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TRANSCRIPT
MathPRE-ASSESSMENT 8
Finding Each Student’s Pathway
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SAMPLEMATERIALINSIDE
2
FINDING EACH STUDENT’S PATHWAY
Math Pre-Assessment is a uniquely designed resource to help educators understand and customize each student’s math education. The resource is developed by a team of expert math educators and backed by research. Math Pre-Assessment enables educators to compare a student’s math understanding to their curriculum, identify gaps in understanding and ensure each student is ready for new curriculum material all with this easy to use assessment tool.
Each pre-assessment is created from a DEVELOPMENTAL TRAJECTORY. These developmental trajectories are research-supported pathways that students go through to understand mathematics concepts and skills as they move along a learning continuum.
Developmental Trajectory
Compare and Order Rational Numbers
Represent Rational Numbers
Add Integers
Add Fractions
Subtract Integers
Subtract Fractions
Multiply Integers
Multiply Fractions
Divide Integers
Divide Fractions
Make Financial Decisions about Sales Tax, Tips, Discounts, Sale Prices
Relate Fractions and Decimals
Make a Budget
Make Financial Decisions about Earning, Spending, Saving, Giving
Spend Responsibly Considering Wants and Needs
Multiply and Divide with Money
Add and Subtract with Money
Identify, Represent, Count Money
Order of Operations
Choose the Appropriate Operation
Prime and Composite Numbers
Factors and Multiples
Estimation Strategies for Division
Divide Multi-Digit Whole Numbers
RemaindersRecall Division
FactsRelate Division
and MultiplicationDivision
Properties Relate Subtraction
and DivisionSingle-Digit
Division
Estimation Strategies for Multiplication
Multiplication Properties
Relate Addition and Multiplication
Single-Digit Multiplication
Subtract Decimals
Subtract Multi-Digit Whole Numbers
Relate Subtraction and Addition
Add Decimals
Add Multi-Digit Whole Numbers
Estimation Strategies for Addition
Subtraction Properties
Addition Properties
Single-Digit Addition
Single-Digit Subtraction
Proportional Reasoning with Rates
Represent Decimals Concretely, Pictorially, Symbolically
Proper Fractions, Improper Fractions, Mixed Numbers
Equivalent Fractions
Compare Integers
Represent Integers
Compare, Order, Relate Whole Numbers
Estimate Quantities
Ordinal Counting
Skip Counting
Count On and Count Back
Counting Principles
Represent Whole Numbers Concretely, Pictorially, Symbolically
Subitize
Represent Quantities with Fractions
Ratios
Meaning of Addition
Meaning of Subtraction
Meaning of Multiplication
Meaning of Division
Even and Odd Numbers
Role Play Financial Situations
COUNTING
PLACE VALUE AND REPRESENTING NUMBERS
FRACTIONS AND DECIMAL NUMBERS
RATIOS, PERCENTS, PROPORTIONAL REASONING
ADDITION
SUBTRACTION
MULTIPLICATION
DIVISION
NUMBER RELATIONSHIPS
FINANCIAL LITERACY
Rote Counting Forward and Backward
Count Objects
Compose and Decompose Numbers
Compare and Order Fractions and Decimals
Mental Math Strategies for Addition
Relate Addition and Subtraction
Recall Addition Facts
Estimation Strategies for Subtraction
Mental Math Strategies for Subtraction
Recall Subtraction Facts
Mental Math Strategies for Multiplication
Recall Multiplication Facts
Relate Multiplication and Division
Mental Math Strategies for Division
Percents
Divide Decimals
Multiply Decimals
Multiply Multi-Digit Whole Numbers
Represent Numbers and Measurements with Exponents
Squares, Square Roots, Cubes
POWERS AND ROOTS
NEL
Applications
Foundational Understandings
NEL
Numbers are used to describe quantities.
A number can be represented concretely, pictorially, and symbolically.
A number can be represented in various equivalent ways.
Our numbersystem is based on 10.
Benchmarks and referents can be used to relate numbers and estimate.
One quantity can represent a number of units of another quantity.
Addition resultsin a total. Subtractionresults in a difference.
Multiplication isrepeated addition.Division is repeatedsubtraction.
The operations of addition, subtraction, multiplication, and division are interrelated.
Financial literacy is the basis for making responsible decisions about money, and considering the impact the decisions have on oneself and on others.
Solving problems helps students learn about numbers, operations, and financial literacy both inside and outside the classroom.
STRAND: NUMBER
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Each of the five strands has a developmental trajectory.
Foundational Understandings are the big ideas of the strand.
The applications identify particular aspects of the foundational understandings.
Each item shows the developmental sequence, or journey, for each application.
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Compare and Order Rational Numbers
Represent Rational Numbers
Add Integers
Add Fractions
Subtract Integers
Subtract Fractions
Multiply Integers
Multiply Fractions
Divide Integers
Divide Fractions
Make Financial Decisions about Sales Tax, Tips, Discounts, Sale Prices
Relate Fractions and Decimals
Make a Budget
Make Financial Decisions about Earning, Spending, Saving, Giving
Spend Responsibly Considering Wants and Needs
Multiply and Divide with Money
Add and Subtract with Money
Identify, Represent, Count Money
Order of Operations
Choose the Appropriate Operation
Prime and Composite Numbers
Factors and Multiples
Estimation Strategies for Division
Divide Multi-Digit Whole Numbers
RemaindersRecall Division
FactsRelate Division
and MultiplicationDivision
Properties Relate Subtraction
and DivisionSingle-Digit
Division
Estimation Strategies for Multiplication
Multiplication Properties
Relate Addition and Multiplication
Single-Digit Multiplication
Subtract Decimals
Subtract Multi-Digit Whole Numbers
Relate Subtraction and Addition
Add Decimals
Add Multi-Digit Whole Numbers
Estimation Strategies for Addition
Subtraction Properties
Addition Properties
Single-Digit Addition
Single-Digit Subtraction
Proportional Reasoning with Rates
Represent Decimals Concretely, Pictorially, Symbolically
Proper Fractions, Improper Fractions, Mixed Numbers
Equivalent Fractions
Compare Integers
Represent Integers
Compare, Order, Relate Whole Numbers
Estimate Quantities
Ordinal Counting
Skip Counting
Count On and Count Back
Counting Principles
Represent Whole Numbers Concretely, Pictorially, Symbolically
Subitize
Represent Quantities with Fractions
Ratios
Meaning of Addition
Meaning of Subtraction
Meaning of Multiplication
Meaning of Division
Even and Odd Numbers
Role Play Financial Situations
COUNTING
PLACE VALUE AND REPRESENTING NUMBERS
FRACTIONS AND DECIMAL NUMBERS
RATIOS, PERCENTS, PROPORTIONAL REASONING
ADDITION
SUBTRACTION
MULTIPLICATION
DIVISION
NUMBER RELATIONSHIPS
FINANCIAL LITERACY
Rote Counting Forward and Backward
Count Objects
Compose and Decompose Numbers
Compare and Order Fractions and Decimals
Mental Math Strategies for Addition
Relate Addition and Subtraction
Recall Addition Facts
Estimation Strategies for Subtraction
Mental Math Strategies for Subtraction
Recall Subtraction Facts
Mental Math Strategies for Multiplication
Recall Multiplication Facts
Relate Multiplication and Division
Mental Math Strategies for Division
Percents
Divide Decimals
Multiply Decimals
Multiply Multi-Digit Whole Numbers
Represent Numbers and Measurements with Exponents
Squares, Square Roots, Cubes
POWERS AND ROOTS
NEL
Applications
Foundational Understandings
NEL
Numbers are used to describe quantities.
A number can be represented concretely, pictorially, and symbolically.
A number can be represented in various equivalent ways.
Our numbersystem is based on 10.
Benchmarks and referents can be used to relate numbers and estimate.
One quantity can represent a number of units of another quantity.
Addition resultsin a total. Subtractionresults in a difference.
Multiplication isrepeated addition.Division is repeatedsubtraction.
The operations of addition, subtraction, multiplication, and division are interrelated.
Financial literacy is the basis for making responsible decisions about money, and considering the impact the decisions have on oneself and on others.
Solving problems helps students learn about numbers, operations, and financial literacy both inside and outside the classroom.
STRAND: NUMBER
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Key Features ■ Provides the developmental trajectories to give a whole picture of math
development from grade 1–8.
■ Assesses whether students have the procedural knowledge and conceptual understandings for the grade specific curriculum.
■ Pre-assessments identify where a student is on the developmental trajectory.
■ Includes next steps for instruction, gap closing or intervention.
■ Tracking tools are provided to keep a record of student readiness.
DRAFT
The trajectory items for the given grade are highlighted.
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HOW IT WORKS
Answering The Question:
● Each item on the trajectory has a pre-assessment
● Pre-assessments take little classroom time
● Easy to administer and score
● Includes suggested answers, rationale and next steps
STOP: student needs gap closing
CAUTION: student may have partial understanding or small gaps
GO: student is ready to learn the grade level curriculum expectation or outcome
PRE-ASSESSMENT ANALYSIS CHART
NEXT STEPS
“Are My Students Ready?”
Resource Overview Grades 1–8
Developmental TrajectoriesFor each of the 5 Strands
Math Pre-AssessmentsFor each item on the trajectory
Scoring Guide and Analysis ChartsProvided for each pre-assessment
Online Teaching CentreDigital access
5
PRE-ASSESSMENT
NELAnalysis Chart pages xx-xx
Name Date
2
Multiplying Fractions MATERIALS• fraction circles (optional)• fraction strips (optional)
What multiplication sentence do the fraction strips show? Select all that apply.
A. 3 3 23
B. 2 3 3 C. 23
3 3 D. 3 3 3
Fill in the missing number. 2 3 13
5 ( )
3
Multiply. 14
3 3
A. 43
B. 23
C. 34
D. 3
Fill in the missing number. 25
3 13
5 2
( )
Multiply. 35
3 34
A. 69
B. 9
20 C.
320
D. 39
Multiply. 123
3 2
Select all that apply.
A. 313
B. 223
C. 323
D. 103
Show What You Know
Use estimation to check if your answer is reasonable. Explain your estimation strategy.
1.
2.
3.
4.
5.
6.
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Initial question reaches back to prerequisite learning.
Assessment question focused on trajectory item.
Show What You Know questions provide opportunities for students to demonstrate their understanding.
DRAFT
6
NEL2
Multiplying Fractions
QUESTIONS RATIONALE SCORING NEXT STEPS
What multiplication sentence do the fraction strips show? Select all that apply.
A. 3 3 23
B. 2 3 3
C. 23
3 3
D. 3 3 3
A, C
Students match a model of multiplication of fractions to a multiplication sentence. Understanding representations of multiplication is important in the development of numeracy.
Look at:• multiplication properties
Provide experience: • using the commutative
property of multiplication with whole numbers (e.g., 4 × 3 = 4 × 3)
For deeper intervention, go to Leaps and Bounds 5/6, pages 86–88.
Fill in the missing number.
2 3 13
5 ( )
32
Students multiply a whole number by the numerator of the unit fraction to find the missing numerator. Knowing that a whole number can be written as a fraction with a denominator of 1 helps to determine fraction products.
Provide experience:• using repeated addition of
fractions to model products
Multiply. 14
3 3
A. 43
B. 23
C. 34
D. 3
C
Students multiply a unit fraction by a whole number. Knowing that a whole number can be written as a fraction with a denominator of 1 helps to determine fraction products.
Provide experience:• using repeated addition of
fractions to model products
Fill in the missing number. 25
3 13
5 2
( )
15
Students multiply 2 proper fractions to find the missing denominator. Knowing a variety of strategies to multiply fractions helps students build conceptual knowledge and gives them more than one method to choose from when solving problems.
Provide experience:• using a grid model or
paper folding to show the denominator by counting the number of units in the grid or folded paper
1.1. incorrect
only one correct
2. incorrect
3.incorrect
4. incorrect
NUMBER MultiplicationMultiply Fractions
MultiplicationEstimation Strategies for Multiplication
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DRAFT
ANALYSIS CHART
Answer provided.
Use of Leaps and Bounds recommended for deeper intervention
Identifies the Strand, the Application(s) and the item(s) for the application.
Student needs gap closing.
Contains the “Look Fors” and an explanation for why the question is included.
Look at: Identify possible items on the trajectory to close gaps.Identify the pre-assessment
7
NEL 3
QUESTIONS RATIONALE SCORING NEXT STEPS
Multiply. 35
3 34
A. 69
B. 920
C. 320
D. 39
B
Students multiply 2 proper fractions using any strategy. Knowing a variety of strategies for fraction multiplication leads to faster and more accurate computations.
Provide experience:• using a grid to model the
fractions (e.g., 35 along one side and 34 along the other)
Multiply. 123
3 2
Select all that apply.
A. 313
B. 223
C. 323
D. 1 03
A, D
Show What You KnowUse estimation to check if your answer is reasonable. Explain your estimation strategy.For example, I know that 1 3 2 = 2; there are 3 thirds in 1 whole, so 4 thirds are a little more than 1. So, my answer should be a little more than 2 1 1 5 3. My answer of 31
3 is reasonable.
Students multiply a mixed number by a whole number using any strategy and use estimation to check the reasonableness of their answer. Estimating is an effective strategy for checking answers.
Provide experience:• using an area model to
multiply a fraction by a whole number
Provide experience:• discussing estimation
strategies with a classmate
Provide experience:• creating various types
of problems involving multiplication of fractions, trading with a classmate, and solving
After the lesson that follows this pre-assessment, use Exit Ticket “Multiplying Fractions” to assess whether students can successfully multiply fractions.
5.incorrect
6.incorrect
inadequate explanation
correct
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DRAFT Student has partial understanding and small gaps.
Provide experience: suggestions for scaffolding understanding of concepts and skills identified in the question.
Use Math Exit Tickets to check for understanding after the lesson.Sample solution provided
Student is ready to learn the trajectory item.
Recommended intervention.
Title ISBN Math Pre-Assessment Grade 1Book + Online Teaching Centre (Ontario) 9780176830892 Book + Online Teaching Centre (WNCP) 9780176833497Book + Online Teaching Centre (BC) 9780176833558 Math Pre-Assessment Grade 2Book + Online Teaching Centre (Ontario) 9780176830908 Book + Online Teaching Centre (WNCP) 9780176833503Book + Online Teaching Centre (BC) 9780176833565Math Pre-Assessment Grade 3Book + Online Teaching Centre (Ontario) 9780176830915Book + Online Teaching Centre (WNCP) 9780176833510
Book + Online Teaching Centre (BC) 9780176833572Math Pre-Assessment Grade 4Book + Online Teaching Centre (Ontario) 9780176830922Book + Online Teaching Centre (WNCP) 9780176833527Book + Online Teaching Centre (BC) 9780176833589Math Pre-Assessment Grade 5Book + Online Teaching Centre (Ontario) 9780176830939Book + Online Teaching Centre (WNCP) 9780176833534Book + Online Teaching Centre (BC) 9780176833596Math Pre-Assessment Grade 6Book + Online Teaching Centre (Ontario) 9780176830946Book + Online Teaching Centre (WNCP) 9780176833541Book + Online Teaching Centre (BC) 9780176833602Math Pre-Assessment Grade 7Book + Online Teaching Centre (Ontario) 9780176903992Math Pre-Assessment Grade 8Book + Online Teaching Centre (Ontario) 9780176904005
Math Pre-Assessment Order Information
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ISBN-10: 0-17-691448-XISBN-13: 978-0-17-691448-6
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