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Major Work of the Grade
Sixth Grade
Alisan Royster
NCCTM Conference 2012
http://www.ncdpi.wikispaces.net
Research
Major Work of the Grade
NC Educators
CCSS Progressions
Smarter Balanced
Assessment Consortium
NC Department of Public
Instruction
• A Critical Area for 6th grade CCSS
• One of the Major Clusters of the Major Work of the Grade identified by NC DPI
Ratio and Proportional Relationships
Ratio and Proportional Relationships
• “Many school mathematics programs fail to develop children’s understanding of ratio comparisons and move directly to formal procedures for solving missing-value proportion problems.”
- The Math Learning Study Committee (2001)
Using Ratio Tables to Solve Ratio Problems
• Travis can run 4 laps in 12 minutes. If he continues to run at that pace, how many minutes will it take Travis to run 28 laps?
Using Ratio Tables to Solve Ratio Problems
• If 6 cheese crackers provide 90 calories, how many cheese crackers would you have to eat to get 300 calories?
Using Ratio Tables to Solve Ratio Problems
• Due to stronger gravity on Jupiter, a person who weighs 160 pounds on Earth would weigh 416 pounds on Jupiter. How much would a person weigh on Jupiter if he weighs 120 pounds on Earth?
Ratio and Proportional Relationships
• “Students should work with physical representations of ratios and proportions before learning how to solve these types of problems symbolically at a more abstract level.”
- Wollman and Karplus (1977)
Group Problem Solving• Find some friends or make some new ones!
You need to get into groups of 4.
• Work together to answer the questions on the cards. Begin by passing out one card to each member of the group.
• You may not look at anyone else’s clue, but you may share your own clue by reading it or telling what’s on your card.
Group Problem Solving• If you have a question, check with your group
first. If your group agrees that no one in the group can answer the question, you may all raise your hand and the teacher will come. Do the same when you’ve solved the problem.
• Be sure everyone participates!
• There are 4 cards with clues essential to the solution; 2 additional provide hints that may be needed by some groups.
Barrel Blunder• Find the salmon-colored cards in your envelope
and distribute your cards to the group.
• Work together to solve the problem without setting up proportions. You may find snap cubes helpful.
• Everyone in your group should raise your hands when you’re in agreement that you’ve correctly solved the problem.
Barrel Blunderoptional additional clues
Barrel Blunder ☜• Hint: One recipe for the
correct mixture of apple juice contains one can of apple juice for every three cans of water. If you mixed up more than one correct recipe, what other combinations of apple juice to water might you have?
Barrel Blunder ☝
• You will need more of the weak mixture (Devon’s) than the strong (Bella’s) to get it to come out right.
Gross-Out Green• Find the green cards in your envelope and
distribute one card to each person in the group.
• Work together to solve the problem without setting up proportions. You may find snap cubes helpful.
• Everyone in your group should raise your hands when you’re in agreement that you’ve correctly solved the problems.
Gross-Out Greenoptional additional clues
Gross-Out Green ☜• Hint: To make your paint
the right color, the overall ratio of Dark Denim to Yo-Yo Yellow to Boring Brown has to be the same as the recipe for Gross-Out Green.
Gross-Out Green☝• Hint: There is some
Midnight Marine already mixed, so think about the colors that went into it as you calculate what you need to make Gross-Out Green.
Connecting Critical Areas to Other Domains
• Understanding of critical areas is strengthened when we make connections throughout the mathematics curriculum
• One obvious connection: Ratio & Proportional Relationships and Expressions & Equations
• Look for other ways to connect Ratio and Proportional Relationships to other domains
Using Proportional Reasoning to Think About
Volume• 6.G.2 Find the volume of a right rectangular
prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism.
Using Proportional Reasoning to Think About
Volume• How can you use the model shown, along with
proportional reasoning, to investigate how many ½ inch cubes it would take to fill various right rectangular prisms?
• Work together with your group to determine the volume of various right rectangular prisms and the number of ½ inch cubes it would take to fill them (see handout).
As You Implement CCSSin Your Classrooms
• Remember that change is a process, not an event!
Lessons for Learning
Selected tasks from the DPI Week-by-Week and Strategies Document
rewritten to align to CCSS
DPI Contact InformationKitty RutherfordElementary Mathematics [email protected]
Johannah MaynorSecondary Mathematics [email protected]
Barbara BissellK – 12 Mathematics Section [email protected]
Susan HartK-12 Program [email protected]
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