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

www.e2math.weebly.comwww.e2math.weebly.com