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
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Math Standard 1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems |
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Benchmark 1.1 : Count with understanding and recognize “how many” in sets of objects |
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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
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| 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 | ||
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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
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| 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 | ||
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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
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| 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 | ||
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Developmental Continuum
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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
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| 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 | ||
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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
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| Math Standard 1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems | ||
| Benchmark 1.6 : Understand and represent commonly used fractions | ||
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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
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| 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 | ||
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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
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| 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 | ||
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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
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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
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| 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 | ||
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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
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| 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 | ||
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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
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| 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 | ||
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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
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| 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 | ||
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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
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| 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 | ||
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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
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| 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 | ||
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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
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| 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 | ||
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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
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| 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 | ||
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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
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| 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 | ||
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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
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| 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 | ||
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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
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| Math Standard 8: Apply appropriate techniques, tools, and formulas to determine measurements | ||
| Benchmark 8.1 : Use tools to measure | ||
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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
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| 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 | ||
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Developmental Continuum Data Analysis & Probability
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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
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| 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 | ||
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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
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| Math Standard 10: Sort and classify objects according to their attributes and organize data about the objects | ||
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Benchmark 10.1 : Represent data using concrete objects, pictures, and graphs |
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Developmental Continuum Data & Probability · Draw a picture to represent data
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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
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| 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 | ||
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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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