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High School Mathematics and PARCC
Presented by Don Biery
Turn to page 1 of your hand out………
BLAH BLAH BLAH BLAH…….
Math is not a subject to just fill curriculumn…….it
is life, it is all around us, hidden in the fabric of
nature.
Common Core and The Modeling
System
The real world is what ParCC is after.
ParCC Modeling Questions
Math must be an interdisciplinary item Departments must meet to work together…..
Classes must be aligned for content to interact i.e. ALG II needs to teach systems of equations before chemistry get
to formulae balancing. Math must have labs…………
Life is biology- Biology is Chemistry – Chemistry is
application of Physics – physics is the application of Math
There are no x’s in the world….
We must teach students to be able to problem solve
not solve problems.
Math Labs = Math
Modeling
PARCC High Level Blueprints - Mathematics
Math item counts per form
Assess- me nt
Ite ms Grade
3
Grade
4
Grade
5
Grade
6
Grade
7
Grade
8
Algebra
I
Math I
Geomet
ry
Math
II
Algebra
II
Math
III
EOY
Type I
1 Point
3
4
2
8
2
8
2
6
2
4
2
6
2
1
1
9
1
9
1
9
1
9
1
9 Type I 2 Point
5
8
8
7
8
5
1
1
1
2
1
2
1
2
1
2
1
4 Type I
4 Point
-
-
-
1
1
2
3
3
3
3
3
2
EOY
TOT
A L
Type I
3
9
3
6
3
6
3
4
3
3
3
3
3
5
3
4
3
4
3
4
3
4
3
5
PBA/M
YA
Type I
1Point
8
8
6
8
8
1
0
1
0
1
0
1
0
1
0
1
0
1
0 Type I
2 Point
2
2
3
2
2
1
-
-
-
-
-
-
Type II 3 Point
2
2
2
2
2
2
2
2
2
2
2
2
Type II
4 Point
2
2
2
2
2
2
2
2
2
2
3
3
Type III
3 Point
2
2
2
2
2
2
2
2
2
2
2
2
Type III
6 Point
1
1
1
1
1
1
2
2
2
2
3
3
PBA/M
YA
TOTA
L
Type I
1
0
1
0
9
1
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
Type
II
4
4
4
4
4
4
4
4
4
4
5
5
Type
III
3
3
3
3
3
3
4
4
4
4
5
5
Overview of Task Types
• The PARCC assessments for mathematics will involve three primary types of tasks: Type I, II, and III.
• Each task type is described on the basis of several factors, principally the purpose of the task in generating
evidence for certain sub claims.
Task Type Description of Task Type
I. Tasks assessing concepts, skills • Balance of conceptual understanding, fluency, and application
and procedures • Can involve any or all mathematical practice standards
• Machine scorable including innovative, computer-based formats
• Will appear on the End of Year and Performance Based Assessment
components
• Sub-claims A, B and E
II. Tasks assessing expressing • Each task calls for written arguments / justifications, critique of
reasoning, or precision in mathematical
mathematical reasoning statements (MP.3, 6). • Can involve other mathematical practice standards
• May include a mix of machine scored and hand scored responses
• Included on the Performance Based Assessment component
• Sub-claim C
III. Tasks assessing modeling / • Each task calls for modeling/application in a real-world context or
scenario (MP.4)
applications • Can involve other mathematical practice standards
• May include a mix of machine scored and hand scored responses
• Included on the Performance Based Assessment component
• Sub-claim D
1. Financial Literacy…..Leads to Better
Understanding and true applicability
Real World Application
2. Algebra: Why we learn Real Analysis…..Be true to
our Students……
Real World Application
3. Geometry: What can I do with this junk?
Real World Application
Labs and the real world…. 1. Give them real problems
to solve 2. Don’t always tell them
what tool to use ---ParCC
Real World Application
Create a Lab:
1. Reason for Lab (UBD)
2. Lab reporting out?
3.Lab Procedures
4. Possible issues……
November 2013
the course, requiring application of knowledge and skills articulated in 7.RP.A, 7.NS.3,
engage with the quantities given in the context. Modeling is a critical component of
complex situation to make a real -world estimate given an unscaffolded situation where
given quantities, their units and the proportional relationships between them. This will
decreasing because each day boxes and popcorn seeds are used. This means that
HS Popcorn Inventory
Type Type III 6 Points
Evidence Statement
HS.D.1-1: Solve multi-step contextual problems with degree of difficulty appropriate to
7.EE, and/or 8.EE.
Most Relevant Standards for Mathematical Content
7.RP.2: Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relations hips.
c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn . d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. 7.RP.3: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
These standards are major content in the seventh grade based on the PARCC Model Content Frameworks.
Most Relevant Standards for Mathematical Practice
Students creating reasoned estimates must be able to reason abstractly and quantitatively in order to build a model of the situation that is accurate enough for the given situation (MP.2 and MP.4). Working with ambiguity is an important part of the modeling skills expected at high school, and this requires students to productively
the high school standards, and this item requires students to create a model from a
a model is a useful tool. To make this model, students will have to reason with the
require students to understand how to use the numbers mathematically, and then be able to periodically check their own understanding of what those numbers mean.
Item Description and Assessment Qualities
This application task requires students to create a reasoned estimate in response to solve a real-world problem. Students must first wrestle with the data displayed on the
Popcorn Inventory page . They should recognize that the amounts in the table are
students should recognize that they are using about 15 medium boxes each day and
about 25-30 small boxes each day.
In order to address the amount of popcorn sold over the weekend, students must first
create a viable estimate of the number of cups of popcorn sold, then use the ratio
cups of popcorn seed:8 cups of popcorn. Students may choose to use this method to estimate the amount of popcorn seed used Sunday through Thursday; however, other
methods could be used to determine the amount of popcorn seed used each day.
Students using this method must be sure to account for the amount o f popcorn seed
used on Sunday because the original information starts from end of day on Sunday.
The final estimate requires students to use the current amount of popcorn seed, the
amount used Friday and Saturday, and the amount used Sunday through Thursda y in
order to estimate the amount of popcorn seeds she should purchase so there are 100-
200 pounds left over next Friday morning.
Note that ratio and proportional relationships are key skills required for college and
career readiness, and this item provides a strong application of that content. Unlike
traditional multiple choice, it is difficult to guess the correct answer or use a choice
elimination strategy.
Scoring Information
Scoring Rubric for HS.D.1-1
Task is worth 6 points. Task can be scored as 0, 1, 2, 3, 4, 5, or 6.
Scoring consists of 2 points for calculation and 4 points for modeling.
Structure (6 points total):
- 2 points for correctly addressing the cups of popcorn seed needed for Sunday-
Thursday
o 1 calculation point for adequate estimate
o 1 modeling point for adequate estimation strategy
- 3 points for correctly addressing the cups of popcorn seed needed for Friday
and Saturday.
o 1 modeling point for adequate estimation strategy for addressing two sizes of boxes for both days.
o 1 modeling point for accurate use of the proportion of popcorn seed to
popcorn
o 1 calculation point for adequate estimate
- 1 point for correctly estimating the amount of popcorn seed that should be
ordered
o 1 modeling point for adequate estimation strategy (the calculation is not as important as the strategy)
Example student response: On Friday and Saturday, they will sell about 500 large boxes (250 + 250 = 500). I found
that they sold about 17 medium boxes ( ) and about 30 small boxes
( ) each day in the table, so they would sell about 68 (2 x 17 for both
days of the week ( ). They will need 80 x 5 or 400 cups of popcorn
–
– days) medium boxes and 120 (2 x 30 for both days) small boxes on Friday and Saturday combined.
That means they need to pop:
Large:
Medium (approx.):
Small (approx.):
I added the three amounts of popcorn to find that they will need about 12,400 cups of
popcorn over the weekend.
Since -cups of popcorn seed makes 8 cups of popcorn, I know that 1 cup of popcorn
seed will make 24 cups of popcorn. That means that they need about
cups of popcorn seed for Friday and Saturday. So, they will need about 525 cups of popcorn seed for the weekend.
According to the table, they used about 80 cups of popcorn seed each of the remaining
– seed for Sunday-Thursday.
I made this list to make sure she buys enough:
( 69.7 cups currrently)
525 cups of popcorn seed for Friday and Saturday
400 cups of popcorn seed for Sunday-Thursday
+ 100 extra cups to make sure she is between 100 and 200 cups on Friday morning
1,025 cups of popcorn seed to order in the morning
NOTE: There are a wide variety of estimation strategies that can receive full credit.
between quantities; graph equations on coordinate axes with labels and
students will have to decontextualize and contextualize the information at
then to interpret the meaning and structure of that model (MP.2). Students
Task has 2 parts.
HS Brett’s race
Type Type III 3 Points
Evidence Statement
HS.D.2-5: Solve multi-step contextual word problems with degree of difficulty appropriate to the course, requiring application of course-level knowledge and skills articulated in A-CED, N-Q, A-SSE.3, A-REI.6, A-REI.12, A-REI.11-2, limited to linear equations and exponential equations with integer exponents.
Clarification: A-CED is the primary content; other listed content elements may be involved in tasks as well.
Most Relevant Standards for Mathematical Content
A-CED Creating Equations A-CED.A Create equations that describe numbers or relationships 2. Create equations in two or more variables to represent relationships
scales.
This standard is major content in the course based on the PARCC Model Content Frameworks.
Most Relevant Standards for Mathematical Practice
This item requires students to model the given situation using equations, then students use that model to determine who will win the race and their margin of victory (MP.4). In order to create and interpret these models,
various points in the solution process to create a mathematical model and
that choose to use the graph may create another model of the situation,
and look for and use structure within that model (MP.7).
Item Description and Assessment Qualities
This application task requires students to use content from widely applicable
algebra standards in order to solve a modeling problem with difficulty
expected in high school. Students first create equations that model the
situation described in the first paragraph. It is important for students to
define their variables when creating equations. Then, students reason with
their models, and perhaps the graphing tool, to interpret the model and
determine the margin of victory. There are a variety of solution methods
that students may use to successfully answer Part B.
Scoring Information
Scoring Rubric for Sample Item HS.D. 2-5
Task is worth 3 points. Task can be scored as 0, 1, 2, or 3.
Scoring for Part A – Formulating the Model – 1 point
3 12
100 = 8 𝑥 + 20 1
3
Student produces two equations to determine the distance in meters from the starting line, of each person as a function of the time x, in seconds since the Olympian starts running.
For example, Brett’s distance y, as related to time, x:
𝑦 = 8 1 𝑥 + 20. Or y =
100 x + 20
The Olympian’s distance y, as related to time, x:
𝑦 = 10 . NOTE: All variables should be defined. The student may choose to define x as time in seconds since Brett starts running.
Scoring for Part B Student earns 1 calculation point for stating the correct winner and the correct margin of victory. Students earn 1 modeling point for providing an accurate justification using the equations in Part A.
Sample Student Response 1:
• For Brett, 𝑦 = 100 when 1 3
80 = 8 𝑥 𝑥 = 9.6
• For the Olympian 𝑦 = 100 when 100 = 10𝑥 𝑥 = 10
. • So, Brett wins the race by
10 – 9.6 = 0.4 seconds.
Sample Student Response 2 :
• When Brett finishes the race at 9.6 seconds, the Olympian is only 10(9.6) = 96 meters from the start. Therefore, Brett was 4 meters ahead of the Olympian when he finished the race.
Note:
• If Part A contains incorrect equations, but Part B is correct based on one or two incorrect equations in Part A, the student is still awarded 1 or 2 points of the 3 possible points.
Task score: The task score is the sum of the points awarded in each component.
1. Always do Lab Your Self…..
2. Don’t always give them the tools, allow them to ask for them
3. Evaluate effectiveness of lab
4. Evaluate effectivness of reporting (group participation)
Lessons Learned from OOOPPPSSS
Discussion: Groups 5 ways to aid in implementation
5 hurdles you see
5 ways to overcome those obstacles.
ParCC and CCSS Curriculumn
