Pre-K to Grade 5
Mathematics Curriculum
Creative Commons License
Materials will be made available on the
EngageNy website
Producing the Modules for NY
Creation of exemplar
lessons by teachers
Review at NYSED
level
Review at the vendor
level
Review at the common
core writers levelJason Zimba, Bill
McCallum, H. Wu
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
Deep Understanding
of Concepts
Application
Fluency is More Than Rote
Facts
• Sustained fluency leads to
concept mastery which support
the learning of new concepts
Math Sprints!
Sprints
Bill Davidson
http://www.youtube.com/watch?v=G
_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 less than 9
1 more, 2 more, 3 more than
7
Comparing numbers leads to
number bonds:


3 is less than 7.
3 and 4 make 7.
Number bonds lead to
addition/subtraction
3
4
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”
Make 10
Make
First. 10
First.
How many glasses of juice are there all together?
How many glasses of juice are there all together?
9+4=
9+4=
8 + 5 = 8 + (2 + 3) = (8 + 2) + 3 = 10 + 3 = 13
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

1 ten + 6 tens + 2 tens = 9 tens
1
267
+ 26
293
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
= 53 tens 4 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
0
1
2
3
2
3
1 three
A “third” unit
0
1 third
1
Third Grade
Count by: 1 third, 2 thirds, 3 thirds, …
Equivalent fractions as unit conversion:


3 tens = 30 ones
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)
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
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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
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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