Pre-K to Grade 5 Mathematics Curriculum

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Producing the Modules for NY Creation of exemplar lessons by teachers Review at the vendor level Review at the common core writers level- Jason Zimba, Bill McCallum, H. Wu Review at NYSED level

Overview Chart

Putting the Shifts into Action Focus: 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 Modules Fluency Application Deep Understanding of Concepts

Fluency is More Than Rote Facts Sustained fluency leads to concept mastery which support the learning of new concepts

Math Sprints!

Sprints Bill Davidson _y9gGnd68M

A Grade-by-Grade Progression of “A Story of Units” Common Core

Pre-Kindergarten Well-planned math program Count to 5 with meaning Explore the definitions of circle, rectangles, etc. “How many” up to 10 using familiarity with 5

Pre-Kindergarten Comparisons: small, big, large, tall, etc. Fluency with meaning of numbers 1-10, counting numbers 1-20.

Kindergarten Same themes as Pre-K Numbers 1-10 with “1 more, 1 less” Comparisons: taller than, shorter than, longer than, heavier than—leading to…

Kindergarten More than, less than: 7 is 2 more than 5 7 is 2 more than 5 7 is 2 less than 9 7 is 2 less than 9 1 more, 2 more, 3 more than 1 more, 2 more, 3 more than Comparing numbers leads to number 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 addition/subtraction 7 34

First Grade Fluency with add/subtract facts begins right away and continues the entire year Main strategy for adding/subtracting across a 10: “make 10” This strategy begins the realization of…

First Grade A major concept goal for first grade: Group “10 ones” as a single unit: 1 ten Module 3 on length provides a few weeks to practice “making a ten” and also allows for a wider variety of word problems “Add within 40” module establishes 1 ten

First Grade “Add within 100” module begins model work with addition and subtraction of two 2-digit numbers In between these two heavy-duty number modules is a module on shapes

Second Grade The first module on “numbers to 20” is the beginning of a yearlong fluency program on numbers and time The second module on measurement plays a key role in grade 2: it establishes the meaning of the term “unit.” Place value units are the study of the third module. In particular, …

Second Grade Place value units are the basis of the algorithms 7 ones + 6 ones = 13 ones = 1 ten 3 ones 7 ones + 6 ones = 13 ones = 1 ten 3 ones 1 ten + 6 tens + 2 tens = 9 tens 1 ten + 6 tens + 2 tens = 9 tens

Second Grade 1 apple, 2 apples, 3 apples,... 1 ten, 2 tens, 3 tens, … leads to 1 three, 2 threes, 3 threes, … 4 threes = 12 ones

Second Grade Last modules end with: Money: dollars, dimes, pennies (and nickels and quarters) Analog clocks (curved number line) Simple fractions and clocks

Third Grade Module 1: Rounding and word problems PV  Comparison  Rounding  Bar Models Place value units: 534 = 5 hundreds 3 tens 4 ones 534 = 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 = 60

Third Grade Module 2: ×/÷ by 2, 3, 4, 5, 10 Module 3: Measurements Module 4: ×/÷ by 6, 7, 8, 9 Module 5: Area Module 2 and Module 4 Module 5: Multiplication and Area

Third Grade A “three” unit A “third” unit third three

Third Grade Count by: 1 third, 2 thirds, 3 thirds, … Equivalent fractions as unit conversion: 3 tens = 30 ones 3 tens = 30 ones 2 thirds = 4 sixths 2 thirds = 4 sixths Module 7: Quadrilaterals and Perimeter

Fourth Grade Module 1: “Big” units and the addition/subtraction algorithms Module 2: Converting metric units—An opportunity to practice mental math and the algorithms! 4 × (1 m 2 cm) = 4 m 8 cm 4 × (1 ten 2 ones) = 4 tens 8 ones, leading to the 1-digit multiplication algorithm of Module 3

Fourth Grade Module 4: Geometry is one of the keys that unlocks Algebra

Fourth Grade Module 5: Fraction operations 3 fourths x 10 = 30 fourths (3 apples x 10 = 30 apples, 3 tens x 10 = 30 tens) 3 fourths x 10 = 30 fourths (3 apples x 10 = 30 apples, 3 tens x 10 = 30 tens) Decimals are a type of fraction, 0.1 = 1/10, but is treated like every other type of unit: 30 hundredths = 3 tenths

Fourth Grade The last module explores multi-digit multiplications, anticipating the full algorithm in grade 5

Fifth Grade Module 1: Decimal number operations: Students practice and hone their 1-digit algorithms in the context of decimal numbers.

Fifth Grade Module 2: All other algorithms are employed in dividing by 2-digit numbers, either in the process or the checking of the answer. Division by a 2-digit number includes estimation strategies, error correction, and successive approximation

Fifth Grade Fraction arithmetic is modeled through the use of number lines and area models Place value also helps: 8 ninths ÷ 2 = 4 ninths 8 tenths ÷ 2 = 4 tenths

Fifth Grade Bar models start to bloom:

Fifth Grade Module 5: Area and Volume Continue to practice ×/÷ of fractions using area problems as the context Continue to practice ×/÷ of fractions using area problems as the context Can begin to ask the question: How does area (or volume) change when a rectangle is scaled by a whole number or fractional scale factor? Can begin to ask the question: How does area (or volume) change when a rectangle is scaled by a whole number or fractional scale factor?

Fifth Grade Coordinate plane follows a PK-6 curriculum sequence: “Number Stairs”  Bar Graphs  Line Plots  Line Graphs Last module knocks on the door of “slope”, leading to…

A Story of Ratios

Must Have’s Grade Level Fluencies Sprints Modeling of word problems Priorities Word Problems Table 1 and 2 Glossary

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