Transcript Document

TOOLS/MODELS
FOR ENGAGE NY
Vanessa Walker PVSD
[email protected]
Goal for tonight:
To provide you with some
background knowledge and
provide an overview of the
tools and models that your
child will be using with the
math curriculum.
BACKGROUND INFORMATION
PREPARING STUDENTS FOR ALGEBRA
THROUGH NUMBERS AND OPERATIONS
PREPARING STUDENTS FOR ALGEBRA
REQUIRES THREE SHIFTS IN MATHEMATICS
1.
Focus: Concentrate where the standards focus.
2.
Coherence: Think across grades, and link to major topics.
Rigor: In major topics, pursue conceptual understanding,
procedural skill and fluency, and application.
3.
SOLID CONCEPTUAL UNDERSTANDING
• Teach more than “how to get the answer”
and instead support students’ ability to
access concepts from a number of
perspectives
• Students are able to see math as more than a
set of mnemonics or discrete procedures
• Conceptual understanding supports the other
aspects of rigor (fluency and application)
SUPPORTING MATHEMATICAL
UNDERSTANDING
ENGAGE NY
MOST LESSONS INCLUDE:
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Fluency Practiceactivity to build fluency
in a concept
Application Problemword problems- apply
math to daily life
Concept
Development- main
objective of the lesson is
taught here
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Problem Set- student
practice sheet
Student Debriefprovides students with
the opportunity to
discuss what they have
learned

Exit Ticket- formative
assessment

Homework- is just like
the problem set
VOCABULARY:
DECOMPOSING & COMPOSING NUMBERS
Break numbers down into their sub-parts: This
concept is used across grade levels.
1.
Decompose numbers into tens
2.
How any number can be created using a variety
of addends (numbers).
For example 5 can be represented by:
0+5; 1 + 4; 2+2 +1; 3 + 2; 5 +0; …
TOOLS/MODELS OF ENGAGE NY
Ten Frame (TK-3rd)
 Arrays & Area Models (1st -5th )
 Base Ten Blocks & Bundles (K-2nd)
 Number Bonds (K-5th)
 Tape Diagram (1st-5th)
 Number Line (K-5th)
 Number Path/Towers (TK-1st)
 Place Value Chart (2nd-5th)
 Number Disks (2nd-5th)
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TEN FRAME
ARRAYS & AREA MODELS
TK, Kinder &
5th Grade
1st
2nd -4th Grade
TK - 1ST GRADE
COUNTING, ADDITION, & SUBTRACTION
Uses the
5-frame & 10-frame
to set the foundation of
decomposing numbers
2ND GRADE
REPEATED ADDITION
MULTIPLICATION
3RD GRADE
13 X 23
MULTIPLICATION
4TH GRADE
26 x 34
(20 + 6) x (30 + 4)
(6 x 34) + (20 x 34)
(6 x 4) + (6 x 30) + (20 x 4) + (20+ 30)
30
6
20
18 tens or 180
6 hundreds or 600
34
x 26
24
180
80
600
884
4
24
8 tens or 80
DIVISION
ANTS MARCHING
The ants are marching in the annual parade. There
are 12 ants.
They must march in equal rows and each row
must have more than one ant.
• Show all the different ways the ants can march in
the parade.
• How many different ways can they march?
Explain your answer.
NUMBER BONDS (K – 5TH GRADE)
TAPE DIAGRAMS
(1ST – 5TH GRADE)
PICTORIAL REPRESENTATION OF
PART-PART-WHOLE
RELATIONSHIP
NUMBER BOND PRIMARY GRADE
NUMBER BOND UPPER GRADES
198 + 54 =
2 + 52
198 + 2 = 200
200 + 52 = 252
TAPE DIAGRAM –BAR MODELS
USED FREQUENTLY WITH WORD
PROBLEMS
John, Emma, and Alice each had 10
raisins. John ate 3 raisins, Emma ate
4 raisins, and Alice ate 5 raisins.
How may raisins do they each have
now?
Write a number bond and a number
sentence for each.

Mathew has 14 blue marbles. His blue marbles
make-up two-fifths of his total number of
marbles. How many marbles does Mathew have?
2/5
14
2
1
= 14
= 7
5
= 5 x 7 = 35
NUMBER LINE &
PLACE VALUE CHART
(& NUMBER CHIPS)
NUMBER LINE
PRIMARY GRADES
NUMBER LINE
UPPER GRADES
PLACE VALUE CHART
FLUENCY
REQUIRED FLUENCIES IN K-6
WHAT SUPPORT CAN BE OFFERED AT HOME?
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Continue to support students in memorizing basic
math facts.
Ask your child to review the day’s lesson by
reviewing the problem set with them.
Solve the problem using traditional methods then
prove any added information.
Read the newsletter that goes along with the
topic.
Homework should provide an opportunity for
“practice.”
TO HELP STUDENTS RETELL
Questions to pose:
 How
did you solve the problem?
 What did you do?
 What strategy did you use?
 What math words did you use or learn?
 What were the steps involved?
 What did you learn today?
 What do(es) __________________ mean to
you?
Prompts to use:
 I solved the problem by …
 The math words I used were …
 The steps I followed were …
 My strategy was successful because
…
 Explain to a young child or someone
that wasn’t involved …
 Draw a picture to show how you
solved the problem.
PVSD WEBSITE
HTTP://WWW.PVSD.K12.CA.US/SITE/DEFAULT.ASPX?PAGEID=1
LET’S SOLVE SOME PROBLEMS
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Bella spilled some pencils on the carpet. Bill
came over to help her pick them up.
Bill found 5 pencils under the desk and Bell
found 4 by the door.
How many pencils did they find together?
Use a ten frame, draw a math picture, write a
number sentence (equation) that tells about the
story.
MULTIPLICATION: USE AN ARRAY TO SOLVE
26 X 48
40
20
6
8
20 x 40 = 800
20 x 8 = 160
6 x 40 = 240
6 x 8 = 48
1248
RIGOR & DEPTH OF KNOWLEDGE (DOK)
DOK Level
1
Title of Level
Recall & Reproduction
Memorize, Repeat, List
2
Skills & Concepts
Classify, Compare, Summarize
3
Strategic Thinking
Develop a logical argument, Critique
4
Extended Thinking
Analyze, Create, Prove
FRACTIONS
5TH GRADE
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https://www.engageny.org/resource/grade-5math-visual-model-representations-tapediagram-and-area-model-5nf1-and-5nf4a