Elem. Diff.Instruc Burlington 1.16 as of 12.22.15x
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Transcript Elem. Diff.Instruc Burlington 1.16 as of 12.22.15x
DIFFERENTIATE
INSTRUCTION
elementary school mathematics
presented by
Judith T. Brendel Ed.M.
educational consultant
BURLINGTON COUNTY PD INSTITUTE – JANUARY 2016
What will you do?
-Participate in an engaging activity focusing on
Math Practices;
Debrief the activity
-Select a 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
DIFFERENTIATE why?
• For students to experience multiple opportunities to
work within the same topic.
• To keep all students actively engaged and interested.
• Meet the different learning style preferences of your
students. Give them different types of activities as they
learn, practice and assess their understanding.
• Meet the different levels of understanding of all the
students in your class.
• Give students experiences outside-their-comfort-zone;
so they learn to persevere and be successful.
Which one Doesn’t Belong
and Why?
RAISE the level of EACH student’s thinking
MONITOR each student’s understanding
CHALLENGE ALL!
B
D
Which one Doesn’t Belong and Why?
A.
B.
C.
D.
How are they the same?
(concept w/o math)
Which one Doesn’t Belong and Why?
A. 5 < 6
B. 6 > 2 + 1
C. 2 + 4 > 1+ 5
D. 9 x 2 > 8 x 3
See ‘A’ above: Compare 2 two-digit numbers
… record results of comparisons with symbols
> = < (use of symbols new to grade-1.)
ABCD monitor each
Which ONE doesn’t belong?
A
B
c
D
Which is the most difficult to solve?
A)
C)
2∆ = 14
2∆ = 14
2
2
∆= 7
∆ + 2 = 14
-2
∆
-2
= 12
B)
-14 = 2 - ∆
+∆
+∆
∆ - 14 = 2
+ 14
+14
∆
= 16
D) ½ ∆ = 14
(2)½ ∆ = 14(2)
∆ = 28
GET THEM MOVING
MAKING DECISIONS
BEING SUCCESSFUL
SEE EACH OTHER THINKING
MOVIE CLIP
Lucy and Ethel
in the
CANDY FACTORY
Google: You tube Lucy Ethel Chocolate Factory
st
21
Century Assembly
Line
WHAT’S WRONG?
• Analyze – supervisor/teacher
• Analyze – teacher/student
no rubric, goals not same, feedback not honest,
no change after feedback
THINK TOGETHER SEPARATELY
ACTIVITIES:
(move-on … or … pass-it on)
CHANGE PROCESS!!!
Move to the right.
21st Century Assembly Line
Move, have fun, see each other
thinking
a. Organize thoughts; show
process;
b. Follow rules; defend/critique
each others work
Arithmetic (p.15) about 8 steps
CHANGE PROCESS!!!
Pass it On
21st Century Assembly Line
PASS IT ON
Move, have fun, see each other thinking
a. Organize thoughts; show
process;
b. Follow rules; defend/critique each
others work
Activity:
* Fractions (grade-4)
* Didi and RenRen
* Plan form (p.16)
* Trip to the Zoo (p.17)
**Create a “Do one.PASS rt.”
Work with a partner .
Use √ List page-4
CAROUSEL
SAME THEME different TYPES of tasks
SAME THEME different LEVELS of difficulty
INDIVIDUAL or PAIRED activity
Activity Grades 2-3:
Activity Grade-4: fractions (14 examples)
Activity Grade-5: (13 examples)
Students move about the room (w/clip board, handout,
pencil) to complete multiple tasks.
• Posted about room are sheets, cards or post-its with
tasks
• Needed tools are at each site
• Answer keys are available to students
**Create “CAROUSEL” tasks
(Create … 3 different levels)
work with a partner _ use √-off List
MATCH Your Partner
ACTIVITY: Students work in pairs. (p.29-30, 31-32)
Each student completes six given examples;
then matches answers with partner.
Set GH(gr. K-2) _ Set GH (gr. 3-5) … then each
creates two new examples with the same
answer.
Match Parts with whole
Activity: Student pairs or groups of 3 (compete)
Envelopes contain:
-Geometry: characteristics and shapes
-Formulas and uses
-Vocabulary words and definitions
Activity: *MATCH CARDS/SLIPS
work in pairs or small groups (p.20-27, 28)
PARTICIPATE:
• Geometry (17)
• 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 (p.28)
work with a partner (use check √ off list p.4)
MAKE it a GAME!!!
MATCH the GRAPH
GEOMETRY
ACTIVITY: Battle-ship-like game (Student pairs)
Play games to practice; improve organization;
improve sequencing, problem-solving,
vocabulary, ….
Match the Graph
• Packet of 4 different games
Equation Tic Tac Toe (use grade 4 and 5)
• What standards are met here?
1
2
3
4
7
5
8
6
9
Math + Fun = more
learning
CHANGE the QUESTIONS
How do PARCC questions look?
A. ….
WRITE
B. ....
DRAW
C. …..
EXPLAIN
SKETCH CONSTRUCT
PROVE
YES? NO?
D. ….
COMPARE
BUILD WHY?
NOT TRUE?
Link MP
5: Use Math Tools Appropriately
The Library of Virtual Manipulatives
http://nlvm.usu.edu/ennav/vlibrary.html
LAB STATIONS
grades K-2
TOPIC: HALF
Station #
• 4 - Trace to make the other half (fraction tiles)
• 5a - Cover half the shape (attribute blocks)
• 5 - Show half (fraction tiles)
• 8 - Write half a sentence then ….
• 11 - Make stand-up pattern (pattern blocks)
• 11A – Use template; trace.match other half
LAB STATIONS grades 3-5
TOPIC: ESTIMATION
Station #
• 8 - Coiled rope: estimate length
• 2 - Overflow the spoon
• 3 - Toothpick count
• 4 - Jellybean mix-up
• 5 - Unifix cubes
RANGE PROBLEMS
NOTE GRADE-LEVEL OPTIONS
Change the Question
How should I write my answer?
WHAT makes
SENSE?
If you have, DISTRIBUTE
Sleeves and Markers
or
Individual White Boards
SEE EACH ONE
THINKING
ORIGINAL
NEW QUESTION same example
1
Add 3/8 and 4/8
Is the sum of these two fractions closer to ½ or closer
to 1 whole? Explain or show how you know.
2
4 x 2/3 =
Estimate your answer. The product is
(a) > 4
b) < 4
(c) < 1
(d) < 2
3
Find the sum
5/12
6/12
7/12
REWRITE this example using only two fractions so
you will get the same answer when they are added.
4
What is the total? How can you tell by just looking at this example that
5 and 5/7, and
your answer will be greater than 10? EXPLAIN in
4 and 6/7
WORDS.
\
Change the Question
not the Textbook
See #2 above: NEW grade-5: Explain why
multiplying a given number by a fraction
less than 1 results in a 1product
smaller than
1
the given number; … 4 ´ 2(5.NF.5.b)
ORIGINAL
NEW QUESTION same example
5
2/3 + ¾ = ?
A. 5/7
B. 17/24
C. 5/12
Choices ‘A’ and ‘B’ are incorrect. What do you think
someone might have thought if they selected one of
these choices?
6
0.25, 50% and 2/3
Create two different examples using these numbers.
Solve them.
7
5/12 + 6/12 + 7/12
What could you add to these three fractions so the
sum would be
A) A mixed number? Add ___ new sum = _____
B) A whole number? Add ___ new sum = _____
C) A negative integer? Add ___ new sum = ____
D) Zero? Add ____ new sum = ____
8
1/20 1/10 1/5
and 1/8
Mark says there is a very easy way to put these
fractions in order without making common
denominators. Explain.
Change the Question
not the Textbook
(grades 4-5) Make 2 groups: WHICH are the easiest
and which are the most difficult to solve? Why?
1
Find the sum: 15.2 + 12.7
6
Which is larger? 2/3 or 7/8
2
Find the sum: 12.8 + 6.29
7
Which is larger? 5/9 or 7/8?
3
Find difference: 16.04 – 1.8
8
Which is closer to ½?
3/8 or 6/10
4
Find difference: 16.98 – 6.25
9
How much time between
2:05 pm and 8:20 pm?
5
Which is larger? 6/9 or 2/3?
10
How much time between
10:05 am and 5:20 pm?
Change the
Homework Question
(grades 4-5 ) Possible Answers
Easier
More Difficult
1
15.2 (easy to line-up)
12.7
27.9 (no regrouping)
2
12.8
6.29 (line up decimals)
19.09 (regroup)
4
16.98
– 6.25
10.73 (no regrouping)
3
16.04
-1. 08 (need to regroup twice)
14.96
5
Which is larger? 6/9 or 2/3?
7
(the same 6/9 reduces to 2/3)
larger? 5/9 or 7/8? Ans.7/8
Need common denom. to
compare 5/9=40/72 7/8=63/72
6
Which is larger? 2/3 or 7/8?
8
7/8. It is only 1/8 away from
1; 2/3 is 1/3 away; 1/3 is
larger than 1/8
Which closer to ½? 3/8 or 6/10
9
8:20 pm
- 2:05 pm is 6 hours 15 min no
regrouping
time between 10:05am &5:20pm
10
10am to12pm = 2, 12pm to 5pm=5
2hr+5hr=7hr (add am + pm hrs)
20-5=15min. Answer: 7 hr.15 min
How to Make Sure a
Butterfly
Doesn’t Fly
How do you get a butterfly?
First, there is the egg which hatches into a
caterpillar. The caterpillar eats and grows. At the
right time, it makes a cocoon out of its own body.
While in the cocoon, the caterpillar changes into a
butterfly.
When the butterfly is ready, it starts to break
through the cocoon.
First a hole appears. Then the butterfly struggles
to come out through the hole. This can take a few
hours.
If you try to “help” the butterfly by cutting the
cocoon, the butterfly will come out easily but it will
never fly. Your “help” has destroyed the butterfly.
The butterfly can fly because it has
to struggle to come out.
The ‘pushing’ forces lots of enzymes from the
body to the wing tips. This strengthens the
muscles, and reduces the body weight. In this
way, the butterfly will be able to fly the moment it
comes out of the cocoon. Otherwise it will simply
fall to the ground, crawl around with a swollen
body and shrunken wings, and soon die.
If the butterfly is not left to struggle
to come out of the cocoon, it will never fly.
We can learn an important lesson from
the butterfly.
If we do not have struggles and challenges in
our work, we will never grow strong and
capable. If life has no difficulties, we will become
weak and helpless.
-- Lim Siong Guan,
Former Secretary, Singapore’s Ministry of Education
Mini-Projects
•
•
•
•
•
•
•
•
Give them choices (4-MATT example)
Online Research
Work in pairs
Collect data
Organize data
Analyze data
Come to conclusions
Explain conclusions
STUDENTS CHOOSE
ACTIVITY:
From 4-MAT 4 ALGEBRA
DRAW …. WRITE …. DISCOVER ….
BUILD …. GRAPH …. MEASURE? ...
PORTFOLIO - Congratulations: Dear Assistant,
Printing day is Tuesday and I need your help! The Arts
section of our local paper is completing a page on
all subjects covered in 5th grade. I need you to cover
the math piece for me … Write a poem, song, rap,
or story about order of operations. Just follow the
attached rubric and you should be fine. Be creative
and watch your spelling, but have fun!
Human Growth and Development: Teachers know and
understand how student learning is influenced by individual
experiences, talents and prior learning ….
Portfolio: A Creative Piece
Special Needs: Teachers engage in activities to: Apply knowledge
of students’ abilities, … talents … to positively impact student
learning.
I HAVE WHO HAS?
• OPERATIONS: MIXED OPERATIONS
PROBLEMS (grades 5-6)
• FRACTIONS, DECIMALS and PERCENTS
(grades 5-6)
EAI – 1-800-770-8010
I Have
0.125
Who has
as a
5.NF.1. Add1/3
and
subtract fractions with unlike denominators
%?
CCSS: Understand the place value system.
5.NBT.3. Read, write, and compare decimals to thousandths.
Where do I find resources?
Illuminations from NCTM website (http://www.nctm.org)
How Do We
Get to School?
Handout
DEVELOP DATA-GRAPH COMPREHENSION
Where do I find resources?
Illuminations from NCTM website (http://www.nctm.org)
CLASSROOM RESOURCES (Interactivities)
Factoriizations: grades 3-6 (Interactive
online)http://www.nctm.org/ClassroomResources/Interactives/Factorize/
Concentration: Pre-K to 2; grades 3-5 (Interactive online)
http://www.nctm.org/ClassroomResources/Interactives/Concentration/
Cubes and Volume: Grades 3-5
http://www.nctm.org/Classroom-Resources/Interactives/Cubes/
Where do I find resources?
Illuminations from NCTM website (http://www.nctm.org)
CLASSROOM RESOURCES
http://illuminations.nctm.org/Search.aspx?view=searc
h&gr=3-5
Pre-K-2, 3-5 Lesson, Interactivities, Worksheets
• Hopping on the Number Line
• What’s Next?
• Exploring Other Number Patterns
• Growing Patterns
www.NCTM.ORG
Classroom Resources
http://illuminations.nctm.org/Search.aspx?view=search&gr=3-5
Grades 3-5 Lesson, Interactivities, Worksheets
• Pitching Cards
• National Population Projections
• State Population Projections
• High Temperature
• Every Beat Of Your Heart
• What's the Beat?
Pan Balance: grades 3-5; 6-8
http://www.nctm.org/Classroom-Resources/Interactives/PanBalance-–-Shapes/
EXIT - closure
•
•
•
•
•
Thoughts
Ideas
Questions
Plans next week, next month
To introduce, practice, review, assess
JUDITH T. BRENDEL
• [email protected]
• [email protected]
KEEP IN TOUCH!