Math Standards

Math Standard 1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems
   
Benchmark 1.1 : Count with understanding and recognize “how many” in sets of objects
    Benchmark1.2 : Use multiple models to develop initial understandings of place value and the base ten number system
    Benchmark1.3 : Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections
    Benchmark1.4 : Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers
    Benchmark1.5: Connect number words and numerals to the quantities that they represent, using various physical models and representation
    Benchmark1.6 : Understand and represent commonly used fractions

Math Standard 2:
Understand meanings of operations and how they relate to one another cardinal numbers and their connections
   
Benchmark 2.1 : Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations
     Benchmark 2.2: Sort, classify, and order objects by size, number , and other properties

Math Standard 3: Understand patterns, relations and functions
    
Benchmark 3.1 : Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another

Math Standard 4: Represent and analyze mathematical situations and structures using algebraic symbols
     
  Benchmark 4.1 : Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations 

Math Standard 5:
Use mathematical models to represent and understand quantitative relationships
       
Benchmark 5.1 : Model situations that involve the addition and subtraction of whole numbers, using objects, pictures and symbols

Math Standard 6: Analyze characteristics and properties of two-and three-dimensional geometric shapes and develop mathematical arguments about geometric shapes
   
Benchmark 6.1 : Will recognize some basic shapes
     Benchmark 6.2 : Describe attributes and parts of two-and-three dimensional shapes
     Benchmark 6.3 : Investigate and predict the results of putting together and taking apart two-and-three dimensional shapes

Math Standard 7: Understand measurable attributes of objects and the units, systems, and processes of measurement
 
  Benchmark 7.1 : Recognize the attributes of length, volume, weight, area, and time
    Benchmark 7.2 : Compare and order objects according to their attributes
    Benchmark 7.3 : Understand how to measure using nonstandard and standard units
    Benchmark 7.4 : Select an appropriate unit and tool for the attribute being measured.

Math Standard 8: Apply appropriate techniques, tools, and formulas to determine measurements
   
Benchmark 8.1 : Use tools to measure
Math Standard 9: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
 
   Benchmark 9.1 :Pose questions and gather data about themselves and their surroundings

Math Standard 10: Sort and classify objects according to their attributes and organize data about the objects
  
  Benchmark 10.1 : Represent data using concrete objects, pictures, and graphs

Math Standard 11: Select and use appropriate statistical methods to analyze data
  
  Benchmark 11.1 : Describe parts of the data and the set of data as a whole to determine what the data shows

 

Math Standard 1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems

Benchmark 1.1 : Count with understanding and recognize “how many” in sets of objects

Developmental Continuum

·    Given a set containing 10 or fewer concrete items, tell how many are in a set by counting the number of items orally using 1:1 correspondence  

·        Given a set of 10 or fewer concrete items, identify and describe one set as  having more, less, or the same number   of members the other set

·    Count in sequence by rote to 20 or higher

·   Use math language to express quantity in everyday experiences

Example Behaviors

As Zavier sets up his farm during center time, he counts his animals as he puts them in the fence.
 

During snack time, Jelani separates her Fruit Loops into color groups. As she looks at her color groups, she exclaims, “I have more pink than blue”.

When she is ‘it’, Ashley counts aloud to 20 while playing hide and seek.

In housekeeping, Carly tells Anna, “We set the table with four plates at home”.

Comments, Strategies, Evaluation

 

 

 

 

 

 

 

 

 

 

 

Math Standard 1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Benchmark 1.2 : Use multiple models to develop initial understandings of place value and the base ten number system

Developmental Continuum

· Begin to understand the it takes 10 ones to equal 1 ten

Example Behaviors

While counting the number of days at school during calendar time, Ryan adds a straw for the day. He relates that the ten straws in the ones place are the same as one bundle in the tens place.

Comments, Strategies, Evaluation

 

 

 

Math Standard 1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Benchmark 1.3 : Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections

Developmental Continuum

· Compares concrete quantities to determine which is more

Example Behaviors

During snack time, the teacher gives Oliver two goldfish crackers and Keelie four goldfish crackers. Oliver says, "Keelie has more goldfish than me".

Comments, Strategies, Evaluation

 

 

 

Math Standard 1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Benchmark 1.4 : Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers

Developmental Continuum

  • Understand how numbers are used in the environment, e.g. house numbers, phone numbers, birthdays
     

 

  • Recognize that a set of objects remains the same amount if physically rearranged
     
  • Realize that the last number counted is the total amount of objects

 

Example Behaviors

When the fire fighter visited the class, she told the children to call 9-1-1 in case of an emergency. Kinsler later went to the telephone in housekeeping and found the 9-1-1.

Bryce makes a tower 5 blocks tall. He tears it down and makes a road with the same blocks. He exclaims, "Look there’s still 5!"

While the class is counting the bears on the growing number line, the teacher stops before they come to the end. Natalie yells out, "You’re still on 10".

Comments, Strategies, Evaluation

 

 

 

 

 

 

 

Math Standard 1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Benchmark 1.5: Connect number words and numerals to the quantities that they represent, using various physical models and representation

Developmental Continuum

· Distinguish one" from "many"

 

· Identify the numeral that matches a quantity 1-10

 

· Write the numeral that corresponds to a given set up to 10

Example Behaviors

While looking at family pictures, Maria says, "My family has one child and Alex’s family has more."

While playing Millie’s Math House on the computer, Robert matches the appropriate number of jelly beans to the corresponding number.

Amaiya draws three flowers in the writing center and writes the numeral 3 above her picture.

Comments, Strategies, Evaluation

 

 

 

 

 

 

Math Standard 1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Benchmark 1.6 : Understand and represent commonly used fractions

Developmental Continuum

· Divide a set of objects into 2 equal groups

· Recognize parts of a whole

Example Behaviors

While playing in housekeeping, Kyle gives Megan some of the food. He says, "One for me, one for you" as he divides up the food.

During a cooking activity, the teacher cuts an apple in two and Stephen says, "Why did you cut the apple in half."

Comments, Strategies, Evaluation

 

 

 

 

Math Standard 2: Understand meanings of operations and how they relate to one another
Benchmark 2.1 : Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations

Developmental Continuum

· Add and subtract whole numbers using up to ten concrete items

Example Behaviors

The teacher asks the group to put ten teddy grahams on the boat. She tells them that 3 swam away. Jonathon eats 3 and shouts, "There are 7 left".

Comments, Strategies, Evaluation

 


 

Math Standard 2: Understand meanings of operations and how they relate to one another
Benchmark 2.2 : Sort, classify, and order objects by size, number, and other properties

Developmental Continuum

Recognize patterns in their environment by color, shape and size

 

Sort and classify objects by one attribute (size, shape, color)

Order 3 objects by size

 

 

Example Behaviors

During group time Trey notices tha T>J> has a pattern on his shirt. "Look, T.J., your shirt has blue, white, blue, white on it."

While in the math center, Mary llines up the puzzle pieces by shapes on the floor.

While on the playground, Johnny, Susie and Bill collect leaves for the classroom. Susie places them in order fromthe smallest to the largest.

Comments, Strategies, Evaluation

 

 

Math Standard 3: Understand patterns, relations and functions
Benchmark 3.1 : Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another

Developmental Continuum

Algebra

· create and extend simple patterns

 

· recognize, duplicate, and extend patterns

Example Behaviors

 

Jada creates a pattern with her fruit loops at the breakfast table using one red, one yellow, one red, one yellow.

Shirley sets up a pattern on the flannel board using 3 shapes. Alice watches Shirley and continues the pattern. Alice exclaims, "Now it’s my turn. Can you finish mine?"

Comments, Strategies, Evaluation

 

 

 

 

 

 

Math Standard 4: Represent and analyze mathematical situations and structures using algebraic symbols
Benchmark 4.1 : Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations

Developmental Continuum

Algebra

· Begin to use language such as less than, more than, or same number as to describe the relative sizes of sets of concrete objects

Example Behaviors

 

Joshua and Joseph are building in blocks. Joshua exclaims that Joseph has more blocks than he does. Joshua asks for two blocks from Joseph. Joshua counts their blocks and says, "Now we have the same."

Comments, Strategies, Evaluation

 

 

 

 

Math Standard 5: Use mathematical models to represent and understand quantitative relationships
Benchmark 5.1 : Model situations that involve the addition and subtraction of whole numbers, using objects, pictures and symbols

Developmental Continuum

Algebra

· Combine two sets of objects and count the results

 

· Given a set of objects, remove some and then count the results

Example Behaviors

 

Sally brings in 5 fall objects for the science center. Jeremiah brings in 2 to add to the collection. Sally says, "Now let’s count to see how many we have."

Rodney and Mickeela are playing store with the cash register. Mickeela takes 2 of the 5 paper dollars out of the cash register. Rodney counts the money and says, "Now we only have 3 left."

Comments, Strategies, Evaluation

 

 

 

 

 

 

Math Standard 6: Analyze characteristics and properties of two-and three-dimensional geometric shapes and develop mathematical arguments about geometric shapes
Benchmark 6.1 : Will recognize some basic shapes

Developmental Continuum

Geometry

· Identify and name basic shapes

 

· Identify, name, model, and draw two-dimensional geometric shapes (circle, square, triangle, rectangle)

· Sort shapes according to attributes

Example Behaviors

 

Four children are playing Shape Bingo. The children take turns calling out the shapes on each card.

After drawing a circle and rectangle, Frankie replicated the shapes using marshmallows, pretzels and cheerios.

Sam and Francesca are playing with attribute blocks. The teacher observes Francesca sorting the triangles by size and color.

Comments, Strategies, Evaluation

 

 

 

 

 

 

 

Math Standard 6: Analyze characteristics and properties of two-and three-dimensional geometric shapes and develop mathematical arguments about geometric shapes
Benchmark 6.2 : Describe attributes and parts of two-and-three dimensional shapes

Developmental Continuum

Geometry

Compare the size (smaller/larger) and shape of plane geometric figures (circles, squares, triangles, rectangles)

Example Behaviors

 

Latasha and Tyler are reading Tonya Hoban’s book, Circles, Triangles and Squares. Latasha says, "Look Tyler, those wheels on the truck are bigger than those on the car."

Comments, Strategies, Evaluation

 

 

 

 

Math Standard 6: Analyze characteristics and properties of two-and three-dimensional geometric shapes and develop mathematical arguments about geometric shapes
Benchmark 6.3 : Investigate and predict the results of putting together and taking apart two-and-three dimensional shapes

Developmental Continuum

Geometry

· Create and duplicate shapes

· Complete simple spatial visualization tasks and purposes

Example Behaviors

 

Using popsicle sticks and string, Zavier makes basic shapes on his paper.

Jasmine builds a car using rectangular and circular bristle blocks and explains, "Look, I made a car like my mommy drives."

Comments, Strategies, Evaluation

 

 

 

 

Math Standard 7: Understand measurable attributes of objects and the units, systems, and processes of measurement
Benchmark 7.1 : Recognize the attributes of length, volume, weight, area, and time

Developmental Continuum

Measurement

· Identify the attribute of length by using manipulatives

· Identify, by picking them up, which of two objects is heavier

 

· Demonstrate (through conversation) a beginning sense of time (yesterday, today, tomorrow)

Example Behaviors

 

Using rectangular wooden blocks, Dale measures the length of her best friend’s body and replies, "You are 14 blocks long."

After going to Harmon’s Farm, Steven replies, "Mrs. Watson, this is not my pumpkin. My pumpkin was heavier than this one."

The teacher asks the children, "Who has been to the State Fair?" Alicia shouts, "I went yesterday" and Thomas announces, "My dad is taking me tomorrow".

Comments, Strategies, Evaluation

 

 

 

 

 

 

 

Math Standard 7: Understand measurable attributes of objects and the units, systems, and processes of measurement
Benchmark 7.2 : Compare and order objects according to their attributes

Developmental Continuum

Measurement

· Use basic comparison words

· Begin comparing two objects by using direct comparisons according to one or more of the following attributes: length (shorter, longer); height (taller, shorter); weight (heavier, lighter)

Example Behaviors

 

During play in the block center, Callie says, "Haley’s car is bigger than mine".

During free play in block center, Trey says, "My tower is taller than yours B.J.".

Comments, Strategies, Evaluation

 

 

Math Standard 7: Understand measurable attributes of objects and the units, systems, and processes of measurement
Benchmark 7.3 : Understand how to measure using nonstandard and standard units

Developmental Continuum

Measurement

· Use nonstandard units of measure to explore, describe, and compare everyday objects

· Use tools to explore measuring

Example Behaviors

The teacher provided string for measuring. After measuring the large pumpkin Jasmine says, "Look Caitlin, my string is longer than yours."

Keith and Phil are experimenting in the rice bin. Keith dumps his cup of rice and says, "My cup holds more rice than yours".

Comments, Strategies, Evaluation

 

 

 

 

 

Math Standard 7: Understand measurable attributes of objects and the units, systems, and processes of measurement
Benchmark 7.4 : Recognize the attributes of length, volume, weight, area, and time

Developmental Continuum

Geometry

Identify the instrument used to measure time (clock)

 Identify the instruments used to measure day, month, and season (calendar) and temperature (thermometer)

Example Behaviors

 

After checking the clock as a class many times, Henry says, "Look, it’s time to go to lunch".

As Joseph approached the calendar he said, "There is a new picture on the calendar, it must be a new month".

The teacher asks, "How do we know if it is hot or cold outside?" Samantha responds by saying, "When there is a lot of red on the thermometer it’s hot. When there is a little red then it’s cold"

Comments, Strategies, Evaluation

 

 

 

 

 

 

 

 

Math Standard 8: Apply appropriate techniques, tools, and formulas to determine measurements
Benchmark 8.1 : Use tools to measure

Developmental Continuum

Measurement

· Shows awareness of time concepts

 

· Categorize and sequence time intervals and use language associated with time in everyday situations

· Use the calendar to identify the days of the week, the months of the year, and yesterday, today, tomorrow.

Example Behaviors

 

After finishing large group, Ben looks at the pictorial daily schedule on the wall and says, "We have centers next".

While walking down the hall after lunch, Zindzi says, "We are going outside next and then our book buddies come today".

Kiara uses the pointer to point to each day of the week on the calendar as the class say’s them aloud.

Comments, Strategies, Evaluation

 

 

 

 

 

Math Standard 9: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
Benchmark 9.1 : Pose questions and gather data about themselves and their surroundings

Developmental Continuum

Data Analysis & Probability

  • Collect data related to familiar experiences by counting

 

Example Behaviors

Students answer the question of the day by identifying their favorite food and placing their name under the picture of the food. Stephanie counts the number of names under each food during group time.

Comments, Strategies, Evaluation

 

 

 

 

Math Standard 9: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
Benchmark 9.2 : Sort and classify objects according to their attributes and organize data about the objects

Developmental Continuum

Data Analysis & Probability

· Sort and classify by a single attribute (color, shape, size)

Example Behaviors

 

While working on Jump Start Preschool, Nathan says, "I put the little people in the same line".

Comments, Strategies, Evaluation

 

 

Math Standard 10: Sort and classify objects according to their attributes and organize data about the objects

Benchmark 10.1 : Represent data using concrete objects, pictures, and graphs

Developmental Continuum

Data & Probability

· Draw a picture to represent data

 

Example Behaviors

 

Sandy drew all the girls in the class on one side of her paper and drew all the boys on the other side.

Comments, Strategies, Evaluation

 

 

 

Math Standard 11: Select and use appropriate statistical methods to analyze data
Benchmark 11.1 : Describe parts of the data and the set of data as a whole to determine what the data shows

Developmental Continuum

Data Analysis & Probability

  • Interpret information on a graph

  • Example Behaviors

     

    After graphing the kinds of pets the children have at home, Janae says, "Most of us have dogs."

    Comments, Strategies, Evaluation

     

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