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Grade 1 Math

GRADE: Kindergarten

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. 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
Patterns and functions help us describe data and physical phenomena and solve a variety of problems. There are patterns all around us. Patterns are repeating sequences that can be created or occur naturally in our world. Patterns help us predict what comes next. Attributes are parts or characteristics of an object. Objects can be sorted or classified by attributes.	What is a pattern? Where can we find patterns in our world? How do you predict what might come next in a pattern? What are some different ways we can group objects?
Knowledge and Skills What students are expected to know and be able to do
Students will know that… Objects can be classified using attributes such as size, shape, color, texture, orientation and use. Patterns are described by rules using the physical attributes and position of various objects in the sequence.	Students will be able to… Describe attributes of objects. Sort and classify objects and describe the rule that was used. Recognize, copy and extend simple patterns of sounds, colors, shapes, textures and numbers. Describe the pattern’s rule and identify patterns in a variety of contexts, such as a poetry, art music, body movement and physical environment. Make comparisons and describe qualitative and quantitative changes of a given pattern (more, less, bigger, smaller, longer, one more, one less).
STAGE 2: DETERMINE ACCEPTABLE EVIDENCE
Performance Task: Authentic application in new context to evaluate student achievement of desired results	Other Evidence: Application that is functional in a classroom context only to evaluate student achievement of desired results
Kindergarten – Algebraic Reasoning Task 1 Directions: Materials: Small classroom objects (paperclips, small toys) Play dough Small rolling pin Teacher: Model rolling out play dough. Show student how to imprint objects into dough. Demonstrate how to create a pattern and repeat it three times. Ask student to tell what comes next. Student: Students print patterns into the play dough with the objects. Students orally describe the pattern. Students tell what part repeats. 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: 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, identify the repeating part or extend the pattern. 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 concept of pattern. He/she can not extend the existing pattern or discuss differentiating attributes. 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

Kindergarten – Algebraic Reasoning

Directions:

Materials:

Small classroom objects (paperclips, small toys)

Play dough

Small rolling pin

Teacher:

Model rolling out play dough.

Show student how to imprint objects into dough.

Demonstrate how to create a pattern and repeat it three times.

Ask student to tell what comes next.

Student:

Students print patterns into the play dough with the objects.

Students orally describe the pattern.

Students tell what part repeats.

Teacher Observations:

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

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

Rubric for scoring: (0-3)

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 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 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.

GRADE: Kindergarten

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
Geometric relationships and measurements help us to solve problems and make sense of our world. Objects can be measured with just about anything. By comparing objects we can determine which object is heavier or lighter, shorter or taller, or which object has more or less. Minutes, hours, days, weeks, months, and years are all means of telling time. Two-dimensional and three-dimensional shapes can be compared by thinking about common characteristics. All objects can be described by their position in space.	What is measurement? How do we use measurement everyday? Why do we measure things? Can everything be measured? 5. How are things shaping up?
Knowledge and Skills What students are expected to know and be able to do
Students will know that… Shapes and solids may be identified and sorted by physical characteristics. Positional language helps describe location, direction, and position of objects and their parts on planes and in space. Calendars and clocks are used to measure and record time. Non-standard units can be used to estimate measures of length, temperature, weight and capacity.	Students will be able to… 1. Sort, order, compare and use comparative language to describe small sets of objects sequenced by size-length, area, volume. 2. Sort, describe likenesses and differences, compare two- and three- dimensional shapes and identify shapes and solids in the environment, such as triangles, squares, rectangles, circles, cubes, spheres, cylinders and cones. 3. Use a variety of materials to create geometric shapes and solids and build copies of simple shapes and designs by direct observation and by visual memory. 1. Describe the position, location and direction of objects, or parts of objects, using terms such as inside, outside, top, bottom, close and closer. 1. Locate a date on the calendar (yesterday, today, and tomorrow) and sequence events using terms like before and after. 1. Estimate the number of objects in a handful, and then count to verify. 2. Estimate the amount of objects in a set using benchmarks of 10, and count to determine if the estimate is more or less. 3. Explore, describe and discuss strategies to estimate length, area, temperature and weight using nonstandard units to compare. 4. Explore using everyday objects as nonstandard units to measure length, area and capacity. 5. Compare the length of two objects using a balance scale and identify which is heavier.
STAGE 2: DETERMINE ACCEPTABLE EVIDENCE
Performance Task(s) Authentic application in new context to evaluate student achievement of desired results	Other Evidence Application that is functional in a classroom context only to evaluate student achievement of desired results
Task 1 Materials: any size, empty gift box; pattern block shapes (square, circle, rectangle and triangle) and geometric solids (sphere, cube, cone and cylinder); teacher recording sheet Teacher: Give the student one of each of the geometric solids and pattern blocks. Have him/her identify each shape. Place the empty box top or bottom on the table. Ask student to complete the following directions. Put the rectangle inside the box. Put the cone on top of the rectangle. Put the circle next to the rectangle. Put the cube near the box. Put the cylinder closer to the box than the cube. Put the sphere inside the box. Put the triangle above the box. Put the square somewhere of your choice and tell me where you put it. Scoring Rubric The student: Score of 3: Meets or exceeds the objectives of the task. Demonstrates a high level of understanding. Student can identify shapes and solids and describe their position in space. Score of 2: Partially meets the objectives of the task. Demonstrates some understanding. Student can either identify shapes and solids or describe their position in space. 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 concept of shapes and positional language. Score of 0: Shows no understanding of the problem or how to arrive at a solution. Task 2 Materials: calendar (either classroom or small, desktop version); A Day in the Life of… worksheet; scissors; glue; crayons; teacher recording sheet Teacher: Show the student a calendar. Ask the following questions: What is this and for what is it used? What is today’s date? What will the date be tomorrow? What was yesterday’s date? 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 words and paste them in chronological order under the correct box. Draw a picture of something you do in the morning, afternoon and night in each of the three boxes, again in chronological order. 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 can locate a date on a calendar. He/she can sequence events. Score of 2: Partially meets the objectives of the task. Demonstrates some understanding. Student can either locate a date on a calendar or sequence events. 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 a calendar or sequential events. He/she can not read a calendar or put events in chronological order. Score of 0: Shows no understanding of the problem or how to arrive at a solution. Task 3 Materials: Tile Challenge worksheet; 1” color tile squares; balance scale; box of classroom objects that fit in the balance scale; overhead projector Teacher: Draw a rectangle on the overhead. Model how to estimate how many tiles will cover the rectangle using one tile as a guide. Write down the estimate for all to see. Cover the rectangle using the tiles. Count how many tiles were used and write down the actual amount. Discuss the difference if applicable. Take the tiles and place them into one side of the balance scale. Find an object in the box whose weight you would like to compare to the tiles. Estimate which side will be heavier. Place the object in the scale and note the actual finding. Student: Complete the Tile Challenge worksheet. Scoring Rubric The student: Score of 3: Meets or exceeds the objectives of the task. Demonstrates a high level of understanding. Student can make a reasonable estimate of area and weight using non-standard units. Score of 2: Partially meets the objectives of the task. Demonstrates some understanding. Student can make a reasonable estimate of area or weight using a non-standard unit. 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 estimation and measurement. Score of 0: Student 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

Kindergarten – Geometry

Directions:

Materials:

Pattern blocks: circle, square, rectangle, triangle

Geometric Solids: sphere, cone, cylinder, cube

Empty gift box

Teacher:

Have student identify each of the shapes and solids.

Record responses.

Place empty box on tabletop.

Ask student to do the tasks and record responses below.

Teacher Record and Student Task List:

sphere _________________ square _________________

cone __________________ circle _________________

rectangle _______________ cylinder ________________

triangle ________________ cube ___________________

1. Put the rectangle inside of the box. _______________________________

2. Put the cone on top of the rectangle. _______________________________

3. Put the circle next to the rectangle. ________________________________

4. Put the cube near the box. __________________________________________

5. Put the cylinder closer to the box than the cube. _________________________

6. Put the sphere inside the box. _______________________________________

7. Put the triangle above the box. ______________________________________

8. Put the square somewhere of your choice and tell me where you put it!

__________________________________________________________________

Scoring Rubric:

The student:

3 Meets or exceeds the objectives of the task. Demonstrates a high level of understanding. Student can identify shapes and solids and describe their position in space.

2 Partially meets the objectives of the task. Demonstrates some understanding. Student can either identify shapes and solids or describe their position in space. He/she can not do both of the above tasks.

1 Does not meet the objectives of the task. Demonstrates poor or incorrect understanding. Student does not clearly understand the concept of shapes and positional language.

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

Name: ________________________________

Date: ______________________

Assessment – Task 2

Kindergarten – Geometry

Directions:

Materials:

Calendar, either classroom or desktop version.

“A Day in the Life of _________” worksheet.

Scissors, glue, crayons

Teacher

Show student a calendar.

Ask questions and record answers.

Teacher Records:

1. What is this? _______________________________________

2. What is it used for? _____________________________________

3. What is today’s date? ____________________________________

4. What is tomorrow? ______________________________________

5.What was yesterday? ______________________________________

Give student “A Day in the Life of ____________” Worksheet

Have student fill in their name on the blank.

Direct student to cut out words and glue them in chronological order under the correct box.

Student draws “something you do in the morning, afternoon and night” in each of the three boxes, again in chronological order.

Students tells teacher about each of his/her pictures.

Rubric for scoring:

The student:

3 Meets or exceeds the objectives of the task. Demonstrates a high level of understanding. Student can locate a date on a calendar. He/she can sequence events.

2 Partially meets the objectives of the task. Demonstrates some understanding. Student can either locate a date on a calendar or sequence events. He/she can not do both 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 a calendar or sequential events. He/she can not read a calendar or put events in chronological order.

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

A Day in the Life of ___________________

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

afternoon morning night

Name: ___________________________________ Date: _____________

Assessment: Task 3

Kindergarten – Geometry

Tile Challenge

Directions:

Look at the first rectangle below.

Estimate how many tiles you think will cover it.

Write your estimate in the top box.

Measure the rectangle with tiles.

Write the actual answer in the bottom box.

Complete for both rectangles.

1.

estimate

actual

2.

estimate

actual

Directions:

Take the tiles from your last rectangle.

Place tiles in one side of the balance scale.

Find an object in the box whose weight you’d like to

compare to the tiles.

Estimate which side will be heavier.

Complete the sentence below.

3. My object will be heavier or lighter than my tiles. (circle one)

4. After comparing my object to the tiles, I found that my

object was heavier or lighter than my tiles. (circle one)

Scoring Rubric

The student:

3 Meets or exceeds the objectives of the task. Demonstrates a high level of understanding. Student can make a reasonable estimate of area and weight using non-standard units.

2 Partially meets the objectives of the task. Demonstrates some understanding. Student can make a reasonable estimate of area or weight using a non-standard unit. He/she can not do both 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 estimation and measurement.

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