solve a story to match a given combination of
symbols and numbers. (M) (+, -, x, <,
>, =) (PSSA)
E. Use concrete objects and symbols to
model the concepts of variables,
expressions, equations and inequalities.
The student will use concrete objects and symbols to model the concepts of
variables, expressions, equations and
inequalities. (M)
18
Strand 2.8 Algebra and Functions Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
F. Explain the meaning of solutions and
symbols.
Explain the meaning of solutions and symbols. (M)
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Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
F. Explain the meaning of solutions and
symbols.
Compare numbers reading the symbols
>, <, =, (e.g., Use the words greater
than, less than, equal to and not equal
to (to thousands). (M) (PSSA)
F. Explain the meaning of solutions and
symbols.
Identify the ordinal position of an object (e.g., 1
st , 2
nd , and 3
rd ). (M)
Read a mathematical number sentence created with <, > and =. (R)
F. Explain the meaning of solutions and
symbols.
Write a mathematical number sentence created with <, > and = for 2-digit
numbers. (R)
G. Gather information and display it in the
form of a table or a chart.
Gather information and display it in the form of a table or a chart.(M)
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Strand 2.8 Algebra and Functions Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
H. Describe and interpret the data shown
in tables and charts.
Describe and interpret the data shown in tables and charts. (M) (PSSA)
Teacher made tests and quizzes
Chapter tests and quizzes
Curriculum-based assessments
Standardized tests
Demonstrations
Performance assessments
Portfolios
Research papers
Essays
Oral presentations
Multi-medial presentations
Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
I Translate information from one type of
display to another.
Translate information from one type of display to another (e.g. convert tally
chart to bar graph). Limit to tally
charts, bar graphs, tables and
pictographs. (PSSA)
J. Demonstrate simple function rules.
Demonstrate simple function rules (one step functions +, -, x). (M) (PSSA)
J. Demonstrate simple function rules.
Determine the missing element in a function table (functions may use +, -,
or x; allowable multiples are 2, 3, or 5.)
Tables must have 3 Ins and 3OUTs
listed. (PSSA)
K. Analyze simple functions and
relationships and locate points on a
simple grid.
Analyze simple functions and relationships. (e.g., What do you do to
3 to get 6?) (M) (PSSA)
Locate points on a simple grid. (M) (PSSA)
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Strand 2.9 Geometry Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
A. Name and label geometric shapes in
two and three dimensions
Name and label geometric shapes in two and three-dimensions. (R)
Circle/sphere, Square/cube,
Triangle/pyramid, Rectangle/prism.
(PSSA)
Teacher made tests and quizzes
Chapter tests and quizzes
Curriculum-based assessments
Standardized tests
Demonstrations
Performance assessments
Portfolios
Research papers
Essays
Oral presentations
Multi-medial presentations
Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
A. Name and label geometric shapes in
two and three dimensions
Describe the difference between an open figure and a closed figure. (R)
Explain the number of sides and corners of shapes. (R)
B. Build geometric shapes using concrete
objects
Build geometric shapes using concrete objects. (R)
C. Draw two and three-dimensional
geometric shapes and construct
rectangles, squares and triangles on the
geoboard and on graph paper satisfying
specific criteria.
Draw two (R) and three-dimensional geometric shapes. (M)
Construct rectangles, squares, and triangles and on graph paper satisfying
specific criteria. (M)
C. Draw two and three-dimensional
geometric shapes and construct
rectangles, squares and triangles on the
geoboard and on graph paper satisfying
specific criteria.
Identify parallel, perpendicular, line segments, and congruent lines. (M)
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Strand 2.9 Geometry Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
D. Find and describe geometric figures in
real life.
Find and describe geometric figures in real life. (R)
Teacher made tests and quizzes
Chapter tests and quizzes
Curriculum-based assessments
Standardized tests
Demonstrations
Performance assessments
Portfolios
Research papers
Essays
Oral presentations
Multi-medial presentations
Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
E. Identify and draw lines of symmetry in
geometric figures.
Identify and draw all lines of symmetry in two-dimensional geometric figures.
(M)
F. Identify symmetry in nature.
Identify symmetry in Nature and in two-dimensional figures
G. Fold paper to demonstrate the
reflections about a line.
Fold paper to demonstrate the reflections about a line. (M)
H. Show relationships between and among
figures using reflections.
Show relationships between and among figures using reflections (e.g.,
tesselations). (M)
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Strand 2.9 Geometry Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
I. Predict how shapes can be changed by
combining or dividing them.
Predict how shapes can be changed by combining or dividing them. (M)
Recognize slides, flips and turns of a simple two-dimensional figure. (M)
(PSSA)
Teacher made tests and quizzes
Chapter tests and quizzes
Curriculum-based assessments
Standardized tests
Demonstrations
Performance assessments
Portfolios
Research papers
Essays
Oral presentations
Multi-medial presentations
Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
23
Strand 2.10 Trigonometry Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
A. Identify right angles in the
environment.
Identify right angles in the environment. (R) (PSSA)
Determine whether an angle is <, >, or = to a right angle. (M)
Teacher made tests and quizzes
Chapter tests and quizzes
Curriculum-based assessments
Standardized tests
Demonstrations
Performance assessments
Portfolios
Research papers
Essays
Oral presentations
Multi-medial presentations
Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
B. Model right angles and right triangles
using concrete objects.
The student will model right angles and right triangles using concrete objects.
(PSSA)
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Strand 2.11 Concepts of Calculus Subject Area: Math Grade: 3
PA Academic Standards Performance Indicators Assessment
A. Identify whole number quantities and
measurements from least to most and
greatest value.
Identify whole number quantities and measurements from least to most and
greatest value from 1 to 10,000. (M)
(PSSA)
Teacher made tests and quizzes
Chapter tests and quizzes
Curriculum-based assessments
Standardized tests
Demonstrations
Performance assessments
Portfolios
Research papers
Essays
Oral presentations
Multi-medial presentations
Experiments
Pennsylvania System of School
Assessment (PSSA) – Grade 3
B. Identify least and greatest values
represented in bar graphs and
pictographs.
Identify least and greatest values in pictographs with variables. (M)
C. Categorize rates of change as faster and
slower.
Categorize rates of change as faster and slower. (M)
D. Continue a pattern of numbers or
objects that could be extended
infinitely.
Continue a pattern of numbers or objects that could be extended
infinitely. (R)
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Adaptations/Modifications for Students with I.E.P.s
Adaptations or modifications to this planned course will allow exceptional students to earn credits toward graduation or develop skills necessary
to make a transition from the school environment to community life and employment. The I.E.P. team has determined that modifications to this
planned course will meet the student’s I.E.P. needs.
Adaptations/Modifications may include but are not limited to:
INSTRUCTION CONTENT - Modification of instructional content and/or instructional approaches - Modification or deletion of some of the essential elements
SETTING - Preferential seating
METHODS
- Additional clarification of content - Occasional need for one to one instruction - Minor adjustments or pacing according to the student’s rate of mastery - Written work is difficult, use verbal/oral approaches - Modifications of assignments/testing - Reasonable extensions of time for task/project completion - Assignment sheet/notebook - Modified/adjusted mastery rates - Modified/adjusted grading criteria - Retesting opportunities
MATERIALS - Supplemental texts and materials - Large print materials for visually impaired students - Outlines and/or study sheets - Carbonless notebook paper - Manipulative learning materials - Alternatives to writing (tape recorder/calculator)
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Strategies and Interventions to Support Students with Mathematics Disabilities
Brittany L. Hott, PhD Laura Isbell, PhD Texas A&M University-‐ Commerce Teresa Oettinger Montani, EdD Fairleigh Dickinson University (December 2014) In the absence of intensive instruction and intervention, students with mathematics difficulties and disabilities lag significantly behind their peers (Jitendra et al., 2013; Sayeski & Paulsen, 2010). Conservative estimates indicate that 25% to 35% of students struggle with mathematics knowledge and application skills in general education classrooms, indicating the presence of mathematics difficulty (Mazzocco, 2007). Additionally, 5% to 8% of all school-‐age students have such significant deficits that impact their ability to solve computation and/or application problems that they require special education services (Geary, 2004). This InfoSheet provides an overview of strategies and resources to support students with, or at-‐risk for, mathematics learning disabilities.
Common Core Mathematics Standards
With the current emphasis on the Common Core State Standards (CCSS; National Governors Association Center for Best Practices [NGA Center], 2010, 2014), it is
essential that students with math difficulties and disabilities be prepared to meet with success on these newly articulated grade level expectations in mathematics. Special education teachers and general education teachers need to have strategies to help students who struggle with mathematics to gain access to the general education curriculum and to meet with success in all areas of math including math literacy and conceptual knowledge (Gargiulo & Metcalf, 2013; Powell, Fuchs, & Fuchs, 2013).
Although the CCSS do not provide a curriculum, they do specify the topics within standards that should be addressed by grade level. CCSS included two major components: Standards for Mathematics Practice and Standards for Mathematics Content. These standards indicate that students should be able to (1) make sense of problems and persevere in solving them, (2) reason abstractly and quantitatively, (3) construct viable arguments and critique the reasoning of others, (4) model with mathematics, (5) use appropriate tools strategically, (6) attend to precision, (7) look for and make use of
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structure, and (8) look for and express regularity in repeated practices. During the elementary years, focus is placed on mathematics fundamentals with the goal of moving from counting skills to multiplying and dividing fractions. By middle school, students are expected to understand geometry, ratios and proportions, and pre-‐ algebra skills. During high school, the focus is on more advanced algebra, functions, modeling, advanced geometry, statistics, and probability content. For a complete listing of grade level standards download the complete set of grade specific standards (www.corestandards.org/the-‐ standards/mathematics).
The Early Learning in Mathematics program (Davis & Jungjohann, 2009) is an example of a core mathematics program that embodies the current thinking on effective instruction in math (Doabler et al., 2012). Both systematic and explicit instruction and detailed coverage of significant areas of content in mathematics are addressed in this program. The successful elements of explicit and systematic instruction incorporated in this program that can also be utilized in other core mathematics instruction include the following:
1. Specific and clear teacher models 2. Examples that are sequenced in level
of difficulty 3. Scaffolding 4. Consistent feedback 5. Frequent opportunity for cumulative
review (NCEERA, 2009) Fuchs and Fuchs (2008) identified seven
principals of effective practice for primary
students with math disabilities. In their article, the authors stated that third grade is a time when mathematical disabilities tend to be identified, and used the seven interventions to illustrate the principles. The seven principles include (1) instructional explicitness, (2) instructional design to minimize the learning challenge, (3) provide strong conceptual knowledge for procedures taught, (4) drill and practice, (5) cumulative review, (6) motivation to help students regulate their attention and behavior and to work hard, and (7) on-‐going progress monitoring. Strategies for Teaching Problem Solving Skills Strategy training has been helpful to students with LD when learning mathematical concepts and procedures. The following are a few examples of strategies that are useful to teachers when instructing students with LD in problem solving. RIDE (Mercer, Mercer, & Pullen, 2011) RIDE is a strategy used to assist students with solving word problems. Students who experience difficulty with abstract reasoning, attention, memory, and/or visual spatial skills may benefit from the strategy. Ensure that steps are taught through demonstration and plenty of opportunities for practice are provided before asking students to independently use the strategy. Visually display the strategy on a chart or class website as a reminder.
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R-- Remember the problem correctly
I-- Identify the relevant information
D-- Determine the operations and unit for expressing the answer E-- Enter the correct numbers, calculate and check the answer
FAST DRAW (Mercer & Miller, 1992) Like RIDE, FAST DRAW is another strategy used to solve word problems. Teach each step in the sequence allowing sufficient time for guided practice prior to asking students
to independently implement the strategy. Create a visual display and post in the classroom or student notebooks to assist students.
F— Find what you’re solving for. A— Ask yourself, “What are the parts of the problem?” S— Set up the numbers. T— Tie down the sign.
D — Discover the sign. R — Read the problem. A — Answer, or draw and check. W— Write the answer.
TINS Strategy (Owen, 2003) The TINS strategy allows students to use different steps to analyze and solve word problems.
T—Thought Think about what you need to do to solve this problem and circle the key words.
I— Information Circle and write the information needed to solve this problem; draw a picture; cross out unneeded information.
N— Number Sentence Write a number sentence to represent the problem. S-- Solution Sentence Write a solution sentence that explains your answer.
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Strategies to Support Vocabulary Development
Strategies that can help students improve their mathematic vocabulary include (a) pre-‐ teach vocabulary, (b) mnemonic techniques, and (c) key word approaches. These strategies are only a few strategies available to help enhance students’ mathematics vocabulary comprehension. Pre-‐teach Vocabulary
• Use representations, both pictorial and concrete, to emphasize the meaning of math vocabulary (Sliva, 2004).
• Pretest students’ knowledge of glossary terms in their math textbook and teach vocabulary that is unknown or incorrect.
Mnemonic Techniques • Teach mnemonic techniques to help
remember word meanings. • Use mnemonic instruction to help
students improve their memory of new information (The Access Center, 2006).
Key Word Approach • Use the keyword approach (e.g.,
visualize a visor as the keyword for
• divisor; visualize quotation marks as the keyword for quotient (Mastropieri & Scruggs, 2002).
Strategies to Assist with Teaching
Algebraic Concepts
Algebra is introduced in elementary school as students learn algebraic reasoning involving patterns, symbolism, and representations. Students experience difficulty with algebra for various reasons including difficulty understanding the vocabulary required for algebraic reasoning, difficulties with problem solving, and difficulties understanding patterns and functions necessary for algebraic reasoning. Possible strategies to assist with teaching algebraic concepts include, but are not limited to, (a) teaching key vocabulary needed for algebra, (b) providing models for identifying and extending patterns, (c) modeling “think aloud” procedures for students to serve as examples for solving equations and word problems, (d) incorporating technology usage (e.g., graphing calculators) (Bryant, 2008), and (e) implementing Star Strategy described below (Gagnon & Maccini, 2001).
S— Search the word problem.
T— Translate the words into an equation in picture form A— Answer the problem R— Review the problem.
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CRA and CSA Instructional Methods Maccini and Gagnon (2005) stated that the STAR strategy incorporates the concrete-‐ Semiconcrete-‐Abstract (CSA) instructional sequence, which gradually advances to abstract ideas using the following progression: (a) concrete stage, (b) semiconcrete stage, and (c) abstract stage. By using the CSA framework teachers can incorporate effective teaching components to teach students effectively and efficiently. Students progressively move through each stage to achieve mastery in a mathematic concept.
Using multiple representations, beginning with the concrete level and moving to the abstract level, is an effective technique in helping struggling learners solve calculation problems. The Concrete-‐Representational-‐ Abstract (CRA) teaching sequence has been found to help students with LD learn procedures and concepts (Flores, Hinton, & Strozier, 2014). During the concrete stage students are in the “doing” stage, during the representational stage students are in the “seeing” stage, and during the abstract phase students are in the “applying” stage. Students move through the phases fluidly.
C— Concrete: students use three-dimensional objects to represent math problems R— Representational: students use pictures to represent math problems A— Abstract: students represent the problem using numerical symbols
C— Concrete: students use three-dimensional objects to represent math problems
S— Semiconcrete: students use two-
dimensional representation to draw pictures of the math problem
A— Abstract: students represent the problem using numerical symbols
Strategies to Assist with the Use of
Metacognitive Skills Metacognition refers to individuals’ awareness of how they think and plan activities. Metacognition also involves strategizing, monitoring success and effort, and knowing when to change directions or to try a different approach to problem solving. Many students with learning difficulties benefit from the use of metacognitive skills to help them focus on what they are doing and to plan for how to employ strategies as needed and change directions when appropriate (Mevarech & Amrany, 2008). A few examples of how to incorporate metacognitive strategies include:
• Demonstrating “think-‐alouds” so students become aware of how one talks oneself through a learning task.
• Demonstrating the use of graphic organizers, schematics, and visual imagery.
• Explicit, direct instruction accompanied by modeling of self-‐ monitoring, self-‐talk, and self-‐checks.
Mathematics Advisory Panels and Their
Reports Developing foundational mathematics skills at the elementary level is essential. Maintaining basic skills acquired during the elementary years is essential as students move toward more advanced computational, place value, and fractional concepts. As
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students move from elementary to secondary mathematics, it is important that students maintain skills mastered and that teachers continue to scaffold instruction and provide supports to ensure that foundational skills
are addressed while affording access to more advanced mathematics concepts. Below are links to various advisory panel recommendations for effectively teaching mathematics.
Panel Link National Commission on Mathematics and Science Teaching for the 21st Century— Before It’s Too Late
http://www.ptec.org/items/detail.cfm?ID=4059
National Research Council—Adding It Up: Helping Children Learn Mathematics
http://www.nap.edu/catalog.php?record_id=9822
RAND Mathematics Study Panel— Mathematical Proficiency for All Students
http://www.rand.org/pubs/monograph_reports/MR1643/index.ht ml
Foundations for Success: The Final Report of the National Mathematics Advisory Panel
http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final- report.pdf
The Access Center’s Math Problem Solving for Primary Elementary Students with Disabilities
http://www.k8accesscenter.org/training_resources/mathprimaryp roblemsolving.asp
The Access Center’s Math Problem Solving for Upper Elementary Students with Disabilities
http://www.k8accesscenter.org/training_resources/MathPrblSlvi ng_upperelem.asp
Resources
There are numerous website and resources available to assist with mathematics
instruction. Following are suggested websites with a summary of resources for teaching a variety of mathematics concepts across levels.
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Website Resource www.cast.org http://www.factmonster.com/math/flashcards.html www.aplusmath.com/flashcards www.flash-cardmachine.com www.academicskillbuilders.com www.sunburst.com www.intellitools.com www.tomsnyder.com www.illuminations.nctm.org www.internet4classrooms.com http://ncisla.wceruw.org/teachers/index.html
• expand learning opportunities through universal design
• increase math fluency with web- based flashcards
• enhance fluency through the use
of web-based flashcards
• enhance fluency with the use of web-based flashcards
• support math and vocabulary
fluency (Brownell, Smith, Crockett, Griffin, 2012)
• research based achievement
solutions; standards based products prescriptive web based instruction K-5, digital classroom
• technology for preK – 8
classrooms, free downloads available.
• software for fluency, word
problems, graphing, etc.
• activities, lessons, standards web links for math education; preK-12.
• Common Core State Standards
internet sites for teaching mathematics in culturally responsive ways
• resources related to supporting
understanding of science and math
References The Access Center. (2006). Using mnemonic
instruction to teach math. Retrieved from http://www.k8accesscenter.org
Brownell, M. T., Smith, S. J., Crockett, J. B., & Griffin, C. C. (2012). Inclusive instruction: Evidence based practices for teaching students with disabilities. New York, NY: The Guilford Press.
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Bryant, D. P. (2008). Teaching mathematics. In D. P. Bryant, D. D. Smith, & B. R. Bryant (Eds.), Teaching students with special needs in inclusive classrooms. Boston, MA: Allyn & Bacon.
Davis, K., & Jungjohann, K. (2009). Early learning in mathematics: Level K. Unpublished curriculum, Center on Teaching and Learning, University of Oregon, Eugene, OR.
Doabler, C. T., Cary, M. S., Jungjohann, K., Clarke, B., Fien, H., Baker, C., Smolkowski, K., & Chard, D. (2012). Enhancing core mathematics instruction for students at risk for mathematics disabilities. Teaching Exceptional Children, 44(4), 48-‐57.
Flores, M. M., Hinton, V., & Strozier, S. (2014). Teaching subtraction and multiplication with regrouping using Concrete-‐Representational-‐ Abstract sequence and the Strategic Instruction Model. Learning Disabilities Research and Practice, 29(2), 75-‐88.
Fuchs, L. S., & Fuchs, D. (2008), Mathematics disabilities in the primary grades: Seven principles of effective practice. Retrieved from www.TeachingLD.org
Gagnon, J., & Maccini, P. (2001). Preparing students with disabilities for algebra. Teaching Exceptional Children, 34(1), 10-‐17.
Gargiulo, R. M., & Metcalf, D. (2013). Teaching in today’s inclusive classrooms: A universal design for learning approach (2nd ed.) Independence, KY: Cengage Learning.
Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4-‐15.
Jitendra, A. K., Rodriguez, M., Kanive, R., Huang, J., Church, C., Conrroy, K. A., & Zaslofsky, A. (2013). Impact of small-‐group tutoring interventions on the mathematical problem solving and achievement of third-‐grade students with mathematics difficulties. Learning Disability Quarterly, 36, 21-‐35.
Maccini, P., & Gagnon, J. (2005). Mathematics strategy instruction (SI) for middle school students with learning disabilities. The Access Center. Retrieved from http://digilib.gmu.edu/jspui/bitstream/1920 /284/1/MathSIforMiddleSchoolStudentswith LD.2.pdf
Mastropieri, M. A., & Scruggs, T. E. (2002). Effective instruction for special education (3rd ed.). Austin, TX: PRO-‐ED.
Mazzocco, M. (2007). Defining and differentiating mathematical learning disabilities and difficulties. In D. Berch & M. Mazzocco (Eds.), Why is math so hard for some children? The nature and origins of mathematics learning difficulties and disabilities (pp. 29-‐47). Baltimore, MD: Paul H. Brooks.
Mercer, C. D., Mercer, A. R., & Pullen, P. C. (2011). Teaching students with learning problems (8th ed.). Upper Saddle River, NJ: Pearson Education.
Mercer, C. D., & Miller, S. P. (1992). Multiplication facts 0 to 81. Lawrence, KS: Edge Enterprises.
Mevarech, Z. R., & Amrany, C. (2008). Immediate and delayed effects of meta-‐cognitive instruction on regulation of cognition and mathematics achievement. Metacognition and Learning, 3(2), 147-‐157.
National Center for Education Evaluation and Regional Assistance. (2009). Assisting students struggling with mathematics: Response to intervention (RtI) for elementary and middle schools (Practice Guide Report No. NCEE 2009-‐ 4060). Washington, DC: Institute of Education Sciences. Retrieved from http://ies.ed.gov/ncee/wwc/pdf/practice_gui des/rti_math_pg_042109.pdf
National Governors Association Center for Best Practices, Council of Chief State School Officers. (2010). Common Core State Standards (Mathematics). Washington, DC: National Association Center for Best Practices, Council of Chief State School Officers. Retrieved from http://www.corestandards.org/assets/CCSSI_ Math%20Standards.pdf
National Governors Association. (2014). Trends in state implementation of the common core state standards: Making the shift to better tests. Retrieved from http://www.nga.org/files/live/sites/NGA/file s/pdf/2014/1404NGACCSSAssessments.pdf
Owen, M. J. (2003). It’s elementary! 275 math word problems book 3. Toronto, Canada: Educator Publishing Service.
Powell, S. R., Fuchs, L. S., & Fuchs, D. (2013). Reaching the mountaintop: Addressing the common core standards in mathematics for
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students with mathematics difficulties. Learning Disabilities Research and Practice, 28, 38-‐48. doi: 10.1111/ldrp.12001
Sayeski, K. L., & Paulsen, K. J. (2010). Mathematics reform curricula and special education: Identifying intersections and implications for
practice. Intervention in School and Clinic, 46, 13-‐21.
Sliva, J. A. (2004). Teaching inclusive mathematics to special learners, K-‐6. Thousand Oaks, CA: Corwin Press.
©2014 Council for Learning Disabilities. CLD grants permission to copy this InfoSheet for educational
purposes. Other InfoSheets are available on our website (www.cldinternational.org).

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