PUHSD

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PUHSD Common Core Integrated Mathematics
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Why change to Integrated Math?

• Common Core materials are more supportive of an
  Integrated Approach.
• There is no algebra gap that occurs in the 2nd
  course (like in Geometry).
• There is a greater focus on data and real world
  problems.

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Pathways

• Integrated Math 1 begins in 2014-2015 school
  year. Algebra 1 will no longer be offered.
• Incoming Freshmen will be enrolled into courses
  based on placement test (similar to last year).
  Most students will start in IM-1.
• Integrated Math 2 begins in 2015-2016 school
  year. Geometry will no longer be offered.
• A diagnostic test will replace the placement test
  for the 2015-2016 school year.

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2014 - 2015
8th Grade Placement Test
IM-1
CC Geom
CC Alg 2
Current 9th, 10th, 11th
Math A
IM-1
CC Geom
Alg 1
CC Alg 2
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Curriculum Path 2014-2015
Placement Test
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Schedule Choice Class of 2018
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2015 - 2016
8th Grade Diagnostic
IM-1
IM-2
IM-1
IM-2
9th, 10th, 11th (from 2014-15)
IM-1
IM-A
IM-2
CC Alg 2
IM-1
IM-2
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Curriculum Path
IM-1/IM-A
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Schedule Choice Class of 2019
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2016 - 2017
8th Grade Diagnostic
IM-1
IM-2
IM-1
IM-2
9th, 10th, 11th (from 2015-16)
IM-1
IM-A
IM-2
IM-3
IM-1
IM-2
IM-3
IM-2
IM-3
Pre Calc
Other Adv
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Realities of Common Core

1. Common core requires a much deeper understanding
   of mathematics that students use.
2. The problems are real world and not just a
   collection of algorithms.
3. 60 of the assessment is Performance Based

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4 Claims

• Claim 1 Concepts and Procedures
• Students can explain and apply mathematical
  concepts and interpret and carry out mathematical
  procedures with precision and fluency.
• Claim 2 Problem Solving
• Students can solve a range of complex, well-posed
  problems in pure and applied mathematics, making
  productive use of knowledge and problem-solving
  strategies.
• Claim 3 Communicating Reason
• Students can clearly and precisely construct
  viable arguments to support their own reasoning
  and to critique the reasoning of others.
• Claim 4 Modeling and Data Analysis
• Students can analyze complex, real-world
  scenarios and can construct and use mathematical
  models to interpret and solve problems.

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What Changes?
Typical Problem from current State Geometry
assessments
A right circular cone has a height of 6 inches
and a diameter of 6 inches. What is the volume
of the cone?
(A) (B)(C)
(D)
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A Common Core Type Question
An ice cream parlor sells ice cream cones which
have three flavors of ice cream. The bottom of
the cone is filled with vanilla ice cream so that
half of the volume of the cone is vanilla. The
top part of the cone is filled with strawberry
ice cream. Finally to top the cone off a
hemisphere (half of a sphere) of chocolate ice
cream is placed on top to the cone. The cone has
a height (h) of 6 inches and a diameter (d) of 6
inches.
(a) What is the volume of all the ice cream used
for the cone? (b) Explain why the height of the
vanilla in the cone is not 3 inches.
T
(c) The company that owns the ice cream parlor
makes several versions of the ice cream treat
which has similar dimensions (the diameter and
the height of the cone are equal). To simplify
ordering they want to find a formula that will
find the volume of the ice cream (both the cone
and the hemisphere) based on the total height (T)
of the ice cream treat. Find a formula that
will calculate the volume based on the value of
T.
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Answers to Problems

• Star Test Type Answer B
• Common Core Problem
• The volume 36? in3 (18? for the cone and 18?
  for the hemisphere)
• The cone is much narrower on the bottom than the
  top. If we fill the vanilla to only 3 inches,
  the volume would be which is not 9?
  in3.
• First start with doing the problem in terms of
  the radius. Since the height of the cone is the
  same as the diameter, the volume of the cone is
  The volume of the hemisphere is The volume in
  terms of r for the figure isThe height of the
  full figure T 3r. ThereforeSubstituting in
  for r we get