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1.PS
Problem Solving
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Students will build new mathematical knowledge through problem solving.
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1.PS.1
Explore, examine, and make observations about a social problem or mathematical situation
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1.PS.2
Interpret information correctly, identify the problem, and generate possible solutions
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Students will solve problems that arise in mathematics and in other contexts.
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1.PS.3
Act out or model with manipulatives activities involving mathematical content from literature and/or story telling
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1.PS.4
Formulate problems and solutions from everyday situations (e.g., counting the number of children in the class or using the calendar to teach counting)
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Students will apply and adapt a variety of appropriate strategies to solve problems.
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1.PS.5
Use informal counting strategies to find solutions
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1.PS.6
Experience teacher-directed questioning process to understand problems
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1.PS.7
Compare and discuss ideas for solving a problem with teacher and/or students to justify their thinking
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1.PS.8
Use manipulatives (e.g., tiles, blocks) to model the action in problems
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1.PS.9
Use drawings/pictures to model the action in problems
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Students will monitor and reflect on the process of mathematical problem solving.
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1.PS.10
Explain to others how a problem was solved, giving strategies and justifications
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1.RP
Reasoning and Proof
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Students will recognize reasoning and proof as fundamental aspects of mathematics.
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1.RP.1
Understand that mathematical statements can be true or false
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1.RP.2
Recognize that mathematical ideas need to be supported by evidence
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Students will make and investigate mathematical conjectures.
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1.RP.3
Investigate the use of knowledgeable guessing as a mathematical tool
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1.RP.4
Explore guesses, using a variety of objects and manipulatives
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Students will develop and evaluate mathematical arguments and proofs.
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1.RP.5
Justify general claims, using manipulatives
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1.RP.6
Develop and explain an argument verbally or with objects
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1.RP.7
Listen to and discuss claims other students make
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Students will select and use various types of reasoning and methods of proof.
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1.RP.8
Use trial and error strategies to verify claims
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1.CM
Communication
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Students will organize and consolidate their mathematical thinking through communication.
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1.CM.1
Understand how to organize their thought processes with teacher guidance
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1.CM.2
Verbally support their reasoning and answer
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Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
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1.CM.3
Share mathematical ideas through the manipulation of objects, drawings, pictures, charts, and symbols in both written and verbal explanations
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Students will analyze and evaluate the mathematical thinking and strategies of others.
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1.CM.4
Listen to solutions shared by other students
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1.CM.5
Formulate mathematically relevant questions
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Students will use the language of mathematics to express mathematical ideas precisely.
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1.CM.6
Use appropriate mathematical terms, vocabulary, and language
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1.CN
Connections
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Students will recognize and use connections among mathematical ideas.
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1.CN.1
Recognize the connections of patterns in their everyday experiences to mathematical ideas
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1.CN.2
Understand the connections between numbers and the quantities they represent
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1.CN.3
Compare the similarities and differences of mathematical ideas
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Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
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1.CN.4
Understand how models of situations involving objects, pictures, and symbols relate to mathematical ideas
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1.CN.5
Understand meanings of operations and how they relate to one another
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1.CN.6
Understand how mathematical models represent quantitative relationships
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Students will recognize and apply mathematics in contexts outside of mathematics.
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1.CN.7
Recognize the presence of mathematics in their daily lives
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1.CN.8
Recognize and apply mathematics to solve problems
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1.CN.9
Recognize and apply mathematics to objects, pictures, and symbols
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1.R
Representation
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Students will create and use representations to organize, record, and communicate mathematical ideas.
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1.R.1
Use multiple representations including verbal and written language, acting out or modeling a situation, drawings, and/or symbols as representations
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1.R.2
Share mental images of mathematical ideas and understandings
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1.R.3
Use standard and nonstandard representations
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Students will select, apply, and translate among mathematical representations to solve problems.
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1.R.4
Connect mathematical representations with problem solving
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Students will use representations to model and interpret physical, social, and mathematical phenomena.
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1.R.5
Use mathematics to show and understand physical phenomena (e.g., estimate and represent the number of apples in a tree)
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1.R.6
Use mathematics to show and understand social phenomena (e.g., count and represent sharing cookies between friends)
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1.R.7
Use mathematics to show and understand mathematical phenomena (e.g., draw pictures to show a story problem, show number value using fingers on your hand)
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1.N
Number Sense and Operations
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Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.
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Number Systems
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1.N.1
Count the items in a collection and know the last counting word tells how many items are in the collection (1 to 100)
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1.N.2
Count out (produce) a collection of a specified size (10 to 100 items), using groups of ten
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1.N.3
Quickly see and label with a number, collections of 1 to 10
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1.N.4
Count by 1's to 100
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1.N.5
Skip count by 10's to 100
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1.N.6
Skip count by 5's to 50
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1.N.7
Skip count by 2's to 20
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1.N.8
Verbally count from a number other than one by 1's
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1.N.9
Count backwards from 20 by 1's
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1.N.10
Draw pictures or other informal symbols to represent a spoken number up to 20
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1.N.11
Identify that spacing of the same number of objects does not affect the quantity (conservation)
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1.N.12
Arrange objects in size order (increasing and decreasing)
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1.N.13
Write numbers to 100
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1.N.14
Read the number words one, two, three...ten
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1.N.15
Explore and use place value
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1.N.16
Compare and order whole numbers up to 100
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1.N.17
Develop an initial understanding of the base ten system:
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1.N.17.a
10 ones = 1 ten
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1.N.17.b
10 tens = 1 hundred
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1.N.18
Use a variety of strategies to compose and decompose one-digit numbers
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1.N.19
Understand the commutative property of addition
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1.N.20
Name the number before and the number after a given number, and name the number(s) between two given numbers up to 100 (with and without the use of a number line or a hundreds chart)
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1.N.21
Use before, after, or between to order numbers to 100 (with or without the use of a number line)
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1.N.22
Use the words higher, lower, greater, and less to compare two numbers
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1.N.23
Use and understand verbal ordinal terms, first to twentieth
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Students will understand meanings of operations and procedures, and how they relate to one another.
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Operations
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1.N.24
Develop and use strategies to solve addition and subtraction word problems
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1.N.25
Represent addition and subtraction word problems and their solutions as number sentences
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1.N.26
Create problem situations that represent a given number sentence
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1.N.27
Use a variety of strategies to solve addition and subtraction problems with one- and two-digit numbers without regrouping
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1.N.28
Demonstrate fluency and apply addition and subtraction facts to and including 10
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1.N.29
Understand that different parts can be added to get the same whole
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Students will compute accurately and make reasonable estimates.
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Estimation
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1.N.30
Estimate the number in a collection to 50 and then compare by counting the actual items in the collection
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1.A
Algebra
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Students will recognize, use, and represent algebraically patterns, relations, and functions.
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Patterns, Relations, and Functions
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1.A.1
Determine and discuss patterns in arithmetic (what comes next in a repeating pattern, using numbers or objects)
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1.G
Geometry
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Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
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Shapes
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1.G.1
Match shapes and parts of shapes to justify congruency
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1.G.2
Recognize, name, describe, create, sort, and compare two-dimensional and three-dimensional shapes
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Students will apply transformations and symmetry to analyze problem solving situations.
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Transformational Geometry
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1.G.3
Experiment with slides, flips, and turns of two-dimensional shapes
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1.G.4
Identify symmetry in two-dimensional shapes
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Students will apply coordinate geometry to analyze problem solving situations.
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Coordinate Geometry
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1.G.5
Recognize geometric shapes and structures in the environment
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1.M
Measurement
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Students will determine what can be measured and how, using appropriate methods and formulas.
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Units of Measurement
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1.M.1
Recognize length as an attribute that can be measured
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1.M.2
Use non-standard units (including finger lengths, paper clips, students' feet and paces) to measure both vertical and horizontal lengths
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1.M.3
Informally explore the standard unit of measure, inch
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Students will use units to give meaning to measurements.
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Units
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1.M.4
Know vocabulary and recognize coins (penny, nickel, dime, quarter)
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1.M.5
Recognize the cent notation as ยข
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1.M.6
Use different combinations of coins to make money amounts up to 25 cents
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1.M.7
Recognize specific times (morning, noon, afternoon, evening)
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1.M.8
Tell time to the hour, using both digital and analog clocks
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1.M.9
Know the days of the week and months of the year in sequence
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1.M.10
Classify months and connect to seasons and other events
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Students will develop strategies for estimating measurements.
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Estimation
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1.M.11
Select and use non-standard units to estimate measurements
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1.S
Statistics and Probability
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Students will collect, organize, display, and analyze data.
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Collection of Data
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1.S.1
Pose questions about themselves and their surroundings
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1.S.2
Collect and record data related to a question
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Organization and Display of Data
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1.S.3
Display data in simple pictographs for quantities up to 20 with units of one
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1.S.4
Display data in bar graphs using concrete objects with intervals of one
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1.S.5
Use Venn diagrams to sort and describe data
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Analysis of Data
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1.S.6
Interpret data in terms of the words: most, least, greater than, less than, or equal to
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1.S.7
Answer simple questions related to data displayed in pictographs (e.g., category with most, how many more in a category compared to another, how many all together in two categories)
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Students will make predictions that are based upon data analysis.
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Predictions from Data
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1.S.8
Discuss conclusions and make predictions in terms of the words likely and unlikely
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Probability: More or less likely (Kindergarten - P.1)
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Probability and statistics: More, less, and equally likely (First grade - P.1)
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Probability and statistics: Certain, probable, unlikely, and impossible (First grade - P.2)
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Probability and statistics: More, less, and equally likely (Second grade - V.1)
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Probability and statistics: Certain, probable, unlikely, and impossible (Second grade - V.2)
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1.S.9
Construct a question that can be answered by using information from a graph
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