Grade 2 Math

Contents Page

Grade 4 Math

 

GRADE:     3

TOPIC:      ALGEBRAIC REASONING: PATTERNS AND FUNCTIONS

 

STAGE 1: IDENTIFY DESIRED RESULTS

Content Standard(s)

Generalizations about what students should know and be able to do

Established Goals:

 

State Standards:

*      Model and describe patterns and functional relationships.

*      Model and analyze quantitative data.

*      Using algebraic symbols to represent and interpret data and physical phenomena.

 

National (NCTM) Standards:

*      Understand patterns, relations, and functions.

*      Represent and analyze mathematical situations and structures using algebraic symbols.

*      Use mathematical models to represent and understand quantitative relationships.

*      Analyze change in various contexts.

 

 

Enduring Understandings

Insights learned from exploring generalizations via the essential questions (Students will understand THAT…)

Essential Questions

Inquiry used to explore generalizations

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?

Knowledge and Skills

What students are expected to know and be able to do

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.

 

STAGE 2: DETERMINE ACCEPTABLE EVIDENCE

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

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

 

STAGE 1: IDENTIFY DESIRED RESULTS

Content Standard(s)

Generalizations about what students should know and be able to do

Established Goals:

State Standards:

*      Develop and apply units, systems, formulas and appropriate tools to estimate and measure.

*      Use spatial reasoning, location and geometric relationships to solve problems.

*      Use attributes of two- and three-dimensional shapes and geometric theorems to describe relationships and communicate ideas based upon those relationships.

 

National (NCTM) Standards

*      Understand measurable attributes of objects and the units, systems, and processes of measurement.

*      Apply appropriate techniques, tools, and formulas to determine measurements.

*      Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

*      Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

*      Apply transformations and use symmetry to analyze mathematical situations.

*      Use visualization, spatial reasoning, and geometric modeling to solve problems.

 

Enduring Understandings

Insights learned from exploring generalizations via the essential questions (Students will understand THAT…)

Essential Questions

Inquiry used to explore generalizations

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?

Knowledge and Skills

What students are expected to know and be able to do

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.

 

 

 

STAGE 2: DETERMINE ACCEPTABLE EVIDENCE

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

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: