Transcript NUMBER SENSE and MATH FLUENCY (grades k-5)

NUMBER SENSE
and
MATH FLUENCY
(grades k-5)
Presenter
JUDITH T. BRENDEL, Ed.M.
[email protected]
http://www.njpsa.org
Click on [FEA PROGRAMS]
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Number Sense and Math Fluency (K-5) Dec. 9, 2015
PowerPoint
Selected 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.
1. 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. UNDERSTANDING
linking topics and thinking across grades
COHERENCY
ORDER doesn’t
matter in ADDITION
3
+ 5
= 5
+3
1 dog + 6 cats = 6 cats + 1 dog
3a + 5b + a = 5b + a + 3a
1 2 3 6
2 1 3 6
+ + =
and
+ + =
8 8 8 8
8 8 8 8
ORDER doesn’tCOHERENCY
matter in MULTIPLICATION
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!
3 x 5 = 5 x 3 or
(8)(9) = (9)(8)
3a(2a) =6a2 and 2a(3a) = 6a2
2x3x5=2x5x3
2x3x5 =
6 x 5 = 30
2x5x3
10 x 3 = 30
4a(3a)(-2b) = -24a2b or 3a(4a)(-2b) = -24a2b
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!
=5
+3
not 8
3cats+2cats+4dogs = 5cats + 4dogs not 9catdogs
2 6 + 6 +5 4 = 3 6 + 5 4
UseMathPractices
“same
format”
to compare
COHERENCY
6: PRECISION
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
3.2 0.857 0.33 0.66
0.33
2/3
6/7
π
π
3.14
3.2
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.
Required Fluencies K-6 without calculators
Grade
K–2
Focus Areas in Support of Rich Instruction and
Expectations of Fluency and Conceptual Understanding
• 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)
15
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
* Folded
strip
activities
0
½
0
¼
0
2/4
1/3
One half
1
¾
2/3
one
fourth
one
fourth
one one
fourth fourth
4/4
3/3
Three thirds
= one whole
FRACTIONS (Concrete objects)
Count the objects
Show me one-half of the objects
Count these objects
Show me one-third of the objects
FRACTIONS (words & symbols)
Circle one half of the stars
Circle 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
3
?
8
10
20
> = <
?
5
?
6
7
8
RESOURCES: Hardcopies_Links
• √Gr. K-5:
• PreK-5:
link to Virginia NumberSense resource (activities)
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-releaseditems
• Gr. 3, 4, 5 EOY and PBA item set:
Student responses with rubrics
Grade 3: items 11-13
Grade 4: items 11-16
Grade 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 formatting
Use 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-gradelevel 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 Work with others
DESIGN your own: minimum 6 steps
-GEOMETRY
•
•
•
•
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 H
PARTICIPATE: 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 student
One for below-level student
One 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 MUSIC
https://www.youtube.com/watch?v=2TWGPFpeyPw
Participate: 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+mod
ules+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 [email protected] )
Sincere thanks
for your participation,
collaboration and dedicated
efforts!!!
Hope to see you again at another
session.
Judy
[email protected]