engageNY/Eureka Math

Elementary Grades

Parent Workshop

Outcomes

• Learn about the components of an

engageNY lesson

• See classroom examples of engageNY math

in action

• Engage in hands-on math activities utilizing

some of the tools and representations from

the engageNY curriculum

• Receive resources to support you student’s

math education

2

Agenda

• Welcome

• Introduction to engageNY and lesson

components

• Overview of sample Tools and

Representations

• Tools and Representation Stations

• Resources/Closure

3

What is Eureka Math?

Eureka Math is an online textbook-like program that

was developed by Common Core, Inc. a

Washington, DC-based not-for-profit organization

(not affiliated with CCSS) that creates content-rich

curriculum tools. The Eureka website is

www.greatminds.net .

Eureka Math provides an easily navigable online

platform for housing the comprehensive

mathematics curriculum Common Core, Inc.

created for the New York State Education

Department (NYSED), which is housed at

www.engageny.org .

What is Eureka Math?

• Eureka Math is an enhanced version of EngageNY

Math.

• “Eureka Math is based on research and

development made possible through a partnership

with the New York State Education Department.

• The modules within Eureka Math are available

online at engageny.org and greatminds.net.

Eureka Math added an “array of online resources

for teachers and parents and professional

development” to support the implementation of the

curriculum.

5

PK-5 A Story of Units

Structured to reflect the instructional shifts:

• Focus – deeply on the concepts prioritized in the

CCSS

• Coherence – learning is connected within and

across grades – each standard is an extension of

previous learning experiences.

• Rigor – pursuits of conceptual understanding,

procedural skills, fluency and application - all with

equal intensity.

6

Focus

Shift 1: Focus

Coherence

Shift 2: Coherence

Rigor

Shift 3: Fluency

Shift 4: Deep Understanding

Shift 5: Application

Shift 6: Dual Intensity

Instructional Shifts Combined

Standards for Mathematical Practices

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Key Points

• A Story of Units: A Curriculum Overview for Grades P-5

provides a curriculum map and sequence of modules

for the year.

• The focus is on strategies and student reasoning, not on

algorithms.

• Each Module builds on the skills and knowledge of the

previous module. Rigorous problems are embedded

throughout the module

9

© 2012 Common Core, Inc. All rights reserved. commoncore.org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios

Review of Module Structure

Module Overview

Topic A Topic B Topic C

Lessons 1 - 2

Lessons 3 - 5

Lessons 6 - 8

11

Lesson Objective/Distribution of Minutes

Lesson Structure

• Fluency

– Fluently…..

• Application Problems*

– ….real-world problems

• Concept Development*

– Understand…..

• Student Debrief

– more engagement in Standards for

Mathematical Practice

12

*May want to change the order.

Fluency

• Fluency is designed to promote

automaticity.

• First three weeks of school- 10 minutes

a day

• Fluency activities for each lesson.

– Sprints --Games

– Math Finger Flash --Personal White Board

– Number Disk Dash Activities

13

Fluency Activities

• Sprint- Divide by 2

• Group Counting

• Personal White Boards- Divide by 3

14

Fluency Activity

2 x 3 =___

2 x 3 = 6

__ 3 = 2

3 x 3 =___

3 x 3 = 9

__ 3 = 3

15

Fluency Activity

9 x 3 =___

9 x 3 = 27

__ 3 = 9

16

Sprints

• They are designed to develop fluency

• They are fast paced

• Teachers assume role of athletic

coach

• They should be fun, adrenaline rich

activities

• Student recognition of increasing

success is critical

– Every improvement is celebrated

17

Sprints

• Each sprint has two parts with closely

related problems on each

• Students complete the two parts in

quick succession

• The goal is improving on the second

part.

• Sprints should take about 8 minutes

18

Other types of fluency practice

Kindergarten

https://www.engageny.org/resource/gr

ade-k-math-fluency-kcc2

Grade 2

https://vimeo.com/72616539

19

Application Problems

• Real world problems

• There is a range of problems presented

within a concept.

• Delivery

– Beginning of the year use more guided

practice.

– Middle and end of the year use more

exploration

20

Page 24 from How to Implement A Story of Units

Application Problems (continued)

• Usually relate to concept

development in lesson

• Suggested use of RDW strategy

• Vignettes are provided and MAY be

used

• Important for students to see

connections between other parts of

the lesson and other concepts.

– Best if students can discover on their own.

21

Application Problem

Mark spends $16 on 2 video games.

Each game costs the same amount.

Find the cost of each game.

?

16 2 = 8

16 Each game costs $8.

22

RDW (Read, Draw, Write)

• Protocol

1. Read

2. Draw and Label

3. Write a number sentence (equation)

4. Write a word sentence (statement).

23

Read, Write, Draw Strategy (RDW)

• Assists students to make sense in

problem solving

• Teacher can model for students first,

then guide students together and

have students apply the strategy on

their own

24

RDW Strategy

• Underline key words

• Circle key numbers

• Underline the question

• Draw a picture (number bond, tape

diagram, array)

• Write an equation

• Write a sentencehttps://www.youtube.com/watch?v=Hn6lKmDe3Gk

25

RDW in Action

Third Grade

• https://youtu.be/Hn6lKmDe3Gk

• Discussion Question

– Share with a partner what you saw in the

video.

26

Concept Development• The major portion of instruction

• New learning is introduced

• Intentionally sequences to build on

prior knowledge

• Concrete- pictorial-abstract

• Includes “how-to” of lesson delivery

through models, sample vignettes, and

dialogue.

27

Page 23 from How to Implement A Story of Units

Concept Development

• Problem Sets

– Classwork

– Students work independently or in pairs

– Follow time recommendation

– Modify number of problems if needed

28

Concept Development

29

Division Problems in Pairs

30

31

Concept Development-Problem Set

Student Debrief

• Objective of the lessons is discussed

and internalized

• Sample dialogue to guide teachers for

eliciting the level of student thinking

required in the lesson.

• Sharing and analyzing student work.

– Standards for Mathematical Practice

32

Page 25 of How to Implement A Story of Units

Student Debrief (continued)

• Conversation

– Establishing routines early in year

– “Pair-share”

– Sentence frames

• Exit Tickets

– End of Student Debrief

– Short, formative assessments

– Students show accountability for day’s

learning

33

34

Student Debrief

35

Student Debrief-Exit Ticket

Lesson Structure• Fluency Practice

• Application Problem

• Conceptual Development

• Problem Set

• Student Debrief/Exit Ticket

• Build automaticity

• Connect to previous learning or to real-life to set the context

• Direct Instruction, model concepts, guided instruction

• Independent Practice

• Summation of lesson

37

Homework

Grade 3 Lesson and Coherence

• Obj.- Interpret the quotient as the

number of groups or the number of

objects in each group using units of 3.

• Prior- divide by 2

• Builds towards students knowing form

memory all products of two one-digit

numbers.

• Anticipates using units of 4

38

TOOLS AND REPRESENTATIONSMODELING MATHEMATICS

39

Making the connection …

Concrete

Pictorial

Abstract9 + 6 = 15

Ali has 4 toy cars. David has 3 toy cars. How

many toy cars do they have together?

4 + 3 = 7

Concrete

Abstract

Use concrete objects to form two groups and put the two groups together.

Representational

4 5,6,7

7 cars

4 5, 6, 7

7 cars

Abstracting to another level.

1,2,3 4 1,2,3

1,2,3,4,5,6,7…7 cars

Progression of Learning

• Students need enough concrete

experiences to develop conceptual

understanding

• Students need experience with visual

models to enable the development of

abstract fluency.

• Students learn “why” behind a math

concept not just the “how” so they can

explain their thinking and justify their

solutions.

43

Suggested Tools and Representations

TAPE DIAGRAMS

44

What are tape diagrams?

• A “thinking tool” that allows students to visually represent a mathematical problem and transform the words into an appropriate numerical operation

• A tool that spans different grade levels

• A picture (or diagram) is worth a thousand words

• Children find equations and abstract calculations difficult to understand. Tape diagrams help to convert the numbers in a problem into pictorial images

• Allows students to comprehend and convert problem situations into relevant mathematical expressions (number sentences) and solve them

– Bridges the learning from primary to secondary (arithmetic method to algebraic method)

Why use tape diagrams? Modeling vs. Conventional Methods

Progression of Tape Diagrams

• Students begin by drawing pictorial models

• Evolves into using bars to represent quantities– Enables students to become more comfortable

using letter symbols to represent quantities later at the secondary level (Algebra)

15

7 ?

The Comparison Model – Grade 1

• There are 2 more dogs than cats. If there are 6 dogs, how many cats are there?

There are 6 dogs. There are 2 more dogs than cats. The difference between the two numbers is 2. There are 4 cats.

The Comparison Model – Grade 2

• Students may draw a pictorial model to represent the problem situation.

Example:

Part-Whole Model – Grade 2

Ben has 6 toy cars. Stacey has 8 toy cars. How many toy cars do they have altogether?

6 + 8 = 14 They have 14 toy cars altogether.

Forms of a Tape Diagram

• Part-Whole Model- Also known as the ‘part-part-whole’ model,

shows the various parts which make up a whole

• Comparison Model- Shows the relationship between two quantities

when they are compared

The Comparison Model

There are 6 dogs. There are 2 more dogs than cats. The difference between the two numbers is 2. There are 4 cats.

Tape DiagramsThe baker packs 36 bran muffins in boxes of 4. Draw and label a tape diagram to find the number of boxes he packs.

36 muffins

4 4 4 4 4 4 4 4 4

Grade 3

Part-Whole Model Multiplication & Division

Variation #1: Given the number of parts and one part, find the whole.

5 children shared a bag of candy bars equally. Each child got 6 candy bars. How many candy bars were inside the bag?

5 x 6 = 30The bag contained 30 candy bars.

Part-Whole Model Fractions

To show a part as a fraction of a whole:

Here, the part is 2

3of the whole.

The Comparison Model Fractions

A is 5 times as much as B. Thus, A is 5 times B. (A =

5 x B) B is1

5as much as A. Thus, B is

1

5of A.

We can also express this relationship as:

B is 1

5times A. (B =

1

5x A)

Jerome, Kevin, and Seth shared a submarine

sandwich. Jerome ate ½ of the sandwich, Kevin

ate1

3of the sandwich, and Seth ate the rest. What

is the ratio of Jerome’s share to Kevin’s share to

Seth’s share?

Kevin

Jerome

Seth

3

2

1

Practice ACT

Question

Tape Diagrams

© 2012 Common Core, Inc. All rights reserved. commoncore.org

A Story of Units

Key Points – Proficiency with Tape Diagrams

59

• When building proficiency in tape diagraming skills start with simple accessible situations and add complexities one at a time.

• Develop habits of mind in students to reflect on the size of bars relative to one another.

• Part-whole models are more helpful when modeling situations where you are given information relative to a whole.

• Compare to models are best when comparing quantities.

© 2012 Common Core, Inc. All rights reserved. commoncore.org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios

Using Tape Diagrams

60

• Promote perseverance in reasoning through problems.

• Develop students’ independence in asking themselves:

–“Can I draw something?”

–“What can I label?”

–“What do I see?”

–“What can I learn from my drawing?”

NUMBER BONDS

Number Bonds

17

10 7

17

- 9

8

Grades K, 1, & 2

10 – 9 = 1 8

34

- 9

21

52

Subtraction Algorithm

34

20

10

4

Number Bond

10-9=1

Number Bonds

-7 + 9 = ___

7 2

2

Makes 0

Grade 6 & 7

First Grade Fluency

w/Number Bonds

https://www.youtube.com/watch?v=y3Pvpin9mtY

ARRAYS

Multiplication as an ArrayKindergarten – arrange items into array

Multiplication as an arrayKindergarten – arrange items into array

5 rows

Multiplication as an array

3 rows

3rd grade – recognize array as multiplication

Multiplication as an array

7 rows

4th & 5th grade – multiply using area model

7 units

4 units

Area Model – 7th Grade – Introduction to Factoring

2

x 6y 4

2x + 12y + 8 = 2(x + 6y + 4)

Algebra I

Student Samples of Arrays- Grade 2

https://www.youtube.com/watch?v=41

9h8ubyCYQ

A Story of Units

Models

• Array and Area Models

• Base Ten Blocks

• Bundles

• Money

• Number Bond

• Number Disks

• Number Line

74

A Story of Units

Models (continued)

• Number Path

• Number Towers

• Place Value Chart

• Rekenrek

• Tape Diagram

• Ten Frame

75

EXPLORATION OF TOOLS/REPRESENTATIONS/MODELS

76

What is 8 + 7?

77

Parent Resources

78

More Resources

• Let’s refer to our handout!

79

5 Powerful Questions to Ask

#1. What do you think?

#2. Why do you think that?

#3. How do you know this?

#4. Can you tell me more?

#5. What questions do you still have?

80

Thank you for your time and ment!

Sheila Walters, Math Coordinator

Sheila_Walters@sccoe.org