Pre-K to Grade 5 Mathematics Curriculum. Creative Commons License Materials will be made available...
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Transcript of Pre-K to Grade 5 Mathematics Curriculum. Creative Commons License Materials will be made available...
Pre-K to Grade 5Pre-K to Grade 5Mathematics CurriculumMathematics Curriculum
Creative Commons License Creative Commons License
Materials will be made available on the Materials will be made available on the EngageNy websiteEngageNy website
Producing the Modules for NYProducing the Modules for NY
Overview ChartOverview Chart
Putting the Shifts into ActionPutting the Shifts into ActionFocus: focus strongly where the standards focus
Coherence: think across grades, and link to major topics in each grade
Rigor: in major topics, pursue with equal intensity
• conceptual understanding• procedural skill and fluency• applications
Connection to the ModulesConnection to the Modules
Fluency
ApplicationDeep Understanding
of Concepts
Fluency is More Than Rote Fluency is More Than Rote FactsFacts
• Sustained fluency leads to concept mastery which support the learning of new concepts
Math Sprints!Math Sprints!
SprintsSprints
Bill Davidson http://www.youtube.com/watch?v=G_y9gGnd68M
A Grade-by-Grade Progression A Grade-by-Grade Progression of “A Story of Units”of “A Story of Units”
Common CoreCommon Core
Pre-KindergartenPre-Kindergarten
Well-planned math programWell-planned math program
Count to 5 with Count to 5 with meaningmeaning
Explore the definitions of Explore the definitions of circle, rectangles, etc.circle, rectangles, etc.
““How many” up to 10 using How many” up to 10 using familiarity with 5familiarity with 5
Pre-KindergartenPre-Kindergarten
Comparisons: small, big, large, tall, etc.Comparisons: small, big, large, tall, etc.
Fluency with meaning of numbers 1-10, Fluency with meaning of numbers 1-10, counting numbers 1-20.counting numbers 1-20.
KindergartenKindergarten
Same themes as Pre-KSame themes as Pre-K
Numbers 1-10 with “1 more, Numbers 1-10 with “1 more, 1 less”1 less”
Comparisons: taller than, Comparisons: taller than, shorter than, longer than, shorter than, longer than, heavier than—leading to…heavier than—leading to…
KindergartenKindergarten
More than, less than:More than, less than: 7 is 2 more than 57 is 2 more than 5 7 is 2 less than 97 is 2 less than 9 1 more, 2 more, 3 more than1 more, 2 more, 3 more than
Comparing numbers leads to number Comparing numbers leads to number bonds:bonds: 3 is less than 7. 3 is less than 7. 3 and 4 make 7.3 and 4 make 7.
Number bonds lead to Number bonds lead to addition/subtractionaddition/subtraction
7
3 4
First GradeFirst GradeFluency with add/subtract facts begins Fluency with add/subtract facts begins right away and continues the entire yearright away and continues the entire year
Main strategy for adding/subtracting Main strategy for adding/subtracting across a 10: “make 10”across a 10: “make 10”
This strategy begins the realization of…This strategy begins the realization of…
First GradeFirst Grade
A major concept goal for first grade: A major concept goal for first grade:
Group “10 ones” as a single unit: 1 ten Group “10 ones” as a single unit: 1 ten
Module 3 on length provides a few weeks Module 3 on length provides a few weeks to practice “making a ten” and also allows to practice “making a ten” and also allows for a wider variety of word problemsfor a wider variety of word problems
““Add within 40” module establishes 1 tenAdd within 40” module establishes 1 ten
First GradeFirst Grade
““Add within 100” module begins model Add within 100” module begins model work with addition and subtraction of two work with addition and subtraction of two 2-digit numbers2-digit numbers
In between these two heavy-duty number In between these two heavy-duty number modules is a module on shapes modules is a module on shapes
Second GradeSecond Grade
The first module on “numbers to 20” is the The first module on “numbers to 20” is the beginning of a yearlong fluency program beginning of a yearlong fluency program on numbers and timeon numbers and time
The second module on measurement The second module on measurement plays a key role in grade 2: it establishes plays a key role in grade 2: it establishes the meaning of the term “unit.”the meaning of the term “unit.”
Place value Place value unitsunits are the study of the third are the study of the third module. In particular, …module. In particular, …
Second GradeSecond Grade
Place value units are the basis of Place value units are the basis of the algorithmsthe algorithms 7 ones + 6 ones = 13 ones7 ones + 6 ones = 13 ones
= 1 ten 3 ones = 1 ten 3 ones
1 ten + 6 tens + 2 tens = 9 tens1 ten + 6 tens + 2 tens = 9 tens
1
2 6 7
+ 2 6
2 9 3
Second GradeSecond Grade
1 apple, 2 apples, 3 apples, ...1 apple, 2 apples, 3 apples, ...1 ten, 2 tens, 3 tens, …1 ten, 2 tens, 3 tens, …
leads to leads to
1 three, 2 threes, 3 threes, …1 three, 2 threes, 3 threes, …
4 threes = 12 ones4 threes = 12 ones
Second GradeSecond Grade
Last modules end with:Last modules end with:
Money: dollars, dimes, pennies (and Money: dollars, dimes, pennies (and nickels and quarters)nickels and quarters)
Analog clocks (curved number line)Analog clocks (curved number line)
Simple fractions and clocksSimple fractions and clocks
Third GradeThird GradeModule 1: Rounding and word problemsModule 1: Rounding and word problems
PVPVComparisonComparisonRoundingRoundingBar ModelsBar Models
Place value units:Place value units: 534 = 5 hundreds 3 tens 4 ones534 = 5 hundreds 3 tens 4 ones
= 53 tens 4 ones= 53 tens 4 ones
= 5 hundreds 34 ones= 5 hundreds 34 ones
6 tens = 6 x 10 = 606 tens = 6 x 10 = 60
Third GradeThird Grade
Module 2: ×/÷ by 2, 3, 4, 5, 10Module 2: ×/÷ by 2, 3, 4, 5, 10
Module 3: MeasurementsModule 3: Measurements
Module 4: ×/÷ by 6, 7, 8, 9Module 4: ×/÷ by 6, 7, 8, 9
Module 5: AreaModule 5: Area
Module 2 and Module 4
Module 5: Multiplication and Area
Third GradeThird Grade
A “three” unitA “three” unit
A “third” unitA “third” unit 0 1 2 3
1 third
0 1 2 3
1 three
Third GradeThird Grade
Count by: 1 third, 2 thirds, 3 thirds, …Count by: 1 third, 2 thirds, 3 thirds, …
Equivalent fractions as unit conversion:Equivalent fractions as unit conversion:
3 tens = 30 ones3 tens = 30 ones 2 thirds = 4 sixths2 thirds = 4 sixths
Module 7: Quadrilaterals and PerimeterModule 7: Quadrilaterals and Perimeter
Fourth GradeFourth Grade
Module 1: “Big” units and the addition/subtraction Module 1: “Big” units and the addition/subtraction algorithmsalgorithms
Module 2: Converting metric units—An opportunity Module 2: Converting metric units—An opportunity to practice mental math and the algorithms!to practice mental math and the algorithms!
4 × (1 m 2 cm) = 4 m 8 cm 4 × (1 m 2 cm) = 4 m 8 cm 4 × (1 ten 2 ones) = 4 tens 8 ones, 4 × (1 ten 2 ones) = 4 tens 8 ones,
leading to the 1-digit multiplication algorithm of leading to the 1-digit multiplication algorithm of Module 3 Module 3
Fourth GradeFourth Grade
Module 4: Geometry is one of the keys Module 4: Geometry is one of the keys that unlocks Algebrathat unlocks Algebra
Fourth GradeFourth Grade
Module 5: Fraction operationsModule 5: Fraction operations 3 fourths x 10 = 30 fourths3 fourths x 10 = 30 fourths
(3 apples x 10 = 30 apples,(3 apples x 10 = 30 apples, 3 tens x 10 = 30 tens) 3 tens x 10 = 30 tens)
Decimals are a type of fraction, 0.1 = 1/10, but is Decimals are a type of fraction, 0.1 = 1/10, but is treated like every other type of unit:treated like every other type of unit:
30 hundredths = 3 tenths30 hundredths = 3 tenths
Fourth GradeFourth Grade
The last module explores multi-digit The last module explores multi-digit multiplications, anticipating the full multiplications, anticipating the full algorithm in grade 5algorithm in grade 5
Fifth GradeFifth Grade
Module 1: Decimal Module 1: Decimal number operations: number operations:
Students practice and Students practice and hone their 1-digit hone their 1-digit algorithms in the algorithms in the context of decimal context of decimal numbers.numbers.
Fifth GradeFifth Grade
Module 2: All other algorithms are Module 2: All other algorithms are employed in dividing by 2-digit numbers, employed in dividing by 2-digit numbers, either in the process or the checking of the either in the process or the checking of the answer.answer.
Division by a 2-digit number includes Division by a 2-digit number includes estimation strategies, error correction, and estimation strategies, error correction, and successive approximationsuccessive approximation
Fifth GradeFifth Grade
Fraction arithmetic is modeled through the Fraction arithmetic is modeled through the use of number lines and area modelsuse of number lines and area models
Place value also helps:Place value also helps:8 ninths ÷ 2 = 4 ninths8 ninths ÷ 2 = 4 ninths8 tenths ÷ 2 = 4 tenths 8 tenths ÷ 2 = 4 tenths
Fifth GradeFifth Grade
Bar models start to bloom:Bar models start to bloom:
Fifth GradeFifth Grade
Module 5: Area and VolumeModule 5: Area and Volume
Continue to practice ×/÷ of fractions using Continue to practice ×/÷ of fractions using area problems as the contextarea problems as the context
Can begin to ask the question: How does Can begin to ask the question: How does area (or volume) change when a rectangle is area (or volume) change when a rectangle is scaled by a whole number or fractional scale scaled by a whole number or fractional scale factor? factor?
Fifth GradeFifth Grade
Coordinate plane follows a PK-6 Coordinate plane follows a PK-6 curriculum sequence:curriculum sequence:
“Number Stairs”“Number Stairs”Bar GraphsBar GraphsLine Line PlotsPlotsLine GraphsLine Graphs
Last module knocks on the door of “slope”, Last module knocks on the door of “slope”, leading to… leading to…
A Story of RatiosA Story of Ratios
Must Have’sMust Have’s
Grade Level FluenciesGrade Level Fluencies
SprintsSprints
Modeling of word problemsModeling of word problems
PrioritiesPriorities
Word ProblemsWord Problems
Table 1 and 2Table 1 and 2
GlossaryGlossary
Stay Updated Stay Updated
New developmentsNew developments
ResourcesResources
ModulesModules
NewsNews
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