1. PUHSD – Common Core Integrated Mathematics

2. 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.

3. Pathways
Integrated Math 1 begins in 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 school year. Geometry will no longer be offered.
A diagnostic test will replace the placement test for the school year.

4. 8th Grade Placement Test
8th Grade Placement Test
IM-1
CC Geom
CC Alg 2
Current 9th, 10th, 11th
Math A
IM-1
In year , students will continue on the current process of taking a placement test if they wish to skip one or more courses at our schools. The placement test will be similar to previous years with the addition of a few common core questions. The criteria to skip Integrated Math 1 will be more strict (80% or better on test to skip IM-1). Since we will not offer IM-2 until , students who start in IM-1 will not be able to double up a math class in that year. For current students who had have not passed Algebra 1 will start in IM-1. Students who finished Algebra 1 in will take Common Core Geometry (following the current courses offered). These students could double up by taking Common Core Algebra 2 in the spring. Current 8th grades that start in Common Core Geometry or Algebra 2 will not be allowed to double up in the 9th grade.
Alg 1
CC Geom
CC Alg 2

5. Integrated Math 1 /Math A College Readiness Math
Curriculum Path –
Integrated Math 1 /Math A
Placement Test
Geometry
Algebra 1
Algebra 2
AP Stats
Trig/Pre-Calc
College Readiness Math
AP Calc AB/BC

6. Schedule Choice – Class of 2018

7. 2015 - 2016 8th Grade Diagnostic IM-1 IM-2 IM-1 IM-2
9th, 10th, 11th (from )
In , all 8th grade students will take a diagnostic exam. This will pre-identify students that may need support or who have sufficient knowledge to be able to begin in Integrated Math 2. The assumption is that the foundation schools will be teaching all 8th graders common core 8th grade math. Advanced students could do additional work beyond the course if they hope to start in IM-2. IM-2 will be the highest placement for any incoming freshmen. This should only be a small number of students. The diagnostic will follow strict common core standards that test the eight mathematical practices. Students will be able to double up in Students who take IM-2 in the fall will be allowed to take Common Core Algebra 2 instead of IM-3 since the courses are relatively similar.
IM-A
IM-1
IM-2
IM-1
IM-2
CC Alg 2

8. College Readiness Math
Curriculum Path
IM-1/IM-A
Diagnostic Test
IM-2
IM-1
College Readiness Math
IM-3
AP Stats
Trig/Pre-Calc
AP Calc AB/BC

9. Schedule Choice – Class of 2019

10. 2016 - 2017 8th Grade Diagnostic IM-1 IM-2 IM-1 IM-2
9th, 10th, 11th (from )
completes the rollout of all three integrated courses.
IM-A
IM-1
IM-2
IM-1
IM-2
IM-3
IM-3
IM-2
IM-3
Pre Calc
Other Adv

11. Realities of Common Core
Common core requires a much deeper understanding of mathematics that students use.
The problems are “real world” and not just a collection of algorithms.
60% of the assessment is “Performance Based”

12. 4 Claims Claim 1: Concepts and Procedures Claim 2: Problem Solving
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.

13. 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?
6 in
(A) (B) (C) (D)

14. 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. h d
(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.

15. 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 is The height of the full figure T = 3r. Therefore Substituting in for r we get