Marie Curie Math & Science Center
 
Andrea L. Holland
Mathematics Grade 2

High risk-low level

Commencement content standard:
 

Standard 3: Mathematics, Science, and Technology. Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics to real world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry. 

 
Benchmark standards: All standards are based on the Elementary level.
 

Content standards

Number and Numeration: Students use number sense and numeration to develop an understanding of multiple uses of numbers in the real world, use of numbers to communicate mathematically, and use of numbers in the development of mathematical ideas.

  Operation: Students use mathematical operations and relationships among them to understand mathematics.

  Pattern: Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.

Performance standards

Number and Numeration

1. Use concrete materials to model numbers and number relationships for whole

numbers and common fractions

2. Relating counting to grouping and to place value

3. Recognize the order of whole numbers and commonly used fractions and decimals

Operation

1. Add, subtract, and divide whole numbers

2. Develop strategies for selecting the appropriate computational and operational 

method in problem solving situations

3. Know single digit addition and subtraction facts

4. Understand the commutative and associative properties

Pattern

1. Recognize, describe, extend, and create a wide variety of patterns

2. Represent and describe mathematical relationships

3. Explore and express relationships using variables and open sentences 

 

Content Standards Or Outcomes
 

The children will be able to use one-to-one counting for items up to 20.

The children will recognize that the addition process is combining parts to make a whole.

The children will use the symbol + to represent the combination of two parts to make a whole.

The children will create, extend, and identify 2 part patterns using a variety of materials.

The children will be able to use Cuisenaire rods to explore number sentences, operations

and their relationship, and the commutative property of addition.

The children will be able to divide groups of objects into equal parts.

The children will successfully add and subtract using 1 digit numbers.

 

Performance Measures

Date:
Child’s Name
Patterns and Cardinal Numbers Rubric

CRITERIA SCORING

Skills

one to one count to 20  4 3 2 1

ordinal numbers to tenth  4 3 2 1

recognize two part pattern by color 4 3 2 1

recognize two part pattern by shape 4 3 2 1

recognize two part pattern by size 4 3 2 1

recognize two part pattern by sound 4 3 2 1

continue a two part pattern 4 3 2 1

divide groups of objects into equal parts 4 3 2 1

add one digit numbers 4 3 2 1

subtract from ten using one digit numbers 4 3 2 1

skip count by 2, 3, 5, 10 4 3 2 1

recognize pattern in math equations 4 3 2 1

use and create number sentences 4 3 2 1

recognize and demonstrate commutative properties of addition 4 3 2 1

recognize and demonstrate associative property of addition 4 3 2 1

DATA COLLECTION

journal exhibits skills 4 3 2 1

journal is neat and readable 4 3 2 1

journal follows correct format including date on each page 4 3 2 1

numbers are written correctly 4 3 2 1

journal shows growth in performance and knowledge 4 3 2 1

 
REFLECTION

demonstrate confidence in skill 4 3 2 1

demonstrate skills to others 4 3 2 1

discusses importance of patterns in Math 4 3 2 1

follow auditory and visual patterns 4 3 2 1
 

DATA

draw representations of two part patterns 4 3 2 1

complete journal with accuracy 4 3 2 1

complete work neatly 4 3 2 1
 

COMPUTER

create a new document and save it 4 3 2 1

enter and edit text 4 3 2 1

open, close, save, and print a document 4 3 2 1

modify style of font and size of text 4 3 2 1

use clip art 4 3 2 1

operate calculator feature 4 3 2 1
 

MATERIALS

use materials appropriately 4 3 2 1

use materials to demonstrate knowledge 4 3 2 1

organize and maintain journal 4 3 2 1

PARAMETERS:

4= Application Mastery (can generate an original problem using the concept and apply it.)

3= Procedural Mastery (can generalize the concept and use it to solve problems without manipulative material).

2= Concept Mastery ( can solve problems and explain the concept used, with or without manipulative materials.)

1= Procedural Exploration (can solve problems based on the concept using real and concrete representative materials. Can explain concept.)

 Enabling Activities:

Lesson: Introduction to materials and rational counting

 Prerequisites: none

Time: 30 minutes

Materials: journal

20 cubes: 10 of one color, 10 of a second color (in a baggy)

colored stickers corresponding to the block’s colors

pencil and crayons

Introduction: Organize class into working pairs. Distribute and organize materials.

Body: Present materials to the children and illicit attributes of the blocks. Encourage playtime with the blocks to explore a variety of uses and structures that may be created. Organize the blocks into a line and ask children to estimate how many blocks they think are there (review the concept of estimation, if necessary). One-to-one count the blocks and determine how many. Encourage partner to monitor that each block is touched and counted. Check for understanding and accuracy. Play with the quantity of blocks to practice rational counting skill.

Questions: What kind of things can you build with the blocks from your bag? Can you guess how many are in the bag? What two colors do you have? Can you show me the color and tell me its name? Can you count them while touching each one? etc.

Literature Link: Today is Monday pictures by Eric Carle

Follow-up activity: Using the journal (date the page), place colored stickers to represent blocks on the paper. Count the number of stickers and place a numeral next to the group.

Conclusion: Display the children’s work in the journal and encourage each child to share one entry. Place materials into a plastic bag and store for the next activity.

Lesson: Creating patterns with sound and color

Prerequisite: none

Time: 50 minutes

Materials: journal

20 cubes: 10 of one color, 10 of a second color (in a baggy)

colored stickers corresponding to the blocks’ colors

pencil and crayons

Introduction: Organize class for large group instruction. Model two part patterns using clap, snap, stomp, pat, etc.

Body: Using a variety of sounds including words, letters numbers, model a variety of patterns and encourage children to mimic and then complete the pattern. Children can demonstrate skill in pairs to allow for checking of comprehension and the security of the child’s feelings within a group setting. Transfer the sounds to color words and pattern two part color patterns. The children will mimic, continue, and then create their own pattern. Children will work in pairs to create a variety of two part patterns.

Questions: Can you hear the pattern that I am making? What two sounds am I using? Can you make the pattern with me? Tell me two colors that you would like to work with? Let’s make a pattern with those two colors.

Literature Link: The Little Fish That Got Away by Bernadine Cook

Follow-up activity: As the pattern is created successfully, use the block stickers to demonstrate the knowledge within the journals. Each child should sticker their pattern and one of his/her partner’s.

Conclusion: Each child may display and model the pattern he/she has created. Journal should display date. Materials should be returned to a plastic bag for the next activity.

Lesson: Symbolic representation of a two part pattern

Time: 50 minutes

Materials: journal

20 cubes: 10 of one color, 10 of a second color (in a baggy)

strips of paper with equally spaced dots

pencil and crayons

Introduction: Organize children into pairs. Review two part pattern using both colors and sounds.

Body: Instruct children to create their own two part patterns. Introduce the strips with the dots. Ask how the children think they can create a pattern using the dot strip. Introduce the bump and straight vocabulary. Encourage children to model with their body’s what a bump might look like and what straight might look like. Model this shapes using the dot strip. Working in pairs have the children create patterns using bump and straight. Encourage the creation of any symbols that might also be appropriate.

Questions: What do you think a bump looks like? What do you think straight looks like? Can you show me? Can you think of some other symbols we can use on the dot strip? What do you think we can use these dot strips for? Can you make a pattern using the dot strip. Show me the bump/straight pattern using your body?

Literature Link: Seven Blind Mice by Ed Young

Follow-up activity: Paste the strip to the journal and have each child model his/her pattern with their bodies. Using Microsoft Word, the children can create bump and straight patterns using the insert lines and freeform line functions.

Conclusion: Each child has the opportunity to demonstrate to the class his/her bump/straight patterns. Patterns may include other activities and may become three of four part. Materials are returned to appropriate place and blocks are returned to the baggy.
 

Lesson: Skip counting by 2, 3, 4, 5, and 10

Time: 5 minutes

Materials: none

Introduction: This activity is done as a regular classroom activity. It will increase knowledge and automaticity.

Body: During circle time the children will use a variety of techniques to skip count in chorus. Using a clap and silent pattern the children will skip count by 3s. Each child will say a number and the group will clap together on the factor of three. (ex. 1, 2, 3 (clap), 4, 5, 6 (clap) 7, 8, 9 (clap)...) When exiting the room the children will be encourage to recite a variety of factors as chosen by the teacher. (ex . As we line-up let’s skip count by two’s.) The children can effectively use this with either a prescribed or random line order.

Questions: Why do you think it is important to skip count? Can you think of any ways that you can use skip counting?

Literature Link: Do You Want To Be My Friend by Eric Carle

Follow-up Activity: The children can use a tape recorder to record the groups counting. Listening to the skip counting during center time will reinforce familiarity and automaticity.

Conclusion: This activity will continue throughout the year and will become increasingly more intricate and complicated.

Lesson: Measuring using non-standard forms of measure(Cuisenaire Rods)

Time: 40 minutes

Materials: Cuisenaire rods and Cuisenaire Graph paper

journal

crayons and pencils

Albert Inchworm’s Inching Around" handout

Introduction: Organize class into working pairs. Introduce Cuisenaire rods and encourage play and exploration time with materials.

Body: After sufficient play time ask the children to create stairs with the Cuisenaire rods. Demonstrate that each color has a unique size and that the rods will be consistent. Using the ones rod have the children explore to locate the longest rod and how many ones it measures. Introduce the concept of "train" to the class and have them create a variety of trains using both size and color as a reference point. Copy and color the pattern onto the graph paper and paste the paper into the journal.

Questions: Why do you think that making the stairs is helpful? Can you think of any other way to group your rods? Show your partner. What color is equal to two ones? three ones? four ones?, etc. Why do you think the patterns are called trains?

Literature Link: Pancakes For Breakfast by Tomie DePaola

Follow-up Activity: Access the Internet site http://www.awl.com/www.cuisenaire.com/hand-kids.html and have each child complete the activity Albert Inchworm: How Big is a Hand? Encourage the children to use a variety of train to measure his/her hand and partner’s hand. Using everyday items measure each item with the rods. Draw the item in your journal and draw the train used to measure it.

Lesson: Associative property of addition

Time: 30 minutes

Material: Cuisenaire rods and Cuisenaire graph paper

journal

crayons and pencils

Introduction: Organize the class into working pairs. Reintroduce the Cuisenaire rods and review the consistency of their values.

Body: Direct the children to create tens using two blocks. After creating as many pairs that equal ten, have them put the like pairs together to represent the associative property of the addition equation. Copy and color the number sentences onto graph paper and transfer it to the journal.

Questions: Are there any number sentences that showed equal numbers. Can you use Cuisenaire rods to show 10 + 0= 10? Do you think this would work for bigger numbers?

Literature Link: Have You Seen My Cat? by Eric Carle

Follow-up Activity: Access the Internet site http://www.awl.com.www.cuisenaire.com/handskids.html and have each child complete the available activities. Expand the concept to real numbers that are larger. Continue the challenge to addition/subtraction association.

Lesson: Patterning in the real world

Time: 50 minutes

Materials: magazines and photographs

journal, crayons, and a pencil

Introductions: We have been exploring math patterns, using real things, now we will identify patterns that we can observed.

Body: Patterns occur in nature and through observation we can identify them. Encourage the children to look around the room and identify patterns (i.e. a stack of dittos stacked right and left) Go outside and look for patterns (shadows of the tree limbs, the bicycle rack etc.). Using the journal draw and color the patterns that the children have observed.

Questions: Why do you think we study patterns in math? Do you think that patterning might help you predict the answers?

Literature Link: The Jacket I Wear In The Snow by Shirley Neitzel

Follow-up Activity: Using the magazines and photographs, look for patterns within the pictures. Cut out the patterns and paste them into the journal. Write a sentence explaining the pattern and why it was created.

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Lesson: Building onto existing patterns

Time: 50 minutes

Materials: different shaped and colored objects in multiples

journal, crayons, and a pencil

Introduction: Organize the class into a circle that flows in a clear path. Allow room for each child to comfortably work without infringing on the space of a neighbor. Demonstrate a simple pattern and ask a volunteer to continue the pattern. Introduce working materials and the concept of working in a round robin.

Body: Each child should create a complex patter with accuracy. After repeating the pattern twice, on the signal move to the nest station. Each child then continues someone else patterns for two repetitions. Continue this procedure until the children are back to their own pattern. Check the work for accuracy. Observe whether the pattern changes. Did it continue in the changed form or was it corrected?

Questions: Was it easy to follow the patterns? What clues did you look for? Did they represent a variety of color, shape, and size? Why would patterns be helpful in completing work?

Literature Link: Have You Seen My Duckling by Nancy Tafuri

Follow-up Activity: Send the materials home in a baggy and encourage the children to have their family play the patterning round robin. Ask the children to report back on their findings and where their family members had difficulty.

Lesson: Using Power Point to create patterns

Time: 150 minutes

Materials: computers with Power Point software

Introduction: Organize children into working pairs. Review patterns and how they can be represented. Introduce Power Point and how to make a presentation.

Body: After demonstrating the variety of possibilities of Power Point, guide each group through the process of making a demonstration. Their presentations should highlight patterns within a variety of formats and skill levels. Present the completed presentations to the whole class

Questions: Can you recognize the patterns within your classmates work? Are the patterns easy to find or are they hidden? Do you think the computer will allow the pattern to go on and on? How could we find out?

Conclusion: Patterns exist in Math and when identified they can help solve problems more efficiently.   Bibliography:

Baratta-Lorton, Mary. Mathematics Their Way. Addison Wesley Publishing Company, CA. 1976. 396pp.

Pearl River School District. A Conceptual Scope and Sequence: Elementary Mathematics K-6. no copyright stated. 60 pp.

Solomon, Pearl. The Curriculum Bridge: From Standards to Actual Classroom Practice. Corwin Press, CA. 1998.

Thiessen, Diane (et al.). Elementary Mathematical Methods. MacMillan Publishing Co., NY. 1989. 642pp.

The University of the State of New York. Mathematics, Science, & Technology Resource Guide. no copyright stated. not paged.

 

St. Thomas Aquinas College, 125 Route 340, Sparkill NY 10976-1050