The Eureka Math Trilogy:
A Story of Units: Grades K-5
A Story of Ratios: Grades 6 - 8
A Story of Functions: Grades 9 - 12
A Story of Units
Grades PK-5
A Story of Ratios
Grades 6 - 8
A Story of Functions:
Grades 9 - 12
NYS COMMON CORE MATHEMATICS CURRICULUM
Test Date
Pre-Kindergarten
A Story of Units
A Story of Units Curriculum Overview
Kindergarten
Grade 1
9/6/12
Grade 2
Grade 3
*M1: Sums and Differences
(10 days)
20 days
M1: Analyze, Sort, Classify,
and Count up to 5
(45 days)
10/10/12
M1: Classify and Count
Numbers to 10
(43 days)
M1: Multiplication and
Division with Factors of 2, 3,
M2: Additi on and Subtraction
4, 5, and 10
with Length, Weight,
(25 days)
M1: Addition and Subtraction
Capacity, and Time
of Numbers to 10 and Fluency
Measurements
(45 days)
(20 days)
20 days
11/8/12
M3: Place Value, Counting,
and Comparison of Numbers
to 1000
(25 days)
M2: Identify and Descri be
Shapes (7 days)
20 days
M2: Analyze, Compare,
Create, and Compose Shapes
(15 days)
12/11/12
M3: Comparison with Length,
Weight, and Numbers to 10
(43 days)
20 days
1/17/13
20 days
M3: Count and Answer "How
Many" Questions up to 10
(50 days)
M2: Place Value,
Comparison, Addition and
Subtraction of Numbers to 20
(35 days)
M4: Additi on and Subtraction
of Numbers to 1000
(35 days)
M3: Ordering and Expressing
Length Measurements as
Numbers
(15 days)
Grade 4
Grade 5
M1: Place Value, Rounding,
Fluency with Addition and
Subtraction Algorithms of
Whole Numbers
(25 days)
M1: Whole Number and
Decimal Fraction Place Value
to the One-Thousandths
(20 days)
*M2: Unit Conversions
(7 days)
M2: Problem Solvi ng with
Mass, Time, and Capacity
(25 days)
M3: Multiplication and
Division with Factors of 6, 7,
8, and 9
(25 days)
M4: Mul tiplication and Area
(20 days)
M3: Multiplication and
Division of up to a 4-Digit
Number by up to a 1-Digit
Number Using Place Value
(43 days)
M4: Addition and
Subtracti on of Angle
Measurements of Planar
Fi gures
(20 days)
2/15/13
20 days
3/22/13
20 days
M4: Describe and Compare
Length, Weight, and Capacity
(35 days)
M4: Place Value,
Comparison, Addition and
M4: Number Pairs, Addition
Subtraction of Numbers to 40
and Subtraction of Numbers
(35 days)
to 10
(47 days)
M5: Identify, Compose, and
Partition Shapes
(15 days)
4/29/13
20 days
M5: Write Numeral s to 5,
Addition and Subtraction
Stories, Count to 20
(35 days)
5/28/13
20 days
6/26/13
M5: Numbers 10-20, Counting
to 100 by 1 and 10
(30 days)
M6: Place Value,
Comparison, Addition and
Subtraction of Numbers to
100
(35 days)
M6: Analyze, Compare,
Create, and Compose Shapes
(10 days)
M5: Preparation for
Multiplication and Division M5: Fractions as Numbers on
Facts
the Number Line
(40 days)
(35 days)
M7: Recognizing Angles,
Faces, and Vertices of
Shapes, Fractions of Shapes
(20 days)
Geometry
Number
20 days
M3: Addition and Subtraction
of Fractions
(22 days)
M4: Multiplication and
Division of Fractions and
Decimal Fractions
(38 days)
M5: Addition and
Multiplication with Volume
and Area
(25 days)
M6: Decimal Fractions
(20 days)
Number and Geometry,
Measurement
20 days
20 days
20 days
20 days
M6: Graph Points on the
Coordinate Plane to Solve
Problems
(40 days)
M7: Word Problems wi th
Geometry and Measurement
(40 days)
M7: Exploring Multiplication
(20 days)
Note that date approximations are based on a first student day of 9/6/12 and last day of 6/26/13 with a testing date of approximately mid-late April.
Key:
20 days
M2: Multi-Digit Whole
Number and Decimal
Fraction Operations
(35 days)
20 days
M5: Order and Operations
with Fractions
(45 days)
M6: Collecting and
Displaying Data (10 days)
M6: Comparison, Addition
and Subtraction with Length
and Money
(30 days)
20 days
Fractions
20 days
Approx. test
date for
grades 3-5
A Story of Ratios
A Story of Functions Curriculum Overview
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Functions
Curriculum Map
Grade 9 -- Algebra I
20 days
20 days
20 days
20 days
20 days
M1:
Relationships Between
Quantities and Reasoning
with Equations and Their
Graphs
(40 days)
M2: Descriptive Statistics
(25 days)
M3:
Linear and Exponential
Functions
State Examinations
(35 days)
Grade 10 -- Geometry
Grade 11 -- Algebra II
M1:
Congruence, Proof, and
Constructions
(45 days)
M1:
Polynomial, Rational, and
Radical Relationships
(45 days)
M2:
Similarity, Proof, and
Trigonometry
(45 days)
State Examinations
M2:
Trigonometric Functions
(20 days)
20 days
20 days
20 days
M4:
Polynomial and Quadratic
Expressions, Equations and
Functions
(30 days)
State Examinations
M5:
A Synthesis of Modeling
with Equations and
Functions (20 days)
Review and Examinations
Review and Examinations
20 days
20 days
20 days
M2:
Vectors and Matrices
(40 days)
20 days
State Examinations
M3:
Rational and Exponential
Functions
(25 days)
20 days
20 days
M4: Connecting Algebra
and Geometry through
Coordinates (25 days)
M5:
Circles with and Without
Coordinates
(25 days)
M1:
Complex Numbers and
Transformations
(40 days)
M3: Functions
(45 days)
M3: Extending to Three
Dimensions (10 days)
20 days
Grade 12 -- Precalculus
M4: Trigonometry
(20 days)
M4:
Inferences and Conclusions
from Data
(40 days)
Review and Examinations
20 days
M5:
Probability and Statistics
(25 days)
Review and Examinations
20 days
20 days
Module
Overview
Topic
Overview
A Lesson
T:
S:
Compare models. What are the similarities and differences between arrays and tape diagrams?
The tape diagram is like a labeled and boxed array.
They both show the 7 piles, 3 papers in each
pile, and 21 papers total.
The labels make the tape diagram a little easier to use.
Problem Set (10 minutes)
Students should do their personal best to complete the
Problem Set within the allotted 10 minutes. Depending on
your class, it may be appropriate to modify the assignment
by specifying which problems they work on first. Some
problems do not specify a method for solving. Students
solve these problems using the RDW approach used for
Application Problems.
Student Debrief (10 minutes)
Lesson Objective: Model division as the unknown factor in
multiplication using arrays and tape diagrams.
The Student Debrief is intended to invite reflection and
active processing of the total lesson experience.
Invite students to review their solutions for the Problem
Set. They should check work by comparing answers with a
partner
before going
answers asCURRICULUM
a class. Look for
NYS COMMON
COREover
MATHEMATICS
misconceptions or misunderstandings that can be
addressed in the Debrief. Guide students in a
conversation to debrief the Problem Set and process the
lesson. You may choose to use any combination of the
ideas below to lead the discussion.
Lesson 11 3•1
Compare Problem 1 and 2. What does the
unknown represent in each problem?
Compare how units are represented in tape
diagrams and in
arrays.
Lesson
11:
Model division as the unknown factor in multiplication using arrays
and tape diagrams.
How can each Date:
model represent
both types of
6/26/13
This work is licensed under a
unknowns?
© 2013 Common Core, Inc. Some rights reserved. commoncore.org
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Compare the way you solved the application
problem with the tape diagram model we learned
today.
Exit Ticket (3 minutes)
After the Student Debrief, instruct students to complete
the Exit Ticket. A review of their work will help you assess
the students’n uderos tanding of the cn cepts that were presented in the lesson today and plan more effectively
for future lessons. You may read the questions aloud to
the students.
1.D.6
Kindergarten:
One object, 1 unit
1 apple, 2 apples, 3 apples, 4 apples
4 apples = 3 apples + 1 apple
4=3+1
4-3=1
Grade 1:
10 ones, a unit of 1 ten
1 ten, 2 tens, 3 tens, 4 tens
4 tens = 40 ones
4 tens = 3 tens + 1 ten
40 = 30 + 10
40 - 30 = 10
Grade 1:
Two different units in a single number
4 tens 3 ones
43 ones
39 + 4 = 43
1
3
Grade 2:
10 tens, a unit of 1 hundred
1 hundred, 2 hundreds, 3 hundreds,
4 hundreds
4 hundreds = 40 tens = 400 ones
4 hundreds = 3 hundreds + 1 hundred
400 = 300 + 100
400 - 300 = 100
Grade 2:
Three different units in a single number.
6 hundreds 4 tens 3 ones
6 hundreds 43 ones
6 meters 43 centimeters
643 ones
643 centimeters
Grade 3:
2 ones, a unit of 1 two,
3 ones, a unit of 1 three....
1 three, 2 threes, 3 threes, 4 threes
1×3
2×3
3×3
How many threes are in 12?
12 ÷ 3 = 4
4×3
Grade 3:
Units and the distributive property
5 threes + 2 threes = 7 threes
5×3 + 2×3
= 15 + 6 = 21
Grades 3 and 4:
Decomposition of one into smaller units.
1 fourth
1×¼
2 fourths 3 fourths
2×¼
1 = 4/4
1=¾+¼
3×¼
4×¼
4 fourths
Grade 4:
Compose, decompose and distribute fractional units.
Grade 4:
Bridge to ratios with multiplicative comparison.
Ben ordered 120 blue markers. He ordered 4 times as
many red markers as blue markers. How many more
red than blue markers did he order?
Grade 5:
Units and fraction of a set
Grade 5:
The conversion of measurement units from smaller
to larger.
Grade 5:
Application of work with fractional units in
measurement conversion.
Grades 4 - 6:
Equivalent fractions and equivalent ratios.
Grade 6:
Ratio word problems.
The students are using 60 yards of red and white streamers to decorate the
gym. The ratio of the length of the red ribbon to the length of the white ribbon
is 1:4. How much more white ribbon is there than red ribbon?
Grade 6:
Points generated
from equivalent
ratios lie on a
straight line on
the coordinate
plane.
Grade 7:
Given any point
on a line through
the origin, the
ratio of y to x is
constant.
Grade 7:
Ratio word problems
The table below shows 6 different sized pans of the same recipe for macaroni
and cheese. If the recipe relating the ratio of ingredients stays the same, how
might it be altered to account for the different sized pans?
Grade 8:
Similar triangles
are used to
show that slope,
which is
determined by
the ratio of the
rise to the run,
makes sense.
Grades 11-12:
On to the functions
of trigonometry
Alignment
Common Core State Standards
• Mathematical Practices
• Instructional Shifts
• Progressions Documents
• Major Content Emphases
• Publishers’ Criteria
EngageNY Mathematics
a.k.a.
Eureka Math
http://www.engageny.org/mathematics
http://commoncore.org/maps/math/home
Robin Ramos
lead writer A Story of Units.
[email protected]