Kindergarten Math

Contents Page

Grade 2 Math

 

GRADE:     1

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.

*      Use 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.     There are patterns all around us.

3.     Patterns are repeating sequences that can be created or occur naturally in our world.

4.     Patterns help us predict what comes next.

5.     Patterns can be represented numerically and graphically.

6.     Classification by attributes highlights similarities and differences allowing us to form unique groups.

7.     We can represent ideas with symbols

 

 

 

1.     What is a pattern?

2.     Where can we find patterns in our world?

3.     How do you predict what might come next in a pattern?

4.     How do patterns help us in math?

5.     How are _______ similar and different?

6.     What are some different ways we can group (sort, classify) objects?

7.     When is sorting helpful?

8.     What do the symbols represent?

 

Knowledge and Skills

What students are expected to know and be able to do

Students will know…

  1. Patterns have rules and can be created using a variety of attributes.

 

 

 

 

 

 

 

 

 

 

 

  1. Problems involving classification and patterns can be solved using graphic organizers such as tables or Venn diagrams.

 

 

 

 

 

  1. Number sentences represent the result of counting, combining and separating sets of objects.

 

 

 

 

Students will be able to…

1.     Recognize, extend, describe and create a variety of simple patterns, and translate the same pattern from one representation (such as color) to another representation (such as shape).

2.     Sort, classify and order objects and numbers based on one and two attributes and describe the rule used.

3.     Describe counting patterns and number patterns on the hundreds chart.

 

 

 

1.     Develop and test generalizations based on observations of patterns and relationships.  Explore simple functions, such as finding any term in a pattern.

 

 

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

Materials:(per pair) Attribute blocks; yarn or a shoelace

Teacher:  Demonstrate how to create a pattern using attribute blocks of different sizes, colors and shapes. Continue the pattern three times. Ask the children to tell what comes next.

Children: Partner A makes a pattern three times with attribute blocks and says it aloud to his/her partner.  Partner B circles the repeating part of the pattern using the yarn or shoelace and extends it. Partners switch roles and repeat.

Scoring Rubric

The student:

Score of 3: Meets or exceeds the objectives of the task.  Demonstrates a high level of understanding.  Student can create a repeating pattern and explain the attributes used.  He/she can identify the repeating part of the pattern and extend it.

Score of 2: Partially meets the objectives of the task.  Demonstrates some understanding. Student can create a pattern, explain the pattern by attributes or identify the repeating part or extend the pattern.  He/she can not do all of the tasks.

Score of 1: Does not meet the objectives of the task.  Demonstrates poor or incorrect understanding. Student does not clearly understand the concept of pattern.  He/she can not extend the existing pattern or discuss differentiating attributes.

Score of 0: Student shows no understanding of the problem or how to arrive at a solution.             

Task 2

Materials:  9 attribute blocks per student; graphic organizer worksheet

Teacher:  Demonstrate how to take the 9 attribute blocks and sort them into two groups.  Describe how you sorted the two groups.  Model how to write the addition sentence that goes with the sorting (____blocks + ____blocks = _____ blocks in all). Hand out the graphic organizer worksheet to each child and explain to students how they will show their work. 

Students:  Sort the 9 attribute blocks into 2 groups.  Using the graphic organizer, draw the groups in the boxes provided, write how the blocks were sorted and write an addition sentence to go with the groups.

 

Scoring Rubric

The student:

Score of 3: Meets or exceeds the objectives of the task.  Demonstrates a high level of understanding.  Student can separate/sort sets of objects and explain the separation.  He/she can write an addition sentence to go with the sorting and complete a graphic organizer.

Score of 2: Partially meets the objectives of the task.  Demonstrates some understanding. Student can separate/sort objects and explain the separation, write an addition sentence to go with the sorting, or complete a graphic organizer.  He/she can not do all of the above tasks.

Score of 1: Does not meet the objectives of the task.  Demonstrates poor or incorrect understanding. Student does not clearly understand the concepts of sorting, representing groups with addition sentences and graphic organizers.

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

 

Teacher Observations

Daily Work

Center Work

Homework

Topic Assessments

District Assessments

 

 

 

 

 

Student Name:  ______________________________________________

 

Date:  _________________________________

 

Assessment – Task 1

Grade 1 – Algebraic Reasoning

 

Directions:

 

Materials (per pair of students): attribute blocks, yarn or a shoelace

 

Teacher: 

*      Demonstrates how to create a pattern using attribute blocks of different

       sizes, colors and shapes. 

*      Continue the pattern three times.

*      Ask the children to tell what comes next.

 

Children:

*      Partner A makes a pattern three times with attribute blocks and says it

          aloud to his/her partner.

*      Partner B circles the repeating part of the pattern using the yarn or shoelace

and extends it.

*      Partners switch roles and repeat.

 

 

Teacher Observations:

 

1.     Child can create a repeating pattern (3 times) and explain the attributes used.

 

2.     Child can identify the repeating part of a pattern and extend it.

 

 

Scoring Rubric

The student:

3   Meets or exceeds the objectives of the task.  Demonstrates a high level of understanding.  Student can create a repeating pattern and explain the attributes used.  He/she can identify the repeating part of the pattern and extend it.

2   Partially meets the objectives of the task.  Demonstrates some understanding. Student can create a pattern, explain the pattern by attributes, identify the repeating part or extend the pattern.  He/she does not complete all of the requirements.

1   Does not meet the objectives of the task.  Demonstrates poor or incorrect understanding. Student does not clearly understand the concept of pattern.  He/she can not extend the existing pattern or discuss differentiating attributes.

0   Student shows no understanding of the problem or how to arrive at a solution.    

 

 

 

 

Name:  _________________________Date: _____________

 

Assessment – Task 2

Grade 1 – Algebraic Reasoning

 

Sort 9 attribute blocks into two groups.

  Draw them below.

 

 

 

 

 

 

 

 

2.  How did you sort your blocks?

 

I sorted the blocks by __________________.

 

 

3.  Write an addition sentence to go with your groups.

 

 

________  +  ________  =  ________ blocks in all

 

        

 

Scoring Rubric:

The student:

3   Meets or exceeds the objectives of the task.  Demonstrates a high level of understanding.  Student can separate/sort sets of objects and explain the separation.  He/she can write an addition sentence to go with the sorting and complete a graphic organizer.

2   Partially meets the objectives of the task.  Demonstrates some understanding. Student can separate/sort objects and explain the separation, write an addition sentence to go with the sorting, or complete a graphic organizer.  He/she can not do all of the above tasks.

1   Does not meet the objectives of the task.  Demonstrates poor or incorrect understanding. Student does not clearly understand the concepts of sorting, representing groups with addition sentences and graphic organizers.

0   Student shows no understanding of the problem or how to arrive at a solution.             

 

 

GRADE:     1

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 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.  Geometric relationships and measurements help us to solve problems and make sense of our world.
  2. Objects have measurable attributes and there are units, systems, and processes of measurement.

3.     Appropriate techniques and tools must be applied to determine measurements.

  1. All objects can be described by their position in space.
  2. Two and three-dimensional shapes can be compared and classified by common characteristics.
  3. Minutes, hours, days, weeks, months and years are all means of telling time

 

 

 

1.     What is measurement?

2.     How do we use measurement every day?

3.     Why do we measure things?

4.     Can everything be measured?

5.     How did people measure things before there were rulers?

6.     How would you know when to come to school if there were no clocks?

7.     How are things shaping up?

 

Knowledge and Skills

What students are expected to know and be able to do

Students will know that…

A.                 Shapes and solids can be classified by common characteristics.

 

 

 

 

 

 

 

B.                 Positional language helps precisely to describe, name and interpret direction and position of objects.

 

 

C.                Calendars and clocks help to plan and sequence events.

 

 

 

 

 

 

 

 

D.                Objects and physical referents can be used as nonstandard units to help make estimates of length, area, volume, weight and temperature.

 

 

 

 

 

 

 

 

 

E.                 Standard units of measure are used to communicate measurement in a universal manner.

 

Students will be able to…

1.     Sort, build, name, and draw two- and three-dimensional objects.

2.     Use a variety of materials to create two- and three-dimensional designs and copy them from visual memory.

3.     Create and explore shapes and designs with a line of symmetry.

 

 

1.     Indicate relative position, direction and location with terms such as inside, outside, top, bottom, left and right.

 

 

1.     Estimate and compare the length of time needed to complete tasks using terms such as longer and shorter.

2.     Use the calendar to identify dates, days, weeks, months and to plan and sequence events.

3.     Tell time to the hour with analog and digital clocks.

 

 

1.     Solve tessellation problems by filling a two-dimensional region with polygons in one or more ways.

2.     Use physical referents to make, describe and use estimates to determine the reasonableness of answers to measurement problems.

3.     Use estimation, physical referents and nonstandard units to sort and compare objects by length, area, volume, weight and temperature.

 

 

1.     Explore using the standard units of inch and centimeter to estimate and measure length.

 

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

Materials:  Growing with Mathematics Grade 1 Assessment book---Topic 7 Check-Up A Form 7.1 pages A-94 and A-95 and Topic 7 Performance Task B Form 7.4 page A-99; unifix cubes

 

Scoring Rubric 

The student:

Score of 3: Meets or exceeds the objectives of the task.  Demonstrates a high level of understanding.  Student can make reasonable estimates of area and weight.  He/she can recognize 2- and 3- dimensional shapes.

Score of 2: Partially meets the objectives of the task.  Demonstrates some understanding. Student can either make reasonable estimates of area and weight or he/she can recognize 2- and 3- dimensional shapes. He/she can not do both of the above tasks.

Score of 1: Does not meet the objectives of the task.  Demonstrates poor or incorrect understanding. Student does not clearly understand the concepts of estimated and actual measurements of area and weight. He/she can not recognize 2- and 3- dimensional shapes. 

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

 

Task 2

Materials: A Day in the Life of… worksheet; scissors; glue; crayons 

Teacher:  Give the student the worksheet.  Model how to complete it.

Student:  Fill in name on the blank following “A Day in the Life of __________.”  Cut out the digital times and paste them in chronological order under the correct box. Draw the hands on the analog clock in the corner of each box to match the digital time. Draw a picture of something you do at each of the given times in each of the three boxes. Tell your teacher about your pictures.

Scoring Rubric

The student:

Score of 3: Meets or exceeds the objectives of the task.  Demonstrates a high level of understanding. .  Student demonstrates a complete understanding of calendar questions and can accurately order and describe daily events. He/she demonstrates a clear understanding of time using both analog and digital clocks.

Score of 2: Partially meets the objectives of the task.  Demonstrates some understanding. Student can only respond to some of the calendar questions accurately.  He/she may or may not be able to order daily events or tell time using an analog or digital clock

Score of 1: Does not meet the objectives of the task.  Demonstrates poor or incorrect understanding. Student does not clearly understand the purpose of a calendar.  He/she can not identify today, tomorrow or yesterday. He/she can not order daily events or understand time using an analog and/or digital clock.

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

 

 

 

Teacher Observations

Daily Work

Center Work

Homework

Topic Assessments

District Assessments

“Calendar Questions” worksheet

 

 

Assessment – Grade 1 -  Geometry and Measurement – Task 2

 

A Day in the Life of ______________________________

 

 

 

    4:00 in the afternoon                   7:00 in the morning                              8:00 at night

 

Scoring Rubric:

The student:

3   Meets or exceeds the objectives of the task.  Demonstrates a high level of understanding. .  Student demonstrates a complete understanding of calendar questions and can accurately order and describe daily events. He/she demonstrates a clear understanding of time using both analog and digital clocks.

2   Partially meets the objectives of the task.  Demonstrates some understanding. Student can only respond to some of the calendar questions accurately.  He/she may or may not be able to order daily events or tell time using an analog or digital clock

1   Does not meet the objectives of the task.  Demonstrates poor or incorrect understanding. Student does not clearly understand the purpose of a calendar.  He/she can not identify today, tomorrow or yesterday. He/she can not order daily events or understand time using an analog and/or digital clock.

0   Student shows no understanding of the problem or how to arrive at a solution.             

 

 

 

Name: ______________________________  Date:  _______

 

“Calendar Questions”

“Other Evidence” Worksheet

Grade 1 – Geometry and Measurement

 

Use your calendar to answer the following questions.

 

1.         What is the month?  ________________________

 

2.         <