engageny/eureka math parent workshop, session 2 · engageny/eureka math parent workshop, session 2...

engageNY/Eureka Math

Parent Workshop, Session 2Saratoga USD

January 20, 2016

Outcomes

2

• Learn about the implementation process

and collaboration occurring in SUSD with the

engageNY/Eureka Math curriculum

• Explore the skills and conceptual

understandings in the domain of Number

and Operations in Base Ten

• Connect learnings in the domain to middle

school mathematics

• Receive resources to support your child’s

math education at home

Agenda

• engageNY/Eureka math

implementation and collaboration

• Number and Operations in Base Ten,

Grades K-5

• The Number System, Grades 6-8

• Resources

• Closure

3

ENGAGENY/EUREKA MATH IMPLEMENTATION AND COLLABORATION IN SUSD

4

THE DOMAIN OF NUMBER AND OPERATIONS IN BASE TEN

5

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

Coherence: Think Across Grades

K 1 2 3 4 5 6 7 8 HS

Counting &

Cardinality

Number and Operations in Base TenRatios and Proportional

RelationshipsNumber &

QuantityNumber and Operations –

FractionsThe Number System

Operations and Algebraic Thinking

Expressions and Equations Algebra

Functions Functions

Geometry Geometry

Measurement and Data Statistics and ProbabilityStatistics &

Probability

Findwell, Bradford & Foughty, Zachary. “”Preparing to Implement the Common Core State Standards for Mathematics. Indiana Department of Education and Ohio Department of Education. March 30, 2011

Focusing Attention Within

Number and Operations

Briars & Mitchell (2010)

Getting Started with the Common Core State Standards

Operations and Algebraic Thinking

Number and Operations -Base Ten

Number and Operations -

Fractions

Expressions and Equations

The NumberSystem

Algebra

K-5 6-8 MS/HS

8 CCSS First Grade Overview

Shift #2: Coherence: Think Across Grades, and

Link to Major Topics Within Grades

• Carefully connect the learning within and across

grades so that students can build new

understanding on foundations built in previous

years.

• Begin to count on solid conceptual understanding of

core content and build on it. Each standard is not a

new event, but an extension of previous learning.

Activity: Card Sort

• In each envelope there are six

standards from the domain of Number

and Operations in Base Ten

• Work with your fellow parents and

organize the strips into the Progression

of Standards from Kindergarten to

Grade 5

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Activity: Card Sort

Answers

• Compose and decompose numbers

11-19 into 10 ones and some further

ones… (KNBT.1)

• Given a two-digit number, mentally

find 10 more or 10 less than the

number, without having to count;

explain the reasoning used. (1.NBT.5)

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Activity: Card Sort

Answers

• Mentally add 1- or 100 to a given

number 100-900, and mentally

subtract 10 or 100 from a given

number 100-900. (2.NBT.8)

• Use place value understanding to

round whole numbers to the nearest

10 or 100. (3.NBT.1)

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Activity: Card Sort

Answers


round multi-digit whole numbers to any

place. (4.NBT.3)


round decimals to any place. (5.NBT.4)

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Got Dots?

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NBT in Kindergarten

• Special attention to 10

• Use of objects, drawings an equations

to describe and explain “teen

numbers”

• Initially, 16 looks like “one six” not “1

ten and 6 ones” (hide zero cards)

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NBT in Kindergarten

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By working with teen numbers in this way in Kindergarten, students gain a foundation for viewing 10 ones as a new unit called a ten in Grade 1.

NBT in Grade 1

• Numbers 11-19 are composed of 1 ten

and some ones

• They view the decade numbers in

spoken and written form.

• The digit in the tens place is more

important for determining the size of

the two-digit number (comparing two

digit numbers)

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NBT in Grade 1

• Adding tens and ones separately is a

general method that can extend to

any sum

• Compute differences to two-digit

numbers of multiples of 10 (ex. 70 – 40

can be viewed as 7 tens minus 4 tens

and represented with models or

drawings.

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NBT in Grade 1

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NBT in Grade 1

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In grade 2, students will compute the difference of any two- digit numbers (not just multiples of ten) with and without decomposing.

NBT in Grade 2

• Students extend their base-ten

understanding to hundreds.

• They add and subtract within 1000 with

decomposing and composing.

• They become fluent with + and – within

100.

• Use of manipulatives, drawings, hide

zero card (three digit)

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NBT in Grade 2

• Saying numbers aloud in terms of their

base ten units. (e.g., 456 is “Four

hundreds five tens six ones”)

• Students begin to work towards

multiplication by skip counting by 5s,

by 10s, by 100s.

• Comparing magnitudes of three-digit

numbers

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NBT in Grade 2

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Grade 2 students mentally add or subtract 10 or 100 to a given number between 100 and 900. They then work to achieve fluency in adding and subtracting within 1000 in Grade 3.

Sample Student Work: Grade 2

• Let’s look at some sample exit tickets

from second graders using the

subtraction algorithm and decomposing/unbundling using a

place value chart!

• Grade 2, Module 5, Lesson 16

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NBT in Grade 2

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NBT in Grade 3

• The major focus is multiplication

• Maintenance of addition and

subtraction within 1000

• Round numbers to the nearest 10 or

100

• Multiply one-digit whole numbers by

multiples of 10 using strategies based

on place value and properties of

operations.

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NBT in Grade 3

• Develop understanding of fractions,

equivalence and comparisons

• Express whole numbers as fractions (ex.

3 = 3/1

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NBT in Grade 3

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NBT in Grade 3

• The Great Round-Up

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NBT in Grade 4

• Read numbers from 1,000 to 1,000,000

• Fractions with denominators of 10 and

100 and decimals to the hundredths

place

• Add and subtract fractions

• Fluent with standard addition and

subtraction algorithms

• Compute product up to four digits

(1x3) and (2x2)

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NBT in Grade 4

• Extend understanding of how to

compute products of one-digit

numbers to multiples of 100. (ex. 6 x

700 as 6 x 7 and shift two places to the

left- 6 groups pf 700 = 4200

• Further explore the relationship

between multiplication and division

• Multiply a fraction by a whole number

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NBT in Grade 4

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NBT in Grade 4

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NBT in Grade 5

• Extend understanding of decimals to

the thousandth place

• Add, subtract, multiply and divide

decimals to the hundredths place

• Fluent in multiplication and division

algorithms

• Introduction of whole number

exponents

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NBT in Grade 5

• Students use the same place value

system to add and subtract decimals

• Multiplication of a fraction by a whole

number or fractions

• Divide unit fractions by a whole

number

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NBT in Grade 5

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NBT in Grade 5

• Rounding decimals to a given place

value using a vertical number line

• Grade 5, Module 1, Lesson 7 Exit Ticket

https://youtu.be/HClHJyoCeMY

37

https://youtu.be/HClHJyoCeMY

CONNECTIONS TO MIDDLE SCHOOL MATH

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The Number System- Grades 6-8

• Students build on concepts developed

in K-5:

– Representation of whole numbers and

fractions on the number line

– Understanding of the properties of

operations

• Students are ready to build new

understandings with fractions and

negative numbers (integers).

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Number Lines

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• The number line is first explicitly

addressed in 2nd grade. References

occur throughout middle school and in

HS Statistics and Probability.

• The number line constitutes a unifying

and coherent representation for the

different sets of numbers which other

models cannot do.

Evolution of the Number Line

Grade Number Line representation

1

3

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4

5

43



7

Algebra II

44

Properties of Operations

• Building understanding of

multiplication and division of rational

numbers relies on a firm understanding

of the properties of operations.

• Students have not been taught the

formal names of the properties but

have used them repeatedly in

elementary grades.

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Properties of Operations on Rational

Numbers (addition)

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Properties of Operations on Rational

Numbers (multiplication)

47

Grade 6

• Students conclude work with

operations of fractions begun in Grade

4 by computing quotients of fractions.

48

Grade 6

• Students consolidate the work of

earlier grades with whole numbers and

decimals and become fluent in the

four operations.

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Grade Knowledge

3 Whole numbers are fractions (ex. 2/1 = 2 wholes)

4 Decimal notation is a way of writing fractions with denominatorsequal to the power of 10 (ex. .10 is equal to 1/10)

6 Whole numbers, decimals and fractions are not wholly different types of numbers but are part of the same number system.

Grade 6

• Use of prime factorization, least

common multiple and greatest

common factor are introduced

formally.

50

Grade 7 and Grade 8

• Students extend their understanding of

operations with fractions to operations

with rational numbers.

• Students know there are numbers that

are not rational and approximate

them by rational numbers. (ex. 1/3 is a

repeating decimal—0.333333 or 0.3

and (pi) does not have a repeating

decimal and therefore is irrational.

51

HELPING STUDENTS WITH MATH

52

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?

53

Questions to Clarify Understanding of

Explanation

• Do you understand your solution?

• Can you explain what you’re thinking?

From Whole Class Mathematics Discussions, Lamberg, Pearson 2012S

PHASE 2: ANALYZING SOLUTIONS

Questions to promote analysis and reflection of

solutions:

– What do you see that is the same about

these solutions?

– What do you see that is different about

these solutions?

– How does this relate to ___?

– Ask students to think about how these

strategies relate to the mathematical

concept being discussed


PHASE 3: DEVELOPING NEW MATHEMATICAL INSIGHTS

(ABSTRACT MATHEMATICAL CONCEPTS)

Questions to Promote Mathematical Insights

•Ask students to summarize key idea.

•Ask questions: Will the rule work all the time? (Making generalizations)

•Ask students to solve a related problem that extends the insights they had gained from the discussion.

•Ask “What if” questions.


Tips

• Emphasize skill, understanding and

application of math

• Talk through the math

• Value process along with final results

• Making mistakes is a part of doing

authentic mathematics

57

Recognize math in everyday life• How many more days?

• Reinforce multiplication and division by

helping your student plan for a major

purchase

• Cooking has endless possibilities to work with

fractions

• Shopping: Which discount or deal is better?

• Discuss the financial side of planning for

college

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Thank you for your time and participation!

Sheila Walters

Math Coordinator

[email protected]

59

mailto:[email protected]

engageny/eureka math parent workshop, session 2 · engageny/eureka math parent workshop, session 2...

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