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K.2.1
Numbers, Number Systems and Number Relationships
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K.2.1.1
Content for Kindergarten
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K.2.1.1.A
Count using whole numbers (to 100) by ones and tens (rote counting)
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K.2.1.1.B
Use concrete objects to represent quantities up to and including 20
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K.2.1.1.C
Represent equivalent forms of the same number through the use of concrete objects and drawings up to and including 20
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K.2.1.1.D
Use concrete objects to separate a set into two equal parts using the terms half and whole
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K.2.1.1.E
Use concrete objects to group into sets of ten
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K.2.1.1.F
Use concrete objects to demonstrate understanding of one-to-one correspondence up to and including 20
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K.2.1.1.G
Count, read, and write whole numbers 0 to 20
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K.2.1.1.H
Identify numbers before, after, and between 0 - 20
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K.2.1.1.I
Estimate using concrete objects up to 100
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K.2.1.1.J
Identify pennies, nickels, dimes, and quarters by name and value
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K.2.1.1.K
Count pennies and dimes
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K.2.1.1.a
Examples
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K.2.1.1.a.1
Practice group and individual rote counting experiences (daily counts, objects in the classroom, counts children in class).
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K.2.1.1.a.2
Represent a given number up to twenty with manipulatives.
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K.2.1.1.a.3
Use manipulatives to demonstrate one-to-one correspondence.
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K.2.1.1.a.4
Examine an object and successfully split it in half.
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K.2.1.1.a.5
Analyze a set of objects and successfully divide them in half.
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K.2.1.1.a.6
Create sets of ten with manipulatives.
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K.2.1.1.a.7
Count a set of manipulatives to match a given number.
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K.2.1.1.a.8
Count manipulatives and establish a number- to -object relationship.
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K.2.1.1.a.9
Use manipulatives to find before, after, and between on a number line.
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K.2.1.1.a.10
Make a reasonable estimation of how many objects are in a container.
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K.2.1.1.a.11
Observe the different characteristics of the penny, nickel, dime and quarter and identify them by name and their given value.
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K.2.1.1.a.12
Count by ones and tens to identify an amount of money.
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K.2.1.1.a.13
Write whole numbers using various tactile materials as well as conventional writing instruments
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K.2.1.1.b
Supportive Practices
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K.2.1.1.b.1
Provide opportunities and support learner's counting during daily everyday activities.
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K.2.1.1.b.2
Model, using the appropriate language/vocabulary, the process of counting with one-to-one correspondence, and write the number signifying that amount.
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K.2.1.1.b.3
Provide opportunities and support learners matching and counting objects (passing out snacks, counting manipulatives, learner's jacket, classroom materials, lunchboxes).
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K.2.1.1.b.4
Provide opportunities and support learners counting with one-to-one correspondence during classroom activities.
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K.2.1.1.b.5
Provide opportunities and support learners using a variety of math manipulative (blocks, pattern blocks, unifix cubes, beans, buttons, colored counters).
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K.2.1.1.b.6
Draw representations to explore one-to-one correspondence.
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K.2.1.1.b.7
Provide opportunities, and support learners counting, reading, and writing numbers during various classroom activities (use various tactile materials).
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K.2.1.1.b.8
Provide opportunities and support learners creating groups of ten during classroom activities (Popsicle sticks, baggies of objects).
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K.2.1.1.b.9
Model, using the appropriate language/vocabulary, the processes of separating sets into equal parts (divide).
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K.2.1.1.b.10
Use correct mathematical language (half, whole, equal/equivalent parts).
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K.2.1.1.b.11
Model, using the appropriate language, the processes of creating and naming patterns.
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K.2.1.1.b.12
Provide and support learners during a variety of experiences with patterns (visual, auditory, tactile, kinesthetic).
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K.2.2
Computation and Estimation
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K.2.2.1
Content for Kindergarten
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K.2.2.1.A
Make estimates of objects in a set up to and including 20
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K.2.2.1.B
Make an estimation and verify by counting
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K.2.2.1.C
Represent addition and subtraction in everyday situations using up to ten concrete objects
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K.2.2.1.D
Use concrete objects to explain the results of joining and separating sets of objects in quantities up to and including ten
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K.2.2.1.E
Separate concrete objects into equal groups
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K.2.2.1.F
Determine the sum of the same two one-digit numbers using concrete objects and/or pictures (3+3=6)
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K.2.2.1.a
Examples
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K.2.2.1.a.1
Estimate how many objects are in a group.
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K.2.2.1.a.2
Check estimate by counting the number of objects.
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K.2.2.1.a.3
Use counters to make sets up to ten.
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K.2.2.1.a.4
Use counters to solve simple math stories
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K.2.2.1.a.5
Draw pictures of two sets of objects, count them together, and explain the process of joining the sets (how many objects are in each group and how many were all together when the two sets were joined.)
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K.2.2.1.a.6
Explore the concepts of addition and subtraction by joining and separating sets.
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K.2.2.1.a.7
Combine two sets of objects (up to five) and find the sum
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K.2.2.1.a.8
Separate a pile of counters into two equal piles.
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K.2.2.1.a.9
Use counting manipulatives to create two sets of the same number, then count them to determine the sum.
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K.2.2.1.a.10
Separate a pile of counters into two equal piles.
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K.2.2.1.a.11
Use counting manipulatives to create two sets of the same number, then count them to determine the sum.
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K.2.2.1.a.12
Create in a math journal or wipe off board the joining , subtracting and dividing of sets of objects after teacher models
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K.2.2.1.a.13
Use mathematical language to explain their work(equals, sum, difference, add, subtract, less, more, equal, same)
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K.2.2.1.b
Supportive Practices
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K.2.2.1.b.1
Model using the appropriate language/vocabulary the process of estimation(less, more, almost, close, nearly
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K.2.2.1.b.2
Provide opportunities and support learners in estimating a quantity (students bring objects from home)
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K.2.2.1.b.3
Provide support for learners estimating and counting the number of objects
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K.2.2.1.b.4
Model, using the appropriate language/vocabulary, the processes of adding, subtracting, and dividing sets.
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K.2.2.1.b.5
Create real life addition and subtraction problems for learners to solve by using pictures and/or concrete manipulatives
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K.2.2.1.b.6
Identify everyday classroom opportunities that involve the operation of addition and/or subtraction.
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K.2.2.1.b.7
Provide opportunities, and support learners using counters or objects to make and count sets(small group, individual, large group)
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K.2.2.1.b.8
Identify everyday classroom opportunities that involve the operation of addition and/or subtraction.
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K.2.2.1.b.9
Provide opportunities, and support learners using counters or objects to make and count sets.
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K.2.2.1.b.10
Provide opportunities, and support learners separating sets of objects and/or counters into two equal groups.
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K.2.2.1.b.11
Create addition problems that join two sets of the same amount of objects (use flannelboard and concrete objects).
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K.2.2.1.b.12
Encourage and support learners in explaining how they applied their skills during mathematical tasks. Provide opportunities for learners to explore and apply understanding of joining, subtracting, and dividing sets in learning centers
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K.2.3
Measurement and Estimation
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K.2.3.1
Content for Kindergarten
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K.2.3.1.A
Understand the spatial concepts of over, under, beside, in, out, around, on and between, above, top, bottom,
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K.2.3.1.B
Compare two objects using direct comparison
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K.2.3.1.C
Estimate and measure objects using nonstandard units
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K.2.3.1.D
Determine the length and height of objects with nonstandard units (e.g. hands, shoe lengths, jelly beans, paper clips)
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K.2.3.1.E
Describe the instruments used for measuring time, length, weight, volume, and temperature
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K.2.3.1.a
Examples
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K.2.3.1.a.1
Engage in teacher-led activities, such as Simon Says, that use spatial words (example: "stand in the circle").
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K.2.3.1.a.2
Use positional vocabulary to describe the relative positions of objects ("The book is on the chair.") ("I am in front of Amanda.").
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K.2.3.1.a.3
Collect two classroom objects and compare them by a defined characteristic (length, height, weight).
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K.2.3.1.a.4
Explore objects to determine which will make a good measuring tool. (classroom objects like paper clips, unifix cubes, new pencils, coins)
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K.2.3.1.a.5
Use multiple units of the same size (nonstandard units) to measure (paperclips, unifix cubes).
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K.2.3.1.a.6
Use nonstandard units to estimate the length of and object.
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K.2.3.1.a.7
Investigate the different ways to measure the various attributes of an object.
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K.2.3.1.a.8
Compare the measurement of different classroom objects.
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K.2.3.1.a.9
Use comparison vocabulary to describe how objects are related by length or height.
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K.2.3.1.a.10
Select appropriate tools for the attribute being measured (e.g. clock to tell time, scale to weigh, measuring cups to help bake a cake).
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K.2.3.1.a.11
Recognize parts of the day and discuss activities that occur in the morning, afternoon, and night.
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K.2.3.1.a.12
Participate using the calendar. Identify the season, the month, and the date of today, tomorrow, and yesterday.
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K.2.3.1.a.13
Observe natural phenomena such as the changing of trees and sunrise/sunset.
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K.2.3.1.a.14
Use pictures, drawings, and words to depict events in the order of occurrence.
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K.2.3.1.a.15
Initiate and respond to questions about the order of events occurring throughout the day.
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K.2.3.1.a.16
Manipulate clocks in the math center.(to given times, specific school events times)
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K.2.3.1.a.17
Arrange their individual clocks to match the teacher's demonstration clock.
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K.2.3.1.a.18
Generate solutions to problems that might arise if we do not pay attention to time
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K.2.3.1.b
Supportive Practices
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K.2.3.1.b.1
Incorporate spatial concept words into directions and sensorimotor activities throughout the day.
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K.2.3.1.b.2
Incorporate comparative and spatial vocabulary to compare, locate, and identify positions in space.
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K.2.3.1.b.3
Use gross motor activities to help children understand and internalize comparative and positional words and phrases.
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K.2.3.1.b.4
Emphasize the daily use of positional words.(in daily conversation, in morning message)
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K.2.3.1.b.5
Model the processes of measurement using standard and nonstandard tools and units while using the appropriate language/vocabulary.
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K.2.3.1.b.6
Provide interesting objects for comparison.
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K.2.3.1.b.7
Demonstrate how to measure objects starting at an end point and adding on cubes until the cubes are equal in length to the object they are measuring.
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K.2.3.1.b.8
Design and provide activities to help children recognize the attributes of length, weight, time, and volume.
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K.2.3.1.b.9
Provide opportunities, and support learners in determining the appropriate measurement tool.
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K.2.3.1.b.10
Provide cooking and mixing activities that use measurement for real life purposes(add simple recipes)
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K.2.3.1.b.11
Create measurement math stories that require students to determine which measuring tool to use ("What would I need to do to find out how long I brush my teeth in the morning?").
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K.2.3.1.b.12
Provide opportunities, and support learners in using standard and nonstandard units to measure objects by more than one attribute.
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K.2.3.1.b.13
Engage children in thinking about the concept of time (number of days at school, season, days of the week, month; do calendar daily, extend calendar questions).
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K.2.3.1.b.14
Engage in conversation about time (why is time important? What might happen if we didn't have or use clocks? What time do you come to school, go to bed, eat dinner?).
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K.2.4
Mathematical Reasoning and Connections
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K.2.4.1
Content for Kindergarten
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K.2.4.1.A
Use math vocabulary comparison terms when making predictions regarding the quantity, size, and shape of objects
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K.2.4.1.B
Identify the use of measurement in everyday situations
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K.2.4.1.a
Examples
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K.2.4.1.a.1
Analyze the size of the container and the objects inside when making an estimate as to the amount.
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K.2.4.1.a.2
Examine the object being measured to determine the appropriate tool and approach.
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K.2.4.1.a.3
Make an estimate by considering the size of the object(s) and its container.
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K.2.4.1.b
Supportive Practices
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K.2.4.1.b.1
Model, using the appropriate language/vocabulary, the process of estimation (size of object, size of container, comparisons of size of containers- big, bigger, small, smaller, quart, pint, gallon, cup).
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K.2.4.1.b.2
Engage learners in recognizing and applying measurement in everyday situations.
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K.2.4.1.b.3
Encourage and support learners in explaining how they applied their skills during mathematical tasks.
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K.2.4.1.b.4
Provide opportunities for learners to explore and apply understanding of estimating and measurement.
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K.2.5
Mathematical Problem Solving and Communication
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K.2.5.1
Content for Kindergarten
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K.2.5.1.A
Identify a problem and analyze possible solutions to determine which is most appropriate
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K.2.5.1.B
Identify what information is needed to solve a problem
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K.2.5.1.C
Demonstrate various strategies to solve a problem
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K.2.5.1.a
Examples
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K.2.5.1.a.1
Identify and think about possible solutions to solve daily problems occurring in and out of the classroom.
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K.2.5.1.a.2
Describe the steps necessary to solve a problem.
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K.2.5.1.a.3
Utilize different strategies and approaches to solve daily problems occurring in and out of the classroom.
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K.2.5.1.b
Supportive Practices
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K.2.5.1.b.1
Model, using the appropriate language/vocabulary, the process of identifying and solving a problem.
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K.2.5.1.b.2
Facilitate classroom discussion to identify the necessary steps and the appropriate order to solve problems occurring in and out of the classroom.
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K.2.5.1.b.3
Create and provide opportunities for learners to engage in problem solving activities role play; use Second Step program).
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K.2.5.1.b.4
Highlight the process versus the product of an activity (give specific examples).
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K.2.5.1.b.5
Ask open-ended questions, encourage conversations, and create classroom activities that encourage learners to explore a variety of possible solutions(set up situations)
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K.2.5.1.b.6
Encourage and support learners to explain their mathematical thinking and work.
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K.2.5.1.b.7
Provide opportunities for learners to explore and apply understanding of problem solving throughout the school day.
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K.2.6
Statistics and Data Analysis
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K.2.6.1
Content for Kindergarten
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K.2.6.1.A
Gather, organize and display data on a bar graph and/or pictograph
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K.2.6.1.B
Analyze a chart or graph that displays data and make a prediction
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K.2.6.1.C
Answer questions based on data shown on graphs or charts
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K.2.6.1.D
Use data from graphs to answer questions and form opinions
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K.2.6.1.a
Examples
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K.2.6.1.a.1
Participate in classroom graphing activities by adding his/her input to a graph.
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K.2.6.1.a.2
Analyze the data on classroom graphs.
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K.2.6.1.a.3
Draw conclusions from the data, applying the data to future events/behaviors.
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K.2.6.1.a.4
Answer the question how many? How many more? How many less? Equal? Why? What? How do you know?
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K.2.6.1.b
Supportive Practices
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K.2.6.1.b.1
Assist learners in "reading" the data, deducing information, drawing conclusions, and applying data to future events/behavior.
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K.2.6.1.b.2
Pose open-ended questions to engage learners in "reading" the data on a graph.
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K.2.6.1.b.3
Provide opportunities for learners to see graphs used in the real world.
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K.2.6.1.b.4
Encourage and support learners in explaining how they applied their skills during mathematical work.
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K.2.6.1.b.5
Provide opportunities for learners to explore and apply understanding of creating and interpreting a graph throughout the school day(can do
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K.2.6.1.b.6
Model, using the appropriate language/vocabulary, the process of graphing (creating a graph, adding, and interpreting the data-use simple yes/no, favorite...)
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K.2.7
Probability and Predictions
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K.2.7.1
Content for Kindergarten
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K.2.7.1.A
State and explain the likelihood of an event using the terms: likely, unlikely, or certain
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K.2.7.1.B
Compare sets of data using the concepts of largest, smallest, most, and least. Explain if an event is fair or unfair
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K.2.7.1.a
Examples
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K.2.7.1.a.1
Determine the likelihood of real life events/things occurring.
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K.2.7.1.a.2
Discuss the fairness or unfairness of classroom situations.
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K.2.7.1.a.3
Predict the results of experiments.
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K.2.7.1.b
Supportive Practices
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K.2.7.1.b.1
Model, using the appropriate language/vocabulary, the process of determining the likelihood of real life events/things occurring (current events)
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K.2.7.1.b.2
Explain examples of activities that are most likely to occur at certain times of the year and explaining the meaning of the words likely, unlikely or certain.
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K.2.7.1.b.3
Engage learners in discussions to determine fair and unfair procedures in and out of the classroom.
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K.2.7.1.b.4
Facilitate predictions of possible results by referring to previous events.
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K.2.7.1.b.5
Encourage and support learners in explaining how they applied their skills during mathematical tasks.
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K.2.8
Algebra and Functions
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K.2.8.1
Content for Kindergarten
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K.2.8.1.A
Identify, describe, and extend patterns based on shape, size, color, sound, or number
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K.2.8.1.B
Use concrete objects to show equal or not equal
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K.2.8.1.C
Recreate a simple story problem using concrete objects or pictures
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K.2.8.1.D
Use concrete objects and trial and error to represent a number story
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K.2.8.1.E
Use concrete objects or pictures to represent a number story that involves a missing addend
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K.2.8.1.F
Explain how solutions are determined
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K.2.8.1.G
Identify the purposes for different mathematical symbols (+, -, and =)
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K.2.8.1.a
Examples
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K.2.8.1.a.1
Sort manipulatives and other objects according to attribute (color, shape, size, function).
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K.2.8.1.a.2
Define sorting rule.
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K.2.8.1.a.3
Recognize, describe, repeat, and extend a pattern
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K.2.8.1.a.4
Use manipulatives to create sets that are equal.
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K.2.8.1.a.5
Determine whether two sets of objects are equal by counting the objects in each set.
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K.2.8.1.a.6
Use concrete manipulatives and/or draw pictures to show the process of addition.
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K.2.8.1.a.7
Use concrete manipulatives to show same, less, more, different, fewer sets
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K.2.8.1.a.8
Use concrete manipulatives and/or draw pictures to determine the missing addend (There were 3 bears at the table. Now there are 5. How many came?)
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K.2.8.1.a.9
Utilize a number line to "count on" from a specified number to reach an end number.
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K.2.8.1.a.10
Use numbers and symbols to represent adding and subtraction of concrete objects or pictures.
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K.2.8.1.a.11
Solve a simple story problem and explain the process.
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K.2.8.1.a.12
Draw story problems and assign the appropriate number to each set, then choose the correct symbol.(record in math journal)
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K.2.8.1.b
Supportive Practices
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K.2.8.1.b.1
Provide a variety of materials for sorting, classifying, and creating patterns(lids, buttons)
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K.2.8.1.b.2
Demonstrate and explain the concept of recognizing, describing, repeating and extending a pattern.
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K.2.8.1.b.3
Provide opportunities and support learners in recognizing, describing, and extending patterns.
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K.2.8.1.b.4
Provide opportunities and support learners in recognizing and describing patterns in the environment(use informational text)
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K.2.8.1.b.5
Model, using the appropriate language/vocabulary, the process of determining equal and not equal sets.
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K.2.8.1.b.6
Support learners in determining whether sets are equal(match 1 to 1;use terms fewer, more)
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K.2.8.1.b.7
Support learners using numbers as they draw pictures to illustrate story problems.
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K.2.8.1.b.8
Support learners in solving the missing addend(given an end number - "5" and a set number - "2", learners will "count on" from "2" to "5" to determine 3 is the missing amount).
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K.2.8.1.b.9
Provide opportunities and support learners in solving real life story problems (use flannelboard or overhead)
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K.2.8.1.b.10
Provide opportunities and support learners in solving story problems with symbolic notation of numbers and adding/subtracting and equal sign(+ = -)
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K.2.8.1.b.11
Encourage and support learners in explaining how they applied their skills during mathematical tasks (retell with manipulatives)
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K.2.8.1.b.12
Provide opportunities for learners to explore and apply understanding of the foundations for algebraic thinking throughout the school day.
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K.2.9
Geometry
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K.2.9.1
Content for Kindergarten
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K.2.9.1.A
Identify common two and three-dimensional geometric shapes
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K.2.9.1.B
Create and reproduce geometric designs using concrete objects
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K.2.9.1.C
Draw and/or construct two-dimensional geometric shapes
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K.2.9.1.D
Name and describe two-dimensional geometric shapes in real life
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K.2.9.1.E
Explore symmetry in nature (leaves, butterflies)
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K.2.9.1.F
Identify a reflection
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K.2.9.1.G
Create a reflection
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K.2.9.1.H
Identify geometric shapes that are turned in different ways
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K.2.9.1.a
Examples
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K.2.9.1.a.1
Explore the environment to locate two and three-dimensional shapes (circle, square, triangle, rectangle, cube, sphere, and cone).
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K.2.9.1.a.2
Name two-dimensional shapes in the environment and describe their properties.
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K.2.9.1.a.3
Create various geometric shapes with manipulatives (pattern blocks, geoboards, and tangrams).
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K.2.9.1.a.4
Determine if shapes folded in half are the same or different (symmetrical or nonsymmetrical).
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K.2.9.1.a.5
Observe items from nature to determine if they are symmetrical or nonsymmetrical.
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K.2.9.1.a.6
Explore the concept of reflection and symmetry.
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K.2.9.1.a.7
Explore geometric shapes turned in different ways.
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K.2.9.1.a.8
Use paint and construction paper to create a symmetrical shape- butterfly for ex.
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K.2.9.1.a.9
Be able to define a reflection as a figure that does not change size. It is often called a flip.
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K.2.9.1.a.10
Explore shapes in their environment
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K.2.9.1.a.11
Use geoboards or peg boards to create geometric shapes
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K.2.9.1.b
Supportive Practices
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K.2.9.1.b.1
Model, using the appropriate language/vocabulary, the process of recognizing, describing the properties, and naming geometric shapes (line segment, diagonal, angle, length, width, height)
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K.2.9.1.b.2
Provide opportunities and support learners in locating geometric shapes within the environment.
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K.2.9.1.b.3
Provide materials/opportunities and support learners in creating shapes (toothpicks, Popsicle sticks, foam shapes, playdoh, Model Magic)
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K.2.9.1.b.4
Provide opportunities and support learners in describing the attributes of shapes
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K.2.9.1.b.5
Model, using the appropriate language/vocabulary, the process of determining whether something is symmetrical.
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K.2.9.1.b.6
Provide opportunities and support learners in determining whether a shape or object is symmetrical Read It Looked Like Spilt Milk
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K.2.9.1.b.7
Support learners in making observations about the symmetry found in nature.
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K.2.9.1.b.8
Model, using the appropriate language/vocabulary, the process of determining whether something is a reflection.
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K.2.9.1.b.9
Model, using the appropriate language/vocabulary, how a shape can be turned in different ways and remains the same shape.
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K.2.9.1.b.10
Encourage and support learners in explaining how they applied their skills during mathematical tasks (math journal)
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K.2.9.1.b.11
Provide opportunities for learners to explore and apply understanding of geometry throughout the school day.
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K.2.10
Trigonometry
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K.2.10.1
Content for Kindergarten
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K.2.10.1.A
Identify triangles in the environment and discuss how they are alike and different
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K.2.10.1.a
Examples
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K.2.10.1.a.1
Identify triangles in everyday situations.
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K.2.10.1.a.2
Identify and describe similarities and differences in triangles found in everyday situations and teacher created learning materials.
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K.2.10.1.b
Supportive Practices
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K.2.10.1.b.1
Model, using the appropriate language/vocabulary, the process of comparing the attributes of triangles(tri=3, 3 angles, 3 sides)
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K.2.10.1.b.2
Provide opportunities and support learners in identifying triangles in the environment.
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K.2.10.1.b.3
Provide opportunities and support learners in comparing the attributes of triangles.
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K.2.10.1.b.4
Encourage and support learners in explaining how they applied their skills during mathematical tasks.
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K.2.10.1.b.5
Provide opportunities for learners to explore and apply understanding of triangles throughout the school day.(use pattern blocks-how many triangles =a hexagon or trapezoid)
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K.2.11
Calculus
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K.2.11.1
Content for Kindergarten
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K.2.11.1.A
Order whole numbers (0-20) from least to greatest value
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K.2.11.1.B
Identify situations that occur in real life that are slow or fast in happening
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K.2.11.1.a
Examples
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K.2.11.1.a.1
Place number cards in order from 0 to 20.
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K.2.11.1.a.2
Visualize and think about two objects (such as a bike and a car) and compare their rates of speed.
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K.2.11.1.a.3
Compare vehicles, pictures of people different ages and discuss the speed or rate of growth
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K.2.11.1.b
Supportive Practices
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K.2.11.1.b.1
Model, using the appropriate language/vocabulary, the process of ordering numbers from least to greatest.
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K.2.11.1.b.2
Use classroom tools such as the number line, or the 100s board, to model strategies that support learning.
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K.2.11.1.b.3
Provide opportunities and support learners in ordering numbers from least to greatest.
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K.2.11.1.b.4
Model, using the appropriate language/vocabulary, the process of deciding which real life event or object is faster and slower.
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K.2.11.1.b.5
Provide opportunities and support learners in deciding which real life object or event is faster or slower(talk about growth)
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K.2.11.1.b.6
Encourage and support learners in explaining how they applied their skills during mathematical tasks (use journals or chart paper)
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K.2.11.1.b.7
Provide opportunities for learners to explore and apply understanding of ordering (from least to greatest, and from slow to fast).
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