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Day 3 EEA Summer 2012

Middle School Mathematics Educators

Outcomes for Day 3

The participants will:• synthesize their knowledge of the CCSS and available resources.

• share projects.

• become aware of expected shifts in mathematics instruction.

• formulate a plan for training teachers at their school.

OUTCOME:The participants will synthesize their knowledge of the CCSS and available resources.

Quiz, Quiz, Trade Warm-Up

Quiz, Quiz, Trade

OUTCOME:

The participants will

share their projects.

Project Presentations

BREAK

Shifts in Mathematics

HERE THERE

OUTCOME:

The participants will become aware of expected shifts in mathematics instruction.

Shifts

Instructional Shifts

1. Focus2. Coherence3. Fluency4. Deep Understanding5. Application6. Dual intensity

Locate “Shifts in Mathematics”

Looks like this

Task:Create a representation on your chart paper that summarizes your group’s assigned “SHIFT”.

Share Your

Shifts

Expected Changes in Mathematics Tasks

In addition to traditional tasks, students also will be asked to complete tasks that:

• assess more than one standard.

• simultaneously assess content and practice standards.

• are not scaffolded.

• take an extended period of time to complete.

• Will they need to stop for gas? Explain your reasoning.

• Suppose they decide to stop for gas and the stop lasts 30 minutes. If they continue their trip at the same speed, at what time will they reach LA?

The figure below shows a conversation between two friends.

Appendix F- ITN 2012-31-PARCC Item Development

270

LET’S LOOK AT A MATHEMATICS TASK OF THE

FUTURE

9:20 AM

Will they need to stop for gas?

Yes, they will need to stop for gas. They have enough gas to travel 262.5 miles but according to the road sign, the distance to Los Angeles is 270 miles

35 miles ? miles

1 gallon 7.5 gall

1 of a 15 gallon tank = 7.5 gallons

2

35miles 7.5 gallons 35 7.5 262.5 miles

1 gall

o

on 1

ns

Solution

• Will they need to stop for gas? Explain your reasoning.

• Suppose they decide to stop for gas and the stop lasts 30 minutes. If they continue their trip at the same speed, at what time will they reach LA?

The figure below shows a conversation between two friends.

Appendix F- ITN 2012-31-PARCC Item Development

270

9:20 AM

• Which “Shifts” and “Changes”

are represented by this task?

• Why do you think so?

LET’S LOOK AT A MATHEMATICS TASK OF THE

FUTURE

Debriefing the Task

• This task draws on content from: • Cluster 7.RP.1-3. Analyze Proportional relationships and use them to solve real world problems.

• The numbers in the task are not limited to integers.

• The task:• is not scaffolded.• takes an extended amount of time to solve. • assesses both content and practice standards.• assesses more than one content standard.

Examples: General CCSSM Content Changes

AWAY FROM TOWARD

Solving equations mechanically

Solving equations as a process of reasoning

Limiting word problems that invite arithmetic skills

Including word problems that invite algebraic approaches

Limiting to integer algebra Including rational number algebra

Mechanically simplifying or expanding expressions

Using properties of operations to rewrite expressions

Appendix F- ITN 2012-31-PARCC Item Development

Examples: Content Changes in Middle School

Ratios and Proportional Reasoning

Focus is on relationships between values, and is tied to direct variation in linear relationships and rates of change (algebra), and to similarity (geometry)

Number SystemFocus is on positive and negative rational numbers (including integers, positive fractions and decimals, negative fractions and decimals), rather than only on integers.

Operations

• Focus is on fluently: (1) dividing multi-digit whole numbers; (2) adding, subtracting, multiplying, and dividing multi-digit decimals; (3) dividing fractions by fractions – Grade 6• Focus is on fluently: (1) adding, subtracting, multiplying, and dividing rational numbers; (2) solving multi-step problems with positive and negative rational numbers in any form; (3) solving word problems leading to one-variable equations – Grade 7• Focus is on fluently: (1) solving one-variable equations with one solution, many solutions, or no solution; (2) using a well-developed set of geometric measurement skills – Grade 8.

MeasurementFocus is on volume of cones and spheres, as well as on cylinders.

Data Displays

• Focus in elementary grades: on bar graphs, scaled picture graphs, and line plots (dot plots)• Focus in middle grades: on box-and-whisker plots (box plots), histograms, and scatter plots.• Circle graphs, stem-and-leaf plots, and line graphs (except in relation to graphing the line of an equation on the coordinate plane) are no longer in middle school.

PatternsFormer focus on arithmetic and geometric patterns in middle school is now covered in the Number Systems domain, culminating with 7.NS: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

ProbabilityProbability is no longer a part of the Elementary mathematics curriculum, but is addressed at the middle school level, beginning with 7.SP.5-8: Investigate chance processes and develop use, and evaluate probability models.

Focus by Content Cluster

Content is prioritized at each grade level. Some Clusters of Standards will require a greater amount of time for instruction. Others will receive less time and focus. However, ALL standards – including the Standards for Mathematical Practice – will be assessed.

Additional Changes in Mathematics

Straightforward items will still be important for students to be able to complete, for example:

In addition, the new assessments will include richer, often open-ended tasks, such as:

What are two different equations with the same solution as 3(y – 1) = 8?

If 3(y – 1) = 8, then what is y?

Additional Changes in Mathematics

Straightforward items will still be important for students to be able to complete, for example:

Donna buys 40 apples at 35 cents each. She eats 2 apples and sells the rest for 45 cents each. How much money does she make?

Additional Changes in Mathematics

In addition, the new assessments will include richer, often open-ended tasks, such as:

Donna buys some apples at 35 cents each. She eats 2 apples and sells the rest for 45 cents each. She makes $4.40. How many apples did she buy?

Additional Changes in Mathematics

Assessments still will include 1-point items:

BUT students also will need to complete multi-part problems:

A bird flies 20 miles in 100 minutes, at a constant speed. At that speed,

• how long will it take the bird to fly 6 miles?• how far will the bird fly in 15 minutes?• how fast will the bird be flying in miles per hour?• what will be the bird’s pace in minutes per mile?

A bird flies 20 miles in 100 minutes, at a constant speed. At that speed, how long will it take the bird to fly 6 miles?

Additional Changes in Mathematics

Away from “integer algebra” in middle school:

If 3(x-5) = 45 then what is x?

Toward rational number algebra in middle school:

Mathematics Instruction of the Future

To successfully implement the Common Core Mathematics Curriculum, what must mathematics teachers:

KEEP DOING???

STOP DOING???

START DOING???

OUTCOME:

The participants will formulate a plan for training teachers at their school.

Reflection

Preparation for School Team Planning

1. Independently prepare discussion points to share with your school team, using ideas from the KEEP-STOP-START activity.

2. Share discussion points with the members of your table group

3. Share discussion highlights with the large group

Engage Me

Internet

Engage Me! - YouTube.wmv

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