number sense and math fluency (grades k-5) presenter judith t. brendel, ed.m....

NUMBER SENSE and

MATH FLUENCY(grades k-5)

PresenterJUDITH T. BRENDEL, Ed.M.edleaderk12@hushmail.com

http://www.njpsa.org

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Number Sense and Math Fluency (K-5) Dec. 9, 2015 PowerPointSelected Handouts

Number & Operations Standard

describes deep and fundamental understanding of, and proficiency with:• Counting (1, 2, 3 … 5, 10, 20 … 98, 97, 96 …)• Numbers (-3,-2,0,2,4…½, ¾ … 0.5, 4.9 … 6:00

A.M.)• Arithmetic (+ - x ÷ ) • an understanding of number systems and their

structures.

Pre-kindergarten through grade 12: students should attain a rich understanding of numbers—

• What they are • How numbers are– represented: objects, numerals, number lines – related to one another – embedded in systems that have structures and

properties; and – used with operations to solve problems

Central to this Standard K-12

is the development of number sense—• the ability to decompose numbers naturally, • use particular numbers like 100 or 1/2 as

referents, • use the relationships among arithmetic

operations to solve problems, • understand the base-ten number system, • estimate and make sense of numbers

(Sowder 1992).

Dual Competencies

1. Knowing basic number combinations—the single-digit addition and multiplication pairs and their counterparts for subtraction and division—is essential.

2. Computational fluency is equally as important—having and using efficient and accurate methods for computing.

Fluency might be manifested in • using a combination of mental strategies and jottings on

paper or • using an algorithm with paper and pencil, particularly when

the numbers are large, to produce accurate results quickly.

OPERATIONS

Instructional programs from pre-k through grade 12 should enable all students to—• understand meanings of operations and how

they relate to one another;

STUDENT learning strategies

Teaching student learning strategies that THEY can use to become more successful learners … more responsible for their own learning.

2. COHERENCY and 4. UNDERSTANDINGlinking topics and thinking across grades

COHERENCY

3 + 5 = 5 + 3

1 dog + 6 cats = 6 cats + 1 dog

3a + 5b + a = 5b + a + 3a

ORDER doesn’t matter in ADDITION

COHERENCYrefers to the fact that each year students learn something that relates and continues from the prior year; topics are related; all is NOT new!

3 x 5 = 5 x 3 or (8)(9) = (9)(8)

3a(2a) =6a2 and 2a(3a) = 6a2

2 x 3 x 5 = 2 x 5 x 3 2 x 3 x 5 = 2 x 5 x 3

6 x 5 = 30 10 x 3 = 30

4a(3a)(-2b) = -24a2b or 3a(4a)(-2b) = -24a2b

ORDER doesn’t matter in MULTIPLICATION

COHERENCYrefers to the fact that each year students learn something that relates and continues from the prior year; topics are related; all is NOT new!

= 5 + 3 not 8

3cats+2cats+4dogs = 5cats + 4dogs not 9catdogs

COMBINE “LIKE” TERMS

COHERENCY

refers to the fact that each year students learn something that relates and continues from the prior year; topics are related; all is NOT new!

Which area is larger? 2’x 3’ or 20”x 38” Why?2’x3’ = 24” x 36” = 863 sq.”

20” x 38” = 760 sq.”

Put in order: 3.2 6/7 0.33 2/3 π 3.2 0.857 0.33 0.66 3.14

0.33 2/3 6/7 π 3.2

Use “same format” to compare

MathPractices 6: PRECISION

FLUENCY and ESTIMATES

Instructional programs from pre-k through grade 12 should enable all students to—• compute fluently and make reasonable

estimates

FLUENCY

• By the end of grade 2, students should know the basic addition and subtraction combinations, should be fluent in adding two-digit numbers, and should have methods for subtracting two-digit numbers.

• At the grades 3–5 level, as students develop the basic

number combinations for multiplication and division, they should also develop reliable algorithms to solve arithmetic problems efficiently and accurately. These methods should be applied to larger numbers and practiced for fluency.

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GradeFocus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding

K–2• Add/subtract within 5/ 10/ 20 (K.OA.5, 1.OA.6, 2.OA.2)• Add/subtract within 100 (2.NBT.5)• Know single-digit sums within 20 (2.OA.2)

3• Multiply/divide within 100 (know single-digit products from

memory) (3.OA.7)• Add/subtract within 1000 (3.NBT.2)

4 • Add/subtract within 1,000,000 (4.NBT.4)

5 • Multi-digit division (5.NBT.5)

6• Multi-digit division (6.NS.2)• Multi-digit decimal operations (6.NS.3)

Required Fluencies K-6 without calculators

ESTIMATES Pre-K to 2

• A key idea is that a number can be decomposed: 24 = ? and ? or 24 = 2 sets of ____?

• Odd numbers

• Even numbers

• Commonly used fractions: ½ of a glass of milk, 1/8 of a pizza

Attendees at today’s workshop have special permission from the author to use material from the Barron’s “Grade 2 Test Practice for Common Core.” (draft from 2016 edition) J. Brendel, author

Grade-2 NUMBER SENSE FRACTIONS

0 ½ 1

0 ¼ 2/4 ¾ 4/4

0 1/3 2/3 3/3

* Folded strip activities

onefourth

onefourth

onefourth

onefourth

One half Three thirds

= one whole

FRACTIONS (Concrete objects)

Count the objectsShow me one-half of the objects

Count these objectsShow me one-third of the objects

FRACTIONS (words & symbols)

Circle one half of the starsCircle one

fourth

Circle one third of the rabbits

ESTIMATES Grades 3 to 5

• Compare fractions to familiar benchmarks: to half or to a whole. Explain why 1/2 + 3/8 must be less than 1

• Explain their method; understand that many methods exist, and see the usefulness of methods that are efficient, accurate, and general.

Grade 3-5 ESTIMATE FRACTIONS

< ½ = ½ > ½ ?

RESOURCES: Hardcopies_Links• √Gr. K-5: link to Virginia NumberSense resource (activities)• PreK-5: link- http://www.engageny.org (curriculum map,

module, lessons, worksheets)• √Gr. 2: Barron’s sample tasks (17p) • √Gr.3,4,5 packets: PARCC sample EOY/PBA ex. 2014-15• Gr. 3-5: link to

http://www.prc.parcconline.org/assessents/parcc-released-items

• Gr. 3, 4, 5 EOY and PBA item set:Student responses with rubrics

Grade 3: items 11-13Grade 4: items 11-16Grade 5: items 11-16

ACTIVITIES (RESOURCES)√

√List: Differentiate Instruction (list) and √Sample Templates (new created 12/3/15 on laptop)√21ST.Century Line: Move right (arithmetic expression) √21ST.Century Line: Pass right(zoo), (write a number … )√Carousel (non-sequential tiered activities)√Match your Partner (sets CD and GF) and blank√Match Games (slips): gr. 2, 3, 4, 5 √Geom.:(17) … Fractions gr.5: (15) … Gr.4:(3) … Gr.3:(3) … newGr.K-2:[AddSubt(2)] … Frac.[Number line(2)] and blank

√BattleShip Game: concrete/template or graph paper√templates(for 22) √attrib.blocks(for 4) √polygons(6 sets for 12)=38 Rulers? folders

What will you do?-Participate in an engaging activity

Debrief the activity

-Select a NS topic/standards for your students-Create a similar activity for your students

Use √off-list (vary ways students demonstrate ….)Use template for formattingUse hardcopy & online resources for content

PARCC released items, EOY/PBA tests,Engageny modules, worksheets, quizzes

Activity #1: 21st Century Assembly Line*do ONE STEP and MOVE RIGHT

(workbook p.15)

PARTICIPATE: Number (arithmetic) activity

DESIGN: an “order of operations” expression or equation appropriate for the student on-grade-level in your class. (minimum 6-8 steps)

Activity #2: 21st Century Assembly Line*do ONE STEP and PASS RIGHT

(Workbook p. 16)

PARTICIPATE: in one/two activities: -TRIP TO THE ZOO scenario-REN REN scenario – geometry -FRACTIONS -GEOMETRY

Work with others DESIGN your own: minimum 6 steps

• Select topic/objectives/standard(s)• Use √off list; vary content items• Vary: MC, SCR, OE, MMC, EOY, PBA• Use resources to find examples/tasks

**Create a “Do one.PASS rt.”Work with a partner . Use √ List

Get content resources: http://www.engageny.org PreK-5 curriculum map: Yellow=number Blue=geometry Green=number/geometry/measurement Pink=fractions

http://www.engageny.org• Click on [ curriculum map ] _ decide module• Select [module] … Select [lesson] ….• Scroll down to [Lesson Problem Set (student

worksheet)] Copy/paste, or take screen-shots• Sample grade-1 module 1: lesson 1

Example #3.

Mary gets stickers at school for good work. She got 7 puffy stickers, 6 smelly stickers, and 3 flat stickers. How many stickers did Mary get at school altogether?

___ + ___ + ___ = ___10 + ___ = ___ Mary got ____ stickers at school.

Activity #3: *MATCH CARDS/SLIPS work in pairs or small groups

PARTICIPATE: (p.19-26) CREATE your own (p.27)

• Geometry (17) (4 match-ups minimum)• Fractions grade-5 (15)• Grade 3 (3)• Grade K-2 (2)• Fraction/Number line (2)• Elementary Number Sense: whole numbers,

fractions, decimals, + - x ÷

**Create a“MATCH SLIPS”set work with a partner . Use √-off List

Activity #4: PARCC grades K-5 (p.28/30)

*MATCH your PARTNER’S ANSWER

PARTICIPATE: Grades K-2: sets G and HPARTICIPATE: Grades 3-5: sets C and D

CREATE: your own. Work with your partner to create three pairs of tasks for your grade.

One for on-level studentOne for below-level studentOne for advanced student

Use Worksheet Template, and Answer-Key Template.

**Create “MATCH YOUR PARTNER’s ANSWER”

work with a partner . Use √-off List

Activity #5: PARCC grades K-5*CAROUSEL ACTIVITIES

INCLUDE CAROUSEL MUSIChttps://www.youtube.com/watch?v=2TWGPFpeyPwParticipate: All students move about the room from one posted task to the next. Using a clip-board is helpful and fun!Grade: Grade:Grade:

*WORK IN TEAMS: Create a Carousel set of 10 tasks

**Create “CAROUSEL” tasks to post (Create a few … 3 different levels)

work with a partner _ use √-off List

Activity #6: PARCC grades K-5 (4 page packet.)

*PLAY a BATTLE-SHIP TYPE GAME

• Use CONCRETE SHAPES (attributed blocks, pattern blocks, fraction tiles, base-ten blocks, snap cubes, ….) or a TEMPLATE to trace. (focus on vocabulary that relate to positions: half-way between, above, below, to the right of, in the middle, ….)

• Use GRAPH PAPER and straight edge to duplicate shape on grid using given dimensions (focus on number sense) in description.

COMMUNICATE: SPEAK MATHEMATICS . LISTEN . FOLLOW DIRECTIONS . BE PRECISE

Search for: Elementary Math Modules Virginia https://www.google.com/search?client=safari&rls=en&q=Elementary+math+modules+Virginia&ie=UTF-

8&oe=UTF-8

(K- 5 Mathematics Module: Number and Number Sense)

Each grade level has 6-22 different activities to facilitate student learning:

Kindergarten sample:Share number cards 1 to 10 with students.

Ask them to tell something about each number shown. Using 10 as an example, students might count the number of fingers they have, share that $10 is a lot of money, or point out that 10 is a number bigger than six. Try a few different numbers to get students talking and sharing what they know about each number.

Screen shot: K-5 Mathematics Module

Gr. 3-5: Other Online Resources

Check out Engage NY and new PARCC released examples grades 3-5 for– Lessons– Videos– Activities for teachers to do

QUESTIONS

Action Planning and Next Steps

• Goals• Action Planning• Next Steps

FEEDBACK

The three most useful things I learned today:

Two things I would share with a colleague:

One question that I have: (Email to edleaderk12@hushmail.com )

Sincere thanks for your participation, collaboration and dedicated efforts!!!

Hope to see you again at another session.

Judy edleaderk12@hushmail.com