Grade 5 Mathematics N5.1 Whole Numbers Represent, describe and compare whole numbers to 1 000 000 in various ways. Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level

Performance Representing Cannot use manipulatives

or draw pictures to represent a given 4-digit number.

Can create 1 picture or model to represent a given 6-digit number.

Can create picture or models to represent a given 6-digit number.

Can use a variety of different manipulatives or pictures to model the value of any 6-digit number.

Cannot write 4 digit numbers.

Can write 5 or 6-digit numbers that do not use zeros as placeholders.

Can write 6-digit numbers that use zeros as placeholders, but may omit the space or insert commas.

Can write 6-digit numbers with the correct spacing and including zeros as placeholders.

Describing Cannot read 4 digit numbers.

Can read 5 and 6 digit numbers with some assistance or can only read numbers to 4 digits.

Can read 6 digit numbers but may hesitate or use the word “and”.

Can read 6 digit numbers without hesitating or using the word “and”.

Cannot explain how a picture or model relates the standard form of a 4-digit number.

Can state somewhat clearly how a model or picture represents the standard form of a 6-digit number.

Can explain how a model or picture relates to a 6-digit number.

Can explain how various pictures or models relate to any given 6-digit number.

Cannot accurately write a 4-digit number in an expanded form.

Can only write a 6-digit number in 1 of the expanded forms or needs assistance to write the expanded forms of a given 6 digit number.

Can write 6 digit numbers in their expanded form.

Can write any 6 digit number in both expanded forms: 30 000 + 500 or (3X10 000) + (5X100), including numbers that contain zeros as placeholders.

Cannot write the expanded form of a 5-digit number when given its expanded form.

May make errors when writing the standard form of a 6-digit number when given its expanded form, esp. if that number requires zeros for placeholders.

Can write the standard form of a 6-digit number when given the expanded form.

Can write the standard form of any given 6-digit number given either of its expanded forms, including the correct use of zeros as placeholders.

Cannot state the value represented by the digits of a 5-digit number.

Makes some errors when stating the values represented by individual digits of a 6-digit number.

Can state the value represented by any digit in a 6-digit number.

Can state the value of any digit in a 6 digit number in 2 or more different ways; 2 000, 2 thousands or 2 X 1 000.

Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level Performance

Comparing Cannot order 3, 5-digit numbers correctly.

Can put 3, 5 digit numbers in ascending or descending order with few errors.

Can put 3, 6-digit numbers in correct ascending or descending order.

Can put more than, 6-digit numbers in correct ascending or descending order.

Cannot determine if a given 5-digit number is greater, less than or equal to another 5-digit number.

Can determine if a 5-digit number is greater, less than or equal to another 5-digit number, but may need to use manipulatives.

Can determine if a 6-digit number is greater, less than or equal to another 6-digit number.

Can easily determine if a 6-digit number is greater, less than or equal to another 6-digit number.

Cannot create a number a specified amount greater or less than a given 5-digit number.

With some assistance or with the use of manipulatives and create a number a specified amount greater or less than a given 6-digit number.

Can create a number a specified amount greater or less than any given 6-digit number.

Can create a number a specified amount greater or less than any given 6 digit number, including times when regrouping is required. e.g. 2000 less than 601 472.

N5.2 Multiplication Analyze models of, develop strategies for, and carry out the multiplication of whole numbers. Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level

Performance Analyze models Cannot model multiplication

beyond basic facts Cannot demonstrate an understanding of multiplication as repeated addition concretely, pictorially or orally Cannot partially explain with manipulatives, pictures or orally why 0 X 0 = 0 Cannot illustrate concretely, with pictures or symbolically the distributive property using expanded notation and partial products

Can model 2-digit X 2-digit in at least 1 of the following ways; arrays, base 10 blocks, partial products or area model and record the process symbolically or model 1-digit X 2-digit numbers in more than 1 way Can demonstrate an understanding of multiplication as repeated addition concretely, pictorially or orally Can partially explain with manipulatives, pictures or orally why 0 X 0 = 0 With help can illustrate concretely, with pictures or symbolically the distributive property using expanded notation and partial products

Can model 2-digit X 2-digit in at least 2 of the following ways; arrays, base 10 blocks, partial products or area model and record the process symbolically Can demonstrate an understanding of multiplication as repeated addition or combining equal groups concretely, pictorially or orally Explain with manipulatives, pictures or orally why 0 X 0 = 0 Illustrate concretely, with pictures or symbolically the distributive property using expanded notation and partial products

Can model 2-digit X 2-digit in more than 2 of the following ways; arrays, base 10 blocks, partial products or area model and record the process symbolically Can clearly demonstrate an understanding of multiplication as repeated addition and combining equal groups concretely, pictorially and orally Explain with manipulatives, pictures and orally why 0 X 0 = 0 Illustrate concretely, with pictures and symbolically the distributive property using expanded notation and partial products

Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level Performance

Develop strategies Cannot use at least 1 of the

following mental strategies to calculate X facts: skip counting, doubling, halving, repeated doubling and halving, 9s patterns, fact families and skip counting from a known fact. Cannot apply halving and doubling strategy to determine a product involving at least one 2-digit factor Cannot apply or explain the distributive property to determine factors that are close to multiples of 10

Can use at least 1 of the following mental strategies to calculate X facts: skip counting, doubling, halving, repeated doubling and halving, 9s patterns, fact families and skip counting from a known fact. With assistance can apply halving and doubling strategy to determine a product involving at least one 2-digit factor Requires assistance to apply or cannot explain the distributive property to determine factors that are close to multiples of 10

Can use at least 3 of the following mental strategies to calculate X facts: skip counting, doubling, halving, repeated doubling and halving, 9s patterns, fact families and skip counting from a known fact. Can apply halving and doubling strategy to determine a product involving at least one 2-digit factor Can apply and explain the distributive property to determine factors that are close to multiples of 10

Can use more than 3 of the following mental strategies to calculate X facts: skip counting, doubling, halving, repeated doubling and halving, 9s patterns, fact families and skip counting from a known fact. Can apply halving and doubling strategy to determine a product involving 2, 2-digit factors Can clearly explain and apply the distributive property to determine factors that are close to multiples of 10

Carry out multiplication Can recall less than half of X facts to 81 Make frequent errors in recalling X facts when carrying out 2-digit X 2-digit numbers and in problem solving Makes frequent errors when multiplying multiples of 10, 100 or 1 000 Cannot multiply 2-digit numbers and makes frequent errors when X multi-digit by 1-digit numbers Cannot explain or justify the process used when multiplying

Makes frequent errors when recalling X facts to 81 Makes few errors recalling X facts when carrying out 2-digit X 2-digit numbers and in problem solving Makes some minor errors when multiplying multiples of 10, 100 or 1 000 Makes frequent minor errors when multiplying 2-digit numbers but makes few errors when X multi-digit by 1-digit numbers Can partially explain but not justify the process used when multiplying 2-digit numbers

Makes few errors when recalling X facts to 81 Makes few errors recalling X facts when carrying out 2-digit X 2-digit numbers and in problem solving Makes few errors when multiplying multiples of 10, 100 or 1 000 Makes few errors when multiplying 2-digit numbers Can explain and justify the process used when multiplying 2-digit numbers

Rarely makes errors when recalling X facts to 81 Rarely makes errors recalling X facts when carrying out 2-digit X 2-digit numbers and in problem solving Rarely makes errors when multiplying multiples of 10, 100 or 1 000 Rarely makes errors when multiplying 2-digit numbers Can clearly explain and justify the process used when multiplying 2-digit numbers

Note: Estimation rubric can be used as it applies to multiplication

N5.3 Division Demonstrate, with and without concrete objects, an understanding of division (3 digit by 1 digit) and interpret remainders when solving problems. Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level

Performance Analyze models Cannot model division

beyond basic facts Cannot apply the following mental strategies to calculate basic division facts; fact families, repeated subtraction or annexing zeros Cannot explain using manipulative, pictures or orally why division by 0 is not possible

Can model division in at least 1 of the following ways, either with manipulatives, pictures and record the process symbolically; repeated subtraction, equal groups or sharing, subtracting equal groups Can apply at least 1 of the following mental strategies to calculate basic division facts; fact families, repeated subtraction or annexing zeros Can partially explain using manipulative, pictures or orally why division by 0 is not possible

Can model division in at least 2 of the following ways, either with manipulatives, pictures and record the process symbolically; repeated subtraction, equal groups or sharing, subtracting equal groups Can apply at least 2 of the following mental strategies to calculate basic division facts; fact families, repeated subtraction or annexing zeros Can explain using manipulative, pictures or orally why division by 0 is not possible

Can model division in more than 2 of the following ways, either with manipulatives, pictures and record the process symbolically; repeated subtraction, equal groups or sharing, subtracting equal groups Can apply all of the following mental strategies to calculate basic division facts; fact families, repeated subtraction or annexing zeros Can clearly explain using manipulative, pictures and orally why division by 0 is not possible

Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level Performance

Note: Estimation rubric can be used as it applies to division

Carry out division Makes frequent, major errors when diving a 3-digit number by a 1-digit number Makes frequent, major errors when dividing 3-digit numbers by 1-digit numbers (concretely, pictorially or symbolically) Recalls less than half of the basic division facts Makes frequent, major errors recalling division facts when dividing larger numbers or solving problems involving division Makes few, major errors when solving problems involving division Cannot use personal strategies to solve division problems or record the process symbolically

Makes frequent, major errors when diving a 3-digit number by a 1-digit number Makes frequent, major errors when dividing 3-digit numbers by 1-digit numbers (concretely, pictorially or symbolically) Recalls less than half of the basic division facts Makes frequent, minor errors when solving problems involving division Can use personal strategies to solve division problems and record the process symbolically but strategy may show flaws in reasoning or may not reach an accurate solution

Makes few minor errors when diving a 3-digit number by a 1-digit number Makes few, minor errors when dividing 3-digit numbers by 1-digit numbers (concretely, pictorially or symbolically) Makes few errors when recalling division facts with dividends to 81 Makes few errors recalling division facts when dividing larger numbers or solving problems involving division Makes few, minor errors when solving problems involving division Can use personal strategies to solve division problems and record the process symbolically

Rarely makes errors when diving a 3-digit number by a 1-digit number Rarely makes errors when dividing 3-digit numbers by 1-digit numbers (concretely, pictorially or symbolically) Rarely makes errors when recalling division facts with dividends to 81 Rarely makes errors in recalling division facts when dividing larger numbers or solving problems involving division Rarely makes errors when solving problems involving division Chooses and applies effective personal strategies to successfully solve division problems and record the process symbolically

Interpret remainders Cannot decide what to do with remainders (disregard, round up, rename as a fraction, or rename as a decimal) or explain the reasoning behind their choice

Can decide what to do with remainders (disregard, round up, rename as a fraction, or rename as a decimal) but cannot explain the reasoning behind their choice or their choice is inappropriate for the situation

Can decide what to do with remainders (disregard, round up, rename as a fraction, or rename as a decimal) and explain the reasoning behind their choice

Can decide what to do with remainders (disregard, round up, rename as a fraction, or rename as a decimal) and clearly explain the reasoning behind their choice

N5.4 Estimating Develop and apply personal strategies for estimation and computation including; front-end rounding, compensation and compatible numbers. Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level

Performance Know whether best to choose an under or over estimate strategy. Identifies whether a specific strategy will result in an under or over estimate and why. Understands when it is appropriate to use an estimate.

Does not understand whether a chosen strategy will result in an under or over estimate Cannot describe situation in which an estimate would be appropriate Chooses random or inappropriate estimation strategies

Can state whether a specific strategy will result in an under or over estimate but cannot explain why Cannot give a clear/logical explanation for why a specific strategy was chosen Limited ability to explain why an under or overestimate is appropriate for a given situation Chooses familiar estimation strategies even thought they might not be the most appropriate.

Can state whether a specific strategy will result in an under or over estimate and can explain why Can explain why an over or under estimate is appropriate for a given situation Chooses a workable and reasonable strategy

Can determine whether specific strategies will result in an over or under estimate and can clearly explain why. Can clearly explain they chose to over or underestimate in a given situation and explains the reasoning behind the chosen method Can explain why a strategy was chosen and how it was applied Chooses the most effective strategy for a given situation

Explain and apply estimation strategies; front end rounding, compatible numbers and compensation

Cannot explain the process or reasoning behind any of the estimation strategies Provides a vague and or inaccurate explanation of their thinking

Can explain the process for applying 1 or 2 of the 3 estimation strategies Provides a partially clear explanation of their thinking

Can clearly explain the process for using all 3 estimation strategies Provides a clear and logical explanation of their thinking

Can clearly explain the process for using all 3 estimation strategies as applied to all 4 operations Provides precise and insightful explanation of their thinking

Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level Performance

Apply estimation strategies; front end rounding, compatible numbers and compensation

Cannot apply estimation strategies to arrive at a reasonable estimate Has difficulty demonstrating computational fluency when estimating

Can apply only 1 or 2 of the estimation strategies to arrive at a reasonable estimate Makes some errors in computation when estimating

Can apply all 3 of the estimation strategies to arrive at a reasonable estimate Makes few minor computational errors when estimating

Can apply all 3 estimation strategies to arrive at a logical estimate in all operations Personalizes estimation strategies to involve numbers that are easy for themselves to work with Demonstrates computational fluency with all 3 estimation strategies that is efficient and flexible

N5.5 Fractions Demonstrate an understanding of fractions by using concrete/pictorial representations to: compare sets of equivalent fractions and compare fractions with like and unlike denominators Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level

Performance Model and demonstrate an understanding of equivalent decimals

Cannot use manipulatives or pictures to model equivalent fractions Cannot explain why 2 fractions are equivalent Cannot verify whether or not 2 fractions are equivalent

Can model equivalent fractions with manipulatives or pictures but may not be able to clearly state why they are equivalent With limited assistance can use manipulatives or pictures to determine if 2 given fractions are equivalent

Can model equivalent fractions with manipulatives or pictures Can state why fractions are equivalent with reference to quantity Can use manipulatives, pictures or symbolic manipulation to determine whether or not 2 give fractions are equivalent

Can model equivalent fractions with a variety of manipulatives Can clearly explain why they are equivalent (with references to meaning of numerators, denominators and quantity) Can determine if 2 given fractions are equivalent using symbolic manipulation and can clearly explain the process used

Create equivalent decimals Cannot create sets of equivalent fractions

Uses concrete or pictorial representations to create sets of equivalent fractions

Uses a symbolic strategy to create sets of equivalent fractions

Uses symbolic strategies to create sets of equivalent fractions and clearly explains why the strategy works (2/3 x 3/3 = 2/3 x 1 …multiplying by 1 doesn’t change the value

Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level Performance

Compare and order fractions

Can compare fractions only if they have like denominators or like numerators Cannot plot fractions on a number line Cannot explain how to use equivalent fractions to compare fractions with unlike denominators

Can compare and order fractions with like denominators or like numerators but requires some assistance to compare and order fractions with unlike denominators With some assistance can plot fractions on a number line Can only partially explain how to use equivalent fractions to compare fractions with unlike denominators

Can compare fractions with like and unlike denominators with or without manipulatives or pictures (by comparing to ½ or using equivalent fractions) Can use equivalent fractions to plot fractions on a number line by Can explain how to use equivalent fractions to compare fractions with unlike denominators

Can compare fractions with like and unlike numerators or denominators symbolically by comparing to benchmarks and using equivalent fractions Can clearly explain the process used to compare fractions Can plot fractions and mixed numbers on a number line

N5.6 Decimal Fractions Describe, represent, compare decimals and relate decimals to fractions Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level

Performance Relating fractions and decimals

Cannot identify equivalent fractions and decimals Cannot create fractions and decimals that are equivalent Cannot write fractions as decimals or vice-versa

Sometimes makes errors when identifying equivalent fractions and decimals Requires assistance to create fraction and decimals that are equivalent Can write fractions with denominators of 10, 100 or 1000 as decimals

Makes few errors when identifying equivalent fractions and decimals Makes few errors when creating fractions and decimals that are equivalent Makes few errors when writing fractions as decimals and vice-versa

Rarely makes errors when identifying equivalent fractions and decimals Rarely makes errors when creating fractions and decimals that are equivalent Rarely makes errors when writing fractions as decimals and vice-versa

Representing and describing decimals

Cannot represent decimals with manipulatives or pictures Cannot describe the value of each digit in a decimal Cannot create equivalent decimals

Require some assistance to represent decimals with manipulatives or pictures Requires assistance to describe the value of each digit in a decimal With some assistance can create equivalent decimals

Can use manipulatives or create a picture to represent decimals Makes few errors when describing the value of each digit in a decimal Can create equivalent decimals

Can represent decimals with a variety of manipulatives and pictures Rarely makes errors when describing the value of each digit in a decimal Can create sets of equivalent decimals

Comparing and Ordering Cannot use benchmarks to order decimals Cannot plot decimals on a number line Cannot compare decimals

Requires some assistance to use benchmarks to order decimals accurately Requires assistance to plot decimals on a number line accurately Makes some errors when comparing decimals

Can use benchmarks to order decimals with few errors Can plot decimals on a number line with few errors Can compare decimals with few errors

Rarely makes errors when using benchmarks to order decimals Rarely makes errors when plotting decimals on a number line Rarely makes errors when comparing decimals

N5.7 Adding and Subtracting Decimals Adds and subtracts decimals to thousandths Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level

Performance Addition Often makes major errors

when adding decimals Cannot use estimation to determine where to place the decimal point when adding decimals Cannot model or draw a picture to represent the determination of a decimal sum, and cannot record the process symbolically

Makes frequent minor errors when adding decimals Makes frequent minor errors when using estimation to determine where to place the decimal point when adding decimals Requires assistance to model or draw a picture to represent the determination of a decimal sum and record the process symbolically

Makes few minor errors when adding decimals Makes few minor errors when using estimation to determine where to place the decimal point when adding decimals Can use manipulates or draw a picture to represent the determination of a decimal sum and record the process symbolically

Rarely makes errors when adding decimals Rarely makes errors when using estimation to determine where to place the decimal point when adding decimals Can use a variety of manipulatives and draw pictures to represent the determination of a decimal sum and record the process symbolically

Subtraction Often makes major errors when subtracting decimals Cannot use estimation to determine where to place the decimal point when subtracting decimals Cannot model or draw a picture to represent the determination of a decimal difference, and cannot record the process symbolically

Makes frequent minor errors when subtracting decimals Makes frequent minor errors when using estimation to determine where to place the decimal point when subtracting decimals Requires assistance to model or draw a picture to represent the determination of a decimal difference and record the process symbolically

Makes few minor errors when subtracting decimals Makes few minor errors when using estimation to determine where to place the decimal point when subtracting decimals Can use manipulates or draw a picture to represent the determination of a decimal difference and record the process symbolically

Rarely makes errors when subtracting decimals Rarely makes errors when using estimation to determine where to place the decimal point when adding decimals Can use a variety of manipulatives and draw pictures to represent the determination of a decimal sum and record the process symbolically

Problem Solving Makes frequent major errors when solving problems involving decimals

Requires assistance to solve problems involving decimals

Makes few minor errors when solving problems involving decimals

Rarely makes errors when solving problems involving decimals

P5.1 /5.2 Patterns P5.1 Represent, analyze and apply patterns using mathematical words and notation P5.2 Write, solve and confirm solutions of sing-variable, one-step equations (with whole numbers) Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level

Performance Describing patterns Cannot use mathematical

language/notation to describe patterns

With assistance uses mathematical language and notation to describe patterns Makes frequent errors when working independently

Make some errors when using mathematical language and notation to describe patterns

Uses mathematical language and notation clearly and concisely to describe patterns, seldom make errors

Representing patterns Cannot create models and pictures for patterns Cannot determine the pattern in a picture or model

Can create models and pictures for patterns Able to create charts and pattern rules for patterns with some assistance

Can create models, pictures, charts, and pattern rules for given patterns

Can create models, pictures, charts and pattern rules for given patterns and can translate a pattern from on form to another

Writing expressions for patterns

Cannot use variables to write expressions for patterns

With assistance can use variable to write expressions for patterns but make frequent errors when doing so independently

Generally accurate when using variables to write expressions for patterns

Accurately uses variable to write expressions for patterns

Analyzing patterns Cannot determine whether or not a number belongs to a given pattern

With assistance can determine whether or not a number belongs to a given pattern but makes frequent errors when working independently (extending patterns, creating chars or solving expressions)

Can determine whether or not a number belongs to a given pattern using at least 1 of the following strategies; extending the pattern, making a chart, or solving the expression by replacing the variable

Can determine whether or not a given number belongs to a pattern by extending the pattern, making a chart and solving the expression by replacing the variable

Writing equations with variable

Cannot write an equation using a variable to describe a pattern

Makes frequent errors or omissions when using variable to write equations for patterns…partially accurate

Generally uses variable to write equations for patterns accurately…makes few errors or omissions

Rarely make errors or omissions when writing equations with variable for patterns

Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level Performance

Solving equations with variables

Cannot solve one-step equations with single variables

With some assistance can solve one-step equations with single variables

Can solve one-step equations with single variables though may make some calculation or procedural errors

Can solve one-step equations with single variables including any operation accurately and consistently

Cannot explain what part of a problem the variable represents

Requires assistance to determine what part of a problem a variable represents

Can clearly explain what part of a problem a variable represents

Can clearly explain what part of a problem a variable represents and its relationship to the equation

Statistics and Probability SP5.1 state the difference between first and second hand data SP5.2 construct and interpret double bar graphs SP5.3 describe, compare, predict and test the likelihood of outcomes in probability situations Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level

Performance First and second hand data Unable to explain or

demonstrate the difference between first and second hand data

Partially able to explain or demonstrate the difference between first and second had data

Able to explain and demonstrate the difference between first and second hand data

Able to clearly demonstrate and explain the difference between first and second had data

Unable to identify data as first or second hand

Not always able to identify whether data is first or second hand

Able to identify examples of first and second hand data

Able to give examples of first and second had data

Unable to create or answer questions based on first and second hand data

Able answer or create logical questions based on first or second hand data

Able to create and answer questions based on first and second hand data

Able to create and answer insightful questions based on first and second hand data

Double bar graphs Often makes major errors when creating double bar graphs (including labels, legends and scales)

Makes frequent minor errors/omissions when creating double bar graphs; including labels, legends and scales

Generally accurate, making few errors or omissions in creating double bar graphs (including labels, legends and scales)

Rarely makes errors or omissions when constructing double bar graphs (including labels, legends and scales)

Draws faulty conclusions when interpreting double bar graphs

Draws basic conclusions when interpreting double bar graphs

Draws appropriate conclusions when interpreting double bar graphs

Draws insightful conclusions when interpreting double bar graphs

Unable to create or answer basic, questions relating the construction or interpretation of double bar graphs

Able to create and answer basic questions relating to the construction and interpretation of double bar graphs

Able to create and answer logical questions related to the construction and interpretation of double bar graphs

Able to create and answer insightful questions related to the construction and interpretation of double bar graphs

Probability outcomes Often inaccurate when categorizing outcomes in probability situations as impossible, possible or certain

Sometimes inaccurate when categorizing outcome in probability situations as impossible, possible or certain

Generally accurate, makes few errors when categorizing outcomes in probability situations as impossible, possible or certain

Mostly accurate; rarely makes errors or omissions when categorizing outcomes in probability situations as impossible, possible or certain

Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level Performance

Has difficulty designing and carrying out probability experiments successfully

With limited help uses strategies with partial success to design and carry out probability experiments

Uses appropriate strategies to design and carry out probability experiments successfully

Uses appropriate, often innovative strategies with a high degree of success to design and conduct probability experiments Designs and successfully carries out effective probability experiments

Is unable to analyze data to make predictions about future outcomes (as impossible, possible or certain)

Analyzes data but superficially and makes simple predictions but may not be able to explain reasons why outcomes are possible, impossible or certain

Analyzes data and makes logical predictions (impossible, possible or certain) and states reasoning behind prediction

Analyzes data and makes insightful predictions about future outcomes as impossible, possible or certain, and clearly states reasons for predictions

Cannot list all the outcomes of a probability experiment or cannot explain why the are equally, more or less like to occur

Can list all the possible outcomes of a probability experiment but explanations of whether they are more, less or equally likely is only partially clear

Can list all possible outcomes of a probability experiment and clearly explains why they are less, equally or more likely to occur

Can list all the outcomes of a probability experiment and precisely explain why they are equally, more or less likely to occur

SS5.1 Shape and Space (area and perimeter) Design and construct different rectangles given perimeter, area or both (whole numbers) Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level

Performance Creating rectangles Unable to create 2 different

rectangles with the same perimeter even with the use of manipulatives or grids

Requires some assistance to create 2 different rectangle with the same perimeter

Able to create 2 different rectangles with the same perimeter

Able to create more tan 2 different rectangles with the same perimeter

Cannot create 2 different rectangles with the same area

Can create 2 different rectangles with the same area

Can create more than 2 different rectangles with the same area

Can create more than 3 different rectangles with the same area

Analyzing rectangles Cannot accurately explain why rectangles with the same perimeters can have different shapes and area

Can give a partially accurate explanation about why rectangles with the same perimeters can have different shapes and areas

Can explain why rectangles with the same perimeter can have different shapes and areas

Can clearly explain why rectangles with the same perimeters can have different shapes and areas

Cannot accurately explain why rectangles with greater areas do not always have greater perimeters (and vice-versa)

Can give a partially accurate explanation of why rectangles with greater areas do not always have greater perimeters (and vice-versa

Can explain why rectangles with greater area do not always have greater perimeters (and vice-versa)

Can clearly explain why rectangles with greater areas do not always have greater perimeters (and vice-versa) and how knowing this could impact choices in real life situations

Cannot explain which rectangles would be appropriate for a given situation

Explanation of which rectangles would be appropriate for a given situation is unclear or show some flaws in the reasoning behind the choice

Can explain which rectangles would be appropriate for a given situation

Can explain which rectangles would be appropriate for a given situation and clearly describe the reasoning behind their choice

Shape and Space (Length) 5.2 select and justify referents for mm and model/describe the relationship between mm, cm and m Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level

Performance Referents for mm Cannot give an appropriate

referent for mm Can give a referent for mm but it may not be the most appropriate

Can give at least 1 appropriate referent for mm

Can give 2 or more appropriate referents for mm

Cannot use referents for mm to determine a reasonable estimate of a linear measurement

Uses referents for mm to determine approximate linear measurements but resulting estimate is not always reasonable

Uses referents for mm to determine acceptable estimates of linear measurements

Uses referents for mm to determine appropriate estimates of linear measurements

Relationship between mm, cm and m

Cannot calculate conversions between mm, cm and m

Requires assistance to calculate conversions between mm, cm and m Makes frequent errors when calculating conversions independently

Makes few minor errors when calculating conversions between mm, cm and m

Calculates conversions between mm, cm and m accurately

Cannot identify the standard unit (mm, cm or m) that would be appropriate for a linear measurement in a given situation

Can identify a standard unit for a given linear measurement situation but that unit may not be the most appropriate choice

Can identify the standard unit (mm, cm or m) that would be appropriate for a linear measurement in a given situation

Identifies the most appropriate standard unit for a linear measurement in a given situation

Shape and Space (Volume)

SS5.3 Measure and record volume in ㎤ or ㎥

Select and justify referents for ㎤ or ㎥

Estimate volume by using referents for ㎤ or ㎥

Construct rectangular prisms for a given volume Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level

Performance Referents Cannot give a referent for

㎤ or ㎥

Often makes errors when identifying which standard unit is represented by a specific referent

Can give at least 1

appropriate referent for ㎤

or ㎥ but cannot clearly

explain the reasoning behind their choice Makes some errors when identifying which standard unit is represented by a specific referent

Can give at least 1

appropriate referent for ㎤

or ㎥ and explain the

reasoning behind their choice Makes few errors when identifying which standard unit is represented by a specific referent

Can give more than 1

appropriate referent for ㎤

or ㎥ and clearly explain

the reasoning behind their choice Rarely makes errors when identifying which standard unit is represented by a specific referent

Cannot use referents to determine acceptable estimates of the volumes of 3-D objects

Can use referents to determine estimates of the volumes of 3-D objects but the resulting estimate may not always be reasonable

Can use referents to determine acceptable estimates of the volumes of 3-D objects

Can use referents to determine appropriate estimates of the volumes of 3-D objects

Measuring Cannot measure and record the volumes of 3-D objects with an acceptable degree of accuracy

Makes frequent minor errors when measuring and recording the volumes of 3-D objects

Makes few minor error when measuring and recording the volumes of 3-D objects

Can accurately measure and record the volumes of 3-D objects

Constructing rectangular prisms

Cannot construct a rectangular prism for a given volume

With assistance can construct a rectangular prism for a given volume

Can construct a rectangular prism for a given volume

Can construct more than 1 rectangular prisms for a given volume

Shape and Space (Capacity) 5.4 Measure and record capacity in ml or L Describe the relationship between ml and L, Select and justify referents for and estimate capacity in ml and L Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level

Performance Referents Cannot give any

appropriate referents for ml and L Cannot identify which standard unit is represented by a specific referent

Can give at least 1 appropriate referent for ml and L but cannot clearly explain the reasoning behind their choice Makes some errors when identifying which standard unit is represented by a specific referent

Can give at least 1 appropriate referent for ml and L and explain the reasoning behind their choice Makes few errors when identifying which standard unit is represented by a specific referent

Can give more than 1 appropriate referent for ml and L and explain the reasoning behind their choice Rarely makes errors when identifying which standard unit is represented by a specific referent

Cannot use referents to determine acceptable estimates of the capacity of containers

Can use referents to determine estimates of the capacities of containers but the resulting estimates may not be reasonable

Can use referents to determine acceptable estimates of the capacities of containers

Can use referents to determine appropriate estimates of containers

Measuring and recording Cannot measure and record the capacity of containers

Makes some errors when measuring and recording the capacity of containers

Makes few minor error when measuring and recording the capacity of containers

Rarely makes errors when measuring and recording the capacity of containers

Relationship between ml and L

Cannot use manipulatives to show the relationship between ml and L

With assistance can use manipulatives to show the relationship between ml and L

Can use manipulatives to show the relationship between ml and L

Can show the relationship between ml and L using a variety of manipulatives

Shape and Space (Geometry) SS5.5 determine if edges and faces of 3-D objects and 2-D shapes are parallel, intersecting, perpendicular, vertical or horizontal Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level

Performance Identifies edges, faces and lines of 2-D shapes and 3-D objects

Often makes major errors/omissions in identifying edges, faces and lines of 2-D shapes and 3-D objects

Makes frequent but minor errors/omissions when identifying edges, faces and lines of 2-D shapes and 3-D objects

Makes few errors/omissions when identifying edges, faces and lines of 2-D shapes and 3-D objects

Rarely makes errors/omission when identifying edges, faces and sides of 2-D shapes and 3-D objects

Determines if edges, faces and lines of 2-D shapes and 3-D objects are parallel, intersecting, perpendicular, vertical or horizontal

Often makes major errors/omissions when determining whether or not edges, faces and lines of 2-D shapes and 3-D objects are parallel, intersecting, perpendicular, vertical or horizontal

Makes frequent minor errors/omissions when determining whether or not edges, faces and lines of 2-D shapes and 3-D objects are parallel, intersecting, perpendicular, vertical or horizontal

Makes few errors/omissions when determining whether or not edges, faces and lines of 2-D shapes and 3-D objects are parallel, intersecting, perpendicular, vertical or horizontal

Rarely makes when determining whether or not edges, faces and lines of 2-D shapes and 3-D objects are parallel, intersecting, perpendicular, vertical or horizontal

Explains what it means for lines, edges or face of 2-D shapes and 3-D objects

Gives a vague or inaccurate description of what it means for a line, edge, or face of a 2-D shape or 3-D object to be parallel, intersecting, perpendicular, vertical or horizontal through physical movement, orally or in writing

Gives a partially accurate description of what it means for a line, edge, or face of a 2-D shape or 3-D object to be parallel, intersecting, perpendicular, vertical or horizontal through physical movement, orally or in writing

Can describe what it means for a line, edge, or face of a 2-D shape or 3-D object to be parallel, intersecting, perpendicular, vertical or horizontal through physical movement, orally or in writing

Can clearly and concisely describe what it means for a line, edge, or face of a 2-D shape or 3-D object to be parallel, intersecting, perpendicular, vertical or horizontal through physical movement, orally or in writing

SS5.6 Shape and Space (Quadrilaterals) Identify and sort quadrilaterals (including rectangles, squares, trapezoids, parallelograms and rhombuses) according to their attributes Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level

Performance Naming Often makes major errors

when naming different types of quadrilaterals (squares, rectangles, trapezoids, parallelograms and rhombuses)

Makes frequent minor errors when naming different types of quadrilaterals (squares, rectangles, trapezoids, parallelograms and rhombuses)

Makes few errors when naming different types of quadrilaterals (squares, rectangles, trapezoids, parallelograms and rhombuses)

Rarely makes errors when naming different types of quadrilaterals (squares, rectangles, trapezoids, parallelograms and rhombuses)

Describing common attributes

Cannot describe the common attributes of quadrilaterals (squares, rectangles, trapezoids, parallelograms and rhombuses)

Can describe some of the common attributes of quadrilaterals (squares, rectangles, trapezoids, parallelograms and rhombuses)

Can describe most of the common attributes of quadrilaterals (squares, rectangles, trapezoids, parallelograms and rhombuses)

Can describe all of the common attributes of quadrilaterals (squares, rectangles, trapezoids, parallelograms and rhombuses)

Sorting Cannot sort quadrilaterals according to their attributes

Makes some errors when sorting quadrilaterals according to their attributes

Makes few errors when sorting quadrilaterals according to their attributes

Can accurately sort quadrilaterals according to the attributes

Common and differing attributes

Cannot identify common and differing attributes of various quadrilaterals

Can identify some common and differing attributes of various quadrilaterals

Makes few errors/omissions when identifying attributes of various quadrilaterals

Rarely makes errors/omissions when identifying attributes of various quadrilaterals

Shape and Space (Transformations) 5.7 identify, create and analyze single transformations of 2-D shapes Experiencing Difficulty Approaching Grade Level At Grade Level Strong Grade Level

Performance Demonstrating rotations, reflections and translations

Makes frequent major errors when performing translations, rotations, and reflections of 2-D shapes concretely, pictorially or physically

Makes frequent minor errors when performing translations, rotations, and reflections of 2-D shapes concretely, pictorially or physically

Makes few, minor errors when performing translations, rotations, and reflections of 2-D shapes concretely, pictorially or physically

Rarely makes errors when performing translations, rotations, and reflections of 2-D shapes concretely, pictorially and physically

Analyzing/describing translations

Makes frequent major errors when drawing 2-D shapes and showing their translations, Cannot record the direction and magnitude of the movements

Can draw 2-D shapes and show their translations Makes frequent minor errors when recording the direction and magnitude of the movements

Can draw 2-D shapes, show their translations Makes few minor errors when recording the directions and magnitudes of the movements

Can draw 2-D shapes, showing their translations Rarely makes errors when recording the directions and magnitudes of movements

Analyzing/describing rotations

Makes frequent major errors when drawing 2-D shapes and showing their rotations Cannot accurately describe the rotations (direction and fraction of the turn or the point or rotation)

Can draw 2-D shapes and show their rotations Makes frequent errors when describing the rotations (including the direction and fraction of the turn and the point of rotation)

Can draw 2-D shapes and show their rotations Makes few minor errors when describing the rotations (including the direction and fraction of the turn and the point of rotation

Can draw 2-D shapes and their rotations Rarely makes errors when describing the rotations (including the direction and fraction of the turn and the point of rotation)

Analyzing/describing reflections

Cannot draw 2-D shapes and show their reflections Cannot identify lines of reflection

Can draw 2-D shapes and show their reflections Often makes errors when identifying lines of reflection

Can draw 2-D shapes and show their reflections Makes few errors when identifying lines of reflection

Can draw 2-D shapes and show their reflections Rarely makes errors when identifying lines of reflection

Identifying translations, reflection, and rotations

Cannot determine whether a given image shows a reflection, rotation, or translation of a given 2-D shape

Frequently makes errors when determining whether a given image shows a reflection, rotation, or translation of a given 2-D shape

Makes few errors when determining whether a given image shows a reflection, rotation, or translation of a given 2-D shape

Accurately determines whether a given image shows a reflection, rotation, or translation of a given 2-D shape