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Common Core Math Grade 6

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Common Core MathGrade 6

Ventura Unified School District

November 2013

Natalie Albrizzio, Secondary Math Specialist

- Shifts in Mathematics
- Content Standards
- Practice Standards
- Smarter Balanced Assessment

- Focus
- Coherence
- Rigor
(see Key Instructional Shifts handout)

- Not all of the content in a given grade is emphasized equally in the standards. Some clusters of standards require a greater instructional emphasis than the others based on the depth of the ideas, the time that they take to master, and/or their importance.
- The bulk of instructional time should be given to “Major” clusters and the standards within them. However, standards in the “Supporting” and “Additional” clusters should not be neglected.
(see “Content Emphases” handout)

- Students complete their study of the four basic arithmetic operations with whole numbers, decimals, and fractions.
- Students extend their understanding of numbers to the system of rational numbers. Students also extend their study of the coordinate plane to include all four quadrants.
- Students begin a formal study of algebraic expressions in Grade 6.
- Students explore inequalities for the first time.
- Students also explore ratios and rates for the first time in Grade 6.
- Statistics is introduced in Grade 6.

To be prepared for grade seven mathematics, students should be able to demonstrate they have have met the fluency expectations for grade six. For sixth graders, the expected fluencies are

- multi-digit whole number division (6.NS.2) and
- multi-digit decimal operations (6.NS.3).
These fluencies and the conceptual understandings that support them are foundational for work with fractions and decimals in grade seven.

Of particular importance for students to attain in grade six are

- skills and understandings of division of fractions by fractions (6.NS.1);
- an understanding of the system of rational numbers (6.NS.5-8);
- the ability to use ratio concepts and reasoning to solve problems (6.RP.1-3);
- the extension of arithmetic to algebraic expressions (6.EE.1-4), including how to reason about and solve one-variable equations and inequalities (6.EE.8-4);
- and the ability to represent and analyze quantitative relationships between dependent and independent variables (6.EE.1-9).

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
(two handouts – one specific to grade 6 and the other with questions)

- William McCallum (The Hunt Institute) http://www.youtube.com/playlist?list=PLD7F4C7DE7CB3D2E6
- Jason Zimba (The Hunt Institute)
- Phil Daro (SERP) http://www.bing.com/videos/search?q=Phil+Daro&FORM=VIRE8&adlt=strict#view=detail&mid=E1D9EE1B4F7598A58827E1D9EE1B4F7598A58827

- Selected Response
- Short Constructed Response
- Extended Constructed Response
- Technology Enhanced
- Performance Tasks
(green handout)

Overall claim for grades 3 – 8:Students can demonstrate progress toward college and career readiness in mathematics.

- Claim #1: Concepts & Procedures
- Claim #2: Problem Solving
- Claim #3: Communicating Reasoning
- Claim #4: Modeling and Data Analysis
(green handout)

Use the following materials to find how Holt is filling the gaps:

- Holt Curriculum Companion TE Course of Study pages xi – xvi
- Holt Course 1: Numbers to Algebra
- Holt 2-column chapter worksheets with standards column left blank
- Grade 6 standards document
DO NOT ASSUME THE PUBLISHER IS ACCURATE!

In your Holt math text book, you will find:

- “Think and Discuss” box at the end of the examples. You can call it “Think and Write”.
- Items towards the end of the problem set that are titled:
- Reasoning
- What’s the Error?
- Write About It
- What’s the Question?
- Challenge

- Labs – great for conceptual understanding.
- “Reading and Writing Math” at the beginning of the chapter.
- “Concept Connection” and “Game Time” at the end of the chapter.
- Cumulative Assessment with Short Response and Extended Response items with rubric.

- Grade 6 CST Released Question.
The weekly milk order for the Tranquility Inn includes 40 gallons of low-fat milk and 15 gallons of chocolate milk. What is the ratio of the number of low-fat gallons to chocolate gallons in the Tranquility Inn’s weekly milk order?

- 3:1
- 5:1
- 5:3
- 8:3

- Grade 6 CST Released Question.
The weekly milk order for the Tranquility Inn includes 40 gallons of low-fat milk and 15 gallons of chocolate milk. What is the ratio of the number of low-fat gallons to chocolate gallons in the Tranquility Inn’s weekly milk order?

- Grade 6 CST Released Question.
The weekly milk order for the Tranquility Inn includes 40 gallons of low-fat milk and 15 gallons of chocolate milk. What is the ratio of the number of low-fat gallons to chocolate gallons in the Tranquility Inn’s weekly milk order?

- They have been around for a long time but are gaining new momentum with Common Core.
- The word “Number” suggests that the focus is on number, and in early grades that is true. Some middle and high school teachers have adopted the “talk” and changed the name to “Math Talks.” This allows the discussion to open up to math in general.
- http://mathtalks.fawnnguyen.com/

An estimation challenge each day building number sense.

- Video about Estimation 180 http://www.youtube.com/watch?feature=player_embedded&v=Rfpu42cS-6Y
- Website: http://www.estimation180.com/
- Handout available on his website with thorough explanation of how to use it.

- Video about Dan Meyer 3 Act Math Tasks http://www.youtube.com/watch?v=8OHvrNAfURw
- Website: https://docs.google.com/spreadsheet/pub?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE&output=html
- Nana’s Chocolate Milk (6.RP.3, MP4)

Asking students to choose their own path and justify it.

- Blog: http://wyrmath.wordpress.com/2013/11/07/would-you-rather-18/

- VUSD Intranet: (more resources than internet)
http://intranet.venturausd.org/cni/mathseco/

- VUSD Internet:
http://vusdmath6-12.weebly.com/

- Compute fluently with multi-digit numbers
- Graph points on the coordinate plane
- Understand absolute value
- Write and solve inequalities
- Find area of shapes by composing or decomposing
- Represent 3-D figures using nets