Grade 3 Math

Contents Page

Grade 5 Math

 

GRADE:     4

TOPIC:      ALGEBRAIC REASONING:  PATTERNS & 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 aid description, understanding and communication about the world.

3.     Rules can be written to describe and extend patterns.

4.     Data can be used to interpret real life events and situations.

5.     When data is used in a variety of ways, our understanding of a problem, situation or event can be more meaningful.

6.     Data can be used to uphold or defeat an opinion.

 

  1. What kind of patterns are in the world around us?
  2. What are solutions of equations?
  3. When is an equation an appropriate problem solving model?
  4. How does data shape our understanding of a situation or event?
  5. Why do variables change their value?
  6. Do variables have value?
  7. Why do we simplify equations?

Knowledge and Skills

What students are expected to know and be able to do

Students will know…

  1. Patterns can be classified as repeating or growing.

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. The equivalence of both sides of an equation is maintained if the same value is added, subtracted, multiplied or divided on each side.

 

 

  1. Variables are used to represent a set of possible values.

 

 

 

Students will be able to…

  1. Recognize a variety of patterns and trends including repeating and growing patterns, make predictions and justify conclusions based on data from tables, graphs and charts.

 

  1. Develop and test generalizations based on observation of patterns and relationships, including geometric transformations such as slides, flips and rotations.

 

  1. Explore extending and comparing arithmetic and geometric sequences.

 

  1. Use equations to describe the rule for a number pattern and to model the solution to word problems.

 

 

 

  1. Use a variable as an unknown quantity in simple equations.

 

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

Goal: The goal is to determine the pattern of gumballs that come out of the broken gumball machine

 

Role: You work for the Chicklet Gumball Company as a vending machine technician.

 

Audience: The manager of  Walmart in Waterford, Connecticut

 

Situation: The gumball machine has been giving out extra gumballs with each additional penny.  Children are excited about this and swarm around the machine in hopes of getting extra gumballs for their money.  This consistent crowd is causing a safety hazard, so the manager would like you to repair the broken machine.  The broken machine is also getting to be very expensive.

 

Product Performance and Purpose:

Before you can reprogram the machine, you need to determine the pattern in which it is dispersing gumballs and record it on a chart. Write a rule or an equation to describe the pattern. Once you figure out the pattern, you need to test it out by seeing what would happen if a person puts in 5 pennies, 10 pennies, or even 100 pennies!

 

Standards and Criteria for Success

Scoring Rubric

The student:

 

Score of 3: Meets or exceeds the expectations of the task.  Demonstrates a high level of understanding.  The student achieves correct solutions to each part of the task.

The math language and representations are accurate and appropriate. The student creates a rule for finding any number of pennies.  All work is shown and labeled.

 

Score of 2: Partially meets the expectations of the task.  Demonstrates some understanding.

The student achieves correct solutions to all parts of the task. Work is clear and labeled.  Some math language is used.

 

Score of 1: Does not meet the objectives of the task.  Demonstrates poor or incorrect understanding. A partial solution is achieved.  The math representation is labeled, but is not organized to show what strategy was used for solving the task.

 

Score of 0: Shows no understanding of the problem or how to arrive at a solution. There are no solutions shown.  No math language is used.  Math language and representations are inaccurate and inappropriate.

 

Task 2

Goal: You will observe patterns and relationships by making conjectures (extending patterns) when you design a tile patio.

 

Role: You work at Tile Works and are hired to design and build an outdoor patio.

 

Audience: The owner of the home, who has hired you.

 

Product Performance and Purpose:

You need to design and build a 10 ft. X 10 ft. tile patio that has a pattern.  You can use tiles with different properties that show the extending pattern (i.e. different colors or sizes).

 

 

Standards and Criteria for Success

Scoring Rubric

The student:

 

Score of 3: Meets or exceeds the expectations of the task.  Demonstrates a high level of understanding. 

 

Score of 2: Partially meets the expectations of the task.  Demonstrates some understanding.

 

Score of 1: Does not meet the objectives of the task.  Demonstrates poor or incorrect understanding.

 

      Score of 0: Shows no understanding of the problem or how to arrive at a solution

 

 

District Assessments

State Assessments

Topic Assessments

Center Work

Group Work

Daily Individual Assignments

Teacher Observations

Math Journal Responses

Self-Assessments

Homework

 

 

 

GRADE:     4

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 communicate ideas and solve problems.

 

National (NCTM) Standards:

*      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.

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

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

 

Enduring Understandings

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

Essential Questions

Inquiry used to explore generalizations

1.      Measuring is a common everyday practice.

2.      We use different units to measure different things.

3.      Benchmarks can help us estimate.

4.      There are appropriate techniques, tools, and formulas to determine measurements.

5.      Geometric relationships and measurements help to solve problems.

6.      The physical world is made up of shapes that can be described by their attributes.

 

 

 

 

1.      Can everything be measured?

2.      Why do we measure things?

3.      Is it necessary for measurement to always be exact?

4.      Why do we use standard units?

5.      How do measurements help you describe things?

6.      How is measurement used in everyday life?

7.      How can geometric shapes be described by their attributes?

8.      Why do we learn geometry?

9.      How is geometry important in real life?

10.  What is geometry?

11. How do geometry concepts affect real life?

Knowledge and Skills

What students are expected to know and be able to do

Students will know…

  1. Lines of symmetry, slides, flips and turns can be used to build, describe, classify and analyze two- and three-dimensional shapes.

 

 

 

 

 

  1. Maps are based on the rectangular coordinate system and help to locate positions and find possible pathways between two points.

 

 

  1. Measurements of length, perimeter and area of squares and rectangles, when organized in a data table, reveal patterns which are generalized as formulas.

 

 

 

 

 

 

 

 

 

  1. Benchmarks (points of reference such as a centimeter-the width of the smallest finger) may be used to make estimates of length, area, volume, weight, temperature and time.  Measurement tools increase the precision of the estimates.