Number Sense
22.5%of exam
Relationships & Proportional Reasoning
38%of exam
Measurement
9.9%of exam
Pedagogy: Growing Success
12.7%of exam
Pedagogy: Learning for All
9.9%of exam
Pedagogy: Curriculum Context
7%of exam
Quick Facts
- Exam
- MPT
- Credential
- Ontario Teacher Certification
- Time
- 180 min (est. 120)
- Pass
- 70% each component
- Cost
- Free
- Scored Qs
- 71 of 75
- Math / Pedagogy
- 50 / 21 Qs
- Retakes
- Unlimited, free
Order of Operations
BEDMAS: Brackets, Exponents, Mult/Div, Add/Sub
B: Brackets firstE: Exponents nextM/D: left to rightA/S: left to right, last
Order & Operations
- BEDMAS order
- Brackets, exponents, mult/div, add/sub
- Same-rank operations
- Work left to right
- Same-sign integers
- Product/quotient is positive
- Different-sign integers
- Product/quotient is negative
- Negative exponent
- Means 1/a^n, not negative
- Product of powers
- Add exponents, same base
- Quotient of powers
- Subtract exponents, same base
- Square root
- Non-negative root of n
Math Question Split
Number Sense 16, Relationships 27, Measurement 7
Number Sense: 16 of 50Proportional Reasoning: 27 of 50Measurement: 7 of 50
Place Value & Fractions
- Expanded form
- Digit x place value, summed
- GCF
- Largest shared factor
- LCM
- Smallest shared multiple
- Dividing fractions
- Multiply by the reciprocal
- Front-end rounding
- Round to leading digit
- No-calculator items
- First 5 math questions only
Financial Literacy Contexts
Earn, purchase, save, invest, borrow, travel
Gross pay minus deductions = netSimple interest: I = Prt onlyCompound: interest earns interest12+ of 50 math Qs
Ratio vs Rate
Ratio
- Same-unit comparison
- e.g. 3 boys to 4 girls
Rate
- Different-unit comparison
- Needs a unit label
Same units vs different units
Financial Literacy Picker
- Compare loan offers→Cost of borrowing(Total repaid minus principal)
- Interest never compounds→Simple interest: I=Prt
- Interest earns interest→Compound interest(Grows faster over time)
- Need take-home pay→Net income(After deductions)
- Need pre-deduction pay→Gross income(Before deductions)
- Splitting income by category→Budget by percentage(Scales automatically with income)
Ratios, Rates & Percent
- Ratio
- Same-unit comparison, e.g. 3:4
- Rate
- Different-unit comparison, needs a label
- Unit rate
- Rate per single unit
- Percent change formula
- Change / original x 100
- Fraction to percent
- Divide, then multiply by 100
- Ontario HST rate
- 13% (5% GST + 8% PST)
- Sale price
- Price x (1-discount rate)
- Cross products
- Cross-multiply: ad=bc
Simple vs Compound Interest
Simple interest
- I = P x r x t
- Same amount every year
Compound interest
- Interest earns interest too
- Grows faster over time
Principal only vs principal + interest
Linear Relations
- Slope
- Rise / run between points
- y = mx + b
- m slope, b y-intercept
- Linear relation
- Constant first differences, straight line
- Non-linear relation
- First differences change, curved graph
- Linear system solution
- Graphs' intersection point (x,y)
- Parallel lines
- Same slope: no solution
- Distributive property
- a(b+c) = ab + ac
- Both-sides equations
- Isolate variable to one side
Theoretical vs Experimental Probability
Theoretical
- Favourable / total outcomes
- Calculated, not tested
Experimental
- From actual trial results
- Approaches theoretical over time
Predicted vs observed
Data & Probability
- Mean
- Sum of values / count
- Median
- Middle value, data ordered
- Mode
- Most frequent value
- Outlier effect
- Skews mean more than median
- Theoretical probability
- Favourable / total outcomes
- Experimental probability
- From actual trial results
- Independent events
- Multiply the two probabilities
Linear vs Non-Linear Relations
Linear
- Constant first differences
- Straight-line graph
Non-linear
- Changing first differences
- Curved graph
Constant vs changing rate
Financial Literacy
- Gross income
- Earnings before any deductions
- Net income
- Pay after tax, deductions
- Simple interest
- I = P x r x t
- Compound interest
- Interest earns interest too
- Cost of borrowing
- Total repaid minus principal
- Budgeting by percent
- Allocate income by share
- Financial literacy share
- 12+ of 50 math Qs
Question Categories
- Knowledge & Understanding
- 20 of 50 Qs (40%)
- Application
- 25 of 50 Qs (50%)
- Thinking
- 5 of 50 Qs (10%)
- Communication
- Not used to categorize Qs
Metric Conversion Factors
Area units squared, volume units cubed
cm to m: divide by 100cm^2 to m^2: divide by 10,000cm^3 to m^3: divide by 1,000,000
Formula Picker
- Right triangle side missing→Pythagorean theorem(a^2+b^2=c^2)
- Trapezoid area needed→(a+b) x h / 2(Formula sheet)
- Circle area needed→pi x r^2(Formula sheet)
- Prism or cylinder volume→Base area x height
- Cylinder surface area→2pi r^2 + 2pi rh
- cm to m conversion→Divide by 100(Length)
- cm^2 to m^2 conversion→Divide by 10,000(Area)
- cm^3 to m^3 conversion→Divide by 1,000,000(Volume)
Measurement Formulas
- Pythagorean theorem
- a^2 + b^2 = c^2
- Trapezoid area
- (a+b) x h / 2
- Circle area
- pi x r^2
- Circle circumference
- 2pi x r
- Rectangle area
- length x width
- Triangle area
- base x height / 2
- Cylinder volume
- pi x r^2 x height
- Cylinder surface area
- 2pi r^2 + 2pi rh
Metric Conversions & Volume
- Length conversion
- 1 m = 100 cm
- Area conversion
- 1 m^2 = 10,000 cm^2
- Volume conversion
- 1 m^3 = 1,000,000 cm^3
- Prism volume
- Base area x height
- Smaller unit convert
- Multiply by conversion factor
- Larger unit convert
- Divide by conversion factor
- Formula sheet
- Given for Measurement questions only
- Perimeter formula
- Sum of all side lengths
Pedagogy Question Split
Growing Success 9, Learning for All 7, Context 5
Growing Success: 9 QsLearning for All: 7 QsCurriculum Context: 5 Qs
Accommodation vs Modification
Accommodation
- Changes access, not content
- Same expectation for all
Modification
- Changes the expectation itself
- Different grade-level target
Access vs expectation
Assessment Type Picker
- Checking progress mid-unit→Assessment for learning(Teacher adjusts next steps)
- Student self-monitors work→Assessment as learning(Self and peer assessment)
- Assigning a final grade→Assessment of learning(Summative, evaluates achievement)
- Same content, easier access→Accommodation(Expectation stays the same)
- Student needs eased expectation→Modification(Changes what is assessed)
Growing Success Terms
- Assessment for learning
- Teacher checks, plans next steps
- Assessment as learning
- Student self-monitors own progress
- Assessment of learning
- Summative, becomes the grade
- Learning goal
- States what students are learning
- Success criteria
- How the goal is met
- Descriptive feedback
- Specific, tied to criteria
- Achievement chart
- K&U, Thinking, Comm, Application
- Accommodation
- Same expectation, different access
- Modification
- Changes the expectation itself
Assessment For vs Of Learning
For learning
- During instruction
- Improves next steps
Of learning
- End of a unit
- Becomes the reported grade
Formative vs summative
Scoring & Format
- tLOFT delivery
- Testlets assembled in real time
- Machine scored
- Results ready within 10 days
- Successful result
- 70%+ on both components
- Not Yet Successful
- Must reattempt the entire test
- Green result light
- At or above 70% threshold
- Amber result light
- Below the 70% threshold
Differentiated Instruction vs UDL
Differentiated instruction
- Responds to this class
- Adjusted after planning
UDL
- Built in from the start
- Necessary for some, good for all
Reactive vs proactive design
Pedagogy Response Picker
- Whole class needs support→Tier 1(Universal instruction)
- Small group falling behind→Tier 2(Targeted support)
- One student needs intensive help→Tier 3(Individualized support)
- Planning before problems arise→UDL(Built in from the start)
- Adjusting an existing lesson→Differentiated instruction(Content, process, or product)
Learning for All Terms
- Differentiated instruction
- Adjust content, process, or product
- UDL
- Necessary for some, good for all
- Tier 1
- Universal, whole-class supports
- Tier 2
- Targeted, small-group supports
- Tier 3
- Individualized, intensive supports
- Class profile
- Whole-class strengths and needs
- Scaffolding
- Temporary support, later withdrawn
- ZPD
- Gap between alone and helped
Curriculum Context Terms
- Six strands (2020)
- SEL, Number, Algebra, Data, Spatial, Financial
- Seven math processes
- Problem solving through communicating
- MTH1W
- De-streamed Grade 9 math course
- 2020 curriculum update
- Added Financial Literacy and SEL
- Grade 9 math, 2021
- Single de-streamed pathway for all
- High-impact practices
- Direct instruction, math talk, more
- Curriculum context source
- Grades 1-8 and Grade 9 docs
Common Traps
Scored vs Field-Test Questions
71 scored questions count ≠ 4 field-test Qs do not
Formula Sheet Scope
Given only for Measurement Qs ≠ Not for other math dimensions
Successful vs Not Yet Successful
Both components pass together ≠ One low score fails everything
No-Calculator Scope
Only first 5 math Qs ≠ Other 45 allow a calculator
Component Weight vs Dimension Weight
Math is 70% of test ≠ Number Sense is 32% of math
Ontario HST Split
13% total sales tax rate ≠ 5% federal, 8% provincial
Application vs Thinking Category
Application: 25 of 50 Qs ≠ Thinking: only 5 of 50
Last Minute
- 1.70% needed on each component
- 2.Math and pedagogy: same attempt
- 3.50 math Qs: 5 no-calculator
- 4.21 pedagogy Qs, 3 dimensions
- 5.4 field-test Qs are unscored
- 6.180-min session, ~120 min needed
- 7.Free test, unlimited retake attempts
- 8.Fail = reattempt the entire test
- 9.Measurement Qs give a formula sheet
- 10.At least 12 Qs: financial literacy
- 11.Results reported within 10 days
- 12.Green = pass; amber = below 70%