1. Math Files Part Two (Older)
Katherine A. Mileto
Math and Science for Young Children
February 21, 2013
Math Files Part Two (Older)
Champlain College
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3. Math Files Part Two (Older)
Geometry
Book(s)
• The Greedy Triangle by Marilyn
Burns
Objective(s)
• Explore attributes of plane shapes
Vocabulary
• Corner(s)
• Angle(s)
• Side(s)
• Point(s)
Skills
• Shape recognition
• Describing attributes
• Comparing Shapes
NCTM (National Council of Teachers of
Mathematics) Expectations
• Recognize, name, build, draw, compare,
and sort two-and three-dimensional shapes.
• Describe attributes and parts of two- and
three-dimensional shapes
Attributes of Plane Shapes
Each plane shape has attributes that make it unique and recognizable. A square has four equal sides and
four corners. A rectangle also has four sides. However, a rectangle has two opposite sides that are long
and two opposite sides that are short. A triangle has three sides and three corners. A circle is a plane
shape that has no sides or corners. Size and color are also attributes. Learning the basic shapes
introduces the children to shape and attribute vocabulary and prepares children for more advanced skills
in geometry and algebra, such as sorting and classifying (Learning Resources 2006).
Naturalistic Activity: At morning meeting read the story, The Greedy Triangle by Marilyn Burns. After
the story introduce the bucket of plane shapes. Show the students all the different shapes in the bucket.
Tell the students that the shapes will be a new addition to the math center. Allow the students to explore
the shapes at planning time. Write what you observe as the students explore the shapes. Take note of who
uses the correct terminology and who needed help with the shape names. Also note if the students
discussed the shapes’ attributes. Remember to make comments to the students as they play like, I see you
used the triangles points to connect the group of triangles together.
Structured Activity: Here is a problem demonstrating attributes of plane shapes.
Nicky and Louisa are drawing shapes on the chalkboard. Nicky draws a shape that has four sides. All the
sides are the same length. Louisa draws a shape that has three sides. What shapes did Nicky and Louisa
draw? Are the shapes the same or different? How can you tell?
Introduce the problem. Then have children do the activity to solve the problem.
Distribute bags filled with several matching pairs of Attribute Blocks to each group.
1. Have children close their eyes, reach into the bag, and pull out a block. Children should say the name
of the shape they chose and note how many sides and corners it has.
2. Next, children should reach into the bag and try to find a shape that matches the first block they chose.
Have children count to make sure that the two blocks have the same number of sides and corners. Ask:
Are the two shapes the same?
3. Finally, have children put their shapes back in the bag and pick out two new blocks that are different
from each other. They should count the number of sides and corners and name the shapes.
Lookout! Some children may confuse the shapes especially the rectangle and the square. If this happens,
show a square and talk about how all the sides are the same. Then lay the square on top of a rectangle and
point out that the rectangle has two long sides and two short sides.
Informal Activity-While the students are playing with the shapes is small groups-
• Hold up a square. Ask: What shape is this? How many sides does it have? How many corners does it
have?
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5. Math Files Part Two (Older)
Operations with Whole Numbers
Book(s)
• Rooster Off to See the World by Eric
Carle
Objective(s)
• Explore different arrangements of the
same number.
Vocabulary
• Arrangement
• Groups
• Shapes
• Numbers-One through Thirty
Skills
• Counting
• Representing numbers
• Visual thinking
NCTM (National Council of Teachers of
Mathematics) Expectations
• Count with understanding and recognize
“how many” in sets of objects.
• Develop understanding of the relative
position and magnitude of whole numbers
and of ordinal and cardinal numbers and
their connections.
• Connect number words and numerals to the
quantities they represent, using various
physical models and representation.
Number Shapes
In this lesson, children develop their “number sense” by investigating numbers in different arrangements.
This kind of work provides children with an opportunity to practice their counting skills, helps children
develop some visual sense about quantity as they see same-number groups arranged in different ways, and
helps children to expand their number sense as they begin to realize that a group of 7, for example, is
always 7 no matter how the group is arranged (Learning Resources 2006).
Naturalistic Activity: During morning meeting read Rooster Off to See the World by Eric Carle. As you
read make sure you point out the illustrations on the page and at the top corners to comment on how the
animals are arranged in groups. Be clear that the animal groups are growing and that the groups are
changing size and shape. After the story, tell the children that the snap ovals and snap cubes will be
available during planning time. Demonstrate with the cubes how to snap them together to make larger
chains or configurations. Show the children how they can take a group of cubes and make an arrangement
with them. During planning time take written observations of how the students are using the snap cubes
and snap ovals. Note if the students are comparing the shapes of cubes/ovals they are creating and if they
are making comments about how may cubes/ovals they are using. Remember to make comments on their
creations such as, I see you used ten ovals and made the letter V, as the children are playing.
Structured Activity: Here is a problem about number arrangements.
Mrs. Kim gave each child some Snap Cubes to build with. Bryan connected his cubes in a line to build a
long stick shape. Tina connected her Cubes in the shape of the letter T. Bran says that his shape has more
Cubes because it is longer than Tina’s shape. Is Bryan correct?
Introduce the problem. Then have children do the activity to solve the problem.
Give 24 Snap Cubes and a Number Shape Worksheet, found in the black line masters section of the lesson
plan book labeled as BLM 2, to each child.
1. Have children build Bryan’s shape in Exercise one on the worksheet. Ash them to count the Cubes and
write the number.
2. Now have children build Tina’s shape in Exercise 1 on the worksheet. Ask them to count the Cubes
and write the number. Ask: Do the shapes have the same number of Cubes? How can you tell?
3. Have children tell how the shapes are the same and how they are different. Then have children repeat
for worksheet Exercise 2.
Lookout! Watch for children who have difficulty understanding that the same number can “look” many
different ways. Give these children 10 Cubes. Have them arrange 5 Cubes in 2 different ways. Then have
children compare the shapes side-by-side and count the number of Cubes in each shape.
Informal Activity- While the students are playing with the snap ovals/cubes is small groups-
• Have children refer to one of the Number Shapes Worksheet (BLM 2) exercises.
• Ask: What does Bryan’s shape look like to you? How many Snap Cubes is it made of? How do you
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7. Math Files Part Two (Older)
Patterns
Books(s)
• Eight Hands Round: A Patchwork
Alphabet by A.W. Paul
Objective
Identify and extend a color pattern.
Vocabulary
• Alternating
• Color Words-Red Green, etc
• Pattern Types AB, AAB, ABC
• Extend
• Create
Skills
• Recognizing patterns
• Extending patterns
• Predicting
NCTM (National Council of Teachers of
Mathematics) Expectations
• Sort, classify, and order objects by size,
number, and other properties.
• Recognize, describe, and extend patterns
such as sequences of sounds and shapes or
simple numeric patterns and translate from
one representation to another.
• Analyze how both repeating and growing
patterns are generated.
Extend Color Patterns
Identifying and extending a color pattern involves recognizing how the colors in the pattern are organized.
Children must understand that patterns involve repetition in order to understand how a pattern should be
extended. Recognition of patterns is one of the most important skills in the development of algebraic
reasoning (Learning Resources 2006).
Naturalistic Activity: During morning meeting read Eight Hands Round: A Patchwork Alphabet by A.W.
Paul to the students. Then use the students to model/play a pattern. Ask the students to identify the pattern
you made. After the correct guess ask the students,” what would come next?” Play this game a few times,
each time using a different pattern type and explain the pattern type’s name to the students. Before you
dismiss the students from the carpet remind them to look for patterns around the room. Tell them you are
going to ask them later, at math time, what patterns they have noticed. Then point out to the students that
the Unifix cubes are in the math center today. During planning time observe the students as they play with
the Unifix cubes. Note if they make patterns and what type. Remember to make comments such as; I see
you used two alternating colors (name the colors used) to make an AB pattern type.
Structured Activity: Here is a problem about identifying and extending a color pattern.
Mr. Matthews is making a path of colored construction paper leading from the inside of the classroom to
the playground. He wants the path to make a color pattern. He has started the pattern in this order: red,
blue, and red, blue, red. What color should go next?
Introduce the problem. Display a simple AB color-pattern train of Unifix cubes. Tell children that a
pattern is a set of things that repeats in order. Explain that a color pattern is a set of colors that repeat in a
specific order. Then have children o the activity to solve the problem. Distribute Cubes to each pair of
children.
1. Have children work in pairs to make a pattern train of Cubes in the following order: red, blue, red, blue,
red.
2. Say: I guess that the next Cube in the patter train is red. Tell children to add a red cube to the end of
the train. Have them examine the train. Then, ask: Was my guess correct? Does the red Cube belong
at the end of the train? Guide children to recognize that the red Cube is not placed correctly. Have
children remove the red Cube from the end of the train.
3. Say: The red Cube was not correct. Ask: What Cube should we try next? Have children add a blue
Cube. Ask: Does the blue Cube belong at the end of the train? Guide children to recognize that the
blue Cube correctly extends the pattern. Then ask children to explain the repeating pattern of the
Cubes in the train (1 red and 1 blue).
Lookout! Some children may have trouble determining the pattern and understand how it was extended,
even after adding the blue cube to its correct place at the end of the rain. Have children start at the
beginning of the train (red, blue, red, blue, red, blue) and break the train apart by color as they explain the
number and color of the Cubes they are removing. Use the cadence of your voice to help establish the
rhythm of the pattern. For example, say: red, blue, (pause), red, blue, and so on.
Informal Activity- While the students are playing with the Unifix cubes is small groups-
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8. Math Files Part Two (Older)
Reflection
Please note that the above lessons are based off of Learning Resources Hand-On Standards (2006) math lessons, for the
Kindergarten Class as a supplement to the math curriculum already in place. The kindergarten class uses Harcourt School Publishers
(HSP) Math (Houghton Mifflin Harcourt 2009). The HSP Math (Houghton Mifflin Harcourt 2009), is a strictly worksheet based
curriculum which allows for very little hands on activities and exploration. Using the adapted lessons allows for some hands on
learning to the math topics covered by the HSP Math (Houghton Mifflin Harcourt 2009), curriculum.
The above topics were chosen because they build upon the foundations of mathematics. Students need to understand and
recognize the ways numbers, patterns, and shapes are used in real world situations (Charlesworth & Lind 2010). I was able to
introduce each topic during morning meeting and then observe how they explored the materials at planning time. Later in the
afternoon I was then able to reflect and review with the students what they did during planning time before the structured math activity
took place. Making the connections with the students prior to the structured lesson helped the students deepen their knowledge of the
subject matter. The students also enjoyed their free exploration time with the materials. There was a lot of, “Oh Ms. Kate look at this
shape I made using 39 snap ovals” and “Ms Kate I can make a hexagon using only triangles”. The students got the opportunity to see
the topic in many contexts, so that they were comfortable playing with the materials and using the vocabulary in everyday situations. I
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9. Math Files Part Two (Older)
also found that my role modeling before the lesson intrigued their interest in manipulating the materials later on in the same day and
weeks later.
References
Charlesworth, R & Lind, K. (2010) Math and science for young children. Wadsworth, New York.
Houghton Mifflin Harcourt (publishers) (2009) Harcourt school publisher (hsp) math. Houghton Mifflin Harcourt Inc.
Learning Resources (publishers) (2006) Hands on standards: Photo-illustrated lessons for teaching math with manipulatives,
grades prek-k. Learning Resources Inc.
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10. Math Files Part Two (Older)
also found that my role modeling before the lesson intrigued their interest in manipulating the materials later on in the same day and
weeks later.
References
Charlesworth, R & Lind, K. (2010) Math and science for young children. Wadsworth, New York.
Houghton Mifflin Harcourt (publishers) (2009) Harcourt school publisher (hsp) math. Houghton Mifflin Harcourt Inc.
Learning Resources (publishers) (2006) Hands on standards: Photo-illustrated lessons for teaching math with manipulatives,
grades prek-k. Learning Resources Inc.
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