Andrea
L. Holland
Mathematics Grade 2
High risklow 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.
ª
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
ª 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 onetoone 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). Onetoone 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
Followup
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
Followup
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
Followup
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 lineup
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
Followup
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 nonstandard 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
Followup
Activity: Access the Internet site http://www.awl.com/www.cuisenaire.com/handkids.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
Followup
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
Followup
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.
0
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
Followup
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:
BarattaLorton,
Mary. Mathematics Their Way. Addison Wesley Publishing Company,
CA. 1976. 396pp.
Pearl
River School District. A Conceptual Scope and Sequence: Elementary
Mathematics K6. 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.
