GRADE: 3
TOPIC: ALGEBRAIC REASONING: PATTERNS AND FUNCTIONS
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STAGE 1:
IDENTIFY DESIRED RESULTS |
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Content Standard(s) Generalizations about what students should know and be able to do |
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Established Goals: State Standards:
National
(NCTM) Standards:
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Enduring Understandings Insights learned from
exploring generalizations via the essential questions (Students will
understand THAT…) |
Essential Questions Inquiry used to explore generalizations |
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1.
Patterns
and functions help us describe data and physical phenomena and solve a
variety of problems. 2.
Patterns enable us to predict. 3.
Patterns are repeating sequences that can be
created or occur naturally in our world. 4.
Equation implies equality. 5. Inequalities can be represented mathematically. 6. Objects can be organized based on various explainable elements and rules. |
1.
When is a pattern useful? 2.
How does a pattern extend? 3.
What does balance have to do with an equation? 4. What is equality? 5. What is inequality? |
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Knowledge and Skills What students are expected to know and be able to do |
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Students will know… A. Patterns that are made with different objects and symbols and that follow the same rule may be classified together. B.
A number sentence with an equal sign
(equation) indicates that both sides of the equal sign represent the same
value and can be modeled with a balance. |
Students will be able to… 1.
Use a variety of materials to construct,
reproduce, describe and extend number and spatial patterns (both repeating
and growing). 2.
Explore and describe patterns and sequences
using tables, graphs and charts. State
rules for simple function tables using numbers and ratios. 3.
Construct, reproduce and extend patterns using
geometric transformation (translations/slides, reflections/flips,
rotations/turns). 4.
Sort and classify the same set of objects in
more than one way and explain the rule for each sort. 5.
Investigate simple combinations, permutations
(arrangements) and simple networks (pathways and maps). 1.
Demonstrate understanding of the = sign as an
equality symbol and explore inequalities and the NOT EQUAL SIGN symbol. 2.
Express mathematical relationships involving
addition, subtraction, multiplication and division as open number sentences
and simple equations e.g. (17 + _ = 72 or A = B + 3) and match to simple
story problems. 3.
Identify specific illustrations of the commutative (3+6 = 6+3) associative (3+6) + 5 = 3+ (6+5) and distributive (5 x 13 = (5 x 10) + (5
x 3) properties with whole numbers and use them to construct estimation and
computation strategies. |
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STAGE 2:
DETERMINE ACCEPTABLE EVIDENCE |
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Performance Task(s) Authentic application in
new context to evaluate student achievement of desired results designed
according to GRASPS (Goal, Role, Audience, Setting Performance, Standards) |
Other Evidence Application that is
functional in a classroom context only to evaluate student achievement of
desired results |
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Task 1 (Assesses: ALG A-1, A-2, A-5) Goal: Correct the test and explain why or why not the problem is
correct. Role: You are a teacher correcting a third grader’s test on
patterns and discussing the results with your student teacher. Situation: You must explain to your student teacher why the children’s
answers are correct or not correct. Scoring Rubric: The student: Score of 3: Meets or exceeds
the objectives of the task.
Demonstrates a high level of understanding. Student explains
all or most answers with clarity and in-depth comprehension. Score of 2: Partially meets the
objectives of the task. Demonstrates
some understanding. Student is able to explain most answers. Score of 1: Does not meet the
objectives of the task. Demonstrates
poor or incorrect understanding. Student explains why some patterns
are correct or not correct. Score of 0: Shows no
understanding of the problem or how to arrive at a solution. Student can’t explain why patterns are
correct or not correct. |
Teacher Observation Center Activities Group Work Journal Entries Class Work Homework Topic Assessments District Assessments State Assessments |
Task 1
(Assesses: ALG A-1, A-2, A-5)
Goal:
Correct the test and explain why or why not the problem is
correct or not.
Role:
You are a teacher correcting a third grader’s test on
patterns and discussing the results with your student teacher.
Situation:
You must explain to your student teacher why the children’s
answers are correct or not.
Scoring Rubric:
The student:
3 Meets or exceeds the objectives
of the task. Demonstrates a high level
of understanding. Student explains all or most answers with clarity and
in depth comprehension.
2 Partially meets the objectives
of the task. Demonstrates some
understanding.
Student is able to explain most answers.
1 Does not meet the objectives of
the task. Demonstrates poor or incorrect
understanding. Student explains why some patterns are correct or not.
0 Student shows no understanding
of the problem or how to arrive at a solution. Student can’t explain why patterns are correct
or not.
STUDENT TESTS TO BE DONE AND ATTACHED
GRADE: 3
TOPIC: GEOMETRY AND MEASUREMENT
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STAGE 1:
IDENTIFY DESIRED RESULTS |
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|
Content Standard(s) Generalizations about what students should know and be able to do |
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|
Established Goals: State Standards:
National (NCTM)
Standards
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Enduring Understandings Insights learned from
exploring generalizations via the essential questions (Students will
understand THAT…) |
Essential Questions Inquiry used to explore generalizations |
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1.
Geometric
relationships and measurements help us to solve problems and make sense of
our world. 2.
The measurement tool must be carefully
examined prior to use. All rulers, for example, are not the same. 3.
Estimation is a helpful skill in daily
activities. 4. The appropriate tool needs to be used when measuring attributes such as length, area, weight, volume, the size of an angle and time. 5. Location may be represented on simple maps. |
1.
Can everything be measured? 2.
How far is far? 3.
Is the measurement tool (ruler, clock) always
right? 4.
How is estimating helpful? 5.
How are maps used? 6.
How do clocks/calendars assist us? 7. To sort or not to sort? 8. What is good
about comparing? |
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Knowledge and Skills What students are expected to know and be able to do |
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Students will know… A. Polygons and solids can be compared and classified using attributes such as number and length of sides, number and kinds of angles, lines of symmetry, parallel sides or faces and congruent parts. B. Calendars and clocks are used to plan events and coordinate meetings. C. Location may be represented on simple maps
using shapes or pictures. D. Estimation and measurement of length,
area, volume, weight and temperature require different tools and units
appropriate for a specific measurement task. |
Students will be able to… 1. Identify angles and classify them as right,
obtuse and acute angles. 2. Explore similarities and differences using
characteristics such as the relationship of sides (parallel, perpendicular),
kinds of angles (acute, right and obtuse), symmetry and congruence to sort
polygons and solids. 3. Build, describe and identify polygons and
solids in various orientations after transformations (slides, flips and
turns), or after combining and subdividing. 4. Use various polygons to investigate ways to
tessellate (tile) a region or shape. 5. Identify, describe, draw and compare
polygons and solids found in the environment – buildings, plants, art, etc. 6. Identify, draw and describe line symmetry in two- and three-dimensional objects. 1. Tell time to the minute, using analog and
digital clocks, and identify a.m. and p.m. 2. Use calendars and clocks to plan and
sequence events. 1. Use coordinate systems to draw and
interpret simple maps. 2. Develop and use nonstandard and standard
referents to estimate length (height), area and volume (capacity). 3. Explain when an estimate is appropriate and
use and describe estimation strategies that can identify a reasonable answer
to a measurement problem. 4. Select and use the appropriate kind of unit
(dimension) for measuring length, perimeter, area, weight, time, temperature,
volume and capacity. 5. Explain the need for standard units of
measure and identify customary and metric units that are used to measure
length, area and volume. 6. Estimate, draw and measure length to the
nearest inch and centimeter using inch tiles, centimeter rods and primary
rulers. 7. Estimate and use concrete objects to
measure perimeter, area, weight, volumes of irregular shaped solids.and
capacity. 8. Explore strategies for estimating and
measuring the perimeters, areas and volumes of irregular shapes and solids. |
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STAGE 2:
DETERMINE ACCEPTABLE EVIDENCE |
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Performance Task(s) Authentic application in
new context to evaluate student achievement of desired results designed
according to GRASPS (Goal, Role, Audience, Setting Performance, Standards) |
Other Evidence Application that is
functional in a classroom context only to evaluate student achievement of
desired results |
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Task 1 (Assesses: GEO A-1, A-2, A-6) Task: The student will sort a set of shapes and write an explanation of why they sorted the shapes the way they did. Then they will sort the same shapes using different attributes, explaining each new way in writing. Materials:
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