4.PS.1

Explore, examine, and make observations about a social problem or mathematical situation

4.PS.2

Understand that some ways of representing a problem are more helpful than others

4.PS.3

Interpret information correctly, identify the problem, and generate possible solutions

4.PS.4

Act out or model with manipulatives activities involving mathematical content from literature

4.PS.5

Formulate problems and solutions from everyday situations

4.PS.6

Translate from a picture/diagram to a numeric expression

4.PS.7

Represent problem situations in oral, written, concrete, pictorial, and graphical forms

4.PS.8

Select an appropriate representation of a problem

4.PS.9

Use trial and error to solve problems

4.PS.10

Use process of elimination to solve problems

4.PS.11

Make pictures/diagrams of problems

4.PS.12

Use physical objects to model problems

4.PS.13

Work in collaboration with others to solve problems

4.PS.14

Make organized lists to solve numerical problems

4.PS.15

Make charts to solve numerical problems

4.PS.16

Analyze problems by identifying relationships

4.PS.17

Analyze problems by identifying relevant versus irrelevant information

4.PS.18

Analyze problems by observing patterns

4.PS.19

State a problem in their own words

4.PS.20

Determine what information is needed to solve a problem

4.PS.21

Discuss with peers to understand a problem situation

4.PS.22

Discuss the efficiency of different representations of a problem

4.PS.23

Verify results of a problem

4.PS.24

Recognize invalid approaches

4.PS.25

Determine whether a solution is reasonable in the context of the original problem

4.RP.1

Use representations to support mathematical ideas

4.RP.2

Determine whether a mathematical statement is true or false and explain why

4.RP.3

Investigate the use of knowledgeable guessing by generalizing mathematical ideas

4.RP.4

Make conjectures from a variety of representations

4.RP.5

Justify general claims or conjectures, using manipulatives, models, and expressions

4.RP.6

Develop and explain an argument using oral, written, concrete, pictorial, and/or graphical forms

4.RP.7

Discuss, listen, and make comments that support or reject claims made by other students

4.RP.8

Support an argument by trying many cases

4.RP.9

Disprove an argument by finding counterexamples

4.CM.1

Understand and explain how to organize their thought process

4.CM.2

Verbally explain their rationale for strategy selection

4.CM.3

Provide reasoning both in written and verbal form

4.CM.4

Organize and accurately label work

4.CM.5

Share organized mathematical ideas through the manipulation of  objects, drawings, pictures, charts, graphs, tables, diagrams, models, symbols, and expressions in written and verbal form

4.CM.6

Answer clarifying questions from others

4.CM.7

Restate mathematical solutions shared by other students

4.CM.8

Consider strategies used and solutions found in relation to their own work

4.CM.9

Increase their use of mathematical vocabulary and language when communicating with others

4.CM.10

Describe objects, relationships, solutions and rationale using appropriate vocabulary

4.CM.11

Decode and comprehend mathematical visuals and symbols to construct meaning

4.CN.1

Recognize, understand, and make connections in their everyday experiences to mathematical ideas

4.CN.2

Compare and contrast mathematical ideas

4.CN.3

Connect and apply mathematical information to solve problems

4.CN.4

Understand multiple representations and how they are related

4.CN.5

Model situations with objects and representations and be able to make observations

4.CN.6

Recognize the presence of mathematics in their daily lives

4.CN.7

Apply mathematics to solve problems that develop outside of  mathematics

4.CN.8

Recognize and apply mathematics to other disciplines

4.R.1

Use verbal and written language, physical models, drawing charts, graphs, tables, symbols, and equations as representations

4.R.2

Share mental images of mathematical ideas and understandings

4.R.3

Recognize and use external mathematical representations

4.R.4

Use standard and nonstandard representations with accuracy and detail

4.R.5

Understand similarities and differences in representations.

4.R.6

Connect mathematical representations with problem solving

4.R.7

Construct effective representations to solve problems

4.R.8

Use mathematics to show and understand physical phenomena (e.g., estimate and represent the number of apples in a tree)

4.R.9

Use mathematics to show and understand social phenomena (e.g., determine the number of buses required for a field trip)

4.R.10

Use mathematics to show and understand mathematical phenomena (e.g., use a multiplication grid to solve odd and even number problems)

4.N.1

Skip count by 1,000’s

4.N.2

Read and write whole numbers to 10,000

4.N.3

Compare and order numbers to 10,000

4.N.4

Understand the place value structure of the base ten number system:

10 ones = 1 ten

10 tens = 1 hundred

10 hundreds = 1 thousand

10 thousands = 1 ten thousand

4.N.5

Recognize equivalent representations for numbers up to four digits and generate them by decomposing and composing numbers

4.N.6

Understand, use, and explain the associative property of multiplication

4.N.7

Develop an understanding of fractions as locations on number lines and as divisions of whole numbers

4.N.8

Recognize and generate equivalent fractions (halves, fourths, thirds, fifths, sixths, and tenths) using manipulatives, visual models, and illustrations

4.N.9

Use concrete materials and visual models to compare and order unit fractions or fractions with the same denominator (with and without the use of a number line)

4.N.10

Develop an understanding of decimals as part of a whole

4.N.11

Read and write decimals to hundredths, using money as a context

4.N.12

Use concrete materials and visual models to compare and order decimals (less than 1) to the hundredths place in the context of money

4.N.13

Develop an understanding of the properties of odd/even numbers as a result of multiplication

4.N.14

Use a variety of strategies to add and subtract numbers up to 10,000

4.N.15

Select appropriate computational and operational methods to solve problems

4.N.16

Understand various meanings of multiplication and division

4.N.17

Use multiplication and division as inverse operations to solve problems

4.N.18

Use a variety of strategies to multiply two-digit numbers by one-digit numbers (with and without regrouping)

4.N.19

Use a variety of strategies to multiply two-digit numbers by two-digit numbers (with and without regrouping)

4.N.20

Develop fluency in multiplying and dividing multiples of 10 and 100 up to 1,000

4.N.21

Use a variety of strategies to divide two-digit dividends by one-digit divisors (with and without remainders)

4.N.22

Interpret the meaning of remainders

4.N.23

Add and subtract proper fractions with common denominators

4.N.24

Express decimals as an equivalent form of fractions to tenths and hundredths

4.N.25

Add and subtract decimals to tenths and hundredths using a hundreds chart

4.N.26

Round numbers less than 1,000 to the nearest tens and hundreds

4.N.27

Check reasonableness of an answer by using estimation

 4.A.1

Evaluate and express relationships using open sentences with one operation

4.A.2

Use the symbols <, >, =, and ≠ (with and without the use of a  number line) to compare whole numbers and unit fractions and decimals (up to hundredths)

4.A.3

Find the value or values that will make an open sentence true, if it contains < or >

4.A.4

Describe, extend, and make generalizations about numeric  () and geometric patterns

4.A.5

Analyze a pattern or a whole-number function and state the rule, given a table or an input/output box

 4.G.1

Identify and name polygons, recognizing that their names are related to the number of sides and angles (triangle, quadrilateral, pentagon, hexagon, and octagon)

4.G.2

Identify points and line segments when drawing a plane figure

4.G.3

Find perimeter of polygons by adding sides 

4.G.4

Find the area of a rectangle by counting the number of squares needed to cover the rectangle

4.G.5

Define and identify vertices, faces, and edges of three-dimensional shapes

4.G.6

Draw and identify intersecting, perpendicular, and parallel lines

4.G.7

Identify points and rays when drawing angles

4.G.8

Classify angles as acute, obtuse, right, and straight

4.M.1

Select tools and units (customary and metric) appropriate for the length measured

4.M.2

Use a ruler to measure to the nearest standard unit (whole, ½ and ¼ inches, whole feet, whole yards, whole centimeters, and whole meters)

4.M.3

Know and understand equivalent standard units of length: 12 inches = 1 foot 3 feet = 1 yard

4.M.4

Select tools and units appropriate to the mass of the object being measured (grams and kilograms)

4.M.5

Measure mass, using grams

4.M.6

Select tools and units appropriate to the capacity being measured (milliliters and liters)

4.M.7

Measure capacity, using milliliters and liters

4.M.8

Make change, using combined coins and dollar amounts

4.M.9

Calculate elapsed time in hours and half hours, not crossing A.M./P.M.

4.M.10

Calculate elapsed time in days and weeks, using a calendar 

4.S.1

Design investigations to address a question from given data

4.S.2

Collect data using observations, surveys, and experiments and record appropriately

4.S.3

Represent data using tables, bar graphs, and pictographs

4.S.4

Read and interpret line graphs

4.S.5

Develop and make predictions that are based on data

4.S.6

Formulate conclusions and make predictions from graphs